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| -rw-r--r-- | SRC/zhesv_rook.f | 295 |
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diff --git a/SRC/chesv_rook.f b/SRC/chesv_rook.f new file mode 100644 index 00000000..4a4569f4 --- /dev/null +++ b/SRC/chesv_rook.f @@ -0,0 +1,295 @@ +*> \brief \b CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CHESV_ROOK + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chesv_rook.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chesv_rook.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chesv_rook.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, +* LWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, LDB, LWORK, N, NRHS +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CHESV_ROOK computes the solution to a complex system of linear equations +*> A * X = B, +*> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS +*> matrices. +*> +*> The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used +*> to factor A as +*> A = U * D * U**T, if UPLO = 'U', or +*> A = L * D * L**T, if UPLO = 'L', +*> where U (or L) is a product of permutation and unit upper (lower) +*> triangular matrices, and D is Hermitian and block diagonal with +*> 1-by-1 and 2-by-2 diagonal blocks. +*> +*> CHETRF_ROOK is called to compute the factorization of a complex +*> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal +*> pivoting method. +*> +*> The factored form of A is then used to solve the system +*> of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of linear equations, i.e., the order of the +*> matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of columns +*> of the matrix B. NRHS >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading +*> N-by-N upper triangular part of A contains the upper +*> triangular part of the matrix A, and the strictly lower +*> triangular part of A is not referenced. If UPLO = 'L', the +*> leading N-by-N lower triangular part of A contains the lower +*> triangular part of the matrix A, and the strictly upper +*> triangular part of A is not referenced. +*> +*> On exit, if INFO = 0, the block diagonal matrix D and the +*> multipliers used to obtain the factor U or L from the +*> factorization A = U*D*U**H or A = L*D*L**H as computed by +*> CHETRF_ROOK. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> Details of the interchanges and the block structure of D. +*> +*> If UPLO = 'U': +*> Only the last KB elements of IPIV are set. +*> +*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were +*> interchanged and D(k,k) is a 1-by-1 diagonal block. +*> +*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and +*> columns k and -IPIV(k) were interchanged and rows and +*> columns k-1 and -IPIV(k-1) were inerchaged, +*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. +*> +*> If UPLO = 'L': +*> Only the first KB elements of IPIV are set. +*> +*> If IPIV(k) > 0, then rows and columns k and IPIV(k) +*> were interchanged and D(k,k) is a 1-by-1 diagonal block. +*> +*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and +*> columns k and -IPIV(k) were interchanged and rows and +*> columns k+1 and -IPIV(k+1) were inerchaged, +*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX array, dimension (LDB,NRHS) +*> On entry, the N-by-NRHS right hand side matrix B. +*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The length of WORK. LWORK >= 1, and for best performance +*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for +*> CHETRF_ROOK. +*> for LWORK < N, TRS will be done with Level BLAS 2 +*> for LWORK >= N, TRS will be done with Level BLAS 3 +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization +*> has been completed, but the block diagonal matrix D is +*> exactly singular, so the solution could not be computed. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2012 +* +*> \ingroup complexHEsolve +*> +*> \verbatim +*> +*> November 2012, Igor Kozachenko, +*> Computer Science Division, +*> University of California, Berkeley +*> +*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, +*> School of Mathematics, +*> University of Manchester +*> +*> \endverbatim +* +* +* ===================================================================== + SUBROUTINE CHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, + $ LWORK, INFO ) +* +* -- LAPACK driver routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2012 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, LDA, LDB, LWORK, N, NRHS +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL LQUERY + INTEGER LWKOPT, NB +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, CHETRF_ROOK, CHETRS_ROOK +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + LQUERY = ( LWORK.EQ.-1 ) + IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN + INFO = -10 + END IF +* + IF( INFO.EQ.0 ) THEN + IF( N.EQ.0 ) THEN + LWKOPT = 1 + ELSE + NB = ILAENV( 1, 'CHETRF_ROOK', UPLO, N, -1, -1, -1 ) + LWKOPT = N*NB + END IF + WORK( 1 ) = LWKOPT + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHESV_ROOK ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Compute the factorization A = U*D*U**H or A = L*D*L**H. +* + CALL CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) + IF( INFO.EQ.0 ) THEN +* +* Solve the system A*X = B, overwriting B with X. +* +* Solve with TRS ( Use Level BLAS 2) +* + CALL CHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* + END IF +* + WORK( 1 ) = LWKOPT +* + RETURN +* +* End of CHESV_ROOK +* + END diff --git a/SRC/zhesv_rook.f b/SRC/zhesv_rook.f new file mode 100644 index 00000000..9d35d650 --- /dev/null +++ b/SRC/zhesv_rook.f @@ -0,0 +1,295 @@ +*> \brief \b ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZHESV_ROOK + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv_rook.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv_rook.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv_rook.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, +* LWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, LDB, LWORK, N, NRHS +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZHESV_ROOK computes the solution to a complex system of linear equations +*> A * X = B, +*> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS +*> matrices. +*> +*> The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used +*> to factor A as +*> A = U * D * U**T, if UPLO = 'U', or +*> A = L * D * L**T, if UPLO = 'L', +*> where U (or L) is a product of permutation and unit upper (lower) +*> triangular matrices, and D is Hermitian and block diagonal with +*> 1-by-1 and 2-by-2 diagonal blocks. +*> +*> ZHETRF_ROOK is called to compute the factorization of a complex +*> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal +*> pivoting method. +*> +*> The factored form of A is then used to solve the system +*> of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of linear equations, i.e., the order of the +*> matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of columns +*> of the matrix B. NRHS >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading +*> N-by-N upper triangular part of A contains the upper +*> triangular part of the matrix A, and the strictly lower +*> triangular part of A is not referenced. If UPLO = 'L', the +*> leading N-by-N lower triangular part of A contains the lower +*> triangular part of the matrix A, and the strictly upper +*> triangular part of A is not referenced. +*> +*> On exit, if INFO = 0, the block diagonal matrix D and the +*> multipliers used to obtain the factor U or L from the +*> factorization A = U*D*U**H or A = L*D*L**H as computed by +*> ZHETRF_ROOK. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> Details of the interchanges and the block structure of D. +*> +*> If UPLO = 'U': +*> Only the last KB elements of IPIV are set. +*> +*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were +*> interchanged and D(k,k) is a 1-by-1 diagonal block. +*> +*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and +*> columns k and -IPIV(k) were interchanged and rows and +*> columns k-1 and -IPIV(k-1) were inerchaged, +*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. +*> +*> If UPLO = 'L': +*> Only the first KB elements of IPIV are set. +*> +*> If IPIV(k) > 0, then rows and columns k and IPIV(k) +*> were interchanged and D(k,k) is a 1-by-1 diagonal block. +*> +*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and +*> columns k and -IPIV(k) were interchanged and rows and +*> columns k+1 and -IPIV(k+1) were inerchaged, +*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX*16 array, dimension (LDB,NRHS) +*> On entry, the N-by-NRHS right hand side matrix B. +*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The length of WORK. LWORK >= 1, and for best performance +*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for +*> ZHETRF_ROOK. +*> for LWORK < N, TRS will be done with Level BLAS 2 +*> for LWORK >= N, TRS will be done with Level BLAS 3 +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization +*> has been completed, but the block diagonal matrix D is +*> exactly singular, so the solution could not be computed. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2012 +* +*> \ingroup complex16HEsolve +*> +*> \verbatim +*> +*> November 2012, Igor Kozachenko, +*> Computer Science Division, +*> University of California, Berkeley +*> +*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, +*> School of Mathematics, +*> University of Manchester +*> +*> \endverbatim +* +* +* ===================================================================== + SUBROUTINE ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, + $ LWORK, INFO ) +* +* -- LAPACK driver routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2012 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, LDA, LDB, LWORK, N, NRHS +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL LQUERY + INTEGER LWKOPT, NB +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZHETRF_ROOK, ZHETRS_ROOK +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + LQUERY = ( LWORK.EQ.-1 ) + IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN + INFO = -10 + END IF +* + IF( INFO.EQ.0 ) THEN + IF( N.EQ.0 ) THEN + LWKOPT = 1 + ELSE + NB = ILAENV( 1, 'ZHETRF_ROOK', UPLO, N, -1, -1, -1 ) + LWKOPT = N*NB + END IF + WORK( 1 ) = LWKOPT + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZHESV_ROOK ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Compute the factorization A = U*D*U**H or A = L*D*L**H. +* + CALL ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) + IF( INFO.EQ.0 ) THEN +* +* Solve the system A*X = B, overwriting B with X. +* +* Solve with TRS ( Use Level BLAS 2) +* + CALL ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* + END IF +* + WORK( 1 ) = LWKOPT +* + RETURN +* +* End of ZHESV_ROOK +* + END |