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version 1.9, 2012/12/14 14:22:49
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*> \brief \b ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. |
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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 ZLA_SYRPVGRW + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syrpvgrw.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/zla_syrpvgrw.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/zla_syrpvgrw.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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* DOUBLE PRECISION FUNCTION ZLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF, |
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* LDAF, IPIV, WORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER*1 UPLO |
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* INTEGER N, INFO, LDA, LDAF |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( LDA, * ), AF( LDAF, * ) |
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* DOUBLE PRECISION WORK( * ) |
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* INTEGER IPIV( * ) |
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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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*> |
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*> ZLA_SYRPVGRW computes the reciprocal pivot growth factor |
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*> norm(A)/norm(U). The "max absolute element" norm is used. If this is |
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*> much less than 1, the stability of the LU factorization of the |
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*> (equilibrated) matrix A could be poor. This also means that the |
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*> solution X, estimated condition numbers, and error bounds could be |
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*> unreliable. |
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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 number of linear equations, i.e., the order of the |
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*> matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> The value of INFO returned from ZSYTRF, .i.e., the pivot in |
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*> column INFO is exactly 0. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,N) |
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*> On entry, the N-by-N matrix A. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in] AF |
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*> \verbatim |
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*> AF is COMPLEX*16 array, dimension (LDAF,N) |
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*> The block diagonal matrix D and the multipliers used to |
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*> obtain the factor U or L as computed by ZSYTRF. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAF |
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*> \verbatim |
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*> LDAF is INTEGER |
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*> The leading dimension of the array AF. LDAF >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (N) |
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*> Details of the interchanges and the block structure of D |
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*> as determined by ZSYTRF. |
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*> \endverbatim |
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*> |
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*> \param[in] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (2*N) |
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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 September 2012 |
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* |
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*> \ingroup complex16SYcomputational |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION ZLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF, |
DOUBLE PRECISION FUNCTION ZLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF, |
$ LDAF, IPIV, WORK ) |
$ LDAF, IPIV, WORK ) |
* |
* |
* -- LAPACK routine (version 3.2.2) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Jason Riedy of Univ. of California Berkeley. -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- June 2010 -- |
* September 2012 |
* |
* |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley and NAG Ltd. -- |
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* |
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IMPLICIT NONE |
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* .. |
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* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER*1 UPLO |
CHARACTER*1 UPLO |
INTEGER N, INFO, LDA, LDAF |
INTEGER N, INFO, LDA, LDAF |
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INTEGER IPIV( * ) |
INTEGER IPIV( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLA_SYRPVGRW computes the reciprocal pivot growth factor |
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* norm(A)/norm(U). The "max absolute element" norm is used. If this is |
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* much less than 1, the stability of the LU factorization of the |
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* (equilibrated) matrix A could be poor. This also means that the |
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* solution X, estimated condition numbers, and error bounds could be |
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* unreliable. |
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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 number of linear equations, i.e., the order of the |
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* matrix A. N >= 0. |
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* |
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* INFO (input) INTEGER |
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* The value of INFO returned from ZSYTRF, .i.e., the pivot in |
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* column INFO is exactly 0. |
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* |
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* NCOLS (input) INTEGER |
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* The number of columns of the matrix A. NCOLS >= 0. |
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* |
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* A (input) COMPLEX*16 array, dimension (LDA,N) |
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* On entry, the N-by-N matrix A. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* AF (input) COMPLEX*16 array, dimension (LDAF,N) |
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* The block diagonal matrix D and the multipliers used to |
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* obtain the factor U or L as computed by ZSYTRF. |
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* |
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* LDAF (input) INTEGER |
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* The leading dimension of the array AF. LDAF >= max(1,N). |
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* |
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* IPIV (input) INTEGER array, dimension (N) |
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* Details of the interchanges and the block structure of D |
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* as determined by ZSYTRF. |
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* |
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* WORK (input) COMPLEX*16 array, dimension (2*N) |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |