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version 1.14, 2016/08/27 15:35:05
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*> \brief \b ZPPTRS |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZPPTRS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptrs.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptrs.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptrs.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 AP( * ), B( LDB, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZPPTRS solves a system of linear equations A*X = B with a Hermitian |
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*> positive definite matrix A in packed storage using the Cholesky |
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*> factorization A = U**H * U or A = L * L**H computed by ZPPTRF. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] NRHS |
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*> \verbatim |
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*> NRHS is INTEGER |
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*> The number of right hand sides, i.e., the number of columns |
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*> of the matrix B. NRHS >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] AP |
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*> \verbatim |
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*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) |
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*> The triangular factor U or L from the Cholesky factorization |
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*> A = U**H * U or A = L * L**H, packed columnwise in a linear |
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*> array. The j-th column of U or L is stored in the array AP |
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*> as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is COMPLEX*16 array, dimension (LDB,NRHS) |
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*> On entry, the right hand side matrix B. |
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*> On exit, the solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) |
SUBROUTINE ZPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 AP( * ), B( LDB, * ) |
COMPLEX*16 AP( * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZPPTRS solves a system of linear equations A*X = B with a Hermitian |
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* positive definite matrix A in packed storage using the Cholesky |
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* factorization A = U**H*U or A = L*L**H computed by ZPPTRF. |
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* |
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* Arguments |
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* ========= |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* NRHS (input) INTEGER |
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* The number of right hand sides, i.e., the number of columns |
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* of the matrix B. NRHS >= 0. |
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* |
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* AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) |
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* The triangular factor U or L from the Cholesky factorization |
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* A = U**H*U or A = L*L**H, packed columnwise in a linear |
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* array. The j-th column of U or L is stored in the array AP |
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* as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; |
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* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. |
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* |
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* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) |
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* On entry, the right hand side matrix B. |
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* On exit, the solution matrix X. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Solve A*X = B where A = U'*U. |
* Solve A*X = B where A = U**H * U. |
* |
* |
DO 10 I = 1, NRHS |
DO 10 I = 1, NRHS |
* |
* |
* Solve U'*X = B, overwriting B with X. |
* Solve U**H *X = B, overwriting B with X. |
* |
* |
CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', N, |
CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', N, |
$ AP, B( 1, I ), 1 ) |
$ AP, B( 1, I ), 1 ) |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
* |
* |
* Solve A*X = B where A = L*L'. |
* Solve A*X = B where A = L * L**H. |
* |
* |
DO 20 I = 1, NRHS |
DO 20 I = 1, NRHS |
* |
* |
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CALL ZTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP, |
CALL ZTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP, |
$ B( 1, I ), 1 ) |
$ B( 1, I ), 1 ) |
* |
* |
* Solve L'*X = Y, overwriting B with X. |
* Solve L**H *X = Y, overwriting B with X. |
* |
* |
CALL ZTPSV( 'Lower', 'Conjugate transpose', 'Non-unit', N, |
CALL ZTPSV( 'Lower', 'Conjugate transpose', 'Non-unit', N, |
$ AP, B( 1, I ), 1 ) |
$ AP, B( 1, I ), 1 ) |