version 1.5, 2011/11/21 20:42:53
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version 1.15, 2018/05/29 07:17:54
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*> \brief \b DLA_GERFSX_EXTENDED |
*> \brief \b DLA_GERFSX_EXTENDED improves the computed solution to a system of linear equations for general matrices by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution. |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download DLA_GERFSX_EXTENDED + dependencies |
*> Download DLA_GERFSX_EXTENDED + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gerfsx_extended.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gerfsx_extended.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gerfsx_extended.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gerfsx_extended.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gerfsx_extended.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gerfsx_extended.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
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* ERRS_N, ERRS_C, RES, AYB, DY, |
* ERRS_N, ERRS_C, RES, AYB, DY, |
* Y_TAIL, RCOND, ITHRESH, RTHRESH, |
* Y_TAIL, RCOND, ITHRESH, RTHRESH, |
* DZ_UB, IGNORE_CWISE, INFO ) |
* DZ_UB, IGNORE_CWISE, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE, |
* INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE, |
* $ TRANS_TYPE, N_NORMS, ITHRESH |
* $ TRANS_TYPE, N_NORMS, ITHRESH |
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* DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), |
* DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), |
* $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) |
* $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
*> |
*> |
*> \verbatim |
*> \verbatim |
*> |
*> |
*> |
*> |
*> DLA_GERFSX_EXTENDED improves the computed solution to a system of |
*> DLA_GERFSX_EXTENDED improves the computed solution to a system of |
*> linear equations by performing extra-precise iterative refinement |
*> linear equations by performing extra-precise iterative refinement |
*> and provides error bounds and backward error estimates for the solution. |
*> and provides error bounds and backward error estimates for the solution. |
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*> |
*> |
*> \param[in,out] Y |
*> \param[in,out] Y |
*> \verbatim |
*> \verbatim |
*> Y is DOUBLE PRECISION array, dimension |
*> Y is DOUBLE PRECISION array, dimension (LDY,NRHS) |
*> (LDY,NRHS) |
|
*> On entry, the solution matrix X, as computed by DGETRS. |
*> On entry, the solution matrix X, as computed by DGETRS. |
*> On exit, the improved solution matrix Y. |
*> On exit, the improved solution matrix Y. |
*> \endverbatim |
*> \endverbatim |
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*> |
*> |
*> \param[in,out] ERRS_N |
*> \param[in,out] ERRS_N |
*> \verbatim |
*> \verbatim |
*> ERRS_N is DOUBLE PRECISION array, dimension |
*> ERRS_N is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) |
*> (NRHS, N_ERR_BNDS) |
|
*> For each right-hand side, this array contains information about |
*> For each right-hand side, this array contains information about |
*> various error bounds and condition numbers corresponding to the |
*> various error bounds and condition numbers corresponding to the |
*> normwise relative error, which is defined as follows: |
*> normwise relative error, which is defined as follows: |
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*> |
*> |
*> \param[in,out] ERRS_C |
*> \param[in,out] ERRS_C |
*> \verbatim |
*> \verbatim |
*> ERRS_C is DOUBLE PRECISION array, dimension |
*> ERRS_C is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) |
*> (NRHS, N_ERR_BNDS) |
|
*> For each right-hand side, this array contains information about |
*> For each right-hand side, this array contains information about |
*> various error bounds and condition numbers corresponding to the |
*> various error bounds and condition numbers corresponding to the |
*> componentwise relative error, which is defined as follows: |
*> componentwise relative error, which is defined as follows: |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date November 2011 |
*> \date June 2017 |
* |
* |
*> \ingroup doubleGEcomputational |
*> \ingroup doubleGEcomputational |
* |
* |
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$ Y_TAIL, RCOND, ITHRESH, RTHRESH, |
$ Y_TAIL, RCOND, ITHRESH, RTHRESH, |
$ DZ_UB, IGNORE_CWISE, INFO ) |
$ DZ_UB, IGNORE_CWISE, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational routine (version 3.7.1) -- |
* -- 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 2011 |
* June 2017 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE, |
INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE, |
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* op(A) = A, A**T, or A**H depending on TRANS (and type). |
* op(A) = A, A**T, or A**H depending on TRANS (and type). |
* |
* |
CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) |
CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) |
CALL DGEMV( TRANS, N, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, |
CALL DGEMV( TRANS, N, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, |
$ RES, 1 ) |
$ RES, 1 ) |
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DO I = 1, N |
DO I = 1, N |