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version 1.4, 2010/08/06 15:32:32 version 1.18, 2023/08/07 08:39:03
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   *> \brief \b DPBCON
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DPBCON + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbcon.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbcon.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbcon.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
   *                          IWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, KD, LDAB, N
   *       DOUBLE PRECISION   ANORM, RCOND
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DPBCON estimates the reciprocal of the condition number (in the
   *> 1-norm) of a real symmetric positive definite band matrix using the
   *> Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.
   *>
   *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
   *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangular factor stored in AB;
   *>          = 'L':  Lower triangular factor stored in AB.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] KD
   *> \verbatim
   *>          KD is INTEGER
   *>          The number of superdiagonals of the matrix A if UPLO = 'U',
   *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   *> \endverbatim
   *>
   *> \param[in] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
   *>          The triangular factor U or L from the Cholesky factorization
   *>          A = U**T*U or A = L*L**T of the band matrix A, stored in the
   *>          first KD+1 rows of the array.  The j-th column of U or L is
   *>          stored in the j-th column of the array AB as follows:
   *>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
   *>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KD+1.
   *> \endverbatim
   *>
   *> \param[in] ANORM
   *> \verbatim
   *>          ANORM is DOUBLE PRECISION
   *>          The 1-norm (or infinity-norm) of the symmetric band 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/(ANORM * AINVNM), where AINVNM is an
   *>          estimate of the 1-norm of inv(A) computed in this routine.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (3*N)
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER 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.
   *
   *> \ingroup doubleOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,        SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
      $                   IWORK, INFO )       $                   IWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- 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 2006  
 *  
 *     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )        DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DPBCON estimates the reciprocal of the condition number (in the  
 *  1-norm) of a real symmetric positive definite band matrix using the  
 *  Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.  
 *  
 *  An estimate is obtained for norm(inv(A)), and the reciprocal of the  
 *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangular factor stored in AB;  
 *          = 'L':  Lower triangular factor stored in AB.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  KD      (input) INTEGER  
 *          The number of superdiagonals of the matrix A if UPLO = 'U',  
 *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.  
 *  
 *  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)  
 *          The triangular factor U or L from the Cholesky factorization  
 *          A = U**T*U or A = L*L**T of the band matrix A, stored in the  
 *          first KD+1 rows of the array.  The j-th column of U or L is  
 *          stored in the j-th column of the array AB as follows:  
 *          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;  
 *          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KD+1.  
 *  
 *  ANORM   (input) DOUBLE PRECISION  
 *          The 1-norm (or infinity-norm) of the symmetric band matrix A.  
 *  
 *  RCOND   (output) DOUBLE PRECISION  
 *          The reciprocal of the condition number of the matrix A,  
 *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an  
 *          estimate of the 1-norm of inv(A) computed in this routine.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)  
 *  
 *  IWORK   (workspace) INTEGER 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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       IF( KASE.NE.0 ) THEN        IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN           IF( UPPER ) THEN
 *  *
 *           Multiply by inv(U').  *           Multiply by inv(U**T).
 *  *
             CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,              CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),       $                   KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
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      $                   INFO )       $                   INFO )
             NORMIN = 'Y'              NORMIN = 'Y'
 *  *
 *           Multiply by inv(L').  *           Multiply by inv(L**T).
 *  *
             CALL DLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,              CALL DLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),       $                   KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
Removed from v.1.4  
changed lines
  Added in v.1.18

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