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| author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
|---|---|---|
| committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
| commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
| tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /BLAS/SRC | |
| parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
| download | lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.gz lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.bz2 lapack-e1d39294aee16fa6db9ba079b14442358217db71.zip | |
Integrating Doxygen in comments
Diffstat (limited to 'BLAS/SRC')
151 files changed, 20133 insertions, 10260 deletions
diff --git a/BLAS/SRC/caxpy.f b/BLAS/SRC/caxpy.f index c0bb7661..3e274e5b 100644 --- a/BLAS/SRC/caxpy.f +++ b/BLAS/SRC/caxpy.f @@ -1,22 +1,71 @@ - SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY) -* .. Scalar Arguments .. - COMPLEX CA - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX CX(*),CY(*) -* .. +*> \brief \b CAXPY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* COMPLEX CA +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* * Purpose * ======= * -* CAXPY constant times a vector plus a vector. +*>\details \b Purpose: +*>\verbatim +*> +*> CAXPY constant times a vector plus a vector. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + COMPLEX CA + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ccopy.f b/BLAS/SRC/ccopy.f index 87446f7b..039a8be8 100644 --- a/BLAS/SRC/ccopy.f +++ b/BLAS/SRC/ccopy.f @@ -1,21 +1,69 @@ - SUBROUTINE CCOPY(N,CX,INCX,CY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX CX(*),CY(*) -* .. +*> \brief \b CCOPY * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CCOPY(N,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* * Purpose * ======= * -* CCOPY copies a vector x to a vector y. +*>\details \b Purpose: +*>\verbatim +*> +*> CCOPY copies a vector x to a vector y. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CCOPY(N,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cdotc.f b/BLAS/SRC/cdotc.f index 025d1636..6903726d 100644 --- a/BLAS/SRC/cdotc.f +++ b/BLAS/SRC/cdotc.f @@ -1,22 +1,70 @@ - COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX CX(*),CY(*) -* .. +*> \brief \b CDOTC * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* * Purpose * ======= * -* forms the dot product of two vectors, conjugating the first -* vector. +*>\details \b Purpose: +*>\verbatim +*> +*> forms the dot product of two vectors, conjugating the first +*> vector. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cdotu.f b/BLAS/SRC/cdotu.f index d31c16f0..00bc019b 100644 --- a/BLAS/SRC/cdotu.f +++ b/BLAS/SRC/cdotu.f @@ -1,21 +1,69 @@ - COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX CX(*),CY(*) -* .. +*> \brief \b CDOTU * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* * Purpose * ======= * -* CDOTU forms the dot product of two vectors. +*>\details \b Purpose: +*>\verbatim +*> +*> CDOTU forms the dot product of two vectors. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cgbmv.f b/BLAS/SRC/cgbmv.f index 6392e1d8..aa8d9d8c 100644 --- a/BLAS/SRC/cgbmv.f +++ b/BLAS/SRC/cgbmv.f @@ -1,134 +1,213 @@ - SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER INCX,INCY,KL,KU,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CGBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER INCX,INCY,KL,KU,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CGBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> CGBMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +*> +*> y := alpha*A**H*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> +*>\endverbatim * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry, KL specifies the number of sub-diagonals of the +*> matrix A. KL must satisfy 0 .le. KL. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry, KU specifies the number of super-diagonals of the +*> matrix A. KU must satisfy 0 .le. KU. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry, the leading ( kl + ku + 1 ) by n part of the +*> array A must contain the matrix of coefficients, supplied +*> column by column, with the leading diagonal of the matrix in +*> row ( ku + 1 ) of the array, the first super-diagonal +*> starting at position 2 in row ku, the first sub-diagonal +*> starting at position 1 in row ( ku + 2 ), and so on. +*> Elements in the array A that do not correspond to elements +*> in the band matrix (such as the top left ku by ku triangle) +*> are not referenced. +*> The following program segment will transfer a band matrix +*> from conventional full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> K = KU + 1 - J +*> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +*> A( K + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( kl + ku + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A**H*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* KL - INTEGER. -* On entry, KL specifies the number of sub-diagonals of the -* matrix A. KL must satisfy 0 .le. KL. -* Unchanged on exit. -* -* KU - INTEGER. -* On entry, KU specifies the number of super-diagonals of the -* matrix A. KU must satisfy 0 .le. KU. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry, the leading ( kl + ku + 1 ) by n part of the -* array A must contain the matrix of coefficients, supplied -* column by column, with the leading diagonal of the matrix in -* row ( ku + 1 ) of the array, the first super-diagonal -* starting at position 2 in row ku, the first sub-diagonal -* starting at position 1 in row ( ku + 2 ), and so on. -* Elements in the array A that do not correspond to elements -* in the band matrix (such as the top left ku by ku triangle) -* are not referenced. -* The following program segment will transfer a band matrix -* from conventional full matrix storage to band storage: -* -* DO 20, J = 1, N -* K = KU + 1 - J -* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) -* A( K + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( kl + ku + 1 ). -* Unchanged on exit. -* -* X - COMPLEX array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cgemm.f b/BLAS/SRC/cgemm.f index 24548db1..daf642d0 100644 --- a/BLAS/SRC/cgemm.f +++ b/BLAS/SRC/cgemm.f @@ -1,133 +1,215 @@ - SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b CGEMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,M,N +* CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CGEMM performs one of the matrix-matrix operations -* -* C := alpha*op( A )*op( B ) + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> CGEMM performs one of the matrix-matrix operations +*> +*> C := alpha*op( A )*op( B ) + beta*C, +*> +*> where op( X ) is one of +*> +*> op( X ) = X or op( X ) = X**T or op( X ) = X**H, +*> +*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) +*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> +*>\endverbatim * -* where op( X ) is one of +* Arguments +* ========= +* +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n', op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't', op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c', op( A ) = A**H. +*> \endverbatim +*> +*> \param[in] TRANSB +*> \verbatim +*> TRANSB is CHARACTER*1 +*> On entry, TRANSB specifies the form of op( B ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSB = 'N' or 'n', op( B ) = B. +*> \endverbatim +*> \verbatim +*> TRANSB = 'T' or 't', op( B ) = B**T. +*> \endverbatim +*> \verbatim +*> TRANSB = 'C' or 'c', op( B ) = B**H. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix +*> op( A ) and of the matrix C. M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix +*> op( B ) and the number of columns of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of columns of the matrix +*> op( A ) and the number of rows of the matrix op( B ). K must +*> be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANSA = 'N' or 'n', and is m otherwise. +*> Before entry with TRANSA = 'N' or 'n', the leading m by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by m part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANSA = 'N' or 'n' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, kb ), where kb is +*> n when TRANSB = 'N' or 'n', and is k otherwise. +*> Before entry with TRANSB = 'N' or 'n', the leading k by n +*> part of the array B must contain the matrix B, otherwise +*> the leading n by k part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANSB = 'N' or 'n' then +*> LDB must be at least max( 1, k ), otherwise LDB must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n matrix +*> ( alpha*op( A )*op( B ) + beta*C ). +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* op( X ) = X or op( X ) = X**T or op( X ) = X**H, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* alpha and beta are scalars, and A, B and C are matrices, with op( A ) -* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n', op( A ) = A. -* -* TRANSA = 'T' or 't', op( A ) = A**T. -* -* TRANSA = 'C' or 'c', op( A ) = A**H. -* -* Unchanged on exit. -* -* TRANSB - CHARACTER*1. -* On entry, TRANSB specifies the form of op( B ) to be used in -* the matrix multiplication as follows: -* -* TRANSB = 'N' or 'n', op( B ) = B. -* -* TRANSB = 'T' or 't', op( B ) = B**T. -* -* TRANSB = 'C' or 'c', op( B ) = B**H. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix -* op( A ) and of the matrix C. M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix -* op( B ) and the number of columns of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of columns of the matrix -* op( A ) and the number of rows of the matrix op( B ). K must -* be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* k when TRANSA = 'N' or 'n', and is m otherwise. -* Before entry with TRANSA = 'N' or 'n', the leading m by k -* part of the array A must contain the matrix A, otherwise -* the leading k by m part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANSA = 'N' or 'n' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, k ). -* Unchanged on exit. -* -* B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is -* n when TRANSB = 'N' or 'n', and is k otherwise. -* Before entry with TRANSB = 'N' or 'n', the leading k by n -* part of the array B must contain the matrix B, otherwise -* the leading n by k part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANSB = 'N' or 'n' then -* LDB must be at least max( 1, k ), otherwise LDB must be at -* least max( 1, n ). -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n matrix -* ( alpha*op( A )*op( B ) + beta*C ). -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER K,LDA,LDB,LDC,M,N + CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cgemv.f b/BLAS/SRC/cgemv.f index d9e55f9a..a341b454 100644 --- a/BLAS/SRC/cgemv.f +++ b/BLAS/SRC/cgemv.f @@ -1,107 +1,183 @@ - SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER INCX,INCY,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CGEMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER INCX,INCY,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CGEMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> CGEMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +*> +*> y := alpha*A**H*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n matrix. +*> +*>\endverbatim * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry with BETA non-zero, the incremented array Y +*> must contain the vector y. On exit, Y is overwritten by the +*> updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A**H*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. -* -* X - COMPLEX array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry with BETA non-zero, the incremented array Y -* must contain the vector y. On exit, Y is overwritten by the -* updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cgerc.f b/BLAS/SRC/cgerc.f index ffc578a1..d6539b01 100644 --- a/BLAS/SRC/cgerc.f +++ b/BLAS/SRC/cgerc.f @@ -1,82 +1,151 @@ - SUBROUTINE CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - COMPLEX ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CGERC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CGERC performs the rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> CGERC performs the rank 1 operation +*> +*> A := alpha*x*y**H + A, +*> +*> where alpha is a scalar, x is an m element vector, y is an n element +*> vector and A is an m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( m - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the m +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. On exit, A is +*> overwritten by the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x is an m element vector, y is an n element -* vector and A is an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( m - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the m -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. On exit, A is -* overwritten by the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cgeru.f b/BLAS/SRC/cgeru.f index 712aba2a..0db12d7b 100644 --- a/BLAS/SRC/cgeru.f +++ b/BLAS/SRC/cgeru.f @@ -1,82 +1,151 @@ - SUBROUTINE CGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - COMPLEX ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CGERU +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CGERU performs the rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> CGERU performs the rank 1 operation +*> +*> A := alpha*x*y**T + A, +*> +*> where alpha is a scalar, x is an m element vector, y is an n element +*> vector and A is an m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( m - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the m +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. On exit, A is +*> overwritten by the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x is an m element vector, y is an n element -* vector and A is an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( m - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the m -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. On exit, A is -* overwritten by the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/chbmv.f b/BLAS/SRC/chbmv.f index e7bacae5..bd3b69c5 100644 --- a/BLAS/SRC/chbmv.f +++ b/BLAS/SRC/chbmv.f @@ -1,136 +1,215 @@ - SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER INCX,INCY,K,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CHBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER INCX,INCY,K,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CHBMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHBMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n hermitian band matrix, with k super-diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the band matrix A is being supplied as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> being supplied. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> being supplied. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of super-diagonals of the +*> matrix A. K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the hermitian matrix, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer the upper +*> triangular part of a hermitian band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the hermitian matrix, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer the lower +*> triangular part of a hermitian band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that the imaginary parts of the diagonal elements need +*> not be set and are assumed to be zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n hermitian band matrix, with k super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the band matrix A is being supplied as -* follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* being supplied. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* being supplied. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of super-diagonals of the -* matrix A. K must satisfy 0 .le. K. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the hermitian matrix, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer the upper -* triangular part of a hermitian band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the hermitian matrix, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer the lower -* triangular part of a hermitian band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that the imaginary parts of the diagonal elements need -* not be set and are assumed to be zero. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - COMPLEX array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* Y - COMPLEX array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/chemm.f b/BLAS/SRC/chemm.f index f5cb17a5..9947cb28 100644 --- a/BLAS/SRC/chemm.f +++ b/BLAS/SRC/chemm.f @@ -1,139 +1,217 @@ - SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b CHEMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER LDA,LDB,LDC,M,N +* CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CHEMM performs one of the matrix-matrix operations -* -* C := alpha*A*B + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> CHEMM performs one of the matrix-matrix operations +*> +*> C := alpha*A*B + beta*C, +*> +*> or +*> +*> C := alpha*B*A + beta*C, +*> +*> where alpha and beta are scalars, A is an hermitian matrix and B and +*> C are m by n matrices. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether the hermitian matrix A +*> appears on the left or right in the operation as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the hermitian matrix A is to be +*> referenced as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of the +*> hermitian matrix is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of the +*> hermitian matrix is to be referenced. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix C. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix C. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> m when SIDE = 'L' or 'l' and is n otherwise. +*> Before entry with SIDE = 'L' or 'l', the m by m part of +*> the array A must contain the hermitian matrix, such that +*> when UPLO = 'U' or 'u', the leading m by m upper triangular +*> part of the array A must contain the upper triangular part +*> of the hermitian matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading m by m lower triangular part of the array A +*> must contain the lower triangular part of the hermitian +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Before entry with SIDE = 'R' or 'r', the n by n part of +*> the array A must contain the hermitian matrix, such that +*> when UPLO = 'U' or 'u', the leading n by n upper triangular +*> part of the array A must contain the upper triangular part +*> of the hermitian matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading n by n lower triangular part of the array A +*> must contain the lower triangular part of the hermitian +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n updated +*> matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*B*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, A is an hermitian matrix and B and -* C are m by n matrices. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether the hermitian matrix A -* appears on the left or right in the operation as follows: -* -* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -* -* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the hermitian matrix A is to be -* referenced as follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of the -* hermitian matrix is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of the -* hermitian matrix is to be referenced. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix C. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix C. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* m when SIDE = 'L' or 'l' and is n otherwise. -* Before entry with SIDE = 'L' or 'l', the m by m part of -* the array A must contain the hermitian matrix, such that -* when UPLO = 'U' or 'u', the leading m by m upper triangular -* part of the array A must contain the upper triangular part -* of the hermitian matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading m by m lower triangular part of the array A -* must contain the lower triangular part of the hermitian -* matrix and the strictly upper triangular part of A is not -* referenced. -* Before entry with SIDE = 'R' or 'r', the n by n part of -* the array A must contain the hermitian matrix, such that -* when UPLO = 'U' or 'u', the leading n by n upper triangular -* part of the array A must contain the upper triangular part -* of the hermitian matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading n by n lower triangular part of the array A -* must contain the lower triangular part of the hermitian -* matrix and the strictly upper triangular part of A is not -* referenced. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, n ). -* Unchanged on exit. -* -* B - COMPLEX array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n updated -* matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER LDA,LDB,LDC,M,N + CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/chemv.f b/BLAS/SRC/chemv.f index 3ddca361..85de0631 100644 --- a/BLAS/SRC/chemv.f +++ b/BLAS/SRC/chemv.f @@ -1,105 +1,178 @@ - SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CHEMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CHEMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHEMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n hermitian matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of A is not referenced. +*> Note that the imaginary parts of the diagonal elements need +*> not be set and are assumed to be zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n hermitian matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of A is not referenced. -* Note that the imaginary parts of the diagonal elements need -* not be set and are assumed to be zero. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cher.f b/BLAS/SRC/cher.f index b8d5ac01..b7ccc0b6 100644 --- a/BLAS/SRC/cher.f +++ b/BLAS/SRC/cher.f @@ -1,92 +1,157 @@ - SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*) -* .. +*> \brief \b CHER +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* CHER performs the hermitian rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHER performs the hermitian rank 1 operation +*> +*> A := alpha*x*x**H + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n hermitian matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> \verbatim +*> X COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n hermitian matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cher2.f b/BLAS/SRC/cher2.f index 3cc1a7d0..ee6e3a44 100644 --- a/BLAS/SRC/cher2.f +++ b/BLAS/SRC/cher2.f @@ -1,103 +1,170 @@ - SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - COMPLEX ALPHA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*),Y(*) -* .. +*> \brief \b CHER2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CHER2 performs the hermitian rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHER2 performs the hermitian rank 2 operation +*> +*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an n +*> by n hermitian matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> \verbatim +*> X COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> \verbatim +*> Y COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an n -* by n hermitian matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cher2k.f b/BLAS/SRC/cher2k.f index 368c1878..3a386fc8 100644 --- a/BLAS/SRC/cher2k.f +++ b/BLAS/SRC/cher2k.f @@ -1,145 +1,224 @@ - SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX ALPHA - REAL BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b CHER2K +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* REAL BETA +* INTEGER K,LDA,LDB,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CHER2K performs one of the hermitian rank 2k operations +*>\details \b Purpose: +*>\verbatim +*> +*> CHER2K performs one of the hermitian rank 2k operations +*> +*> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, +*> +*> or +*> +*> C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, +*> +*> where alpha and beta are scalars with beta real, C is an n by n +*> hermitian matrix and A and B are n by k matrices in the first case +*> and k by n matrices in the second case. +*> +*>\endverbatim * -* C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, -* -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*B**H + +*> conjg( alpha )*B*A**H + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**H*B + +*> conjg( alpha )*B**H*A + +*> beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrices A and B, and on entry with +*> TRANS = 'C' or 'c', K specifies the number of rows of the +*> matrices A and B. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, kb ), where kb is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array B must contain the matrix B, otherwise +*> the leading k by n part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDB must be at least max( 1, n ), otherwise LDB must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars with beta real, C is an n by n -* hermitian matrix and A and B are n by k matrices in the first case -* and k by n matrices in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*B**H + -* conjg( alpha )*B*A**H + -* beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**H*B + -* conjg( alpha )*B**H*A + -* beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrices A and B, and on entry with -* TRANS = 'C' or 'c', K specifies the number of rows of the -* matrices A and B. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array B must contain the matrix B, otherwise -* the leading k by n part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDB must be at least max( 1, n ), otherwise LDB must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. +*> Ed Anderson, Cray Research Inc. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. -* -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. -* Ed Anderson, Cray Research Inc. +* .. Scalar Arguments .. + COMPLEX ALPHA + REAL BETA + INTEGER K,LDA,LDB,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cherk.f b/BLAS/SRC/cherk.f index b2c1d556..66913b6e 100644 --- a/BLAS/SRC/cherk.f +++ b/BLAS/SRC/cherk.f @@ -1,125 +1,199 @@ - SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),C(LDC,*) -* .. +*> \brief \b CHERK +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER K,LDA,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CHERK performs one of the hermitian rank k operations -* -* C := alpha*A*A**H + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> CHERK performs one of the hermitian rank k operations +*> +*> C := alpha*A*A**H + beta*C, +*> +*> or +*> +*> C := alpha*A**H*A + beta*C, +*> +*> where alpha and beta are real scalars, C is an n by n hermitian +*> matrix and A is an n by k matrix in the first case and a k by n +*> matrix in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrix A, and on entry with +*> TRANS = 'C' or 'c', K specifies the number of rows of the +*> matrix A. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**H*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are real scalars, C is an n by n hermitian -* matrix and A is an n by k matrix in the first case and a k by n -* matrix in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrix A, and on entry with -* TRANS = 'C' or 'c', K specifies the number of rows of the -* matrix A. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. +*> Ed Anderson, Cray Research Inc. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * -* Level 3 Blas routine. -* -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1. -* Ed Anderson, Cray Research Inc. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER K,LDA,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/chpmv.f b/BLAS/SRC/chpmv.f index 264bdb24..857293aa 100644 --- a/BLAS/SRC/chpmv.f +++ b/BLAS/SRC/chpmv.f @@ -1,102 +1,173 @@ - SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX AP(*),X(*),Y(*) -* .. +*> \brief \b CHPMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CHPMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHPMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n hermitian matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. +*> Note that the imaginary parts of the diagonal elements need +*> not be set and are assumed to be zero. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n hermitian matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* AP - COMPLEX array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. -* Note that the imaginary parts of the diagonal elements need -* not be set and are assumed to be zero. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/chpr.f b/BLAS/SRC/chpr.f index 747b74af..1cdcf62f 100644 --- a/BLAS/SRC/chpr.f +++ b/BLAS/SRC/chpr.f @@ -1,89 +1,154 @@ - SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX AP(*),X(*) -* .. +*> \brief \b CHPR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX AP(*),X(*) +* .. +* * Purpose * ======= * -* CHPR performs the hermitian rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHPR performs the hermitian rank 1 operation +*> +*> A := alpha*x*x**H + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n hermitian matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is COMPLEX array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n hermitian matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* AP - COMPLEX array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/chpr2.f b/BLAS/SRC/chpr2.f index 71734cee..2a44bb95 100644 --- a/BLAS/SRC/chpr2.f +++ b/BLAS/SRC/chpr2.f @@ -1,100 +1,167 @@ - SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) -* .. Scalar Arguments .. - COMPLEX ALPHA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX AP(*),X(*),Y(*) -* .. +*> \brief \b CHPR2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* CHPR2 performs the hermitian rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> CHPR2 performs the hermitian rank 2 operation +*> +*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an +*> n by n hermitian matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> \verbatim +*> Y COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is COMPLEX array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an -* n by n hermitian matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* AP - COMPLEX array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/crotg.f b/BLAS/SRC/crotg.f index 360028cc..f4800229 100644 --- a/BLAS/SRC/crotg.f +++ b/BLAS/SRC/crotg.f @@ -1,14 +1,55 @@ +*> \brief \b CROTG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CROTG(CA,CB,C,S) +* +* .. Scalar Arguments .. +* COMPLEX CA,CB,S +* REAL C +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CROTG determines a complex Givens rotation. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* +* ===================================================================== SUBROUTINE CROTG(CA,CB,C,S) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* * .. Scalar Arguments .. COMPLEX CA,CB,S REAL C * .. * -* Purpose -* ======= -* -* CROTG determines a complex Givens rotation. -* * ===================================================================== * * .. Local Scalars .. diff --git a/BLAS/SRC/cscal.f b/BLAS/SRC/cscal.f index ce1ae155..0e2dc6a1 100644 --- a/BLAS/SRC/cscal.f +++ b/BLAS/SRC/cscal.f @@ -1,23 +1,72 @@ - SUBROUTINE CSCAL(N,CA,CX,INCX) -* .. Scalar Arguments .. - COMPLEX CA - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX CX(*) -* .. +*> \brief \b CSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE CSCAL(N,CA,CX,INCX) +* +* .. Scalar Arguments .. +* COMPLEX CA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*) +* .. +* * Purpose * ======= * -* CSCAL scales a vector by a constant. +*>\details \b Purpose: +*>\verbatim +*> +*> CSCAL scales a vector by a constant. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CSCAL(N,CA,CX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + COMPLEX CA + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX CX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/csrot.f b/BLAS/SRC/csrot.f index 4178079a..02a7a38c 100644 --- a/BLAS/SRC/csrot.f +++ b/BLAS/SRC/csrot.f @@ -1,5 +1,110 @@ +*> \brief \b CSROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CSROT( N, CX, INCX, CY, INCY, C, S ) +* +* .. Scalar Arguments .. +* INTEGER INCX, INCY, N +* REAL C, S +* .. +* .. Array Arguments .. +* COMPLEX CX( * ), CY( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CSROT applies a plane rotation, where the cos and sin (c and s) are real +*> and the vectors cx and cy are complex. +*> jack dongarra, linpack, 3/11/78. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the vectors cx and cy. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in,out] CX +*> \verbatim +*> CX is COMPLEX array, dimension at least +*> ( 1 + ( N - 1 )*abs( INCX ) ). +*> Before entry, the incremented array CX must contain the n +*> element vector cx. On exit, CX is overwritten by the updated +*> vector cx. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> CX. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] CY +*> \verbatim +*> CY is COMPLEX array, dimension at least +*> ( 1 + ( N - 1 )*abs( INCY ) ). +*> Before entry, the incremented array CY must contain the n +*> element vector cy. On exit, CY is overwritten by the updated +*> vector cy. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> CY. INCY must not be zero. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is REAL +*> On entry, C specifies the cosine, cos. +*> \endverbatim +*> +*> \param[in] S +*> \verbatim +*> S is REAL +*> On entry, S specifies the sine, sin. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* +* ===================================================================== SUBROUTINE CSROT( N, CX, INCX, CY, INCY, C, S ) * +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* * .. Scalar Arguments .. INTEGER INCX, INCY, N REAL C, S @@ -8,51 +113,6 @@ COMPLEX CX( * ), CY( * ) * .. * -* Purpose -* ======= -* -* CSROT applies a plane rotation, where the cos and sin (c and s) are real -* and the vectors cx and cy are complex. -* jack dongarra, linpack, 3/11/78. -* -* Arguments -* ========== -* -* N (input) INTEGER -* On entry, N specifies the order of the vectors cx and cy. -* N must be at least zero. -* Unchanged on exit. -* -* CX (input) COMPLEX array, dimension at least -* ( 1 + ( N - 1 )*abs( INCX ) ). -* Before entry, the incremented array CX must contain the n -* element vector cx. On exit, CX is overwritten by the updated -* vector cx. -* -* INCX (input) INTEGER -* On entry, INCX specifies the increment for the elements of -* CX. INCX must not be zero. -* Unchanged on exit. -* -* CY (input) COMPLEX array, dimension at least -* ( 1 + ( N - 1 )*abs( INCY ) ). -* Before entry, the incremented array CY must contain the n -* element vector cy. On exit, CY is overwritten by the updated -* vector cy. -* -* INCY (input) INTEGER -* On entry, INCY specifies the increment for the elements of -* CY. INCY must not be zero. -* Unchanged on exit. -* -* C (input) REAL -* On entry, C specifies the cosine, cos. -* Unchanged on exit. -* -* S (input) REAL -* On entry, S specifies the sine, sin. -* Unchanged on exit. -* * ===================================================================== * * .. Local Scalars .. diff --git a/BLAS/SRC/csscal.f b/BLAS/SRC/csscal.f index 8ec2eade..2af05c22 100644 --- a/BLAS/SRC/csscal.f +++ b/BLAS/SRC/csscal.f @@ -1,23 +1,72 @@ - SUBROUTINE CSSCAL(N,SA,CX,INCX) -* .. Scalar Arguments .. - REAL SA - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX CX(*) -* .. +*> \brief \b CSSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE CSSCAL(N,SA,CX,INCX) +* +* .. Scalar Arguments .. +* REAL SA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*) +* .. +* * Purpose * ======= * -* CSSCAL scales a complex vector by a real constant. +*>\details \b Purpose: +*>\verbatim +*> +*> CSSCAL scales a complex vector by a real constant. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CSSCAL(N,SA,CX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + REAL SA + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX CX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/cswap.f b/BLAS/SRC/cswap.f index 1e267179..12a6f193 100644 --- a/BLAS/SRC/cswap.f +++ b/BLAS/SRC/cswap.f @@ -1,21 +1,69 @@ - SUBROUTINE CSWAP(N,CX,INCX,CY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX CX(*),CY(*) -* .. +*> \brief \b CSWAP * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CSWAP(N,CX,INCX,CY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*),CY(*) +* .. +* * Purpose * ======= * -* CSWAP interchanges two vectors. +*>\details \b Purpose: +*>\verbatim +*> +*> CSWAP interchanges two vectors. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CSWAP(N,CX,INCX,CY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX CX(*),CY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/csymm.f b/BLAS/SRC/csymm.f index c925a778..326dcf0d 100644 --- a/BLAS/SRC/csymm.f +++ b/BLAS/SRC/csymm.f @@ -1,137 +1,215 @@ - SUBROUTINE CSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b CSYMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER LDA,LDB,LDC,M,N +* CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CSYMM performs one of the matrix-matrix operations -* -* C := alpha*A*B + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> CSYMM performs one of the matrix-matrix operations +*> +*> C := alpha*A*B + beta*C, +*> +*> or +*> +*> C := alpha*B*A + beta*C, +*> +*> where alpha and beta are scalars, A is a symmetric matrix and B and +*> C are m by n matrices. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether the symmetric matrix A +*> appears on the left or right in the operation as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the symmetric matrix A is to be +*> referenced as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix C. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix C. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> m when SIDE = 'L' or 'l' and is n otherwise. +*> Before entry with SIDE = 'L' or 'l', the m by m part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading m by m upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading m by m lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Before entry with SIDE = 'R' or 'r', the n by n part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading n by n upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading n by n lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n updated +*> matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*B*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, A is a symmetric matrix and B and -* C are m by n matrices. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether the symmetric matrix A -* appears on the left or right in the operation as follows: -* -* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -* -* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the symmetric matrix A is to be -* referenced as follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of the -* symmetric matrix is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of the -* symmetric matrix is to be referenced. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix C. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix C. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* m when SIDE = 'L' or 'l' and is n otherwise. -* Before entry with SIDE = 'L' or 'l', the m by m part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading m by m upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading m by m lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Before entry with SIDE = 'R' or 'r', the n by n part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading n by n upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading n by n lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, n ). -* Unchanged on exit. -* -* B - COMPLEX array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n updated -* matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER LDA,LDB,LDC,M,N + CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/csyr2k.f b/BLAS/SRC/csyr2k.f index ed1a56cd..0b424b45 100644 --- a/BLAS/SRC/csyr2k.f +++ b/BLAS/SRC/csyr2k.f @@ -1,136 +1,212 @@ - SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b CSYR2K +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CSYR2K performs one of the symmetric rank 2k operations -* -* C := alpha*A*B**T + alpha*B*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> CSYR2K performs one of the symmetric rank 2k operations +*> +*> C := alpha*A*B**T + alpha*B*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A and B are n by k matrices in the first case and k by n +*> matrices in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + +*> beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrices A and B, and on entry with +*> TRANS = 'T' or 't', K specifies the number of rows of the +*> matrices A and B. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> \verbatim +*> A COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, kb ), where kb is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array B must contain the matrix B, otherwise +*> the leading k by n part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDB must be at least max( 1, n ), otherwise LDB must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A and B are n by k matrices in the first case and k by n -* matrices in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + -* beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + -* beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrices A and B, and on entry with -* TRANS = 'T' or 't', K specifies the number of rows of the -* matrices A and B. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array B must contain the matrix B, otherwise -* the leading k by n part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDB must be at least max( 1, n ), otherwise LDB must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER K,LDA,LDB,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/csyrk.f b/BLAS/SRC/csyrk.f index 7b346ff0..be0a0b93 100644 --- a/BLAS/SRC/csyrk.f +++ b/BLAS/SRC/csyrk.f @@ -1,119 +1,193 @@ - SUBROUTINE CSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),C(LDC,*) -* .. +*> \brief \b CSYRK +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA,BETA +* INTEGER K,LDA,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),C(LDC,*) +* .. +* * Purpose * ======= * -* CSYRK performs one of the symmetric rank k operations -* -* C := alpha*A*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> CSYRK performs one of the symmetric rank k operations +*> +*> C := alpha*A*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A is an n by k matrix in the first case and a k by n matrix +*> in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrix A, and on entry with +*> TRANS = 'T' or 't', K specifies the number of rows of the +*> matrix A. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A is an n by k matrix in the first case and a k by n matrix -* in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrix A, and on entry with -* TRANS = 'T' or 't', K specifies the number of rows of the -* matrix A. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - COMPLEX . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA,BETA + INTEGER K,LDA,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctbmv.f b/BLAS/SRC/ctbmv.f index 37e0e7f8..1a7820e2 100644 --- a/BLAS/SRC/ctbmv.f +++ b/BLAS/SRC/ctbmv.f @@ -1,141 +1,218 @@ - SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*) -* .. +*> \brief \b CTBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* CTBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> CTBMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, or x := A**H*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**H*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* x := A*x, or x := A**T*x, or x := A**H*x, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**H*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctbsv.f b/BLAS/SRC/ctbsv.f index bdbd9a3f..f7eb02c5 100644 --- a/BLAS/SRC/ctbsv.f +++ b/BLAS/SRC/ctbsv.f @@ -1,144 +1,221 @@ - SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*) -* .. +*> \brief \b CTBSV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* CTBSV solves one of the systems of equations +*>\details \b Purpose: +*>\verbatim +*> +*> CTBSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, or A**H*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular band matrix, with ( k + 1 ) +*> diagonals. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* A*x = b, or A**T*x = b, or A**H*x = b, +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**H*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular band matrix, with ( k + 1 ) -* diagonals. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**H*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctpmv.f b/BLAS/SRC/ctpmv.f index 53b1b165..d20c624f 100644 --- a/BLAS/SRC/ctpmv.f +++ b/BLAS/SRC/ctpmv.f @@ -1,101 +1,170 @@ - SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX AP(*),X(*) -* .. -* -* Purpose -* ======= -* -* CTPMV performs one of the matrix-vector operations +*> \brief \b CTPMV * -* x := A*x, or x := A**T*x, or x := A**H*x, +* =========== DOCUMENTATION =========== * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix, supplied in packed form. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**H*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> CTPMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, or x := A**H*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix, supplied in packed form. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**H*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - COMPLEX array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup complex_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctpsv.f b/BLAS/SRC/ctpsv.f index 3a7da00c..5fba7a90 100644 --- a/BLAS/SRC/ctpsv.f +++ b/BLAS/SRC/ctpsv.f @@ -1,103 +1,172 @@ - SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX AP(*),X(*) -* .. +*> \brief \b CTPSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* CTPSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, or A**H*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix, supplied in packed form. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**H*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> CTPSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, or A**H*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix, supplied in packed form. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**H*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - COMPLEX array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup complex_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctrmm.f b/BLAS/SRC/ctrmm.f index e05a623e..8d95a5e7 100644 --- a/BLAS/SRC/ctrmm.f +++ b/BLAS/SRC/ctrmm.f @@ -1,129 +1,208 @@ - SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - COMPLEX ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b CTRMM * -* CTRMM performs one of the matrix-matrix operations +* =========== DOCUMENTATION =========== * -* B := alpha*op( A )*B, or B := alpha*B*op( A ) +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, B is an m by n matrix, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T or op( A ) = A**H. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) multiplies B from -* the left or right as follows: -* -* SIDE = 'L' or 'l' B := alpha*op( A )*B. -* -* SIDE = 'R' or 'r' B := alpha*B*op( A ). -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**H. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> CTRMM performs one of the matrix-matrix operations +*> +*> B := alpha*op( A )*B, or B := alpha*B*op( A ) +*> +*> where alpha is a scalar, B is an m by n matrix, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T or op( A ) = A**H. +*> +*>\endverbatim * -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) multiplies B from +*> the left or right as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' B := alpha*op( A )*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' B := alpha*B*op( A ). +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**H. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, k ), where k is m +*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B, and on exit is overwritten by the +*> transformed matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - COMPLEX array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B, and on exit is overwritten by the -* transformed matrix. +*> \ingroup complex_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctrmv.f b/BLAS/SRC/ctrmv.f index ac0afb73..f432c96f 100644 --- a/BLAS/SRC/ctrmv.f +++ b/BLAS/SRC/ctrmv.f @@ -1,104 +1,175 @@ - SUBROUTINE CTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*) -* .. +*> \brief \b CTRMV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* CTRMV performs one of the matrix-vector operations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* x := A*x, or x := A**T*x, or x := A**H*x, -* -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**H*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE CTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> CTRMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, or x := A**H*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**H*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup complex_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctrsm.f b/BLAS/SRC/ctrsm.f index 2aeb8727..3fd4635e 100644 --- a/BLAS/SRC/ctrsm.f +++ b/BLAS/SRC/ctrsm.f @@ -1,131 +1,211 @@ - SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - COMPLEX ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b CTRSM * -* CTRSM solves one of the matrix equations +* =========== DOCUMENTATION =========== * -* op( A )*X = alpha*B, or X*op( A ) = alpha*B, +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, X and B are m by n matrices, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T or op( A ) = A**H. -* -* The matrix X is overwritten on B. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) appears on the left -* or right of X as follows: -* -* SIDE = 'L' or 'l' op( A )*X = alpha*B. -* -* SIDE = 'R' or 'r' X*op( A ) = alpha*B. -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**H. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* COMPLEX ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> CTRSM solves one of the matrix equations +*> +*> op( A )*X = alpha*B, or X*op( A ) = alpha*B, +*> +*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T or op( A ) = A**H. +*> +*> The matrix X is overwritten on B. +*> +*>\endverbatim * -* ALPHA - COMPLEX . -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) appears on the left +*> or right of X as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' op( A )*X = alpha*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' X*op( A ) = alpha*B. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**H. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, k ), +*> where k is m when SIDE = 'L' or 'l' +*> and k is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the right-hand side matrix B, and on exit is +*> overwritten by the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - COMPLEX array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the right-hand side matrix B, and on exit is -* overwritten by the solution matrix X. +*> \ingroup complex_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ctrsv.f b/BLAS/SRC/ctrsv.f index 93e7e44f..52fdb37b 100644 --- a/BLAS/SRC/ctrsv.f +++ b/BLAS/SRC/ctrsv.f @@ -1,106 +1,177 @@ - SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX A(LDA,*),X(*) -* .. +*> \brief \b CTRSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* CTRSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, or A**H*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**H*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> CTRSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, or A**H*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**H*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup complex_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dasum.f b/BLAS/SRC/dasum.f index e673554c..b6609ded 100644 --- a/BLAS/SRC/dasum.f +++ b/BLAS/SRC/dasum.f @@ -1,22 +1,70 @@ - DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. +*> \brief \b DASUM * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*) +* .. +* * Purpose * ======= * -* DASUM takes the sum of the absolute values. +*>\details \b Purpose: +*>\verbatim +*> +*> DASUM takes the sum of the absolute values. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/daxpy.f b/BLAS/SRC/daxpy.f index ddc7449a..b21a9654 100644 --- a/BLAS/SRC/daxpy.f +++ b/BLAS/SRC/daxpy.f @@ -1,23 +1,72 @@ - SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) -* .. Scalar Arguments .. - DOUBLE PRECISION DA - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. +*> \brief \b DAXPY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DA +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* * Purpose * ======= * -* DAXPY constant times a vector plus a vector. -* uses unrolled loops for increments equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> DAXPY constant times a vector plus a vector. +*> uses unrolled loops for increments equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + DOUBLE PRECISION DA + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dcabs1.f b/BLAS/SRC/dcabs1.f index 73a51fbe..f290b05c 100644 --- a/BLAS/SRC/dcabs1.f +++ b/BLAS/SRC/dcabs1.f @@ -1,13 +1,53 @@ +*> \brief \b DCABS1 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DCABS1(Z) +* +* .. Scalar Arguments .. +* COMPLEX*16 Z +* .. +* .. +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DCABS1 computes absolute value of a double complex number +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* +* ===================================================================== DOUBLE PRECISION FUNCTION DCABS1(Z) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* * .. Scalar Arguments .. COMPLEX*16 Z * .. * .. -* Purpose -* ======= -* -* DCABS1 computes absolute value of a double complex number -* * ===================================================================== * * .. Intrinsic Functions .. diff --git a/BLAS/SRC/dcopy.f b/BLAS/SRC/dcopy.f index a4414509..35d0f4de 100644 --- a/BLAS/SRC/dcopy.f +++ b/BLAS/SRC/dcopy.f @@ -1,22 +1,70 @@ - SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. +*> \brief \b DCOPY * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* * Purpose * ======= * -* DCOPY copies a vector, x, to a vector, y. -* uses unrolled loops for increments equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> DCOPY copies a vector, x, to a vector, y. +*> uses unrolled loops for increments equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ddot.f b/BLAS/SRC/ddot.f index 33719eed..13acc405 100644 --- a/BLAS/SRC/ddot.f +++ b/BLAS/SRC/ddot.f @@ -1,22 +1,70 @@ - DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. +*> \brief \b DDOT * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* * Purpose * ======= * -* DDOT forms the dot product of two vectors. -* uses unrolled loops for increments equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> DDOT forms the dot product of two vectors. +*> uses unrolled loops for increments equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dgbmv.f b/BLAS/SRC/dgbmv.f index 1fd5a589..92dacb42 100644 --- a/BLAS/SRC/dgbmv.f +++ b/BLAS/SRC/dgbmv.f @@ -1,131 +1,211 @@ - SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,KL,KU,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. +*> \brief \b DGBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER INCX,INCY,KL,KU,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DGBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> DGBMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry, KL specifies the number of sub-diagonals of the +*> matrix A. KL must satisfy 0 .le. KL. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry, KU specifies the number of super-diagonals of the +*> matrix A. KU must satisfy 0 .le. KU. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry, the leading ( kl + ku + 1 ) by n part of the +*> array A must contain the matrix of coefficients, supplied +*> column by column, with the leading diagonal of the matrix in +*> row ( ku + 1 ) of the array, the first super-diagonal +*> starting at position 2 in row ku, the first sub-diagonal +*> starting at position 1 in row ( ku + 2 ), and so on. +*> Elements in the array A that do not correspond to elements +*> in the band matrix (such as the top left ku by ku triangle) +*> are not referenced. +*> The following program segment will transfer a band matrix +*> from conventional full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> K = KU + 1 - J +*> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +*> A( K + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( kl + ku + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* KL - INTEGER. -* On entry, KL specifies the number of sub-diagonals of the -* matrix A. KL must satisfy 0 .le. KL. -* Unchanged on exit. -* -* KU - INTEGER. -* On entry, KU specifies the number of super-diagonals of the -* matrix A. KU must satisfy 0 .le. KU. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry, the leading ( kl + ku + 1 ) by n part of the -* array A must contain the matrix of coefficients, supplied -* column by column, with the leading diagonal of the matrix in -* row ( ku + 1 ) of the array, the first super-diagonal -* starting at position 2 in row ku, the first sub-diagonal -* starting at position 1 in row ( ku + 2 ), and so on. -* Elements in the array A that do not correspond to elements -* in the band matrix (such as the top left ku by ku triangle) -* are not referenced. -* The following program segment will transfer a band matrix -* from conventional full matrix storage to band storage: -* -* DO 20, J = 1, N -* K = KU + 1 - J -* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) -* A( K + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( kl + ku + 1 ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dgemm.f b/BLAS/SRC/dgemm.f index 7ac8c46b..64737822 100644 --- a/BLAS/SRC/dgemm.f +++ b/BLAS/SRC/dgemm.f @@ -1,133 +1,215 @@ - SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b DGEMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,M,N +* CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* DGEMM performs one of the matrix-matrix operations -* -* C := alpha*op( A )*op( B ) + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> DGEMM performs one of the matrix-matrix operations +*> +*> C := alpha*op( A )*op( B ) + beta*C, +*> +*> where op( X ) is one of +*> +*> op( X ) = X or op( X ) = X**T, +*> +*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) +*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> +*>\endverbatim * -* where op( X ) is one of +* Arguments +* ========= +* +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n', op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't', op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c', op( A ) = A**T. +*> \endverbatim +*> +*> \param[in] TRANSB +*> \verbatim +*> TRANSB is CHARACTER*1 +*> On entry, TRANSB specifies the form of op( B ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSB = 'N' or 'n', op( B ) = B. +*> \endverbatim +*> \verbatim +*> TRANSB = 'T' or 't', op( B ) = B**T. +*> \endverbatim +*> \verbatim +*> TRANSB = 'C' or 'c', op( B ) = B**T. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix +*> op( A ) and of the matrix C. M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix +*> op( B ) and the number of columns of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of columns of the matrix +*> op( A ) and the number of rows of the matrix op( B ). K must +*> be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANSA = 'N' or 'n', and is m otherwise. +*> Before entry with TRANSA = 'N' or 'n', the leading m by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by m part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANSA = 'N' or 'n' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is +*> n when TRANSB = 'N' or 'n', and is k otherwise. +*> Before entry with TRANSB = 'N' or 'n', the leading k by n +*> part of the array B must contain the matrix B, otherwise +*> the leading n by k part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANSB = 'N' or 'n' then +*> LDB must be at least max( 1, k ), otherwise LDB must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n matrix +*> ( alpha*op( A )*op( B ) + beta*C ). +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* op( X ) = X or op( X ) = X**T, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* alpha and beta are scalars, and A, B and C are matrices, with op( A ) -* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level3 * -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n', op( A ) = A. -* -* TRANSA = 'T' or 't', op( A ) = A**T. -* -* TRANSA = 'C' or 'c', op( A ) = A**T. -* -* Unchanged on exit. -* -* TRANSB - CHARACTER*1. -* On entry, TRANSB specifies the form of op( B ) to be used in -* the matrix multiplication as follows: -* -* TRANSB = 'N' or 'n', op( B ) = B. -* -* TRANSB = 'T' or 't', op( B ) = B**T. -* -* TRANSB = 'C' or 'c', op( B ) = B**T. