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version 1.3, 2010/08/06 15:28:50 version 1.15, 2017/06/17 10:54:07
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   *> \brief \b ZGBCON
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZGBCON + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbcon.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbcon.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbcon.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
   *                          WORK, RWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          NORM
   *       INTEGER            INFO, KL, KU, LDAB, N
   *       DOUBLE PRECISION   ANORM, RCOND
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         AB( LDAB, * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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.
   *>
   *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
   *> condition number is computed as
   *>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] NORM
   *> \verbatim
   *>          NORM is CHARACTER*1
   *>          Specifies whether the 1-norm condition number or the
   *>          infinity-norm condition number is required:
   *>          = '1' or 'O':  1-norm;
   *>          = 'I':         Infinity-norm.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] KL
   *> \verbatim
   *>          KL is INTEGER
   *>          The number of subdiagonals within the band of A.  KL >= 0.
   *> \endverbatim
   *>
   *> \param[in] KU
   *> \verbatim
   *>          KU is INTEGER
   *>          The number of superdiagonals within the band of A.  KU >= 0.
   *> \endverbatim
   *>
   *> \param[in] AB
   *> \verbatim
   *>          AB is COMPLEX*16 array, dimension (LDAB,N)
   *>          Details of the LU factorization of the band matrix A, as
   *>          computed by ZGBTRF.  U is stored as an upper triangular band
   *>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
   *>          the multipliers used during the factorization are stored in
   *>          rows KL+KU+2 to 2*KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>          The pivot indices; for 1 <= i <= N, row i of the matrix was
   *>          interchanged with row IPIV(i).
   *> \endverbatim
   *>
   *> \param[in] ANORM
   *> \verbatim
   *>          ANORM is DOUBLE PRECISION
   *>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
   *>          If NORM = 'I', the infinity-norm of the original matrix A.
   *> \endverbatim
   *>
   *> \param[out] RCOND
   *> \verbatim
   *>          RCOND is DOUBLE PRECISION
   *>          The reciprocal of the condition number of the matrix A,
   *>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (2*N)
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0: if INFO = -i, the i-th argument had an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \date December 2016
   *
   *> \ingroup complex16GBcomputational
   *
   *  =====================================================================
       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 3.7.0) --
 *  -- 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
 *  
 *     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          NORM        CHARACTER          NORM
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       COMPLEX*16         AB( LDAB, * ), WORK( * )        COMPLEX*16         AB( LDAB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  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.  
 *  
 *  An estimate is obtained for norm(inv(A)), and the reciprocal of the  
 *  condition number is computed as  
 *     RCOND = 1 / ( norm(A) * norm(inv(A)) ).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  NORM    (input) CHARACTER*1  
 *          Specifies whether the 1-norm condition number or the  
 *          infinity-norm condition number is required:  
 *          = '1' or 'O':  1-norm;  
 *          = 'I':         Infinity-norm.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  KL      (input) INTEGER  
 *          The number of subdiagonals within the band of A.  KL >= 0.  
 *  
 *  KU      (input) INTEGER  
 *          The number of superdiagonals within the band of A.  KU >= 0.  
 *  
 *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)  
 *          Details of the LU factorization of the band matrix A, as  
 *          computed by ZGBTRF.  U is stored as an upper triangular band  
 *          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and  
 *          the multipliers used during the factorization are stored in  
 *          rows KL+KU+2 to 2*KL+KU+1.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.  
 *  
 *  IPIV    (input) INTEGER array, dimension (N)  
 *          The pivot indices; for 1 <= i <= N, row i of the matrix was  
 *          interchanged with row IPIV(i).  
 *  
 *  ANORM   (input) DOUBLE PRECISION  
 *          If NORM = '1' or 'O', the 1-norm of the original matrix A.  
 *          If NORM = 'I', the infinity-norm of the original matrix A.  
 *  
 *  RCOND   (output) DOUBLE PRECISION  
 *          The reciprocal of the condition number of the matrix A,  
 *          computed as RCOND = 1/(norm(A) * norm(inv(A))).  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0: if INFO = -i, the i-th argument had an illegal value  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. 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
Removed from v.1.3  
changed lines
  Added in v.1.15

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