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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/stzrzf.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
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Integrating Doxygen in comments
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1 files changed, 147 insertions, 80 deletions
diff --git a/SRC/stzrzf.f b/SRC/stzrzf.f index 99d8f308..bab4a738 100644 --- a/SRC/stzrzf.f +++ b/SRC/stzrzf.f @@ -1,102 +1,169 @@ - SUBROUTINE STZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) +*> \brief \b STZRZF * -* -- LAPACK routine (version 3.3.1) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- -* @generated s +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - REAL A( LDA, * ), TAU( * ), WORK( * ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE STZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, LWORK, M, N +* .. +* .. Array Arguments .. +* REAL A( LDA, * ), TAU( * ), WORK( * ) +* .. +* * Purpose * ======= * -* STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A -* to upper triangular form by means of orthogonal transformations. -* -* The upper trapezoidal matrix A is factored as -* -* A = ( R 0 ) * Z, -* -* where Z is an N-by-N orthogonal matrix and R is an M-by-M upper -* triangular matrix. +*>\details \b Purpose: +*>\verbatim +*> +*> STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A +*> to upper triangular form by means of orthogonal transformations. +*> +*> The upper trapezoidal matrix A is factored as +*> +*> A = ( R 0 ) * Z, +*> +*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper +*> triangular matrix. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= M. -* -* A (input/output) REAL array, dimension (LDA,N) -* On entry, the leading M-by-N upper trapezoidal part of the -* array A must contain the matrix to be factorized. -* On exit, the leading M-by-M upper triangular part of A -* contains the upper triangular matrix R, and elements M+1 to -* N of the first M rows of A, with the array TAU, represent the -* orthogonal matrix Z as a product of M elementary reflectors. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* TAU (output) REAL array, dimension (M) -* The scalar factors of the elementary reflectors. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= M. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> On entry, the leading M-by-N upper trapezoidal part of the +*> array A must contain the matrix to be factorized. +*> On exit, the leading M-by-M upper triangular part of A +*> contains the upper triangular matrix R, and elements M+1 to +*> N of the first M rows of A, with the array TAU, represent the +*> orthogonal matrix Z as a product of M elementary reflectors. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is REAL array, dimension (M) +*> The scalar factors of the elementary reflectors. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL 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 dimension of the array WORK. LWORK >= max(1,M). +*> For optimum performance LWORK >= M*NB, where NB is +*> the optimal blocksize. +*> \endverbatim +*> \verbatim +*> 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 +*> \endverbatim +*> +* +* Authors +* ======= * -* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LWORK (input) INTEGER -* The dimension of the array WORK. LWORK >= max(1,M). -* For optimum performance LWORK >= M*NB, where NB is -* the optimal blocksize. +*> \date November 2011 * -* 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. +*> \ingroup realOTHERcomputational * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Based on contributions by +*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA +*> +*> The factorization is obtained by Householder's method. The kth +*> transformation matrix, Z( k ), which is used to introduce zeros into +*> the ( m - k + 1 )th row of A, is given in the form +*> +*> Z( k ) = ( I 0 ), +*> ( 0 T( k ) ) +*> +*> where +*> +*> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), +*> ( 0 ) +*> ( z( k ) ) +*> +*> tau is a scalar and z( k ) is an ( n - m ) element vector. +*> tau and z( k ) are chosen to annihilate the elements of the kth row +*> of X. +*> +*> The scalar tau is returned in the kth element of TAU and the vector +*> u( k ) in the kth row of A, such that the elements of z( k ) are +*> in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in +*> the upper triangular part of A. +*> +*> Z is given by +*> +*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE STZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * -* Based on contributions by -* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA -* -* The factorization is obtained by Householder's method. The kth -* transformation matrix, Z( k ), which is used to introduce zeros into -* the ( m - k + 1 )th row of A, is given in the form -* -* Z( k ) = ( I 0 ), -* ( 0 T( k ) ) -* -* where -* -* T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), -* ( 0 ) -* ( z( k ) ) -* -* tau is a scalar and z( k ) is an ( n - m ) element vector. -* tau and z( k ) are chosen to annihilate the elements of the kth row -* of X. -* -* The scalar tau is returned in the kth element of TAU and the vector -* u( k ) in the kth row of A, such that the elements of z( k ) are -* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in -* the upper triangular part of A. -* -* Z is given by +* -- LAPACK computational routine (version 3.3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). +* .. Scalar Arguments .. + INTEGER INFO, LDA, LWORK, M, N +* .. +* .. Array Arguments .. + REAL A( LDA, * ), TAU( * ), WORK( * ) +* .. * * ===================================================================== * |