version 1.7, 2012/07/31 11:06:39
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version 1.18, 2023/08/07 08:39:28
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*> \brief \b ZLA_SYRFSX_EXTENDED |
*> \brief \b ZLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric indefinite 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 ZLA_SYRFSX_EXTENDED + dependencies |
*> Download ZLA_SYRFSX_EXTENDED + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syrfsx_extended.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syrfsx_extended.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_syrfsx_extended.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_syrfsx_extended.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_syrfsx_extended.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_syrfsx_extended.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
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* AYB, DY, Y_TAIL, RCOND, ITHRESH, |
* AYB, DY, Y_TAIL, RCOND, ITHRESH, |
* RTHRESH, DZ_UB, IGNORE_CWISE, |
* RTHRESH, DZ_UB, IGNORE_CWISE, |
* INFO ) |
* 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, |
* $ N_NORMS, ITHRESH |
* $ N_NORMS, ITHRESH |
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* $ ERR_BNDS_NORM( NRHS, * ), |
* $ ERR_BNDS_NORM( NRHS, * ), |
* $ ERR_BNDS_COMP( NRHS, * ) |
* $ ERR_BNDS_COMP( NRHS, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> In addition to normwise error bound, the code provides maximum |
*> In addition to normwise error bound, the code provides maximum |
*> componentwise error bound if possible. See comments for ERR_BNDS_NORM |
*> componentwise error bound if possible. See comments for ERR_BNDS_NORM |
*> and ERR_BNDS_COMP for details of the error bounds. Note that this |
*> and ERR_BNDS_COMP for details of the error bounds. Note that this |
*> subroutine is only resonsible for setting the second fields of |
*> subroutine is only responsible for setting the second fields of |
*> ERR_BNDS_NORM and ERR_BNDS_COMP. |
*> ERR_BNDS_NORM and ERR_BNDS_COMP. |
*> \endverbatim |
*> \endverbatim |
* |
* |
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*> \verbatim |
*> \verbatim |
*> PREC_TYPE is INTEGER |
*> PREC_TYPE is INTEGER |
*> Specifies the intermediate precision to be used in refinement. |
*> Specifies the intermediate precision to be used in refinement. |
*> The value is defined by ILAPREC(P) where P is a CHARACTER and |
*> The value is defined by ILAPREC(P) where P is a CHARACTER and P |
*> P = 'S': Single |
*> = 'S': Single |
*> = 'D': Double |
*> = 'D': Double |
*> = 'I': Indigenous |
*> = 'I': Indigenous |
*> = 'X', 'E': Extra |
*> = 'X' or 'E': Extra |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] UPLO |
*> \param[in] UPLO |
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*> |
*> |
*> \param[in,out] Y |
*> \param[in,out] Y |
*> \verbatim |
*> \verbatim |
*> Y is COMPLEX*16 array, dimension |
*> Y is COMPLEX*16 array, dimension (LDY,NRHS) |
*> (LDY,NRHS) |
|
*> On entry, the solution matrix X, as computed by ZSYTRS. |
*> On entry, the solution matrix X, as computed by ZSYTRS. |
*> On exit, the improved solution matrix Y. |
*> On exit, the improved solution matrix Y. |
*> \endverbatim |
*> \endverbatim |
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*> |
*> |
*> \param[in,out] ERR_BNDS_NORM |
*> \param[in,out] ERR_BNDS_NORM |
*> \verbatim |
*> \verbatim |
*> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension |
*> ERR_BNDS_NORM 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] ERR_BNDS_COMP |
*> \param[in,out] ERR_BNDS_COMP |
*> \verbatim |
*> \verbatim |
*> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension |
*> ERR_BNDS_COMP 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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*> information as described below. There currently are up to three |
*> information as described below. There currently are up to three |
*> pieces of information returned for each right-hand side. If |
*> pieces of information returned for each right-hand side. If |
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then |
*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then |
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most |
*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most |
*> the first (:,N_ERR_BNDS) entries are returned. |
*> the first (:,N_ERR_BNDS) entries are returned. |
*> |
*> |
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith |
*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith |
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*> DZ_UB is DOUBLE PRECISION |
*> DZ_UB is DOUBLE PRECISION |
*> Determines when to start considering componentwise convergence. |
*> Determines when to start considering componentwise convergence. |
*> Componentwise convergence is only considered after each component |
*> Componentwise convergence is only considered after each component |
*> of the solution Y is stable, which we definte as the relative |
*> of the solution Y is stable, which we define as the relative |
*> change in each component being less than DZ_UB. The default value |
*> change in each component being less than DZ_UB. The default value |
*> is 0.25, requiring the first bit to be stable. See LAWN 165 for |
*> is 0.25, requiring the first bit to be stable. See LAWN 165 for |
*> more details. |
*> more details. |
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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 |
|
* |
* |
*> \ingroup complex16SYcomputational |
*> \ingroup complex16SYcomputational |
* |
* |
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$ RTHRESH, DZ_UB, IGNORE_CWISE, |
$ RTHRESH, DZ_UB, IGNORE_CWISE, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational routine -- |
* -- 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 |
|
* |
* |
* .. 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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END DO |
END DO |
* |
* |
RETURN |
RETURN |
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* |
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* End of ZLA_SYRFSX_EXTENDED |
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* |
END |
END |