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix -* op( A ) and of the matrix C. M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix -* op( B ) and the number of columns of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of columns of the matrix -* op( A ) and the number of rows of the matrix op( B ). K must -* be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is -* k when TRANSA = 'N' or 'n', and is m otherwise. -* Before entry with TRANSA = 'N' or 'n', the leading m by k -* part of the array A must contain the matrix A, otherwise -* the leading k by m part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANSA = 'N' or 'n' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, k ). -* Unchanged on exit. -* -* B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is -* n when TRANSB = 'N' or 'n', and is k otherwise. -* Before entry with TRANSB = 'N' or 'n', the leading k by n -* part of the array B must contain the matrix B, otherwise -* the leading n by k part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANSB = 'N' or 'n' then -* LDB must be at least max( 1, k ), otherwise LDB must be at -* least max( 1, n ). -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n matrix -* ( alpha*op( A )*op( B ) + beta*C ). -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER K,LDA,LDB,LDC,M,N + CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dgemv.f b/BLAS/SRC/dgemv.f index a4125941..c428737a 100644 --- a/BLAS/SRC/dgemv.f +++ b/BLAS/SRC/dgemv.f @@ -1,105 +1,181 @@ - SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. +*> \brief \b DGEMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER INCX,INCY,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DGEMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> DGEMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry with BETA non-zero, the incremented array Y +*> must contain the vector y. On exit, Y is overwritten by the +*> updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry with BETA non-zero, the incremented array Y -* must contain the vector y. On exit, Y is overwritten by the -* updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dger.f b/BLAS/SRC/dger.f index 1d95257e..c0e6059c 100644 --- a/BLAS/SRC/dger.f +++ b/BLAS/SRC/dger.f @@ -1,82 +1,151 @@ - SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. +*> \brief \b DGER +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DGER performs the rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> DGER performs the rank 1 operation +*> +*> A := alpha*x*y**T + A, +*> +*> where alpha is a scalar, x is an m element vector, y is an n element +*> vector and A is an m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( m - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the m +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. On exit, A is +*> overwritten by the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x is an m element vector, y is an n element -* vector and A is an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( m - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the m -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. On exit, A is -* overwritten by the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dnrm2.f b/BLAS/SRC/dnrm2.f index 480c912a..7d4a005d 100644 --- a/BLAS/SRC/dnrm2.f +++ b/BLAS/SRC/dnrm2.f @@ -1,25 +1,73 @@ - DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION X(*) -* .. +*> \brief \b DNRM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION X(*) +* .. +* * Purpose * ======= * -* DNRM2 returns the euclidean norm of a vector via the function -* name, so that +*>\details \b Purpose: +*>\verbatim +*> +*> DNRM2 returns the euclidean norm of a vector via the function +*> name, so that +*> +*> DNRM2 := sqrt( x'*x ) +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 * -* DNRM2 := sqrt( x'*x ) * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> -- This version written on 25-October-1982. +*> Modified on 14-October-1993 to inline the call to DLASSQ. +*> Sven Hammarling, Nag Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- This version written on 25-October-1982. -* Modified on 14-October-1993 to inline the call to DLASSQ. -* Sven Hammarling, Nag Ltd. +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/drot.f b/BLAS/SRC/drot.f index a02bda37..355e17f8 100644 --- a/BLAS/SRC/drot.f +++ b/BLAS/SRC/drot.f @@ -1,22 +1,71 @@ - SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) -* .. Scalar Arguments .. - DOUBLE PRECISION C,S - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. +*> \brief \b DROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION C,S +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* * Purpose * ======= * -* DROT applies a plane rotation. +*>\details \b Purpose: +*>\verbatim +*> +*> DROT applies a plane rotation. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + DOUBLE PRECISION C,S + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/drotg.f b/BLAS/SRC/drotg.f index 3819f473..dcf3e135 100644 --- a/BLAS/SRC/drotg.f +++ b/BLAS/SRC/drotg.f @@ -1,17 +1,62 @@ - SUBROUTINE DROTG(DA,DB,C,S) -* .. Scalar Arguments .. - DOUBLE PRECISION C,DA,DB,S -* .. +*> \brief \b DROTG +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DROTG(DA,DB,C,S) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION C,DA,DB,S +* .. +* * Purpose * ======= * -* DROTG construct givens plane rotation. +*>\details \b Purpose: +*>\verbatim +*> +*> DROTG construct givens plane rotation. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DROTG(DA,DB,C,S) * -* jack dongarra, linpack, 3/11/78. +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION C,DA,DB,S +* .. * * ===================================================================== * diff --git a/BLAS/SRC/drotm.f b/BLAS/SRC/drotm.f index a245116d..4d523113 100644 --- a/BLAS/SRC/drotm.f +++ b/BLAS/SRC/drotm.f @@ -1,54 +1,116 @@ - SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DPARAM(5),DX(*),DY(*) -* .. +*> \brief \b DROTM * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN -* (DY**T) +* Definition +* ========== * -* DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE -* LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY. -* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. -* -* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 +* SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DPARAM(5),DX(*),DY(*) +* .. +* +* Purpose +* ======= * -* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) -* H=( ) ( ) ( ) ( ) -* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). -* SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. +*>\details \b Purpose: +*>\verbatim +*> +*> APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX +*> +*> (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN +*> (DY**T) +*> +*> DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE +*> LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY. +*> WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +*> +*> DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 +*> +*> (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) +*> H=( ) ( ) ( ) ( ) +*> (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). +*> SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* number of elements in input vector(s) +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> number of elements in input vector(s) +*> \endverbatim +*> +*> \param[in,out] DX +*> \verbatim +*> DX is DOUBLE PRECISION array, dimension N +*> double precision vector with N elements +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> storage spacing between elements of DX +*> \endverbatim +*> +*> \param[in,out] DY +*> \verbatim +*> DY is DOUBLE PRECISION array, dimension N +*> double precision vector with N elements +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> storage spacing between elements of DY +*> \endverbatim +*> +*> \param[in,out] DPARAM +*> \verbatim +*> DPARAM is DOUBLE PRECISION array, dimension 5 +*> DPARAM(1)=DFLAG +*> DPARAM(2)=DH11 +*> DPARAM(3)=DH21 +*> DPARAM(4)=DH12 +*> DPARAM(5)=DH22 +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* DX (input/output) DOUBLE PRECISION array, dimension N -* double precision vector with N elements +*> \date November 2011 * -* INCX (input) INTEGER -* storage spacing between elements of DX +*> \ingroup double_blas_level1 * -* DY (input/output) DOUBLE PRECISION array, dimension N -* double precision vector with N elements +* ===================================================================== + SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM) * -* INCY (input) INTEGER -* storage spacing between elements of DY +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* DPARAM (input/output) DOUBLE PRECISION array, dimension 5 -* DPARAM(1)=DFLAG -* DPARAM(2)=DH11 -* DPARAM(3)=DH21 -* DPARAM(4)=DH12 -* DPARAM(5)=DH22 +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DPARAM(5),DX(*),DY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/drotmg.f b/BLAS/SRC/drotmg.f index 108c7949..694d37aa 100644 --- a/BLAS/SRC/drotmg.f +++ b/BLAS/SRC/drotmg.f @@ -1,50 +1,108 @@ - SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM) -* .. Scalar Arguments .. - DOUBLE PRECISION DD1,DD2,DX1,DY1 -* .. -* .. Array Arguments .. - DOUBLE PRECISION DPARAM(5) -* .. -* -* Purpose -* ======= +*> \brief \b DROTMG * -* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS -* THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)* -* DY2)**T. -* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* =========== DOCUMENTATION =========== * -* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) -* H=( ) ( ) ( ) ( ) -* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). -* LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 -* RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE -* VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) +* Definition +* ========== * -* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE -* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE -* OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. +* SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DD1,DD2,DX1,DY1 +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DPARAM(5) +* .. +* +* Purpose +* ======= * +*>\details \b Purpose: +*>\verbatim +*> +*> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS +*> THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T. +*> WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +*> +*> DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 +*> +*> (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) +*> H=( ) ( ) ( ) ( ) +*> (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). +*> LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 +*> RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE +*> VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) +*> +*> THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE +*> INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE +*> OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. +*> +*> +*>\endverbatim * * Arguments * ========= * -* DD1 (input/output) DOUBLE PRECISION +*> \param[in,out] DD1 +*> \verbatim +*> DD1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DD2 +*> \verbatim +*> DD2 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DX1 +*> \verbatim +*> DX1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] DY1 +*> \verbatim +*> DY1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DPARAM +*> \verbatim +*> DPARAM is DOUBLE PRECISION array, dimension 5 +*> DPARAM(1)=DFLAG +*> DPARAM(2)=DH11 +*> DPARAM(3)=DH21 +*> DPARAM(4)=DH12 +*> DPARAM(5)=DH22 +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 * -* DD2 (input/output) DOUBLE PRECISION +*> \ingroup double_blas_level1 * -* DX1 (input/output) DOUBLE PRECISION +* ===================================================================== + SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM) * -* DY1 (input) DOUBLE PRECISION +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* DPARAM (input/output) DOUBLE PRECISION array, dimension 5 -* DPARAM(1)=DFLAG -* DPARAM(2)=DH11 -* DPARAM(3)=DH21 -* DPARAM(4)=DH12 -* DPARAM(5)=DH22 +* .. Scalar Arguments .. + DOUBLE PRECISION DD1,DD2,DX1,DY1 +* .. +* .. Array Arguments .. + DOUBLE PRECISION DPARAM(5) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsbmv.f b/BLAS/SRC/dsbmv.f index e7973517..09c53e1f 100644 --- a/BLAS/SRC/dsbmv.f +++ b/BLAS/SRC/dsbmv.f @@ -1,134 +1,211 @@ - SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,K,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. +*> \brief \b DSBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER INCX,INCY,K,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DSBMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSBMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n symmetric band matrix, with k super-diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the band matrix A is being supplied as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> being supplied. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> being supplied. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of super-diagonals of the +*> matrix A. K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the symmetric matrix, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer the upper +*> triangular part of a symmetric band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the symmetric matrix, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer the lower +*> triangular part of a symmetric band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n symmetric band matrix, with k super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the band matrix A is being supplied as -* follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* being supplied. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* being supplied. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of super-diagonals of the -* matrix A. K must satisfy 0 .le. K. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the symmetric matrix, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer the upper -* triangular part of a symmetric band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the symmetric matrix, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer the lower -* triangular part of a symmetric band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dscal.f b/BLAS/SRC/dscal.f index 986c24eb..50dd2eb5 100644 --- a/BLAS/SRC/dscal.f +++ b/BLAS/SRC/dscal.f @@ -1,24 +1,73 @@ - SUBROUTINE DSCAL(N,DA,DX,INCX) -* .. Scalar Arguments .. - DOUBLE PRECISION DA - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. +*> \brief \b DSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE DSCAL(N,DA,DX,INCX) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*) +* .. +* * Purpose * ======= * -* DSCAL scales a vector by a constant. -* uses unrolled loops for increment equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> DSCAL scales a vector by a constant. +*> uses unrolled loops for increment equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSCAL(N,DA,DX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + DOUBLE PRECISION DA + INTEGER INCX,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsdot.f b/BLAS/SRC/dsdot.f index 8f8ebfdb..cb8de30c 100644 --- a/BLAS/SRC/dsdot.f +++ b/BLAS/SRC/dsdot.f @@ -1,66 +1,138 @@ - DOUBLE PRECISION FUNCTION DSDOT(N,SX,INCX,SY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SX(*),SY(*) -* .. -* -* AUTHORS -* ======= -* Lawson, C. L., (JPL), Hanson, R. J., (SNLA), -* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL) -* +*> \brief \b DSDOT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DSDOT(N,SX,INCX,SY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* +* AUTHORS +* ======= +* Lawson, C. L., (JPL), Hanson, R. J., (SNLA), +* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL) +* * Purpose * ======= -* Compute the inner product of two vectors with extended -* precision accumulation and result. * -* Returns D.P. dot product accumulated in D.P., for S.P. SX and SY -* DSDOT = sum for I = 0 to N-1 of SX(LX+I*INCX) * SY(LY+I*INCY), -* where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is -* defined in a similar way using INCY. +*>\details \b Purpose: +*>\verbatim +*> Compute the inner product of two vectors with extended +*> precision accumulation and result. +*> +*> Returns D.P. dot product accumulated in D.P., for S.P. SX and SY +*> DSDOT = sum for I = 0 to N-1 of SX(LX+I*INCX) * SY(LY+I*INCY), +*> where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +*> defined in a similar way using INCY. +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* number of elements in input vector(s) -* -* SX (input) REAL array, dimension(N) -* single precision vector with N elements +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> number of elements in input vector(s) +*> \endverbatim +*> +*> \param[in] SX +*> \verbatim +*> SX is REAL array, dimension(N) +*> single precision vector with N elements +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> storage spacing between elements of SX +*> \endverbatim +*> +*> \param[in] SY +*> \verbatim +*> SY is REAL array, dimension(N) +*> single precision vector with N elements +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> storage spacing between elements of SY +*> \endverbatim +*> +*> \param[out] DSDOT +*> \verbatim +*> DSDOT is DOUBLE PRECISION +*> DSDOT double precision dot product (zero if N.LE.0) +*> \endverbatim +*> +* +* Authors +* ======= * -* INCX (input) INTEGER -* storage spacing between elements of SX +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* SY (input) REAL array, dimension(N) -* single precision vector with N elements +*> \date November 2011 * -* INCY (input) INTEGER -* storage spacing between elements of SY +*> \ingroup double_blas_level1 * -* DSDOT (output) DOUBLE PRECISION -* DSDOT double precision dot product (zero if N.LE.0) * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> REFERENCES +*> +*> C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +*> Krogh, Basic linear algebra subprograms for Fortran +*> usage, Algorithm No. 539, Transactions on Mathematical +*> Software 5, 3 (September 1979), pp. 308-323. +*> +*> REVISION HISTORY (YYMMDD) +*> +*> 791001 DATE WRITTEN +*> 890831 Modified array declarations. (WRB) +*> 890831 REVISION DATE from Version 3.2 +*> 891214 Prologue converted to Version 4.0 format. (BAB) +*> 920310 Corrected definition of LX in DESCRIPTION. (WRB) +*> 920501 Reformatted the REFERENCES section. (WRB) +*> 070118 Reformat to LAPACK style (JL) +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DSDOT(N,SX,INCX,SY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SX(*),SY(*) +* .. * -* REFERENCES -* -* C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. -* Krogh, Basic linear algebra subprograms for Fortran -* usage, Algorithm No. 539, Transactions on Mathematical -* Software 5, 3 (September 1979), pp. 308-323. -* -* REVISION HISTORY (YYMMDD) -* -* 791001 DATE WRITTEN -* 890831 Modified array declarations. (WRB) -* 890831 REVISION DATE from Version 3.2 -* 891214 Prologue converted to Version 4.0 format. (BAB) -* 920310 Corrected definition of LX in DESCRIPTION. (WRB) -* 920501 Reformatted the REFERENCES section. (WRB) -* 070118 Reformat to LAPACK style (JL) +* AUTHORS +* ======= +* Lawson, C. L., (JPL), Hanson, R. J., (SNLA), +* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL) * * ===================================================================== * diff --git a/BLAS/SRC/dspmv.f b/BLAS/SRC/dspmv.f index 4067b0e3..b0c0ceda 100644 --- a/BLAS/SRC/dspmv.f +++ b/BLAS/SRC/dspmv.f @@ -1,100 +1,171 @@ - SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION AP(*),X(*),Y(*) -* .. +*> \brief \b DSPMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DSPMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSPMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n symmetric matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is DOUBLE PRECISION array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n symmetric matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* AP - DOUBLE PRECISION array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dspr.f b/BLAS/SRC/dspr.f index 64567fc7..87fd3bc8 100644 --- a/BLAS/SRC/dspr.f +++ b/BLAS/SRC/dspr.f @@ -1,86 +1,151 @@ - SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION AP(*),X(*) -* .. +*> \brief \b DSPR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP(*),X(*) +* .. +* * Purpose * ======= * -* DSPR performs the symmetric rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSPR performs the symmetric rank 1 operation +*> +*> A := alpha*x*x**T + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n symmetric matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is DOUBLE PRECISION array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n symmetric matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* AP - DOUBLE PRECISION array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dspr2.f b/BLAS/SRC/dspr2.f index 22900ad0..54553ec1 100644 --- a/BLAS/SRC/dspr2.f +++ b/BLAS/SRC/dspr2.f @@ -1,97 +1,166 @@ - SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION AP(*),X(*),Y(*) -* .. +*> \brief \b DSPR2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DSPR2 performs the symmetric rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSPR2 performs the symmetric rank 2 operation +*> +*> A := alpha*x*y**T + alpha*y*x**T + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an +*> n by n symmetric matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is DOUBLE PRECISION array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + alpha*y*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an -* n by n symmetric matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* AP - DOUBLE PRECISION array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dswap.f b/BLAS/SRC/dswap.f index 93db05cb..27760582 100644 --- a/BLAS/SRC/dswap.f +++ b/BLAS/SRC/dswap.f @@ -1,22 +1,70 @@ - SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. +*> \brief \b DSWAP * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* * Purpose * ======= * -* interchanges two vectors. -* uses unrolled loops for increments equal one. +*>\details \b Purpose: +*>\verbatim +*> +*> interchanges two vectors. +*> uses unrolled loops for increments equal one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsymm.f b/BLAS/SRC/dsymm.f index d9d3c96a..f3537fa9 100644 --- a/BLAS/SRC/dsymm.f +++ b/BLAS/SRC/dsymm.f @@ -1,137 +1,215 @@ - SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b DSYMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER LDA,LDB,LDC,M,N +* CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* DSYMM performs one of the matrix-matrix operations -* -* C := alpha*A*B + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> DSYMM performs one of the matrix-matrix operations +*> +*> C := alpha*A*B + beta*C, +*> +*> or +*> +*> C := alpha*B*A + beta*C, +*> +*> where alpha and beta are scalars, A is a symmetric matrix and B and +*> C are m by n matrices. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether the symmetric matrix A +*> appears on the left or right in the operation as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the symmetric matrix A is to be +*> referenced as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix C. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix C. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is +*> m when SIDE = 'L' or 'l' and is n otherwise. +*> Before entry with SIDE = 'L' or 'l', the m by m part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading m by m upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading m by m lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Before entry with SIDE = 'R' or 'r', the n by n part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading n by n upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading n by n lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n updated +*> matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*B*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, A is a symmetric matrix and B and -* C are m by n matrices. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level3 * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether the symmetric matrix A -* appears on the left or right in the operation as follows: -* -* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -* -* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the symmetric matrix A is to be -* referenced as follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of the -* symmetric matrix is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of the -* symmetric matrix is to be referenced. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix C. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix C. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is -* m when SIDE = 'L' or 'l' and is n otherwise. -* Before entry with SIDE = 'L' or 'l', the m by m part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading m by m upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading m by m lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Before entry with SIDE = 'R' or 'r', the n by n part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading n by n upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading n by n lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, n ). -* Unchanged on exit. -* -* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n updated -* matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER LDA,LDB,LDC,M,N + CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsymv.f b/BLAS/SRC/dsymv.f index 5fa4341a..5dfc7ea9 100644 --- a/BLAS/SRC/dsymv.f +++ b/BLAS/SRC/dsymv.f @@ -1,103 +1,176 @@ - SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. +*> \brief \b DSYMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DSYMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSYMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n symmetric matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of A is not referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n symmetric matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of A is not referenced. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsyr.f b/BLAS/SRC/dsyr.f index 5cc4bcb5..81a01078 100644 --- a/BLAS/SRC/dsyr.f +++ b/BLAS/SRC/dsyr.f @@ -1,89 +1,156 @@ - SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. +*> \brief \b DSYR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* DSYR performs the symmetric rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSYR performs the symmetric rank 1 operation +*> +*> A := alpha*x*x**T + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n symmetric matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n symmetric matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsyr2.f b/BLAS/SRC/dsyr2.f index b2b2f3d7..7b72a342 100644 --- a/BLAS/SRC/dsyr2.f +++ b/BLAS/SRC/dsyr2.f @@ -1,100 +1,171 @@ - SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. +*> \brief \b DSYR2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* DSYR2 performs the symmetric rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> DSYR2 performs the symmetric rank 2 operation +*> +*> A := alpha*x*y**T + alpha*y*x**T + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an n +*> by n symmetric matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + alpha*y*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an n -* by n symmetric matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsyr2k.f b/BLAS/SRC/dsyr2k.f index 7289b055..3c2de59a 100644 --- a/BLAS/SRC/dsyr2k.f +++ b/BLAS/SRC/dsyr2k.f @@ -1,140 +1,219 @@ - SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b DSYR2K +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* DSYR2K performs one of the symmetric rank 2k operations -* -* C := alpha*A*B**T + alpha*B*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> DSYR2K performs one of the symmetric rank 2k operations +*> +*> C := alpha*A*B**T + alpha*B*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A and B are n by k matrices in the first case and k by n +*> matrices in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + +*> beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrices A and B, and on entry with +*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number +*> of rows of the matrices A and B. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array B must contain the matrix B, otherwise +*> the leading k by n part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDB must be at least max( 1, n ), otherwise LDB must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A and B are n by k matrices in the first case and k by n -* matrices in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + -* beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + -* beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + -* beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrices A and B, and on entry with -* TRANS = 'T' or 't' or 'C' or 'c', K specifies the number -* of rows of the matrices A and B. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array B must contain the matrix B, otherwise -* the leading k by n part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDB must be at least max( 1, n ), otherwise LDB must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. -* +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER K,LDA,LDB,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dsyrk.f b/BLAS/SRC/dsyrk.f index 00fb33ae..df232ff4 100644 --- a/BLAS/SRC/dsyrk.f +++ b/BLAS/SRC/dsyrk.f @@ -1,121 +1,196 @@ - SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),C(LDC,*) -* .. +*> \brief \b DSYRK +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER K,LDA,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),C(LDC,*) +* .. +* * Purpose * ======= * -* DSYRK performs one of the symmetric rank k operations -* -* C := alpha*A*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> DSYRK performs one of the symmetric rank k operations +*> +*> C := alpha*A*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A is an n by k matrix in the first case and a k by n matrix +*> in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrix A, and on entry with +*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number +*> of rows of the matrix A. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A is an n by k matrix in the first case and a k by n matrix -* in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrix A, and on entry with -* TRANS = 'T' or 't' or 'C' or 'c', K specifies the number -* of rows of the matrix A. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER K,LDA,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtbmv.f b/BLAS/SRC/dtbmv.f index 4f8778ad..ad062ca9 100644 --- a/BLAS/SRC/dtbmv.f +++ b/BLAS/SRC/dtbmv.f @@ -1,141 +1,218 @@ - SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. +*> \brief \b DTBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* DTBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> DTBMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**T*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* x := A*x, or x := A**T*x, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**T*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtbsv.f b/BLAS/SRC/dtbsv.f index 621c1ec7..9a2b8429 100644 --- a/BLAS/SRC/dtbsv.f +++ b/BLAS/SRC/dtbsv.f @@ -1,144 +1,221 @@ - SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. +*> \brief \b DTBSV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* DTBSV solves one of the systems of equations +*>\details \b Purpose: +*>\verbatim +*> +*> DTBSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular band matrix, with ( k + 1 ) +*> diagonals. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* A*x = b, or A**T*x = b, +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular band matrix, with ( k + 1 ) -* diagonals. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup double_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**T*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtpmv.f b/BLAS/SRC/dtpmv.f index 1def763e..b11f4dbe 100644 --- a/BLAS/SRC/dtpmv.f +++ b/BLAS/SRC/dtpmv.f @@ -1,101 +1,170 @@ - SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION AP(*),X(*) -* .. -* -* Purpose -* ======= -* -* DTPMV performs one of the matrix-vector operations +*> \brief \b DTPMV * -* x := A*x, or x := A**T*x, +* =========== DOCUMENTATION =========== * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix, supplied in packed form. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**T*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> DTPMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix, supplied in packed form. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**T*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is DOUBLE PRECISION array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - DOUBLE PRECISION array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup double_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtpsv.f b/BLAS/SRC/dtpsv.f index 49b65237..bd7c5ec3 100644 --- a/BLAS/SRC/dtpsv.f +++ b/BLAS/SRC/dtpsv.f @@ -1,103 +1,172 @@ - SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION AP(*),X(*) -* .. +*> \brief \b DTPSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* DTPSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix, supplied in packed form. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**T*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> DTPSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix, supplied in packed form. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is DOUBLE PRECISION array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - DOUBLE PRECISION array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup double_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtrmm.f b/BLAS/SRC/dtrmm.f index fc03769f..9e4cc226 100644 --- a/BLAS/SRC/dtrmm.f +++ b/BLAS/SRC/dtrmm.f @@ -1,129 +1,206 @@ - SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b DTRMM * -* DTRMM performs one of the matrix-matrix operations +* =========== DOCUMENTATION =========== * -* B := alpha*op( A )*B, or B := alpha*B*op( A ), +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, B is an m by n matrix, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) multiplies B from -* the left or right as follows: -* -* SIDE = 'L' or 'l' B := alpha*op( A )*B. -* -* SIDE = 'R' or 'r' B := alpha*B*op( A ). -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**T. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> DTRMM performs one of the matrix-matrix operations +*> +*> B := alpha*op( A )*B, or B := alpha*B*op( A ), +*> +*> where alpha is a scalar, B is an m by n matrix, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T. +*> +*>\endverbatim * -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) multiplies B from +*> the left or right as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' B := alpha*op( A )*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' B := alpha*B*op( A ). +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**T. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> \verbatim +*> A DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m +*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B, and on exit is overwritten by the +*> transformed matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B, and on exit is overwritten by the -* transformed matrix. +*> \ingroup double_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtrmv.f b/BLAS/SRC/dtrmv.f index 5356cbbc..c4864bf5 100644 --- a/BLAS/SRC/dtrmv.f +++ b/BLAS/SRC/dtrmv.f @@ -1,104 +1,175 @@ - SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. +*> \brief \b DTRMV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* DTRMV performs one of the matrix-vector operations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* x := A*x, or x := A**T*x, -* -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**T*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> DTRMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**T*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup double_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtrsm.f b/BLAS/SRC/dtrsm.f index dec5c8d0..3a91fd43 100644 --- a/BLAS/SRC/dtrsm.f +++ b/BLAS/SRC/dtrsm.f @@ -1,132 +1,212 @@ - SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b DTRSM * -* DTRSM solves one of the matrix equations +* =========== DOCUMENTATION =========== * -* op( A )*X = alpha*B, or X*op( A ) = alpha*B, +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, X and B are m by n matrices, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T. -* -* The matrix X is overwritten on B. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) appears on the left -* or right of X as follows: -* -* SIDE = 'L' or 'l' op( A )*X = alpha*B. -* -* SIDE = 'R' or 'r' X*op( A ) = alpha*B. -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**T. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> DTRSM solves one of the matrix equations +*> +*> op( A )*X = alpha*B, or X*op( A ) = alpha*B, +*> +*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T. +*> +*> The matrix X is overwritten on B. +*> +*>\endverbatim * -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) appears on the left +*> or right of X as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' op( A )*X = alpha*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' X*op( A ) = alpha*B. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**T. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), +*> where k is m when SIDE = 'L' or 'l' +*> and k is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the right-hand side matrix B, and on exit is +*> overwritten by the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the right-hand side matrix B, and on exit is -* overwritten by the solution matrix X. +*> \ingroup double_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. -* +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dtrsv.f b/BLAS/SRC/dtrsv.f index f901e699..4a0845b7 100644 --- a/BLAS/SRC/dtrsv.f +++ b/BLAS/SRC/dtrsv.f @@ -1,104 +1,171 @@ - SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. -* -* Purpose -* ======= -* -* DTRSV solves one of the systems of equations -* -* A*x = b, or A**T*x = b, +*> \brief \b DTRSV * -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix. +* =========== DOCUMENTATION =========== * -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**T*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. +* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> DTRSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> \verbatim +*> Level 2 Blas routine. +*> \endverbatim +*> \verbatim +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> \endverbatim +*> +* +* Authors +* ======= * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* X - DOUBLE PRECISION array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \date November 2011 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. +*> \ingroup double_blas_level1 * +* ===================================================================== + SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dzasum.f b/BLAS/SRC/dzasum.f index 992b3a5c..ea61e0bb 100644 --- a/BLAS/SRC/dzasum.f +++ b/BLAS/SRC/dzasum.f @@ -1,22 +1,70 @@ - DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*) -* .. +*> \brief \b DZASUM * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*) +* .. +* * Purpose * ======= * -* DZASUM takes the sum of the absolute values. +*>\details \b Purpose: +*>\verbatim +*> +*> DZASUM takes the sum of the absolute values. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/dznrm2.f b/BLAS/SRC/dznrm2.f index a5e3da08..4a6b7573 100644 --- a/BLAS/SRC/dznrm2.f +++ b/BLAS/SRC/dznrm2.f @@ -1,25 +1,73 @@ - DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 X(*) -* .. +*> \brief \b DZNRM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX*16 X(*) +* .. +* * Purpose * ======= * -* DZNRM2 returns the euclidean norm of a vector via the function -* name, so that +*>\details \b Purpose: +*>\verbatim +*> +*> DZNRM2 returns the euclidean norm of a vector via the function +*> name, so that +*> +*> DZNRM2 := sqrt( x**H*x ) +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 * -* DZNRM2 := sqrt( x**H*x ) * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> -- This version written on 25-October-1982. +*> Modified on 14-October-1993 to inline the call to ZLASSQ. +*> Sven Hammarling, Nag Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- This version written on 25-October-1982. -* Modified on 14-October-1993 to inline the call to ZLASSQ. -* Sven Hammarling, Nag Ltd. +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX*16 X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/icamax.f b/BLAS/SRC/icamax.f index 2c941f97..5e060ec0 100644 --- a/BLAS/SRC/icamax.f +++ b/BLAS/SRC/icamax.f @@ -1,22 +1,70 @@ - INTEGER FUNCTION ICAMAX(N,CX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX CX(*) -* .. +*> \brief \b ICAMAX * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* INTEGER FUNCTION ICAMAX(N,CX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*) +* .. +* * Purpose * ======= * -* ICAMAX finds the index of element having max. absolute value. +*>\details \b Purpose: +*>\verbatim +*> +*> ICAMAX finds the index of element having max. absolute value. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup aux_blas +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + INTEGER FUNCTION ICAMAX(N,CX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX CX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/idamax.f b/BLAS/SRC/idamax.f index 2cc0f9a5..e10fa057 100644 --- a/BLAS/SRC/idamax.f +++ b/BLAS/SRC/idamax.f @@ -1,22 +1,70 @@ - INTEGER FUNCTION IDAMAX(N,DX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. +*> \brief \b IDAMAX * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* INTEGER FUNCTION IDAMAX(N,DX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*) +* .. +* * Purpose * ======= * -* IDAMAX finds the index of element having max. absolute value. +*>\details \b Purpose: +*>\verbatim +*> +*> IDAMAX finds the index of element having max. absolute value. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup aux_blas +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + INTEGER FUNCTION IDAMAX(N,DX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/isamax.f b/BLAS/SRC/isamax.f index 26a98dd5..4e03d89a 100644 --- a/BLAS/SRC/isamax.f +++ b/BLAS/SRC/isamax.f @@ -1,22 +1,70 @@ - INTEGER FUNCTION ISAMAX(N,SX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - REAL SX(*) -* .. +*> \brief \b ISAMAX * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* INTEGER FUNCTION ISAMAX(N,SX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* REAL SX(*) +* .. +* * Purpose * ======= * -* ISAMAX finds the index of element having max. absolute value. +*>\details \b Purpose: +*>\verbatim +*> +*> ISAMAX finds the index of element having max. absolute value. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup aux_blas +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + INTEGER FUNCTION ISAMAX(N,SX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + REAL SX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/izamax.f b/BLAS/SRC/izamax.f index 9ab4b45d..592c3363 100644 --- a/BLAS/SRC/izamax.f +++ b/BLAS/SRC/izamax.f @@ -1,22 +1,70 @@ - INTEGER FUNCTION IZAMAX(N,ZX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*) -* .. +*> \brief \b IZAMAX * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* INTEGER FUNCTION IZAMAX(N,ZX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*) +* .. +* * Purpose * ======= * -* IZAMAX finds the index of element having max. absolute value. +*>\details \b Purpose: +*>\verbatim +*> +*> IZAMAX finds the index of element having max. absolute value. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup aux_blas +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 1/15/85. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + INTEGER FUNCTION IZAMAX(N,ZX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 1/15/85. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/lsame.f b/BLAS/SRC/lsame.f index f5369026..7c0c8a07 100644 --- a/BLAS/SRC/lsame.f +++ b/BLAS/SRC/lsame.f @@ -1,26 +1,68 @@ - LOGICAL FUNCTION LSAME(CA,CB) +*> \brief \b LSAME * -* -- LAPACK auxiliary routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - CHARACTER CA,CB -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* LOGICAL FUNCTION LSAME(CA,CB) +* +* .. Scalar Arguments .. +* CHARACTER CA,CB +* .. +* * Purpose * ======= * -* LSAME returns .TRUE. if CA is the same letter as CB regardless of -* case. +*>\details \b Purpose: +*>\verbatim +*> +*> LSAME returns .TRUE. if CA is the same letter as CB regardless of +*> case. +*> +*>\endverbatim * * Arguments * ========= * -* CA (input) CHARACTER*1 +*> \param[in] CA +*> \verbatim +*> CA is CHARACTER*1 +*> \endverbatim +*> +*> \param[in] CB +*> \verbatim +*> CB is CHARACTER*1 +*> CA and CB specify the single characters to be compared. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 * -* CB (input) CHARACTER*1 -* CA and CB specify the single characters to be compared. +*> \ingroup aux_blas +* +* ===================================================================== + LOGICAL FUNCTION LSAME(CA,CB) +* +* -- Reference BLAS level1 routine (version 3.1) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CA,CB +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sasum.f b/BLAS/SRC/sasum.f index 1e3f7db8..400eab05 100644 --- a/BLAS/SRC/sasum.f +++ b/BLAS/SRC/sasum.f @@ -1,23 +1,71 @@ - REAL FUNCTION SASUM(N,SX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - REAL SX(*) -* .. +*> \brief \b SASUM * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SASUM(N,SX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* REAL SX(*) +* .. +* * Purpose * ======= * -* SASUM takes the sum of the absolute values. -* uses unrolled loops for increment equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> SASUM takes the sum of the absolute values. +*> uses unrolled loops for increment equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SASUM(N,SX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + REAL SX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/saxpy.f b/BLAS/SRC/saxpy.f index c0d8b3a0..648be35f 100644 --- a/BLAS/SRC/saxpy.f +++ b/BLAS/SRC/saxpy.f @@ -1,23 +1,72 @@ - SUBROUTINE SAXPY(N,SA,SX,INCX,SY,INCY) -* .. Scalar Arguments .. - REAL SA - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SX(*),SY(*) -* .. +*> \brief \b SAXPY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE SAXPY(N,SA,SX,INCX,SY,INCY) +* +* .. Scalar Arguments .. +* REAL SA +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* * Purpose * ======= * -* SAXPY constant times a vector plus a vector. -* uses unrolled loops for increments equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> SAXPY constant times a vector plus a vector. +*> uses unrolled loops for increments equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SAXPY(N,SA,SX,INCX,SY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + REAL SA + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SX(*),SY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/scabs1.f b/BLAS/SRC/scabs1.f index eccb9f61..f17280fe 100644 --- a/BLAS/SRC/scabs1.f +++ b/BLAS/SRC/scabs1.f @@ -1,12 +1,52 @@ - REAL FUNCTION SCABS1(Z) -* .. Scalar Arguments .. - COMPLEX Z -* .. +*> \brief \b SCABS1 +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SCABS1(Z) +* +* .. Scalar Arguments .. +* COMPLEX Z +* .. +* * Purpose * ======= * -* SCABS1 computes absolute value of a complex number +*>\details \b Purpose: +*>\verbatim +*> +*> SCABS1 computes absolute value of a complex number +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* +* ===================================================================== + REAL FUNCTION SCABS1(Z) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + COMPLEX Z +* .. * * ===================================================================== * diff --git a/BLAS/SRC/scasum.f b/BLAS/SRC/scasum.f index d090110c..dde1badb 100644 --- a/BLAS/SRC/scasum.f +++ b/BLAS/SRC/scasum.f @@ -1,23 +1,71 @@ - REAL FUNCTION SCASUM(N,CX,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX CX(*) -* .. +*> \brief \b SCASUM * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SCASUM(N,CX,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX CX(*) +* .. +* * Purpose * ======= * -* SCASUM takes the sum of the absolute values of a complex vector and -* returns a single precision result. +*>\details \b Purpose: +*>\verbatim +*> +*> SCASUM takes the sum of the absolute values of a complex vector and +*> returns a single precision result. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SCASUM(N,CX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX CX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/scnrm2.f b/BLAS/SRC/scnrm2.f index 1738c315..8b3f8e06 100644 --- a/BLAS/SRC/scnrm2.f +++ b/BLAS/SRC/scnrm2.f @@ -1,25 +1,73 @@ - REAL FUNCTION SCNRM2(N,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX X(*) -* .. +*> \brief \b SCNRM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* REAL FUNCTION SCNRM2(N,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX X(*) +* .. +* * Purpose * ======= * -* SCNRM2 returns the euclidean norm of a vector via the function -* name, so that +*>\details \b Purpose: +*>\verbatim +*> +*> SCNRM2 returns the euclidean norm of a vector via the function +*> name, so that +*> +*> SCNRM2 := sqrt( x**H*x ) +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 * -* SCNRM2 := sqrt( x**H*x ) * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> -- This version written on 25-October-1982. +*> Modified on 14-October-1993 to inline the call to CLASSQ. +*> Sven Hammarling, Nag Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SCNRM2(N,X,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- This version written on 25-October-1982. -* Modified on 14-October-1993 to inline the call to CLASSQ. -* Sven Hammarling, Nag Ltd. +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/scopy.f b/BLAS/SRC/scopy.f index 905a64cb..f8b5d676 100644 --- a/BLAS/SRC/scopy.f +++ b/BLAS/SRC/scopy.f @@ -1,22 +1,70 @@ - SUBROUTINE SCOPY(N,SX,INCX,SY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SX(*),SY(*) -* .. +*> \brief \b SCOPY * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SCOPY(N,SX,INCX,SY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* * Purpose * ======= * -* SCOPY copies a vector, x, to a vector, y. -* uses unrolled loops for increments equal to 1. +*>\details \b Purpose: +*>\verbatim +*> +*> SCOPY copies a vector, x, to a vector, y. +*> uses unrolled loops for increments equal to 1. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SCOPY(N,SX,INCX,SY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SX(*),SY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sdot.f b/BLAS/SRC/sdot.f index 4629bbba..d3429a24 100644 --- a/BLAS/SRC/sdot.f +++ b/BLAS/SRC/sdot.f @@ -1,22 +1,70 @@ - REAL FUNCTION SDOT(N,SX,INCX,SY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SX(*),SY(*) -* .. +*> \brief \b SDOT * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SDOT(N,SX,INCX,SY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* * Purpose * ======= * -* SDOT forms the dot product of two vectors. -* uses unrolled loops for increments equal to one. +*>\details \b Purpose: +*>\verbatim +*> +*> SDOT forms the dot product of two vectors. +*> uses unrolled loops for increments equal to one. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SDOT(N,SX,INCX,SY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SX(*),SY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sdsdot.f b/BLAS/SRC/sdsdot.f index b84a6c51..7be8af19 100644 --- a/BLAS/SRC/sdsdot.f +++ b/BLAS/SRC/sdsdot.f @@ -1,4 +1,150 @@ +*> \brief \b SDSDOT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* REAL FUNCTION SDSDOT(N,SB,SX,INCX,SY,INCY) +* +* .. Scalar Arguments .. +* REAL SB +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* +* PURPOSE +* ======= +* +* Compute the inner product of two vectors with extended +* precision accumulation. +* +* Returns S.P. result with dot product accumulated in D.P. +* SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY), +* where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +* defined in a similar way using INCY. +* +* AUTHOR +* ====== +* Lawson, C. L., (JPL), Hanson, R. J., (SNLA), +* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL) +* +* ARGUMENTS +* ========= +* +* N (input) INTEGER +* number of elements in input vector(s) +* +* SB (input) REAL +* single precision scalar to be added to inner product +* +* SX (input) REAL array, dimension (N) +* single precision vector with N elements +* +* INCX (input) INTEGER +* storage spacing between elements of SX +* +* SY (input) REAL array, dimension (N) +* single precision vector with N elements +* +* INCY (input) INTEGER +* storage spacing between elements of SY +* +* SDSDOT (output) REAL +* single precision dot product (SB if N .LE. 0) +* +* Further Details +* =============== +* +* REFERENCES +* +* C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +* Krogh, Basic linear algebra subprograms for Fortran +* usage, Algorithm No. 539, Transactions on Mathematical +* Software 5, 3 (September 1979), pp. 308-323. +* +* REVISION HISTORY (YYMMDD) +* +* 791001 DATE WRITTEN +* 890531 Changed all specific intrinsics to generic. (WRB) +* 890831 Modified array declarations. (WRB) +* 890831 REVISION DATE from Version 3.2 +* 891214 Prologue converted to Version 4.0 format. (BAB) +* 920310 Corrected definition of LX in DESCRIPTION. (WRB) +* 920501 Reformatted the REFERENCES section. (WRB) +* 070118 Reformat to LAPACK coding style +* +* ===================================================================== +* +* .. Local Scalars .. +* DOUBLE PRECISION DSDOT +* INTEGER I,KX,KY,NS +* .. +* .. Intrinsic Functions .. +* INTRINSIC DBLE +* .. +* DSDOT = SB +* IF (N.LE.0) THEN +* SDSDOT = DSDOT +* RETURN +* END IF +* IF (INCX.EQ.INCY .AND. INCX.GT.0) THEN +* +* Code for equal and positive increments. +* +* NS = N*INCX +* DO I = 1,NS,INCX +* DSDOT = DSDOT + DBLE(SX(I))*DBLE(SY(I)) +* END DO +* ELSE +* +* Code for unequal or nonpositive increments. +* +* KX = 1 +* KY = 1 +* IF (INCX.LT.0) KX = 1 + (1-N)*INCX +* IF (INCY.LT.0) KY = 1 + (1-N)*INCY +* DO I = 1,N +* DSDOT = DSDOT + DBLE(SX(KX))*DBLE(SY(KY)) +* KX = KX + INCX +* KY = KY + INCY +* END DO +* END IF +* SDSDOT = DSDOT +* RETURN +* END +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* +* ===================================================================== REAL FUNCTION SDSDOT(N,SB,SX,INCX,SY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* * .. Scalar Arguments .. REAL SB INTEGER INCX,INCY,N diff --git a/BLAS/SRC/sgbmv.f b/BLAS/SRC/sgbmv.f index 9c81731a..774dcda0 100644 --- a/BLAS/SRC/sgbmv.f +++ b/BLAS/SRC/sgbmv.f @@ -1,131 +1,211 @@ - SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER INCX,INCY,KL,KU,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*),Y(*) -* .. +*> \brief \b SGBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER INCX,INCY,KL,KU,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SGBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> SGBMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry, KL specifies the number of sub-diagonals of the +*> matrix A. KL must satisfy 0 .le. KL. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry, KU specifies the number of super-diagonals of the +*> matrix A. KU must satisfy 0 .le. KU. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry, the leading ( kl + ku + 1 ) by n part of the +*> array A must contain the matrix of coefficients, supplied +*> column by column, with the leading diagonal of the matrix in +*> row ( ku + 1 ) of the array, the first super-diagonal +*> starting at position 2 in row ku, the first sub-diagonal +*> starting at position 1 in row ( ku + 2 ), and so on. +*> Elements in the array A that do not correspond to elements +*> in the band matrix (such as the top left ku by ku triangle) +*> are not referenced. +*> The following program segment will transfer a band matrix +*> from conventional full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> K = KU + 1 - J +*> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +*> A( K + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( kl + ku + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is REAL array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* KL - INTEGER. -* On entry, KL specifies the number of sub-diagonals of the -* matrix A. KL must satisfy 0 .le. KL. -* Unchanged on exit. -* -* KU - INTEGER. -* On entry, KU specifies the number of super-diagonals of the -* matrix A. KU must satisfy 0 .le. KU. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry, the leading ( kl + ku + 1 ) by n part of the -* array A must contain the matrix of coefficients, supplied -* column by column, with the leading diagonal of the matrix in -* row ( ku + 1 ) of the array, the first super-diagonal -* starting at position 2 in row ku, the first sub-diagonal -* starting at position 1 in row ( ku + 2 ), and so on. -* Elements in the array A that do not correspond to elements -* in the band matrix (such as the top left ku by ku triangle) -* are not referenced. -* The following program segment will transfer a band matrix -* from conventional full matrix storage to band storage: -* -* DO 20, J = 1, N -* K = KU + 1 - J -* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) -* A( K + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( kl + ku + 1 ). -* Unchanged on exit. -* -* X - REAL array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - REAL array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sgemm.f b/BLAS/SRC/sgemm.f index 36c00d03..8ef99eac 100644 --- a/BLAS/SRC/sgemm.f +++ b/BLAS/SRC/sgemm.f @@ -1,133 +1,215 @@ - SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - REAL A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b SGEMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,M,N +* CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. +* REAL A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* SGEMM performs one of the matrix-matrix operations -* -* C := alpha*op( A )*op( B ) + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> SGEMM performs one of the matrix-matrix operations +*> +*> C := alpha*op( A )*op( B ) + beta*C, +*> +*> where op( X ) is one of +*> +*> op( X ) = X or op( X ) = X**T, +*> +*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) +*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> +*>\endverbatim * -* where op( X ) is one of +* Arguments +* ========= +* +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n', op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't', op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c', op( A ) = A**T. +*> \endverbatim +*> +*> \param[in] TRANSB +*> \verbatim +*> TRANSB is CHARACTER*1 +*> On entry, TRANSB specifies the form of op( B ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSB = 'N' or 'n', op( B ) = B. +*> \endverbatim +*> \verbatim +*> TRANSB = 'T' or 't', op( B ) = B**T. +*> \endverbatim +*> \verbatim +*> TRANSB = 'C' or 'c', op( B ) = B**T. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix +*> op( A ) and of the matrix C. M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix +*> op( B ) and the number of columns of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of columns of the matrix +*> op( A ) and the number of rows of the matrix op( B ). K must +*> be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANSA = 'N' or 'n', and is m otherwise. +*> Before entry with TRANSA = 'N' or 'n', the leading m by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by m part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANSA = 'N' or 'n' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is REAL array of DIMENSION ( LDB, kb ), where kb is +*> n when TRANSB = 'N' or 'n', and is k otherwise. +*> Before entry with TRANSB = 'N' or 'n', the leading k by n +*> part of the array B must contain the matrix B, otherwise +*> the leading n by k part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANSB = 'N' or 'n' then +*> LDB must be at least max( 1, k ), otherwise LDB must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is REAL array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n matrix +*> ( alpha*op( A )*op( B ) + beta*C ). +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* op( X ) = X or op( X ) = X**T, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* alpha and beta are scalars, and A, B and C are matrices, with op( A ) -* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level3 * -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n', op( A ) = A. -* -* TRANSA = 'T' or 't', op( A ) = A**T. -* -* TRANSA = 'C' or 'c', op( A ) = A**T. -* -* Unchanged on exit. -* -* TRANSB - CHARACTER*1. -* On entry, TRANSB specifies the form of op( B ) to be used in -* the matrix multiplication as follows: -* -* TRANSB = 'N' or 'n', op( B ) = B. -* -* TRANSB = 'T' or 't', op( B ) = B**T. -* -* TRANSB = 'C' or 'c', op( B ) = B**T. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix -* op( A ) and of the matrix C. M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix -* op( B ) and the number of columns of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of columns of the matrix -* op( A ) and the number of rows of the matrix op( B ). K must -* be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, ka ), where ka is -* k when TRANSA = 'N' or 'n', and is m otherwise. -* Before entry with TRANSA = 'N' or 'n', the leading m by k -* part of the array A must contain the matrix A, otherwise -* the leading k by m part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANSA = 'N' or 'n' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, k ). -* Unchanged on exit. -* -* B - REAL array of DIMENSION ( LDB, kb ), where kb is -* n when TRANSB = 'N' or 'n', and is k otherwise. -* Before entry with TRANSB = 'N' or 'n', the leading k by n -* part of the array B must contain the matrix B, otherwise -* the leading n by k part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANSB = 'N' or 'n' then -* LDB must be at least max( 1, k ), otherwise LDB must be at -* least max( 1, n ). -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - REAL array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n matrix -* ( alpha*op( A )*op( B ) + beta*C ). -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER K,LDA,LDB,LDC,M,N + CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. + REAL A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sgemv.f b/BLAS/SRC/sgemv.f index afae2698..315a6822 100644 --- a/BLAS/SRC/sgemv.f +++ b/BLAS/SRC/sgemv.f @@ -1,105 +1,181 @@ - SUBROUTINE SGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER INCX,INCY,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*),Y(*) -* .. +*> \brief \b SGEMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER INCX,INCY,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SGEMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> SGEMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is REAL array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry with BETA non-zero, the incremented array Y +*> must contain the vector y. On exit, Y is overwritten by the +*> updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. -* -* X - REAL array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - REAL array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry with BETA non-zero, the incremented array Y -* must contain the vector y. On exit, Y is overwritten by the -* updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sger.f b/BLAS/SRC/sger.f index 828b7454..46ff76fb 100644 --- a/BLAS/SRC/sger.f +++ b/BLAS/SRC/sger.f @@ -1,82 +1,149 @@ - SUBROUTINE SGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*),Y(*) -* .. +*> \brief \b SGER +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SGER performs the rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> SGER performs the rank 1 operation +*> +*> A := alpha*x*y**T + A, +*> +*> where alpha is a scalar, x is an m element vector, y is an n element +*> vector and A is an m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> \verbatim +*> X REAL array of dimension at least +*> ( 1 + ( m - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the m +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. On exit, A is +*> overwritten by the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x is an m element vector, y is an n element -* vector and A is an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( m - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the m -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. On exit, A is -* overwritten by the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/snrm2.f b/BLAS/SRC/snrm2.f index 1c336dac..6e122ccc 100644 --- a/BLAS/SRC/snrm2.f +++ b/BLAS/SRC/snrm2.f @@ -1,25 +1,73 @@ - REAL FUNCTION SNRM2(N,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - REAL X(*) -* .. +*> \brief \b SNRM2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* REAL FUNCTION SNRM2(N,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* REAL X(*) +* .. +* * Purpose * ======= * -* SNRM2 returns the euclidean norm of a vector via the function -* name, so that +*>\details \b Purpose: +*>\verbatim +*> +*> SNRM2 returns the euclidean norm of a vector via the function +*> name, so that +*> +*> SNRM2 := sqrt( x'*x ). +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 * -* SNRM2 := sqrt( x'*x ). * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> -- This version written on 25-October-1982. +*> Modified on 14-October-1993 to inline the call to SLASSQ. +*> Sven Hammarling, Nag Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + REAL FUNCTION SNRM2(N,X,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- This version written on 25-October-1982. -* Modified on 14-October-1993 to inline the call to SLASSQ. -* Sven Hammarling, Nag Ltd. +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + REAL X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/srot.f b/BLAS/SRC/srot.f index b53b0fdb..50e20ed8 100644 --- a/BLAS/SRC/srot.f +++ b/BLAS/SRC/srot.f @@ -1,22 +1,71 @@ - SUBROUTINE SROT(N,SX,INCX,SY,INCY,C,S) -* .. Scalar Arguments .. - REAL C,S - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SX(*),SY(*) -* .. +*> \brief \b SROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE SROT(N,SX,INCX,SY,INCY,C,S) +* +* .. Scalar Arguments .. +* REAL C,S +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* * Purpose * ======= * -* applies a plane rotation. +*>\details \b Purpose: +*>\verbatim +*> +*> applies a plane rotation. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SROT(N,SX,INCX,SY,INCY,C,S) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + REAL C,S + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SX(*),SY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/srotg.f b/BLAS/SRC/srotg.f index 4f4258be..666d5501 100644 --- a/BLAS/SRC/srotg.f +++ b/BLAS/SRC/srotg.f @@ -1,17 +1,62 @@ - SUBROUTINE SROTG(SA,SB,C,S) -* .. Scalar Arguments .. - REAL C,S,SA,SB -* .. +*> \brief \b SROTG +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SROTG(SA,SB,C,S) +* +* .. Scalar Arguments .. +* REAL C,S,SA,SB +* .. +* * Purpose * ======= * -* SROTG construct givens plane rotation. +*>\details \b Purpose: +*>\verbatim +*> +*> SROTG construct givens plane rotation. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SROTG(SA,SB,C,S) * -* jack dongarra, linpack, 3/11/78. +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL C,S,SA,SB +* .. * * ===================================================================== * diff --git a/BLAS/SRC/srotm.f b/BLAS/SRC/srotm.f index 4eeaa4f0..be84807f 100644 --- a/BLAS/SRC/srotm.f +++ b/BLAS/SRC/srotm.f @@ -1,55 +1,117 @@ - SUBROUTINE SROTM(N,SX,INCX,SY,INCY,SPARAM) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SPARAM(5),SX(*),SY(*) -* .. -* -* Purpose -* ======= -* -* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX +*> \brief \b SROTM * -* (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN -* (SX**T) +* =========== DOCUMENTATION =========== * -* SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE -* LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. -* WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 +* Definition +* ========== * -* (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) -* H=( ) ( ) ( ) ( ) -* (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). -* SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM. +* SUBROUTINE SROTM(N,SX,INCX,SY,INCY,SPARAM) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SPARAM(5),SX(*),SY(*) +* .. +* +* Purpose +* ======= * +*>\details \b Purpose: +*>\verbatim +*> +*> APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX +*> +*> (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN +*> (SX**T) +*> +*> SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE +*> LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. +*> WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +*> +*> SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 +*> +*> (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) +*> H=( ) ( ) ( ) ( ) +*> (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). +*> SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM. +*> +*> +*>\endverbatim * * Arguments * ========= * -* N (input) INTEGER -* number of elements in input vector(s) +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> number of elements in input vector(s) +*> \endverbatim +*> +*> \param[in,out] SX +*> \verbatim +*> SX is REAL array, dimension N +*> double precision vector with N elements +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> storage spacing between elements of SX +*> \endverbatim +*> +*> \param[in,out] SY +*> \verbatim +*> SY is REAL array, dimension N +*> double precision vector with N elements +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> storage spacing between elements of SY +*> \endverbatim +*> +*> \param[in,out] SPARAM +*> \verbatim +*> SPARAM is REAL array, dimension 5 +*> SPARAM(1)=SFLAG +*> SPARAM(2)=SH11 +*> SPARAM(3)=SH21 +*> SPARAM(4)=SH12 +*> SPARAM(5)=SH22 +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* SX (input/output) REAL array, dimension N -* double precision vector with N elements +*> \date November 2011 * -* INCX (input) INTEGER -* storage spacing between elements of SX +*> \ingroup single_blas_level1 * -* SY (input/output) REAL array, dimension N -* double precision vector with N elements +* ===================================================================== + SUBROUTINE SROTM(N,SX,INCX,SY,INCY,SPARAM) * -* INCY (input) INTEGER -* storage spacing between elements of SY +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* SPARAM (input/output) REAL array, dimension 5 -* SPARAM(1)=SFLAG -* SPARAM(2)=SH11 -* SPARAM(3)=SH21 -* SPARAM(4)=SH12 -* SPARAM(5)=SH22 +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SPARAM(5),SX(*),SY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/srotmg.f b/BLAS/SRC/srotmg.f index aae4f284..62a76e42 100644 --- a/BLAS/SRC/srotmg.f +++ b/BLAS/SRC/srotmg.f @@ -1,52 +1,108 @@ - SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM) -* .. Scalar Arguments .. - REAL SD1,SD2,SX1,SY1 -* .. -* .. Array Arguments .. - REAL SPARAM(5) -* .. +*> \brief \b SROTMG * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS -* THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)* -* SY2)**T. -* WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 +* Definition +* ========== * -* (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) -* H=( ) ( ) ( ) ( ) -* (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). -* LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 -* RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE -* VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) -* -* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE -* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE -* OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. +* SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM) +* +* .. Scalar Arguments .. +* REAL SD1,SD2,SX1,SY1 +* .. +* .. Array Arguments .. +* REAL SPARAM(5) +* .. +* +* Purpose +* ======= * +*>\details \b Purpose: +*>\verbatim +*> +*> CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS +*> THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T. +*> WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. +*> +*> SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 +*> +*> (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) +*> H=( ) ( ) ( ) ( ) +*> (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). +*> LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 +*> RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE +*> VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) +*> +*> THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE +*> INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE +*> OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. +*> +*> +*>\endverbatim * * Arguments * ========= * +*> \param[in,out] SD1 +*> \verbatim +*> SD1 is REAL +*> \endverbatim +*> +*> \param[in,out] SD2 +*> \verbatim +*> SD2 is REAL +*> \endverbatim +*> +*> \param[in,out] SX1 +*> \verbatim +*> SX1 is REAL +*> \endverbatim +*> +*> \param[in] SY1 +*> \verbatim +*> SY1 is REAL +*> \endverbatim +*> +*> \param[in,out] SPARAM +*> \verbatim +*> SPARAM is REAL array, dimension 5 +*> SPARAM(1)=SFLAG +*> SPARAM(2)=SH11 +*> SPARAM(3)=SH21 +*> SPARAM(4)=SH12 +*> SPARAM(5)=SH22 +*> \endverbatim +*> +* +* Authors +* ======= * -* SD1 (input/output) REAL +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* SD2 (input/output) REAL +*> \date November 2011 * -* SX1 (input/output) REAL +*> \ingroup single_blas_level1 * -* SY1 (input) REAL +* ===================================================================== + SUBROUTINE SROTMG(SD1,SD2,SX1,SY1,SPARAM) * +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* SPARAM (input/output) REAL array, dimension 5 -* SPARAM(1)=SFLAG -* SPARAM(2)=SH11 -* SPARAM(3)=SH21 -* SPARAM(4)=SH12 -* SPARAM(5)=SH22 +* .. Scalar Arguments .. + REAL SD1,SD2,SX1,SY1 +* .. +* .. Array Arguments .. + REAL SPARAM(5) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssbmv.f b/BLAS/SRC/ssbmv.f index 88b4adc1..82f76ceb 100644 --- a/BLAS/SRC/ssbmv.f +++ b/BLAS/SRC/ssbmv.f @@ -1,134 +1,211 @@ - SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER INCX,INCY,K,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*),Y(*) -* .. +*> \brief \b SSBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER INCX,INCY,K,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SSBMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSBMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n symmetric band matrix, with k super-diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the band matrix A is being supplied as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> being supplied. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> being supplied. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of super-diagonals of the +*> matrix A. K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the symmetric matrix, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer the upper +*> triangular part of a symmetric band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the symmetric matrix, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer the lower +*> triangular part of a symmetric band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is REAL array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n symmetric band matrix, with k super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the band matrix A is being supplied as -* follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* being supplied. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* being supplied. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of super-diagonals of the -* matrix A. K must satisfy 0 .le. K. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the symmetric matrix, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer the upper -* triangular part of a symmetric band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the symmetric matrix, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer the lower -* triangular part of a symmetric band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - REAL array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* Y - REAL array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sscal.f b/BLAS/SRC/sscal.f index dd0a68d9..d3d7130a 100644 --- a/BLAS/SRC/sscal.f +++ b/BLAS/SRC/sscal.f @@ -1,24 +1,73 @@ - SUBROUTINE SSCAL(N,SA,SX,INCX) -* .. Scalar Arguments .. - REAL SA - INTEGER INCX,N -* .. -* .. Array Arguments .. - REAL SX(*) -* .. +*> \brief \b SSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE SSCAL(N,SA,SX,INCX) +* +* .. Scalar Arguments .. +* REAL SA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* REAL SX(*) +* .. +* * Purpose * ======= * -* scales a vector by a constant. -* uses unrolled loops for increment equal to 1. +*>\details \b Purpose: +*>\verbatim +*> +*> scales a vector by a constant. +*> uses unrolled loops for increment equal to 1. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSCAL(N,SA,SX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + REAL SA + INTEGER INCX,N +* .. +* .. Array Arguments .. + REAL SX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sspmv.f b/BLAS/SRC/sspmv.f index c9518517..e2485a27 100644 --- a/BLAS/SRC/sspmv.f +++ b/BLAS/SRC/sspmv.f @@ -1,100 +1,171 @@ - SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL AP(*),X(*),Y(*) -* .. +*> \brief \b SSPMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SSPMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSPMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n symmetric matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is REAL array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n symmetric matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* AP - REAL array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sspr.f b/BLAS/SRC/sspr.f index 6c2a21c6..55b120e8 100644 --- a/BLAS/SRC/sspr.f +++ b/BLAS/SRC/sspr.f @@ -1,86 +1,151 @@ - SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL AP(*),X(*) -* .. +*> \brief \b SSPR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL AP(*),X(*) +* .. +* * Purpose * ======= * -* SSPR performs the symmetric rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSPR performs the symmetric rank 1 operation +*> +*> A := alpha*x*x**T + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n symmetric matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is REAL array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n symmetric matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* AP - REAL array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sspr2.f b/BLAS/SRC/sspr2.f index 51831071..6450dbcc 100644 --- a/BLAS/SRC/sspr2.f +++ b/BLAS/SRC/sspr2.f @@ -1,97 +1,164 @@ - SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL AP(*),X(*),Y(*) -* .. +*> \brief \b SSPR2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SSPR2 performs the symmetric rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSPR2 performs the symmetric rank 2 operation +*> +*> A := alpha*x*y**T + alpha*y*x**T + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an +*> n by n symmetric matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> \verbatim +*> X REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is REAL array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the symmetric matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + alpha*y*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an -* n by n symmetric matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* AP - REAL array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the symmetric matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/sswap.f b/BLAS/SRC/sswap.f index e1a75f49..d0dcddfa 100644 --- a/BLAS/SRC/sswap.f +++ b/BLAS/SRC/sswap.f @@ -1,22 +1,70 @@ - SUBROUTINE SSWAP(N,SX,INCX,SY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - REAL SX(*),SY(*) -* .. +*> \brief \b SSWAP * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SSWAP(N,SX,INCX,SY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* REAL SX(*),SY(*) +* .. +* * Purpose * ======= * -* interchanges two vectors. -* uses unrolled loops for increments equal to 1. +*>\details \b Purpose: +*>\verbatim +*> +*> interchanges two vectors. +*> uses unrolled loops for increments equal to 1. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup single_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSWAP(N,SX,INCX,SY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + REAL SX(*),SY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssymm.f b/BLAS/SRC/ssymm.f index 5182672e..2253c537 100644 --- a/BLAS/SRC/ssymm.f +++ b/BLAS/SRC/ssymm.f @@ -1,137 +1,215 @@ - SUBROUTINE SSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b SSYMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER LDA,LDB,LDC,M,N +* CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* SSYMM performs one of the matrix-matrix operations -* -* C := alpha*A*B + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> SSYMM performs one of the matrix-matrix operations +*> +*> C := alpha*A*B + beta*C, +*> +*> or +*> +*> C := alpha*B*A + beta*C, +*> +*> where alpha and beta are scalars, A is a symmetric matrix and B and +*> C are m by n matrices. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether the symmetric matrix A +*> appears on the left or right in the operation as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the symmetric matrix A is to be +*> referenced as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix C. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix C. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, ka ), where ka is +*> m when SIDE = 'L' or 'l' and is n otherwise. +*> Before entry with SIDE = 'L' or 'l', the m by m part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading m by m upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading m by m lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Before entry with SIDE = 'R' or 'r', the n by n part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading n by n upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading n by n lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is REAL array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is REAL array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n updated +*> matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*B*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, A is a symmetric matrix and B and -* C are m by n matrices. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level3 * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether the symmetric matrix A -* appears on the left or right in the operation as follows: -* -* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -* -* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the symmetric matrix A is to be -* referenced as follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of the -* symmetric matrix is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of the -* symmetric matrix is to be referenced. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix C. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix C. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, ka ), where ka is -* m when SIDE = 'L' or 'l' and is n otherwise. -* Before entry with SIDE = 'L' or 'l', the m by m part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading m by m upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading m by m lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Before entry with SIDE = 'R' or 'r', the n by n part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading n by n upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading n by n lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, n ). -* Unchanged on exit. -* -* B - REAL array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - REAL array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n updated -* matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER LDA,LDB,LDC,M,N + CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssymv.f b/BLAS/SRC/ssymv.f index a43bd9b0..6660a329 100644 --- a/BLAS/SRC/ssymv.f +++ b/BLAS/SRC/ssymv.f @@ -1,103 +1,176 @@ - SUBROUTINE SSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*),Y(*) -* .. +*> \brief \b SSYMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SSYMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSYMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n symmetric matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of A is not referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n symmetric matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of A is not referenced. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssyr.f b/BLAS/SRC/ssyr.f index 1a546009..05c49151 100644 --- a/BLAS/SRC/ssyr.f +++ b/BLAS/SRC/ssyr.f @@ -1,89 +1,156 @@ - SUBROUTINE SSYR(UPLO,N,ALPHA,X,INCX,A,LDA) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*) -* .. +*> \brief \b SSYR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSYR(UPLO,N,ALPHA,X,INCX,A,LDA) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* SSYR performs the symmetric rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSYR performs the symmetric rank 1 operation +*> +*> A := alpha*x*x**T + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n symmetric matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n symmetric matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSYR(UPLO,N,ALPHA,X,INCX,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssyr2.f b/BLAS/SRC/ssyr2.f index 545cfe55..b96e2184 100644 --- a/BLAS/SRC/ssyr2.f +++ b/BLAS/SRC/ssyr2.f @@ -1,100 +1,169 @@ - SUBROUTINE SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*),Y(*) -* .. +*> \brief \b SSYR2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* SSYR2 performs the symmetric rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> SSYR2 performs the symmetric rank 2 operation +*> +*> A := alpha*x*y**T + alpha*y*x**T + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an n +*> by n symmetric matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> \verbatim +*> X REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + alpha*y*x**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an n -* by n symmetric matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssyr2k.f b/BLAS/SRC/ssyr2k.f index c9f44aa8..a0bfee72 100644 --- a/BLAS/SRC/ssyr2k.f +++ b/BLAS/SRC/ssyr2k.f @@ -1,140 +1,219 @@ - SUBROUTINE SSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b SSYR2K +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* SSYR2K performs one of the symmetric rank 2k operations -* -* C := alpha*A*B**T + alpha*B*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> SSYR2K performs one of the symmetric rank 2k operations +*> +*> C := alpha*A*B**T + alpha*B*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A and B are n by k matrices in the first case and k by n +*> matrices in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + +*> beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrices A and B, and on entry with +*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number +*> of rows of the matrices A and B. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is REAL array of DIMENSION ( LDB, kb ), where kb is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array B must contain the matrix B, otherwise +*> the leading k by n part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDB must be at least max( 1, n ), otherwise LDB must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is REAL array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A and B are n by k matrices in the first case and k by n -* matrices in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + -* beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + -* beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + -* beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrices A and B, and on entry with -* TRANS = 'T' or 't' or 'C' or 'c', K specifies the number -* of rows of the matrices A and B. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* B - REAL array of DIMENSION ( LDB, kb ), where kb is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array B must contain the matrix B, otherwise -* the leading k by n part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDB must be at least max( 1, n ), otherwise LDB must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - REAL array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. -* +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER K,LDA,LDB,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ssyrk.f b/BLAS/SRC/ssyrk.f index 33b7296f..9d294f13 100644 --- a/BLAS/SRC/ssyrk.f +++ b/BLAS/SRC/ssyrk.f @@ -1,121 +1,196 @@ - SUBROUTINE SSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* .. Scalar Arguments .. - REAL ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),C(LDC,*) -* .. +*> \brief \b SSYRK +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) +* +* .. Scalar Arguments .. +* REAL ALPHA,BETA +* INTEGER K,LDA,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),C(LDC,*) +* .. +* * Purpose * ======= * -* SSYRK performs one of the symmetric rank k operations -* -* C := alpha*A*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> SSYRK performs one of the symmetric rank k operations +*> +*> C := alpha*A*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A is an n by k matrix in the first case and a k by n matrix +*> in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrix A, and on entry with +*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number +*> of rows of the matrix A. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is REAL +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is REAL array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A is an n by k matrix in the first case and a k by n matrix -* in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrix A, and on entry with -* TRANS = 'T' or 't' or 'C' or 'c', K specifies the number -* of rows of the matrix A. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - REAL . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - REAL array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + REAL ALPHA,BETA + INTEGER K,LDA,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/stbmv.f b/BLAS/SRC/stbmv.f index 7446b4e6..5c1190a8 100644 --- a/BLAS/SRC/stbmv.f +++ b/BLAS/SRC/stbmv.f @@ -1,141 +1,218 @@ - SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*) -* .. +*> \brief \b STBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* STBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> STBMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**T*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* x := A*x, or x := A**T*x, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**T*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/stbsv.f b/BLAS/SRC/stbsv.f index d6d247e2..2bdb4824 100644 --- a/BLAS/SRC/stbsv.f +++ b/BLAS/SRC/stbsv.f @@ -1,144 +1,221 @@ - SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*) -* .. +*> \brief \b STBSV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* STBSV solves one of the systems of equations +*>\details \b Purpose: +*>\verbatim +*> +*> STBSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular band matrix, with ( k + 1 ) +*> diagonals. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* A*x = b, or A**T*x = b, +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular band matrix, with ( k + 1 ) -* diagonals. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup single_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**T*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/stpmv.f b/BLAS/SRC/stpmv.f index 573288e6..a32cf73f 100644 --- a/BLAS/SRC/stpmv.f +++ b/BLAS/SRC/stpmv.f @@ -1,101 +1,170 @@ - SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - REAL AP(*),X(*) -* .. -* -* Purpose -* ======= -* -* STPMV performs one of the matrix-vector operations +*> \brief \b STPMV * -* x := A*x, or x := A**T*x, +* =========== DOCUMENTATION =========== * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix, supplied in packed form. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**T*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> STPMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix, supplied in packed form. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**T*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is REAL array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - REAL array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup single_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/stpsv.f b/BLAS/SRC/stpsv.f index aca8a7fc..d54a5da4 100644 --- a/BLAS/SRC/stpsv.f +++ b/BLAS/SRC/stpsv.f @@ -1,103 +1,172 @@ - SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - REAL AP(*),X(*) -* .. +*> \brief \b STPSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* STPSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix, supplied in packed form. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**T*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> STPSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix, supplied in packed form. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is REAL array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - REAL array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup single_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/strmm.f b/BLAS/SRC/strmm.f index 9d76a16d..c366891e 100644 --- a/BLAS/SRC/strmm.f +++ b/BLAS/SRC/strmm.f @@ -1,129 +1,208 @@ - SUBROUTINE STRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b STRMM * -* STRMM performs one of the matrix-matrix operations +* =========== DOCUMENTATION =========== * -* B := alpha*op( A )*B, or B := alpha*B*op( A ), +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, B is an m by n matrix, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) multiplies B from -* the left or right as follows: -* -* SIDE = 'L' or 'l' B := alpha*op( A )*B. -* -* SIDE = 'R' or 'r' B := alpha*B*op( A ). -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**T. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE STRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> STRMM performs one of the matrix-matrix operations +*> +*> B := alpha*op( A )*B, or B := alpha*B*op( A ), +*> +*> where alpha is a scalar, B is an m by n matrix, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T. +*> +*>\endverbatim * -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) multiplies B from +*> the left or right as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' B := alpha*op( A )*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' B := alpha*B*op( A ). +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**T. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, k ), where k is m +*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is REAL array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B, and on exit is overwritten by the +*> transformed matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - REAL array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - REAL array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B, and on exit is overwritten by the -* transformed matrix. +*> \ingroup single_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/strmv.f b/BLAS/SRC/strmv.f index f20cfa2d..dcfa15d1 100644 --- a/BLAS/SRC/strmv.f +++ b/BLAS/SRC/strmv.f @@ -1,104 +1,175 @@ - SUBROUTINE STRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*) -* .. +*> \brief \b STRMV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* STRMV performs one of the matrix-vector operations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* x := A*x, or x := A**T*x, -* -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**T*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE STRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> STRMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**T*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup single_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/strsm.f b/BLAS/SRC/strsm.f index 88880696..0568d971 100644 --- a/BLAS/SRC/strsm.f +++ b/BLAS/SRC/strsm.f @@ -1,132 +1,212 @@ - SUBROUTINE STRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - REAL ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b STRSM * -* STRSM solves one of the matrix equations +* =========== DOCUMENTATION =========== * -* op( A )*X = alpha*B, or X*op( A ) = alpha*B, +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, X and B are m by n matrices, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T. -* -* The matrix X is overwritten on B. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) appears on the left -* or right of X as follows: -* -* SIDE = 'L' or 'l' op( A )*X = alpha*B. -* -* SIDE = 'R' or 'r' X*op( A ) = alpha*B. -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**T. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE STRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* REAL ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> STRSM solves one of the matrix equations +*> +*> op( A )*X = alpha*B, or X*op( A ) = alpha*B, +*> +*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T. +*> +*> The matrix X is overwritten on B. +*> +*>\endverbatim * -* ALPHA - REAL . -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) appears on the left +*> or right of X as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' op( A )*X = alpha*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' X*op( A ) = alpha*B. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**T. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, k ), +*> where k is m when SIDE = 'L' or 'l' +*> and k is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is REAL array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the right-hand side matrix B, and on exit is +*> overwritten by the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - REAL array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - REAL array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the right-hand side matrix B, and on exit is -* overwritten by the solution matrix X. +*> \ingroup single_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. -* +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + REAL ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/strsv.f b/BLAS/SRC/strsv.f index 02420fbf..c4b3f546 100644 --- a/BLAS/SRC/strsv.f +++ b/BLAS/SRC/strsv.f @@ -1,106 +1,177 @@ - SUBROUTINE STRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - REAL A(LDA,*),X(*) -* .. +*> \brief \b STRSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* STRSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**T*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE STRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* REAL A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> STRSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**T*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - REAL array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - REAL array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup single_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + REAL A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/xerbla.f b/BLAS/SRC/xerbla.f index 3a84150e..5d287b91 100644 --- a/BLAS/SRC/xerbla.f +++ b/BLAS/SRC/xerbla.f @@ -1,33 +1,76 @@ - SUBROUTINE XERBLA( SRNAME, INFO ) +*> \brief \b XERBLA * -* -- LAPACK auxiliary routine (preliminary version) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - CHARACTER*(*) SRNAME - INTEGER INFO -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE XERBLA( SRNAME, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER*(*) SRNAME +* INTEGER INFO +* .. +* * Purpose * ======= * -* XERBLA is an error handler for the LAPACK routines. -* It is called by an LAPACK routine if an input parameter has an -* invalid value. A message is printed and execution stops. -* -* Installers may consider modifying the STOP statement in order to -* call system-specific exception-handling facilities. +*>\details \b Purpose: +*>\verbatim +*> +*> XERBLA is an error handler for the LAPACK routines. +*> It is called by an LAPACK routine if an input parameter has an +*> invalid value. A message is printed and execution stops. +*> +*> Installers may consider modifying the STOP statement in order to +*> call system-specific exception-handling facilities. +*> +*>\endverbatim * * Arguments * ========= * -* SRNAME (input) CHARACTER*(*) -* The name of the routine which called XERBLA. +*> \param[in] SRNAME +*> \verbatim +*> SRNAME is CHARACTER*(*) +*> The name of the routine which called XERBLA. +*> \endverbatim +*> +*> \param[in] INFO +*> \verbatim +*> INFO is INTEGER +*> The position of the invalid parameter in the parameter list +*> of the calling routine. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* INFO (input) INTEGER -* The position of the invalid parameter in the parameter list -* of the calling routine. +*> \date November 2011 +* +*> \ingroup aux_blas +* +* ===================================================================== + SUBROUTINE XERBLA( SRNAME, INFO ) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER*(*) SRNAME + INTEGER INFO +* .. * * ===================================================================== * diff --git a/BLAS/SRC/xerbla_array.f b/BLAS/SRC/xerbla_array.f index 350b59bc..c6173eee 100644 --- a/BLAS/SRC/xerbla_array.f +++ b/BLAS/SRC/xerbla_array.f @@ -1,51 +1,98 @@ - SUBROUTINE XERBLA_ARRAY(SRNAME_ARRAY, SRNAME_LEN, INFO) +*> \brief \b XERBLA_ARRAY * -* -- LAPACK auxiliary routine (version 3.0) -- -* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -* September 19, 2006 +* =========== DOCUMENTATION =========== * - IMPLICIT NONE -* .. Scalar Arguments .. - INTEGER SRNAME_LEN, INFO -* .. -* .. Array Arguments .. - CHARACTER(1) SRNAME_ARRAY(SRNAME_LEN) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE XERBLA_ARRAY(SRNAME_ARRAY, SRNAME_LEN, INFO) +* +* .. Scalar Arguments .. +* INTEGER SRNAME_LEN, INFO +* .. +* .. Array Arguments .. +* CHARACTER(1) SRNAME_ARRAY(SRNAME_LEN) +* .. +* * Purpose * ======= * -* XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK -* and BLAS error handler. Rather than taking a Fortran string argument -* as the function's name, XERBLA_ARRAY takes an array of single -* characters along with the array's length. XERBLA_ARRAY then copies -* up to 32 characters of that array into a Fortran string and passes -* that to XERBLA. If called with a non-positive SRNAME_LEN, -* XERBLA_ARRAY will call XERBLA with a string of all blank characters. -* -* Say some macro or other device makes XERBLA_ARRAY available to C99 -* by a name lapack_xerbla and with a common Fortran calling convention. -* Then a C99 program could invoke XERBLA via: -* { -* int flen = strlen(__func__); -* lapack_xerbla(__func__, &flen, &info); -* } -* -* Providing XERBLA_ARRAY is not necessary for intercepting LAPACK -* errors. XERBLA_ARRAY calls XERBLA. +*>\details \b Purpose: +*>\verbatim +*> +*> XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK +*> and BLAS error handler. Rather than taking a Fortran string argument +*> as the function's name, XERBLA_ARRAY takes an array of single +*> characters along with the array's length. XERBLA_ARRAY then copies +*> up to 32 characters of that array into a Fortran string and passes +*> that to XERBLA. If called with a non-positive SRNAME_LEN, +*> XERBLA_ARRAY will call XERBLA with a string of all blank characters. +*> +*> Say some macro or other device makes XERBLA_ARRAY available to C99 +*> by a name lapack_xerbla and with a common Fortran calling convention. +*> Then a C99 program could invoke XERBLA via: +*> { +*> int flen = strlen(__func__); +*> lapack_xerbla(__func__, &flen, &info); +*> } +*> +*> Providing XERBLA_ARRAY is not necessary for intercepting LAPACK +*> errors. XERBLA_ARRAY calls XERBLA. +*> +*>\endverbatim * * Arguments * ========= * -* SRNAME_ARRAY (input) CHARACTER(1) array, dimension (SRNAME_LEN) -* The name of the routine which called XERBLA_ARRAY. +*> \param[in] SRNAME_ARRAY +*> \verbatim +*> SRNAME_ARRAY is CHARACTER(1) array, dimension (SRNAME_LEN) +*> The name of the routine which called XERBLA_ARRAY. +*> \endverbatim +*> +*> \param[in] SRNAME_LEN +*> \verbatim +*> SRNAME_LEN is INTEGER +*> The length of the name in SRNAME_ARRAY. +*> \endverbatim +*> +*> \param[in] INFO +*> \verbatim +*> INFO is INTEGER +*> The position of the invalid parameter in the parameter list +*> of the calling routine. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* SRNAME_LEN (input) INTEGER -* The length of the name in SRNAME_ARRAY. +*> \date November 2011 * -* INFO (input) INTEGER -* The position of the invalid parameter in the parameter list -* of the calling routine. +*> \ingroup aux_blas +* +* ===================================================================== + SUBROUTINE XERBLA_ARRAY(SRNAME_ARRAY, SRNAME_LEN, INFO) +* +* -- Reference BLAS level1 routine (version 3.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER SRNAME_LEN, INFO +* .. +* .. Array Arguments .. + CHARACTER(1) SRNAME_ARRAY(SRNAME_LEN) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zaxpy.f b/BLAS/SRC/zaxpy.f index 07afb5f3..0daa8870 100644 --- a/BLAS/SRC/zaxpy.f +++ b/BLAS/SRC/zaxpy.f @@ -1,22 +1,71 @@ - SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) -* .. Scalar Arguments .. - COMPLEX*16 ZA - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. +*> \brief \b ZAXPY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ZA +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*),ZY(*) +* .. +* * Purpose * ======= * -* ZAXPY constant times a vector plus a vector. +*>\details \b Purpose: +*>\verbatim +*> +*> ZAXPY constant times a vector plus a vector. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + COMPLEX*16 ZA + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*),ZY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zcopy.f b/BLAS/SRC/zcopy.f index 1038cb96..93ee92d0 100644 --- a/BLAS/SRC/zcopy.f +++ b/BLAS/SRC/zcopy.f @@ -1,21 +1,69 @@ - SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. +*> \brief \b ZCOPY * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*),ZY(*) +* .. +* * Purpose * ======= * -* ZCOPY copies a vector, x, to a vector, y. +*>\details \b Purpose: +*>\verbatim +*> +*> ZCOPY copies a vector, x, to a vector, y. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, linpack, 4/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, linpack, 4/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*),ZY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zdotc.f b/BLAS/SRC/zdotc.f index 2f6b6532..4ed407d0 100644 --- a/BLAS/SRC/zdotc.f +++ b/BLAS/SRC/zdotc.f @@ -1,21 +1,69 @@ - COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. +*> \brief \b ZDOTC * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*),ZY(*) +* .. +* * Purpose * ======= * -* ZDOTC forms the dot product of a vector. +*>\details \b Purpose: +*>\verbatim +*> +*> ZDOTC forms the dot product of a vector. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*),ZY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zdotu.f b/BLAS/SRC/zdotu.f index 1722c8af..9d481a97 100644 --- a/BLAS/SRC/zdotu.f +++ b/BLAS/SRC/zdotu.f @@ -1,21 +1,69 @@ - COMPLEX*16 FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. +*> \brief \b ZDOTU * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* COMPLEX*16 FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*),ZY(*) +* .. +* * Purpose * ======= * -* ZDOTU forms the dot product of two vectors. +*>\details \b Purpose: +*>\verbatim +*> +*> ZDOTU forms the dot product of two vectors. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + COMPLEX*16 FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*),ZY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zdrot.f b/BLAS/SRC/zdrot.f index 20d04361..3caaaca6 100644 --- a/BLAS/SRC/zdrot.f +++ b/BLAS/SRC/zdrot.f @@ -1,5 +1,110 @@ +*> \brief \b ZDROT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZDROT( N, CX, INCX, CY, INCY, C, S ) +* +* .. Scalar Arguments .. +* INTEGER INCX, INCY, N +* DOUBLE PRECISION C, S +* .. +* .. Array Arguments .. +* COMPLEX*16 CX( * ), CY( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> Applies a plane rotation, where the cos and sin (c and s) are real +*> and the vectors cx and cy are complex. +*> jack dongarra, linpack, 3/11/78. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the vectors cx and cy. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in,out] CX +*> \verbatim +*> CX is COMPLEX*16 array, dimension at least +*> ( 1 + ( N - 1 )*abs( INCX ) ). +*> Before entry, the incremented array CX must contain the n +*> element vector cx. On exit, CX is overwritten by the updated +*> vector cx. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> CX. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] CY +*> \verbatim +*> CY is COMPLEX*16 array, dimension at least +*> ( 1 + ( N - 1 )*abs( INCY ) ). +*> Before entry, the incremented array CY must contain the n +*> element vector cy. On exit, CY is overwritten by the updated +*> vector cy. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> CY. INCY must not be zero. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION +*> On entry, C specifies the cosine, cos. +*> \endverbatim +*> +*> \param[in] S +*> \verbatim +*> S is DOUBLE PRECISION +*> On entry, S specifies the sine, sin. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* +* ===================================================================== SUBROUTINE ZDROT( N, CX, INCX, CY, INCY, C, S ) * +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* * .. Scalar Arguments .. INTEGER INCX, INCY, N DOUBLE PRECISION C, S @@ -8,51 +113,6 @@ COMPLEX*16 CX( * ), CY( * ) * .. * -* Purpose -* ======= -* -* Applies a plane rotation, where the cos and sin (c and s) are real -* and the vectors cx and cy are complex. -* jack dongarra, linpack, 3/11/78. -* -* Arguments -* ========== -* -* N (input) INTEGER -* On entry, N specifies the order of the vectors cx and cy. -* N must be at least zero. -* Unchanged on exit. -* -* CX (input) COMPLEX*16 array, dimension at least -* ( 1 + ( N - 1 )*abs( INCX ) ). -* Before entry, the incremented array CX must contain the n -* element vector cx. On exit, CX is overwritten by the updated -* vector cx. -* -* INCX (input) INTEGER -* On entry, INCX specifies the increment for the elements of -* CX. INCX must not be zero. -* Unchanged on exit. -* -* CY (input) COMPLEX*16 array, dimension at least -* ( 1 + ( N - 1 )*abs( INCY ) ). -* Before entry, the incremented array CY must contain the n -* element vector cy. On exit, CY is overwritten by the updated -* vector cy. -* -* INCY (input) INTEGER -* On entry, INCY specifies the increment for the elements of -* CY. INCY must not be zero. -* Unchanged on exit. -* -* C (input) DOUBLE PRECISION -* On entry, C specifies the cosine, cos. -* Unchanged on exit. -* -* S (input) DOUBLE PRECISION -* On entry, S specifies the sine, sin. -* Unchanged on exit. -* * ===================================================================== * * .. Local Scalars .. diff --git a/BLAS/SRC/zdscal.f b/BLAS/SRC/zdscal.f index d4d96c75..327309cf 100644 --- a/BLAS/SRC/zdscal.f +++ b/BLAS/SRC/zdscal.f @@ -1,23 +1,72 @@ - SUBROUTINE ZDSCAL(N,DA,ZX,INCX) -* .. Scalar Arguments .. - DOUBLE PRECISION DA - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*) -* .. +*> \brief \b ZDSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE ZDSCAL(N,DA,ZX,INCX) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*) +* .. +* * Purpose * ======= * -* ZDSCAL scales a vector by a constant. +*>\details \b Purpose: +*>\verbatim +*> +*> ZDSCAL scales a vector by a constant. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZDSCAL(N,DA,ZX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + DOUBLE PRECISION DA + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zgbmv.f b/BLAS/SRC/zgbmv.f index 3000be42..216cb5b8 100644 --- a/BLAS/SRC/zgbmv.f +++ b/BLAS/SRC/zgbmv.f @@ -1,134 +1,213 @@ - SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,KL,KU,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZGBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER INCX,INCY,KL,KU,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZGBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> ZGBMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +*> +*> y := alpha*A**H*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> +*>\endverbatim * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> On entry, KL specifies the number of sub-diagonals of the +*> matrix A. KL must satisfy 0 .le. KL. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> On entry, KU specifies the number of super-diagonals of the +*> matrix A. KU must satisfy 0 .le. KU. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry, the leading ( kl + ku + 1 ) by n part of the +*> array A must contain the matrix of coefficients, supplied +*> column by column, with the leading diagonal of the matrix in +*> row ( ku + 1 ) of the array, the first super-diagonal +*> starting at position 2 in row ku, the first sub-diagonal +*> starting at position 1 in row ( ku + 2 ), and so on. +*> Elements in the array A that do not correspond to elements +*> in the band matrix (such as the top left ku by ku triangle) +*> are not referenced. +*> The following program segment will transfer a band matrix +*> from conventional full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> K = KU + 1 - J +*> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) +*> A( K + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( kl + ku + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX*16 array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A**H*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n band matrix, with kl sub-diagonals and ku super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* KL - INTEGER. -* On entry, KL specifies the number of sub-diagonals of the -* matrix A. KL must satisfy 0 .le. KL. -* Unchanged on exit. -* -* KU - INTEGER. -* On entry, KU specifies the number of super-diagonals of the -* matrix A. KU must satisfy 0 .le. KU. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry, the leading ( kl + ku + 1 ) by n part of the -* array A must contain the matrix of coefficients, supplied -* column by column, with the leading diagonal of the matrix in -* row ( ku + 1 ) of the array, the first super-diagonal -* starting at position 2 in row ku, the first sub-diagonal -* starting at position 1 in row ( ku + 2 ), and so on. -* Elements in the array A that do not correspond to elements -* in the band matrix (such as the top left ku by ku triangle) -* are not referenced. -* The following program segment will transfer a band matrix -* from conventional full matrix storage to band storage: -* -* DO 20, J = 1, N -* K = KU + 1 - J -* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) -* A( K + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( kl + ku + 1 ). -* Unchanged on exit. -* -* X - COMPLEX*16 array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER INCX,INCY,KL,KU,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zgemm.f b/BLAS/SRC/zgemm.f index 8954cbfb..6aaf515e 100644 --- a/BLAS/SRC/zgemm.f +++ b/BLAS/SRC/zgemm.f @@ -1,133 +1,215 @@ - SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b ZGEMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,M,N +* CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZGEMM performs one of the matrix-matrix operations -* -* C := alpha*op( A )*op( B ) + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> ZGEMM performs one of the matrix-matrix operations +*> +*> C := alpha*op( A )*op( B ) + beta*C, +*> +*> where op( X ) is one of +*> +*> op( X ) = X or op( X ) = X**T or op( X ) = X**H, +*> +*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) +*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> +*>\endverbatim * -* where op( X ) is one of +* Arguments +* ========= +* +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n', op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't', op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c', op( A ) = A**H. +*> \endverbatim +*> +*> \param[in] TRANSB +*> \verbatim +*> TRANSB is CHARACTER*1 +*> On entry, TRANSB specifies the form of op( B ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSB = 'N' or 'n', op( B ) = B. +*> \endverbatim +*> \verbatim +*> TRANSB = 'T' or 't', op( B ) = B**T. +*> \endverbatim +*> \verbatim +*> TRANSB = 'C' or 'c', op( B ) = B**H. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix +*> op( A ) and of the matrix C. M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix +*> op( B ) and the number of columns of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of columns of the matrix +*> op( A ) and the number of rows of the matrix op( B ). K must +*> be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANSA = 'N' or 'n', and is m otherwise. +*> Before entry with TRANSA = 'N' or 'n', the leading m by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by m part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANSA = 'N' or 'n' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is +*> n when TRANSB = 'N' or 'n', and is k otherwise. +*> Before entry with TRANSB = 'N' or 'n', the leading k by n +*> part of the array B must contain the matrix B, otherwise +*> the leading n by k part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANSB = 'N' or 'n' then +*> LDB must be at least max( 1, k ), otherwise LDB must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n matrix +*> ( alpha*op( A )*op( B ) + beta*C ). +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* op( X ) = X or op( X ) = X**T or op( X ) = X**H, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* alpha and beta are scalars, and A, B and C are matrices, with op( A ) -* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n', op( A ) = A. -* -* TRANSA = 'T' or 't', op( A ) = A**T. -* -* TRANSA = 'C' or 'c', op( A ) = A**H. -* -* Unchanged on exit. -* -* TRANSB - CHARACTER*1. -* On entry, TRANSB specifies the form of op( B ) to be used in -* the matrix multiplication as follows: -* -* TRANSB = 'N' or 'n', op( B ) = B. -* -* TRANSB = 'T' or 't', op( B ) = B**T. -* -* TRANSB = 'C' or 'c', op( B ) = B**H. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix -* op( A ) and of the matrix C. M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix -* op( B ) and the number of columns of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of columns of the matrix -* op( A ) and the number of rows of the matrix op( B ). K must -* be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* k when TRANSA = 'N' or 'n', and is m otherwise. -* Before entry with TRANSA = 'N' or 'n', the leading m by k -* part of the array A must contain the matrix A, otherwise -* the leading k by m part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANSA = 'N' or 'n' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, k ). -* Unchanged on exit. -* -* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is -* n when TRANSB = 'N' or 'n', and is k otherwise. -* Before entry with TRANSB = 'N' or 'n', the leading k by n -* part of the array B must contain the matrix B, otherwise -* the leading n by k part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANSB = 'N' or 'n' then -* LDB must be at least max( 1, k ), otherwise LDB must be at -* least max( 1, n ). -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n matrix -* ( alpha*op( A )*op( B ) + beta*C ). -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER K,LDA,LDB,LDC,M,N + CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zgemv.f b/BLAS/SRC/zgemv.f index 9415940e..9eaf4450 100644 --- a/BLAS/SRC/zgemv.f +++ b/BLAS/SRC/zgemv.f @@ -1,107 +1,183 @@ - SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZGEMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER INCX,INCY,LDA,M,N +* CHARACTER TRANS +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZGEMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> ZGEMV performs one of the matrix-vector operations +*> +*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +*> +*> y := alpha*A**H*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are vectors and A is an +*> m by n matrix. +*> +*>\endverbatim * -* y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or +* Arguments +* ========= +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX*16 array of DIMENSION at least +*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' +*> and at least +*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. +*> Before entry with BETA non-zero, the incremented array Y +*> must contain the vector y. On exit, Y is overwritten by the +*> updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A**H*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are vectors and A is an -* m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -* -* TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -* -* TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. -* -* X - COMPLEX*16 array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of DIMENSION at least -* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -* and at least -* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -* Before entry with BETA non-zero, the incremented array Y -* must contain the vector y. On exit, Y is overwritten by the -* updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER INCX,INCY,LDA,M,N + CHARACTER TRANS +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zgerc.f b/BLAS/SRC/zgerc.f index a8872b49..9457319f 100644 --- a/BLAS/SRC/zgerc.f +++ b/BLAS/SRC/zgerc.f @@ -1,82 +1,151 @@ - SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZGERC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZGERC performs the rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZGERC performs the rank 1 operation +*> +*> A := alpha*x*y**H + A, +*> +*> where alpha is a scalar, x is an m element vector, y is an n element +*> vector and A is an m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( m - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the m +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. On exit, A is +*> overwritten by the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x is an m element vector, y is an n element -* vector and A is an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( m - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the m -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. On exit, A is -* overwritten by the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zgeru.f b/BLAS/SRC/zgeru.f index 3ece8018..26acb99f 100644 --- a/BLAS/SRC/zgeru.f +++ b/BLAS/SRC/zgeru.f @@ -1,82 +1,151 @@ - SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZGERU +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZGERU performs the rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZGERU performs the rank 1 operation +*> +*> A := alpha*x*y**T + A, +*> +*> where alpha is a scalar, x is an m element vector, y is an n element +*> vector and A is an m by n matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix A. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( m - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the m +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry, the leading m by n part of the array A must +*> contain the matrix of coefficients. On exit, A is +*> overwritten by the updated matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**T + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x is an m element vector, y is an n element -* vector and A is an m by n matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix A. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( m - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the m -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry, the leading m by n part of the array A must -* contain the matrix of coefficients. On exit, A is -* overwritten by the updated matrix. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zhbmv.f b/BLAS/SRC/zhbmv.f index 90988684..0adaec41 100644 --- a/BLAS/SRC/zhbmv.f +++ b/BLAS/SRC/zhbmv.f @@ -1,136 +1,215 @@ - SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,K,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZHBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER INCX,INCY,K,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZHBMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHBMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n hermitian band matrix, with k super-diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the band matrix A is being supplied as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> being supplied. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> being supplied. