version 1.6, 2010/08/13 21:04:01
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version 1.9, 2011/11/21 20:43:07
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*> \brief \b ZGBCON |
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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 ZGBCON + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbcon.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/zgbcon.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/zgbcon.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 ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, |
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* WORK, RWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER NORM |
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* INTEGER INFO, KL, KU, LDAB, 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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* DOUBLE PRECISION RWORK( * ) |
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* COMPLEX*16 AB( LDAB, * ), 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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*> ZGBCON estimates the reciprocal of the condition number of a complex |
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*> general band matrix A, in either the 1-norm or the infinity-norm, |
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*> using the LU factorization computed by ZGBTRF. |
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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 |
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*> RCOND = 1 / ( norm(A) * 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] NORM |
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*> \verbatim |
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*> NORM is CHARACTER*1 |
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*> Specifies whether the 1-norm condition number or the |
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*> infinity-norm condition number is required: |
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*> = '1' or 'O': 1-norm; |
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*> = 'I': Infinity-norm. |
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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] KL |
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*> \verbatim |
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*> KL is INTEGER |
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*> The number of subdiagonals within the band of A. KL >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KU |
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*> \verbatim |
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*> KU is INTEGER |
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*> The number of superdiagonals within the band of A. KU >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] AB |
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*> \verbatim |
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*> AB is COMPLEX*16 array, dimension (LDAB,N) |
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*> Details of the LU factorization of the band matrix A, as |
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*> computed by ZGBTRF. U is stored as an upper triangular band |
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*> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and |
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*> the multipliers used during the factorization are stored in |
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*> rows KL+KU+2 to 2*KL+KU+1. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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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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*> The pivot indices; for 1 <= i <= N, row i of the matrix was |
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*> interchanged with row IPIV(i). |
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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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*> If NORM = '1' or 'O', the 1-norm of the original matrix A. |
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*> If NORM = 'I', the infinity-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/(norm(A) * norm(inv(A))). |
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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] RWORK |
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*> \verbatim |
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*> RWORK is DOUBLE PRECISION array, dimension (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 complex16GBcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, |
SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, |
$ WORK, RWORK, INFO ) |
$ WORK, RWORK, 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 |
* |
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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 NORM |
CHARACTER NORM |
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COMPLEX*16 AB( LDAB, * ), WORK( * ) |
COMPLEX*16 AB( LDAB, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZGBCON estimates the reciprocal of the condition number of a complex |
|
* general band matrix A, in either the 1-norm or the infinity-norm, |
|
* using the LU factorization computed by ZGBTRF. |
|
* |
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* An estimate is obtained for norm(inv(A)), and the reciprocal of the |
|
* condition number is computed as |
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* RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
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* |
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* Arguments |
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* ========= |
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* |
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* NORM (input) CHARACTER*1 |
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* Specifies whether the 1-norm condition number or the |
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* infinity-norm condition number is required: |
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* = '1' or 'O': 1-norm; |
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* = 'I': Infinity-norm. |
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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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* KL (input) INTEGER |
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* The number of subdiagonals within the band of A. KL >= 0. |
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* |
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* KU (input) INTEGER |
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* The number of superdiagonals within the band of A. KU >= 0. |
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* |
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* AB (input) COMPLEX*16 array, dimension (LDAB,N) |
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* Details of the LU factorization of the band matrix A, as |
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* computed by ZGBTRF. U is stored as an upper triangular band |
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* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and |
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* the multipliers used during the factorization are stored in |
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* rows KL+KU+2 to 2*KL+KU+1. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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* |
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* IPIV (input) INTEGER array, dimension (N) |
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* The pivot indices; for 1 <= i <= N, row i of the matrix was |
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* interchanged with row IPIV(i). |
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* |
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* ANORM (input) DOUBLE PRECISION |
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* If NORM = '1' or 'O', the 1-norm of the original matrix A. |
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* If NORM = 'I', the infinity-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/(norm(A) * norm(inv(A))). |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (2*N) |
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* |
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* RWORK (workspace) DOUBLE PRECISION array, dimension (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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$ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO ) |
$ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO ) |
ELSE |
ELSE |
* |
* |
* Multiply by inv(U'). |
* Multiply by inv(U**H). |
* |
* |
CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit', |
CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit', |
$ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK, |
$ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* Multiply by inv(L'). |
* Multiply by inv(L**H). |
* |
* |
IF( LNOTI ) THEN |
IF( LNOTI ) THEN |
DO 30 J = N - 1, 1, -1 |
DO 30 J = N - 1, 1, -1 |