version 1.1.1.1, 2010/01/26 15:22:45
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version 1.16, 2017/06/17 11:07:01
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*> \brief \b ZSYCON |
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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 ZSYCON + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsycon.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/zsycon.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/zsycon.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 ZSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, |
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* INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, LDA, N |
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* DOUBLE PRECISION ANORM, RCOND |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* COMPLEX*16 A( LDA, * ), WORK( * ) |
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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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*> ZSYCON estimates the reciprocal of the condition number (in the |
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*> 1-norm) of a complex symmetric matrix A using the factorization |
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*> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. |
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*> |
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*> An estimate is obtained for norm(inv(A)), and the reciprocal of the |
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*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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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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*> Specifies whether the details of the factorization are stored |
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*> as an upper or lower triangular matrix. |
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*> = 'U': Upper triangular, form is A = U*D*U**T; |
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*> = 'L': Lower triangular, form is A = L*D*L**T. |
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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] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,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] 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] 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] ANORM |
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*> \verbatim |
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*> ANORM is DOUBLE PRECISION |
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*> The 1-norm of the original matrix A. |
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*> \endverbatim |
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*> |
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*> \param[out] RCOND |
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*> \verbatim |
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*> RCOND is DOUBLE PRECISION |
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*> The reciprocal of the condition number of the matrix A, |
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*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an |
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*> estimate of the 1-norm of inv(A) computed in this routine. |
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*> \endverbatim |
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*> |
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*> \param[out] 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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*> \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 December 2016 |
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* |
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*> \ingroup complex16SYcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, |
SUBROUTINE ZSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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 |
* December 2016 |
* |
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* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 A( LDA, * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZSYCON estimates the reciprocal of the condition number (in the |
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* 1-norm) of a complex symmetric matrix A using the factorization |
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* A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. |
|
* |
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* An estimate is obtained for norm(inv(A)), and the reciprocal of the |
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* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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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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* Specifies whether the details of the factorization are stored |
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* as an upper or lower triangular matrix. |
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* = 'U': Upper triangular, form is A = U*D*U**T; |
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* = 'L': Lower triangular, form is A = L*D*L**T. |
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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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* A (input) COMPLEX*16 array, dimension (LDA,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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* 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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* 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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* ANORM (input) DOUBLE PRECISION |
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* The 1-norm of the original matrix A. |
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* |
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* RCOND (output) DOUBLE PRECISION |
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* The reciprocal of the condition number of the matrix A, |
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* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an |
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* estimate of the 1-norm of inv(A) computed in this routine. |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (2*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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) |
CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) |
IF( KASE.NE.0 ) THEN |
IF( KASE.NE.0 ) THEN |
* |
* |
* Multiply by inv(L*D*L') or inv(U*D*U'). |
* Multiply by inv(L*D*L**T) or inv(U*D*U**T). |
* |
* |
CALL ZSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO ) |
CALL ZSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO ) |
GO TO 30 |
GO TO 30 |