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry, K specifies the number of super-diagonals of the +*> matrix A. K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the hermitian matrix, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer the upper +*> triangular part of a hermitian band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the hermitian matrix, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer the lower +*> triangular part of a hermitian band matrix from conventional +*> full matrix storage to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that the imaginary parts of the diagonal elements need +*> not be set and are assumed to be zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the +*> vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX*16 array of DIMENSION at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the +*> vector y. On exit, Y is overwritten by the updated vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n hermitian band matrix, with k super-diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the band matrix A is being supplied as -* follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* being supplied. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* being supplied. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry, K specifies the number of super-diagonals of the -* matrix A. K must satisfy 0 .le. K. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the hermitian matrix, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer the upper -* triangular part of a hermitian band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the hermitian matrix, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer the lower -* triangular part of a hermitian band matrix from conventional -* full matrix storage to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that the imaginary parts of the diagonal elements need -* not be set and are assumed to be zero. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - COMPLEX*16 array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the -* vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of DIMENSION at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the -* vector y. On exit, Y is overwritten by the updated vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER INCX,INCY,K,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zhemm.f b/BLAS/SRC/zhemm.f index 0537e919..8d7218c3 100644 --- a/BLAS/SRC/zhemm.f +++ b/BLAS/SRC/zhemm.f @@ -1,139 +1,217 @@ - SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b ZHEMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER LDA,LDB,LDC,M,N +* CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZHEMM performs one of the matrix-matrix operations -* -* C := alpha*A*B + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> ZHEMM performs one of the matrix-matrix operations +*> +*> C := alpha*A*B + beta*C, +*> +*> or +*> +*> C := alpha*B*A + beta*C, +*> +*> where alpha and beta are scalars, A is an hermitian matrix and B and +*> C are m by n matrices. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether the hermitian matrix A +*> appears on the left or right in the operation as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the hermitian matrix A is to be +*> referenced as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of the +*> hermitian matrix is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of the +*> hermitian matrix is to be referenced. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix C. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix C. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> m when SIDE = 'L' or 'l' and is n otherwise. +*> Before entry with SIDE = 'L' or 'l', the m by m part of +*> the array A must contain the hermitian matrix, such that +*> when UPLO = 'U' or 'u', the leading m by m upper triangular +*> part of the array A must contain the upper triangular part +*> of the hermitian matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading m by m lower triangular part of the array A +*> must contain the lower triangular part of the hermitian +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Before entry with SIDE = 'R' or 'r', the n by n part of +*> the array A must contain the hermitian matrix, such that +*> when UPLO = 'U' or 'u', the leading n by n upper triangular +*> part of the array A must contain the upper triangular part +*> of the hermitian matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading n by n lower triangular part of the array A +*> must contain the lower triangular part of the hermitian +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n updated +*> matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*B*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, A is an hermitian matrix and B and -* C are m by n matrices. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether the hermitian matrix A -* appears on the left or right in the operation as follows: -* -* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -* -* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the hermitian matrix A is to be -* referenced as follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of the -* hermitian matrix is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of the -* hermitian matrix is to be referenced. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix C. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix C. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* m when SIDE = 'L' or 'l' and is n otherwise. -* Before entry with SIDE = 'L' or 'l', the m by m part of -* the array A must contain the hermitian matrix, such that -* when UPLO = 'U' or 'u', the leading m by m upper triangular -* part of the array A must contain the upper triangular part -* of the hermitian matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading m by m lower triangular part of the array A -* must contain the lower triangular part of the hermitian -* matrix and the strictly upper triangular part of A is not -* referenced. -* Before entry with SIDE = 'R' or 'r', the n by n part of -* the array A must contain the hermitian matrix, such that -* when UPLO = 'U' or 'u', the leading n by n upper triangular -* part of the array A must contain the upper triangular part -* of the hermitian matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading n by n lower triangular part of the array A -* must contain the lower triangular part of the hermitian -* matrix and the strictly upper triangular part of A is not -* referenced. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, n ). -* Unchanged on exit. -* -* B - COMPLEX*16 array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n updated -* matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER LDA,LDB,LDC,M,N + CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zhemv.f b/BLAS/SRC/zhemv.f index 8e61e93b..c566a1fe 100644 --- a/BLAS/SRC/zhemv.f +++ b/BLAS/SRC/zhemv.f @@ -1,105 +1,178 @@ - SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZHEMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZHEMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHEMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n hermitian matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of A is not referenced. +*> Note that the imaginary parts of the diagonal elements need +*> not be set and are assumed to be zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n hermitian matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of A is not referenced. -* Note that the imaginary parts of the diagonal elements need -* not be set and are assumed to be zero. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zher.f b/BLAS/SRC/zher.f index 898a1e03..b2af0227 100644 --- a/BLAS/SRC/zher.f +++ b/BLAS/SRC/zher.f @@ -1,92 +1,159 @@ - SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*) -* .. +*> \brief \b ZHER +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* ZHER performs the hermitian rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHER performs the hermitian rank 1 operation +*> +*> A := alpha*x*x**H + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n hermitian matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n hermitian matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zher2.f b/BLAS/SRC/zher2.f index bb414e9e..0c4f94d9 100644 --- a/BLAS/SRC/zher2.f +++ b/BLAS/SRC/zher2.f @@ -1,103 +1,174 @@ - SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. +*> \brief \b ZHER2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* INTEGER INCX,INCY,LDA,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZHER2 performs the hermitian rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHER2 performs the hermitian rank 2 operation +*> +*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an n +*> by n hermitian matrix. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array A is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of A +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of A +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of A is not referenced. On exit, the +*> upper triangular part of the array A is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of A is not referenced. On exit, the +*> lower triangular part of the array A is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an n -* by n hermitian matrix. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array A is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of A -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of A -* is to be referenced. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of A is not referenced. On exit, the -* upper triangular part of the array A is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of A is not referenced. On exit, the -* lower triangular part of the array A is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + INTEGER INCX,INCY,LDA,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zher2k.f b/BLAS/SRC/zher2k.f index e5f7be83..bfcf27fd 100644 --- a/BLAS/SRC/zher2k.f +++ b/BLAS/SRC/zher2k.f @@ -1,145 +1,225 @@ - SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - DOUBLE PRECISION BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b ZHER2K +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* DOUBLE PRECISION BETA +* INTEGER K,LDA,LDB,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZHER2K performs one of the hermitian rank 2k operations +*>\details \b Purpose: +*>\verbatim +*> +*> ZHER2K performs one of the hermitian rank 2k operations +*> +*> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, +*> +*> or +*> +*> C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, +*> +*> where alpha and beta are scalars with beta real, C is an n by n +*> hermitian matrix and A and B are n by k matrices in the first case +*> and k by n matrices in the second case. +*> +*>\endverbatim * -* C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, -* -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*B**H + +*> conjg( alpha )*B*A**H + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**H*B + +*> conjg( alpha )*B**H*A + +*> beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrices A and B, and on entry with +*> TRANS = 'C' or 'c', K specifies the number of rows of the +*> matrices A and B. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 . +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array B must contain the matrix B, otherwise +*> the leading k by n part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDB must be at least max( 1, n ), otherwise LDB must +*> be at least max( 1, k ). +*> Unchanged on exit. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION . +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars with beta real, C is an n by n -* hermitian matrix and A and B are n by k matrices in the first case -* and k by n matrices in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*B**H + -* conjg( alpha )*B*A**H + -* beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**H*B + -* conjg( alpha )*B**H*A + -* beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrices A and B, and on entry with -* TRANS = 'C' or 'c', K specifies the number of rows of the -* matrices A and B. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array B must contain the matrix B, otherwise -* the leading k by n part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDB must be at least max( 1, n ), otherwise LDB must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. +*> Ed Anderson, Cray Research Inc. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. -* -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. -* Ed Anderson, Cray Research Inc. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + DOUBLE PRECISION BETA + INTEGER K,LDA,LDB,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zherk.f b/BLAS/SRC/zherk.f index af04413a..f1795c40 100644 --- a/BLAS/SRC/zherk.f +++ b/BLAS/SRC/zherk.f @@ -1,125 +1,199 @@ - SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),C(LDC,*) -* .. +*> \brief \b ZHERK +* +* =========== DOCUMENTATION =========== * +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA,BETA +* INTEGER K,LDA,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZHERK performs one of the hermitian rank k operations -* -* C := alpha*A*A**H + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> ZHERK performs one of the hermitian rank k operations +*> +*> C := alpha*A*A**H + beta*C, +*> +*> or +*> +*> C := alpha*A**H*A + beta*C, +*> +*> where alpha and beta are real scalars, C is an n by n hermitian +*> matrix and A is an n by k matrix in the first case and a k by n +*> matrix in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrix A, and on entry with +*> TRANS = 'C' or 'c', K specifies the number of rows of the +*> matrix A. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION . +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION. +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the hermitian matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the hermitian matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**H*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are real scalars, C is an n by n hermitian -* matrix and A is an n by k matrix in the first case and a k by n -* matrix in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. -* -* TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrix A, and on entry with -* TRANS = 'C' or 'c', K specifies the number of rows of the -* matrix A. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - DOUBLE PRECISION. -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the hermitian matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the hermitian matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. +*> Ed Anderson, Cray Research Inc. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * -* Level 3 Blas routine. -* -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. -* Ed Anderson, Cray Research Inc. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER K,LDA,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zhpmv.f b/BLAS/SRC/zhpmv.f index 514cd20a..2304ed87 100644 --- a/BLAS/SRC/zhpmv.f +++ b/BLAS/SRC/zhpmv.f @@ -1,102 +1,173 @@ - SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*),Y(*) -* .. +*> \brief \b ZHPMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZHPMV performs the matrix-vector operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHPMV performs the matrix-vector operation +*> +*> y := alpha*A*x + beta*y, +*> +*> where alpha and beta are scalars, x and y are n element vectors and +*> A is an n by n hermitian matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX*16 array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. +*> Note that the imaginary parts of the diagonal elements need +*> not be set and are assumed to be zero. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then Y need not be set on input. +*> \endverbatim +*> +*> \param[in,out] Y +*> \verbatim +*> Y is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. On exit, Y is overwritten by the updated +*> vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* y := alpha*A*x + beta*y, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, x and y are n element vectors and -* A is an n by n hermitian matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* AP - COMPLEX*16 array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. -* Note that the imaginary parts of the diagonal elements need -* not be set and are assumed to be zero. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then Y need not be set on input. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. On exit, Y is overwritten by the updated -* vector y. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zhpr.f b/BLAS/SRC/zhpr.f index 859805d2..d80e359f 100644 --- a/BLAS/SRC/zhpr.f +++ b/BLAS/SRC/zhpr.f @@ -1,89 +1,154 @@ - SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*) -* .. +*> \brief \b ZHPR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION ALPHA +* INTEGER INCX,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 AP(*),X(*) +* .. +* * Purpose * ======= * -* ZHPR performs the hermitian rank 1 operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHPR performs the hermitian rank 1 operation +*> +*> A := alpha*x*x**H + A, +*> +*> where alpha is a real scalar, x is an n element vector and A is an +*> n by n hermitian matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION. +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is COMPLEX*16 array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a real scalar, x is an n element vector and A is an -* n by n hermitian matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - DOUBLE PRECISION. -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* AP - COMPLEX*16 array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zhpr2.f b/BLAS/SRC/zhpr2.f index 48b3591f..0d0c4ea5 100644 --- a/BLAS/SRC/zhpr2.f +++ b/BLAS/SRC/zhpr2.f @@ -1,100 +1,169 @@ - SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER INCX,INCY,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*),Y(*) -* .. +*> \brief \b ZHPR2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* INTEGER INCX,INCY,N +* CHARACTER UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 AP(*),X(*),Y(*) +* .. +* * Purpose * ======= * -* ZHPR2 performs the hermitian rank 2 operation +*>\details \b Purpose: +*>\verbatim +*> +*> ZHPR2 performs the hermitian rank 2 operation +*> +*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> +*> where alpha is a scalar, x and y are n element vectors and A is an +*> n by n hermitian matrix, supplied in packed form. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the matrix A is supplied in the packed +*> array AP as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' The upper triangular part of A is +*> supplied in AP. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' The lower triangular part of A is +*> supplied in AP. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCY ) ). +*> Before entry, the incremented array Y must contain the n +*> element vector y. +*> \endverbatim +*> +*> \param[in] INCY +*> \verbatim +*> INCY is INTEGER +*> On entry, INCY specifies the increment for the elements of +*> Y. INCY must not be zero. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is COMPLEX*16 array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) +*> and a( 2, 2 ) respectively, and so on. On exit, the array +*> AP is overwritten by the upper triangular part of the +*> updated matrix. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular part of the hermitian matrix +*> packed sequentially, column by column, so that AP( 1 ) +*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) +*> and a( 3, 1 ) respectively, and so on. On exit, the array +*> AP is overwritten by the lower triangular part of the +*> updated matrix. +*> Note that the imaginary parts of the diagonal elements need +*> not be set, they are assumed to be zero, and on exit they +*> are set to zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A := alpha*x*y**H + conjg( alpha )*y*x**H + A, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha is a scalar, x and y are n element vectors and A is an -* n by n hermitian matrix, supplied in packed form. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the matrix A is supplied in the packed -* array AP as follows: -* -* UPLO = 'U' or 'u' The upper triangular part of A is -* supplied in AP. -* -* UPLO = 'L' or 'l' The lower triangular part of A is -* supplied in AP. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. -* Unchanged on exit. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. -* -* Y - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCY ) ). -* Before entry, the incremented array Y must contain the n -* element vector y. -* Unchanged on exit. -* -* INCY - INTEGER. -* On entry, INCY specifies the increment for the elements of -* Y. INCY must not be zero. -* Unchanged on exit. -* -* AP - COMPLEX*16 array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -* and a( 2, 2 ) respectively, and so on. On exit, the array -* AP is overwritten by the upper triangular part of the -* updated matrix. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular part of the hermitian matrix -* packed sequentially, column by column, so that AP( 1 ) -* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -* and a( 3, 1 ) respectively, and so on. On exit, the array -* AP is overwritten by the lower triangular part of the -* updated matrix. -* Note that the imaginary parts of the diagonal elements need -* not be set, they are assumed to be zero, and on exit they -* are set to zero. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + INTEGER INCX,INCY,N + CHARACTER UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 AP(*),X(*),Y(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zrotg.f b/BLAS/SRC/zrotg.f index c25fa654..daa0f667 100644 --- a/BLAS/SRC/zrotg.f +++ b/BLAS/SRC/zrotg.f @@ -1,14 +1,55 @@ +*> \brief \b ZROTG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZROTG(CA,CB,C,S) +* +* .. Scalar Arguments .. +* COMPLEX*16 CA,CB,S +* DOUBLE PRECISION C +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZROTG determines a double complex Givens rotation. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* +* ===================================================================== SUBROUTINE ZROTG(CA,CB,C,S) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* * .. Scalar Arguments .. COMPLEX*16 CA,CB,S DOUBLE PRECISION C * .. * -* Purpose -* ======= -* -* ZROTG determines a double complex Givens rotation. -* * ===================================================================== * * .. Local Scalars .. diff --git a/BLAS/SRC/zscal.f b/BLAS/SRC/zscal.f index d5acf683..67148062 100644 --- a/BLAS/SRC/zscal.f +++ b/BLAS/SRC/zscal.f @@ -1,23 +1,72 @@ - SUBROUTINE ZSCAL(N,ZA,ZX,INCX) -* .. Scalar Arguments .. - COMPLEX*16 ZA - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*) -* .. +*> \brief \b ZSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE ZSCAL(N,ZA,ZX,INCX) +* +* .. Scalar Arguments .. +* COMPLEX*16 ZA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*) +* .. +* * Purpose * ======= * -* ZSCAL scales a vector by a constant. +*>\details \b Purpose: +*>\verbatim +*> +*> ZSCAL scales a vector by a constant. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZSCAL(N,ZA,ZX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 3/93 to return if incx .le. 0. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + COMPLEX*16 ZA + INTEGER INCX,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zswap.f b/BLAS/SRC/zswap.f index d3bb047e..8000bfc2 100644 --- a/BLAS/SRC/zswap.f +++ b/BLAS/SRC/zswap.f @@ -1,21 +1,69 @@ - SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. +*> \brief \b ZSWAP * +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* COMPLEX*16 ZX(*),ZY(*) +* .. +* * Purpose * ======= * -* ZSWAP interchanges two vectors. +*>\details \b Purpose: +*>\verbatim +*> +*> ZSWAP interchanges two vectors. +*> +*>\endverbatim +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_blas_level1 +* * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> jack dongarra, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* jack dongarra, 3/11/78. -* modified 12/3/93, array(1) declarations changed to array(*) +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + COMPLEX*16 ZX(*),ZY(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zsymm.f b/BLAS/SRC/zsymm.f index e0192e9f..6ceda01d 100644 --- a/BLAS/SRC/zsymm.f +++ b/BLAS/SRC/zsymm.f @@ -1,137 +1,215 @@ - SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b ZSYMM +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER LDA,LDB,LDC,M,N +* CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZSYMM performs one of the matrix-matrix operations -* -* C := alpha*A*B + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> ZSYMM performs one of the matrix-matrix operations +*> +*> C := alpha*A*B + beta*C, +*> +*> or +*> +*> C := alpha*B*A + beta*C, +*> +*> where alpha and beta are scalars, A is a symmetric matrix and B and +*> C are m by n matrices. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether the symmetric matrix A +*> appears on the left or right in the operation as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the symmetric matrix A is to be +*> referenced as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of the +*> symmetric matrix is to be referenced. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of the matrix C. +*> M must be at least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of the matrix C. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> m when SIDE = 'L' or 'l' and is n otherwise. +*> Before entry with SIDE = 'L' or 'l', the m by m part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading m by m upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading m by m lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> Before entry with SIDE = 'R' or 'r', the n by n part of +*> the array A must contain the symmetric matrix, such that +*> when UPLO = 'U' or 'u', the leading n by n upper triangular +*> part of the array A must contain the upper triangular part +*> of the symmetric matrix and the strictly lower triangular +*> part of A is not referenced, and when UPLO = 'L' or 'l', +*> the leading n by n lower triangular part of the array A +*> must contain the lower triangular part of the symmetric +*> matrix and the strictly upper triangular part of A is not +*> referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), otherwise LDA must be at +*> least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. When BETA is +*> supplied as zero then C need not be set on input. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry, the leading m by n part of the array C must +*> contain the matrix C, except when beta is zero, in which +*> case C need not be set on entry. +*> On exit, the array C is overwritten by the m by n updated +*> matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*B*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, A is a symmetric matrix and B and -* C are m by n matrices. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether the symmetric matrix A -* appears on the left or right in the operation as follows: -* -* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -* -* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the symmetric matrix A is to be -* referenced as follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of the -* symmetric matrix is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of the -* symmetric matrix is to be referenced. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of the matrix C. -* M must be at least zero. -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the number of columns of the matrix C. -* N must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* m when SIDE = 'L' or 'l' and is n otherwise. -* Before entry with SIDE = 'L' or 'l', the m by m part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading m by m upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading m by m lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Before entry with SIDE = 'R' or 'r', the n by n part of -* the array A must contain the symmetric matrix, such that -* when UPLO = 'U' or 'u', the leading n by n upper triangular -* part of the array A must contain the upper triangular part -* of the symmetric matrix and the strictly lower triangular -* part of A is not referenced, and when UPLO = 'L' or 'l', -* the leading n by n lower triangular part of the array A -* must contain the lower triangular part of the symmetric -* matrix and the strictly upper triangular part of A is not -* referenced. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), otherwise LDA must be at -* least max( 1, n ). -* Unchanged on exit. -* -* B - COMPLEX*16 array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. When BETA is -* supplied as zero then C need not be set on input. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry, the leading m by n part of the array C must -* contain the matrix C, except when beta is zero, in which -* case C need not be set on entry. -* On exit, the array C is overwritten by the m by n updated -* matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER LDA,LDB,LDC,M,N + CHARACTER SIDE,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zsyr2k.f b/BLAS/SRC/zsyr2k.f index a9bd0f4d..898febce 100644 --- a/BLAS/SRC/zsyr2k.f +++ b/BLAS/SRC/zsyr2k.f @@ -1,136 +1,214 @@ - SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. +*> \brief \b ZSYR2K +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER K,LDA,LDB,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZSYR2K performs one of the symmetric rank 2k operations -* -* C := alpha*A*B**T + alpha*B*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> ZSYR2K performs one of the symmetric rank 2k operations +*> +*> C := alpha*A*B**T + alpha*B*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A and B are n by k matrices in the first case and k by n +*> matrices in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + +*> beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + +*> beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrices A and B, and on entry with +*> TRANS = 'T' or 't', K specifies the number of rows of the +*> matrices A and B. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array B must contain the matrix B, otherwise +*> the leading k by n part of the array B must contain the +*> matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDB must be at least max( 1, n ), otherwise LDB must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*B + alpha*B**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A and B are n by k matrices in the first case and k by n -* matrices in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + -* beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + -* beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrices A and B, and on entry with -* TRANS = 'T' or 't', K specifies the number of rows of the -* matrices A and B. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array B must contain the matrix B, otherwise -* the leading k by n part of the array B must contain the -* matrix B. -* Unchanged on exit. -* -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDB must be at least max( 1, n ), otherwise LDB must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER K,LDA,LDB,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/zsyrk.f b/BLAS/SRC/zsyrk.f index b2acf31e..db6d567a 100644 --- a/BLAS/SRC/zsyrk.f +++ b/BLAS/SRC/zsyrk.f @@ -1,119 +1,193 @@ - SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),C(LDC,*) -* .. +*> \brief \b ZSYRK +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA,BETA +* INTEGER K,LDA,LDC,N +* CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),C(LDC,*) +* .. +* * Purpose * ======= * -* ZSYRK performs one of the symmetric rank k operations -* -* C := alpha*A*A**T + beta*C, +*>\details \b Purpose: +*>\verbatim +*> +*> ZSYRK performs one of the symmetric rank k operations +*> +*> C := alpha*A*A**T + beta*C, +*> +*> or +*> +*> C := alpha*A**T*A + beta*C, +*> +*> where alpha and beta are scalars, C is an n by n symmetric matrix +*> and A is an n by k matrix in the first case and a k by n matrix +*> in the second case. +*> +*>\endverbatim * -* or +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the upper or lower +*> triangular part of the array C is to be referenced as +*> follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' Only the upper triangular part of C +*> is to be referenced. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' Only the lower triangular part of C +*> is to be referenced. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix C. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with TRANS = 'N' or 'n', K specifies the number +*> of columns of the matrix A, and on entry with +*> TRANS = 'T' or 't', K specifies the number of rows of the +*> matrix A. K must be at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is +*> k when TRANS = 'N' or 'n', and is n otherwise. +*> Before entry with TRANS = 'N' or 'n', the leading n by k +*> part of the array A must contain the matrix A, otherwise +*> the leading k by n part of the array A must contain the +*> matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When TRANS = 'N' or 'n' +*> then LDA must be at least max( 1, n ), otherwise LDA must +*> be at least max( 1, k ). +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is COMPLEX*16 +*> On entry, BETA specifies the scalar beta. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array of DIMENSION ( LDC, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array C must contain the upper +*> triangular part of the symmetric matrix and the strictly +*> lower triangular part of C is not referenced. On exit, the +*> upper triangular part of the array C is overwritten by the +*> upper triangular part of the updated matrix. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array C must contain the lower +*> triangular part of the symmetric matrix and the strictly +*> upper triangular part of C is not referenced. On exit, the +*> lower triangular part of the array C is overwritten by the +*> lower triangular part of the updated matrix. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> On entry, LDC specifies the first dimension of C as declared +*> in the calling (sub) program. LDC must be at least +*> max( 1, n ). +*> \endverbatim +*> +* +* Authors +* ======= * -* C := alpha*A**T*A + beta*C, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where alpha and beta are scalars, C is an n by n symmetric matrix -* and A is an n by k matrix in the first case and a k by n matrix -* in the second case. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level3 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the upper or lower -* triangular part of the array C is to be referenced as -* follows: -* -* UPLO = 'U' or 'u' Only the upper triangular part of C -* is to be referenced. -* -* UPLO = 'L' or 'l' Only the lower triangular part of C -* is to be referenced. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -* -* TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix C. N must be -* at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with TRANS = 'N' or 'n', K specifies the number -* of columns of the matrix A, and on entry with -* TRANS = 'T' or 't', K specifies the number of rows of the -* matrix A. K must be at least zero. -* Unchanged on exit. -* -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is -* k when TRANS = 'N' or 'n', and is n otherwise. -* Before entry with TRANS = 'N' or 'n', the leading n by k -* part of the array A must contain the matrix A, otherwise -* the leading k by n part of the array A must contain the -* matrix A. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When TRANS = 'N' or 'n' -* then LDA must be at least max( 1, n ), otherwise LDA must -* be at least max( 1, k ). -* Unchanged on exit. -* -* BETA - COMPLEX*16 . -* On entry, BETA specifies the scalar beta. -* Unchanged on exit. -* -* C - COMPLEX*16 array of DIMENSION ( LDC, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array C must contain the upper -* triangular part of the symmetric matrix and the strictly -* lower triangular part of C is not referenced. On exit, the -* upper triangular part of the array C is overwritten by the -* upper triangular part of the updated matrix. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array C must contain the lower -* triangular part of the symmetric matrix and the strictly -* upper triangular part of C is not referenced. On exit, the -* lower triangular part of the array C is overwritten by the -* lower triangular part of the updated matrix. -* -* LDC - INTEGER. -* On entry, LDC specifies the first dimension of C as declared -* in the calling (sub) program. LDC must be at least -* max( 1, n ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA,BETA + INTEGER K,LDA,LDC,N + CHARACTER TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),C(LDC,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztbmv.f b/BLAS/SRC/ztbmv.f index 2d2fbe17..781ac531 100644 --- a/BLAS/SRC/ztbmv.f +++ b/BLAS/SRC/ztbmv.f @@ -1,141 +1,218 @@ - SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*) -* .. +*> \brief \b ZTBMV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* ZTBMV performs one of the matrix-vector operations +*>\details \b Purpose: +*>\verbatim +*> +*> ZTBMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, or x := A**H*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**H*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is (input/output) COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* x := A*x, or x := A**T*x, or x := A**H*x, +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular band matrix, with ( k + 1 ) diagonals. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**H*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztbsv.f b/BLAS/SRC/ztbsv.f index 80ebb740..b4828146 100644 --- a/BLAS/SRC/ztbsv.f +++ b/BLAS/SRC/ztbsv.f @@ -1,144 +1,221 @@ - SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,K,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*) -* .. +*> \brief \b ZTBSV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,K,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*) +* .. +* * Purpose * ======= * -* ZTBSV solves one of the systems of equations +*>\details \b Purpose: +*>\verbatim +*> +*> ZTBSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, or A**H*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular band matrix, with ( k + 1 ) +*> diagonals. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* A*x = b, or A**T*x = b, or A**H*x = b, +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**H*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> On entry with UPLO = 'U' or 'u', K specifies the number of +*> super-diagonals of the matrix A. +*> On entry with UPLO = 'L' or 'l', K specifies the number of +*> sub-diagonals of the matrix A. +*> K must satisfy 0 .le. K. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) +*> by n part of the array A must contain the upper triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row +*> ( k + 1 ) of the array, the first super-diagonal starting at +*> position 2 in row k, and so on. The top left k by k triangle +*> of the array A is not referenced. +*> The following program segment will transfer an upper +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = K + 1 - J +*> DO 10, I = MAX( 1, J - K ), J +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) +*> by n part of the array A must contain the lower triangular +*> band part of the matrix of coefficients, supplied column by +*> column, with the leading diagonal of the matrix in row 1 of +*> the array, the first sub-diagonal starting at position 1 in +*> row 2, and so on. The bottom right k by k triangle of the +*> array A is not referenced. +*> The following program segment will transfer a lower +*> triangular band matrix from conventional full matrix storage +*> to band storage: +*> \endverbatim +*> \verbatim +*> DO 20, J = 1, N +*> M = 1 - J +*> DO 10, I = J, MIN( N, J + K ) +*> A( M + I, J ) = matrix( I, J ) +*> 10 CONTINUE +*> 20 CONTINUE +*> \endverbatim +*> \verbatim +*> Note that when DIAG = 'U' or 'u' the elements of the array A +*> corresponding to the diagonal elements of the matrix are not +*> referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> ( k + 1 ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular band matrix, with ( k + 1 ) -* diagonals. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. +*> \date November 2011 * -* Arguments -* ========== +*> \ingroup complex16_blas_level2 * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**H*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. -* -* K - INTEGER. -* On entry with UPLO = 'U' or 'u', K specifies the number of -* super-diagonals of the matrix A. -* On entry with UPLO = 'L' or 'l', K specifies the number of -* sub-diagonals of the matrix A. -* K must satisfy 0 .le. K. -* Unchanged on exit. -* -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) -* by n part of the array A must contain the upper triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row -* ( k + 1 ) of the array, the first super-diagonal starting at -* position 2 in row k, and so on. The top left k by k triangle -* of the array A is not referenced. -* The following program segment will transfer an upper -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = K + 1 - J -* DO 10, I = MAX( 1, J - K ), J -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) -* by n part of the array A must contain the lower triangular -* band part of the matrix of coefficients, supplied column by -* column, with the leading diagonal of the matrix in row 1 of -* the array, the first sub-diagonal starting at position 1 in -* row 2, and so on. The bottom right k by k triangle of the -* array A is not referenced. -* The following program segment will transfer a lower -* triangular band matrix from conventional full matrix storage -* to band storage: -* -* DO 20, J = 1, N -* M = 1 - J -* DO 10, I = J, MIN( N, J + K ) -* A( M + I, J ) = matrix( I, J ) -* 10 CONTINUE -* 20 CONTINUE -* -* Note that when DIAG = 'U' or 'u' the elements of the array A -* corresponding to the diagonal elements of the matrix are not -* referenced, but are assumed to be unity. -* Unchanged on exit. -* -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* ( k + 1 ). -* Unchanged on exit. -* -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. -* -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,K,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztpmv.f b/BLAS/SRC/ztpmv.f index 33f4b52f..d4f71a47 100644 --- a/BLAS/SRC/ztpmv.f +++ b/BLAS/SRC/ztpmv.f @@ -1,101 +1,170 @@ - SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*) -* .. -* -* Purpose -* ======= -* -* ZTPMV performs one of the matrix-vector operations +*> \brief \b ZTPMV * -* x := A*x, or x := A**T*x, or x := A**H*x, +* =========== DOCUMENTATION =========== * -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix, supplied in packed form. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**H*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> ZTPMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, or x := A**H*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix, supplied in packed form. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**H*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX*16 array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is (input/output) COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - COMPLEX*16 array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup complex16_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztpsv.f b/BLAS/SRC/ztpsv.f index 55eaf9e1..e12c1e9c 100644 --- a/BLAS/SRC/ztpsv.f +++ b/BLAS/SRC/ztpsv.f @@ -1,103 +1,172 @@ - SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*) -* .. +*> \brief \b ZTPSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* ZTPSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, or A**H*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix, supplied in packed form. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**H*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 AP(*),X(*) +* .. +* +* Purpose +* ======= * -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +*>\details \b Purpose: +*>\verbatim +*> +*> ZTPSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, or A**H*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix, supplied in packed form. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**H*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX*16 array of DIMENSION at least +*> ( ( n*( n + 1 ) )/2 ). +*> Before entry with UPLO = 'U' or 'u', the array AP must +*> contain the upper triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) +*> respectively, and so on. +*> Before entry with UPLO = 'L' or 'l', the array AP must +*> contain the lower triangular matrix packed sequentially, +*> column by column, so that AP( 1 ) contains a( 1, 1 ), +*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) +*> respectively, and so on. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* AP - COMPLEX*16 array of DIMENSION at least -* ( ( n*( n + 1 ) )/2 ). -* Before entry with UPLO = 'U' or 'u', the array AP must -* contain the upper triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -* respectively, and so on. -* Before entry with UPLO = 'L' or 'l', the array AP must -* contain the lower triangular matrix packed sequentially, -* column by column, so that AP( 1 ) contains a( 1, 1 ), -* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -* respectively, and so on. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced, but are assumed to be unity. -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup complex16_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 AP(*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztrmm.f b/BLAS/SRC/ztrmm.f index e02efd43..a54a53c1 100644 --- a/BLAS/SRC/ztrmm.f +++ b/BLAS/SRC/ztrmm.f @@ -1,129 +1,208 @@ - SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b ZTRMM * -* ZTRMM performs one of the matrix-matrix operations +* =========== DOCUMENTATION =========== * -* B := alpha*op( A )*B, or B := alpha*B*op( A ) +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, B is an m by n matrix, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T or op( A ) = A**H. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) multiplies B from -* the left or right as follows: -* -* SIDE = 'L' or 'l' B := alpha*op( A )*B. -* -* SIDE = 'R' or 'r' B := alpha*B*op( A ). -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**H. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> ZTRMM performs one of the matrix-matrix operations +*> +*> B := alpha*op( A )*B, or B := alpha*B*op( A ) +*> +*> where alpha is a scalar, B is an m by n matrix, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T or op( A ) = A**H. +*> +*>\endverbatim * -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) multiplies B from +*> the left or right as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' B := alpha*op( A )*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' B := alpha*B*op( A ). +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**H. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m +*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is (input/output) COMPLEX*16 array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the matrix B, and on exit is overwritten by the +*> transformed matrix. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - COMPLEX*16 array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the matrix B, and on exit is overwritten by the -* transformed matrix. +*> \ingroup complex16_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztrmv.f b/BLAS/SRC/ztrmv.f index 345c8cd9..2c491498 100644 --- a/BLAS/SRC/ztrmv.f +++ b/BLAS/SRC/ztrmv.f @@ -1,104 +1,175 @@ - SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*) -* .. +*> \brief \b ZTRMV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* ZTRMV performs one of the matrix-vector operations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* x := A*x, or x := A**T*x, or x := A**H*x, -* -* where x is an n element vector and A is an n by n unit, or non-unit, -* upper or lower triangular matrix. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the operation to be performed as -* follows: -* -* TRANS = 'N' or 'n' x := A*x. -* -* TRANS = 'T' or 't' x := A**T*x. -* -* TRANS = 'C' or 'c' x := A**H*x. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> ZTRMV performs one of the matrix-vector operations +*> +*> x := A*x, or x := A**T*x, or x := A**H*x, +*> +*> where x is an n element vector and A is an n by n unit, or non-unit, +*> upper or lower triangular matrix. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the operation to be performed as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' x := A*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' x := A**T*x. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' x := A**H*x. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is (input/output) COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element vector x. On exit, X is overwritten with the +*> tranformed vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element vector x. On exit, X is overwritten with the -* tranformed vector x. +*> \ingroup complex16_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> The vector and matrix arguments are not referenced when N = 0, or M = 0 +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. -* The vector and matrix arguments are not referenced when N = 0, or M = 0 +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztrsm.f b/BLAS/SRC/ztrsm.f index 4cfe33b8..fae9928a 100644 --- a/BLAS/SRC/ztrsm.f +++ b/BLAS/SRC/ztrsm.f @@ -1,131 +1,211 @@ - SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*) -* .. -* -* Purpose -* ======= +*> \brief \b ZTRSM * -* ZTRSM solves one of the matrix equations +* =========== DOCUMENTATION =========== * -* op( A )*X = alpha*B, or X*op( A ) = alpha*B, +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* where alpha is a scalar, X and B are m by n matrices, A is a unit, or -* non-unit, upper or lower triangular matrix and op( A ) is one of -* -* op( A ) = A or op( A ) = A**T or op( A ) = A**H. -* -* The matrix X is overwritten on B. -* -* Arguments +* Definition * ========== * -* SIDE - CHARACTER*1. -* On entry, SIDE specifies whether op( A ) appears on the left -* or right of X as follows: -* -* SIDE = 'L' or 'l' op( A )*X = alpha*B. -* -* SIDE = 'R' or 'r' X*op( A ) = alpha*B. -* -* Unchanged on exit. -* -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix A is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANSA - CHARACTER*1. -* On entry, TRANSA specifies the form of op( A ) to be used in -* the matrix multiplication as follows: -* -* TRANSA = 'N' or 'n' op( A ) = A. -* -* TRANSA = 'T' or 't' op( A ) = A**T. -* -* TRANSA = 'C' or 'c' op( A ) = A**H. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit triangular -* as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. -* -* Unchanged on exit. -* -* M - INTEGER. -* On entry, M specifies the number of rows of B. M must be at -* least zero. -* Unchanged on exit. +* SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* +* .. Scalar Arguments .. +* COMPLEX*16 ALPHA +* INTEGER LDA,LDB,M,N +* CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= * -* N - INTEGER. -* On entry, N specifies the number of columns of B. N must be -* at least zero. -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> ZTRSM solves one of the matrix equations +*> +*> op( A )*X = alpha*B, or X*op( A ) = alpha*B, +*> +*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or +*> non-unit, upper or lower triangular matrix and op( A ) is one of +*> +*> op( A ) = A or op( A ) = A**T or op( A ) = A**H. +*> +*> The matrix X is overwritten on B. +*> +*>\endverbatim * -* ALPHA - COMPLEX*16 . -* On entry, ALPHA specifies the scalar alpha. When alpha is -* zero then A is not referenced and B need not be set before -* entry. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> On entry, SIDE specifies whether op( A ) appears on the left +*> or right of X as follows: +*> \endverbatim +*> \verbatim +*> SIDE = 'L' or 'l' op( A )*X = alpha*B. +*> \endverbatim +*> \verbatim +*> SIDE = 'R' or 'r' X*op( A ) = alpha*B. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix A is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANSA +*> \verbatim +*> TRANSA is CHARACTER*1 +*> On entry, TRANSA specifies the form of op( A ) to be used in +*> the matrix multiplication as follows: +*> \endverbatim +*> \verbatim +*> TRANSA = 'N' or 'n' op( A ) = A. +*> \endverbatim +*> \verbatim +*> TRANSA = 'T' or 't' op( A ) = A**T. +*> \endverbatim +*> \verbatim +*> TRANSA = 'C' or 'c' op( A ) = A**H. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit triangular +*> as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> On entry, M specifies the number of rows of B. M must be at +*> least zero. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the number of columns of B. N must be +*> at least zero. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, ALPHA specifies the scalar alpha. When alpha is +*> zero then A is not referenced and B need not be set before +*> entry. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, k ), +*> where k is m when SIDE = 'L' or 'l' +*> and k is n when SIDE = 'R' or 'r'. +*> Before entry with UPLO = 'U' or 'u', the leading k by k +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading k by k +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. When SIDE = 'L' or 'l' then +*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +*> then LDA must be at least max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX*16 array of DIMENSION ( LDB, n ). +*> Before entry, the leading m by n part of the array B must +*> contain the right-hand side matrix B, and on exit is +*> overwritten by the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> On entry, LDB specifies the first dimension of B as declared +*> in the calling (sub) program. LDB must be at least +*> max( 1, m ). +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m -* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -* Before entry with UPLO = 'U' or 'u', the leading k by k -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading k by k -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. When SIDE = 'L' or 'l' then -* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -* then LDA must be at least max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* B - COMPLEX*16 array of DIMENSION ( LDB, n ). -* Before entry, the leading m by n part of the array B must -* contain the right-hand side matrix B, and on exit is -* overwritten by the solution matrix X. +*> \ingroup complex16_blas_level3 * -* LDB - INTEGER. -* On entry, LDB specifies the first dimension of B as declared -* in the calling (sub) program. LDB must be at least -* max( 1, m ). -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 3 Blas routine. +*> +*> -- Written on 8-February-1989. +*> Jack Dongarra, Argonne National Laboratory. +*> Iain Duff, AERE Harwell. +*> Jeremy Du Croz, Numerical Algorithms Group Ltd. +*> Sven Hammarling, Numerical Algorithms Group Ltd. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * -* Level 3 Blas routine. +* -- Reference BLAS level3 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 8-February-1989. -* Jack Dongarra, Argonne National Laboratory. -* Iain Duff, AERE Harwell. -* Jeremy Du Croz, Numerical Algorithms Group Ltd. -* Sven Hammarling, Numerical Algorithms Group Ltd. +* .. Scalar Arguments .. + COMPLEX*16 ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),B(LDB,*) +* .. * * ===================================================================== * diff --git a/BLAS/SRC/ztrsv.f b/BLAS/SRC/ztrsv.f index 2527445f..3696075b 100644 --- a/BLAS/SRC/ztrsv.f +++ b/BLAS/SRC/ztrsv.f @@ -1,106 +1,177 @@ - SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*) -* .. +*> \brief \b ZTRSV * -* Purpose -* ======= +* =========== DOCUMENTATION =========== * -* ZTRSV solves one of the systems of equations +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* A*x = b, or A**T*x = b, or A**H*x = b, -* -* where b and x are n element vectors and A is an n by n unit, or -* non-unit, upper or lower triangular matrix. -* -* No test for singularity or near-singularity is included in this -* routine. Such tests must be performed before calling this routine. -* -* Arguments +* Definition * ========== * -* UPLO - CHARACTER*1. -* On entry, UPLO specifies whether the matrix is an upper or -* lower triangular matrix as follows: -* -* UPLO = 'U' or 'u' A is an upper triangular matrix. -* -* UPLO = 'L' or 'l' A is a lower triangular matrix. -* -* Unchanged on exit. -* -* TRANS - CHARACTER*1. -* On entry, TRANS specifies the equations to be solved as -* follows: -* -* TRANS = 'N' or 'n' A*x = b. -* -* TRANS = 'T' or 't' A**T*x = b. -* -* TRANS = 'C' or 'c' A**H*x = b. -* -* Unchanged on exit. -* -* DIAG - CHARACTER*1. -* On entry, DIAG specifies whether or not A is unit -* triangular as follows: -* -* DIAG = 'U' or 'u' A is assumed to be unit triangular. -* -* DIAG = 'N' or 'n' A is not assumed to be unit -* triangular. +* SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) +* +* .. Scalar Arguments .. +* INTEGER INCX,LDA,N +* CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. +* COMPLEX*16 A(LDA,*),X(*) +* .. +* +* Purpose +* ======= * -* Unchanged on exit. +*>\details \b Purpose: +*>\verbatim +*> +*> ZTRSV solves one of the systems of equations +*> +*> A*x = b, or A**T*x = b, or A**H*x = b, +*> +*> where b and x are n element vectors and A is an n by n unit, or +*> non-unit, upper or lower triangular matrix. +*> +*> No test for singularity or near-singularity is included in this +*> routine. Such tests must be performed before calling this routine. +*> +*>\endverbatim * -* N - INTEGER. -* On entry, N specifies the order of the matrix A. -* N must be at least zero. -* Unchanged on exit. +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> On entry, UPLO specifies whether the matrix is an upper or +*> lower triangular matrix as follows: +*> \endverbatim +*> \verbatim +*> UPLO = 'U' or 'u' A is an upper triangular matrix. +*> \endverbatim +*> \verbatim +*> UPLO = 'L' or 'l' A is a lower triangular matrix. +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> On entry, TRANS specifies the equations to be solved as +*> follows: +*> \endverbatim +*> \verbatim +*> TRANS = 'N' or 'n' A*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'T' or 't' A**T*x = b. +*> \endverbatim +*> \verbatim +*> TRANS = 'C' or 'c' A**H*x = b. +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> On entry, DIAG specifies whether or not A is unit +*> triangular as follows: +*> \endverbatim +*> \verbatim +*> DIAG = 'U' or 'u' A is assumed to be unit triangular. +*> \endverbatim +*> \verbatim +*> DIAG = 'N' or 'n' A is not assumed to be unit +*> triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> On entry, N specifies the order of the matrix A. +*> N must be at least zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array of DIMENSION ( LDA, n ). +*> Before entry with UPLO = 'U' or 'u', the leading n by n +*> upper triangular part of the array A must contain the upper +*> triangular matrix and the strictly lower triangular part of +*> A is not referenced. +*> Before entry with UPLO = 'L' or 'l', the leading n by n +*> lower triangular part of the array A must contain the lower +*> triangular matrix and the strictly upper triangular part of +*> A is not referenced. +*> Note that when DIAG = 'U' or 'u', the diagonal elements of +*> A are not referenced either, but are assumed to be unity. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> On entry, LDA specifies the first dimension of A as declared +*> in the calling (sub) program. LDA must be at least +*> max( 1, n ). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array of dimension at least +*> ( 1 + ( n - 1 )*abs( INCX ) ). +*> Before entry, the incremented array X must contain the n +*> element right-hand side vector b. On exit, X is overwritten +*> with the solution vector x. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> On entry, INCX specifies the increment for the elements of +*> X. INCX must not be zero. +*> \endverbatim +*> +* +* Authors +* ======= * -* A - COMPLEX*16 array of DIMENSION ( LDA, n ). -* Before entry with UPLO = 'U' or 'u', the leading n by n -* upper triangular part of the array A must contain the upper -* triangular matrix and the strictly lower triangular part of -* A is not referenced. -* Before entry with UPLO = 'L' or 'l', the leading n by n -* lower triangular part of the array A must contain the lower -* triangular matrix and the strictly upper triangular part of -* A is not referenced. -* Note that when DIAG = 'U' or 'u', the diagonal elements of -* A are not referenced either, but are assumed to be unity. -* Unchanged on exit. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA - INTEGER. -* On entry, LDA specifies the first dimension of A as declared -* in the calling (sub) program. LDA must be at least -* max( 1, n ). -* Unchanged on exit. +*> \date November 2011 * -* X - COMPLEX*16 array of dimension at least -* ( 1 + ( n - 1 )*abs( INCX ) ). -* Before entry, the incremented array X must contain the n -* element right-hand side vector b. On exit, X is overwritten -* with the solution vector x. +*> \ingroup complex16_blas_level2 * -* INCX - INTEGER. -* On entry, INCX specifies the increment for the elements of -* X. INCX must not be zero. -* Unchanged on exit. * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Level 2 Blas routine. +*> +*> -- Written on 22-October-1986. +*> Jack Dongarra, Argonne National Lab. +*> Jeremy Du Croz, Nag Central Office. +*> Sven Hammarling, Nag Central Office. +*> Richard Hanson, Sandia National Labs. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * -* Level 2 Blas routine. +* -- Reference BLAS level2 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* -- Written on 22-October-1986. -* Jack Dongarra, Argonne National Lab. -* Jeremy Du Croz, Nag Central Office. -* Sven Hammarling, Nag Central Office. -* Richard Hanson, Sandia National Labs. +* .. Scalar Arguments .. + INTEGER INCX,LDA,N + CHARACTER DIAG,TRANS,UPLO +* .. +* .. Array Arguments .. + COMPLEX*16 A(LDA,*),X(*) +* .. * * ===================================================================== * |