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version 1.3, 2010/08/06 15:28:54 version 1.18, 2023/08/07 08:39:22
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   *> \brief \b ZHBGST
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZHBGST + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgst.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgst.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgst.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
   *                          LDX, WORK, RWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO, VECT
   *       INTEGER            INFO, KA, KB, LDAB, LDBB, LDX, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
   *      $                   X( LDX, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHBGST reduces a complex Hermitian-definite banded generalized
   *> eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
   *> such that C has the same bandwidth as A.
   *>
   *> B must have been previously factorized as S**H*S by ZPBSTF, using a
   *> split Cholesky factorization. A is overwritten by C = X**H*A*X, where
   *> X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
   *> bandwidth of A.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] VECT
   *> \verbatim
   *>          VECT is CHARACTER*1
   *>          = 'N':  do not form the transformation matrix X;
   *>          = 'V':  form X.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangle of A is stored;
   *>          = 'L':  Lower triangle of A is stored.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrices A and B.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] KA
   *> \verbatim
   *>          KA is INTEGER
   *>          The number of superdiagonals of the matrix A if UPLO = 'U',
   *>          or the number of subdiagonals if UPLO = 'L'.  KA >= 0.
   *> \endverbatim
   *>
   *> \param[in] KB
   *> \verbatim
   *>          KB is INTEGER
   *>          The number of superdiagonals of the matrix B if UPLO = 'U',
   *>          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] AB
   *> \verbatim
   *>          AB is COMPLEX*16 array, dimension (LDAB,N)
   *>          On entry, the upper or lower triangle of the Hermitian band
   *>          matrix A, stored in the first ka+1 rows of the array.  The
   *>          j-th column of A is stored in the j-th column of the array AB
   *>          as follows:
   *>          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
   *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
   *>
   *>          On exit, the transformed matrix X**H*A*X, stored in the same
   *>          format as A.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KA+1.
   *> \endverbatim
   *>
   *> \param[in] BB
   *> \verbatim
   *>          BB is COMPLEX*16 array, dimension (LDBB,N)
   *>          The banded factor S from the split Cholesky factorization of
   *>          B, as returned by ZPBSTF, stored in the first kb+1 rows of
   *>          the array.
   *> \endverbatim
   *>
   *> \param[in] LDBB
   *> \verbatim
   *>          LDBB is INTEGER
   *>          The leading dimension of the array BB.  LDBB >= KB+1.
   *> \endverbatim
   *>
   *> \param[out] X
   *> \verbatim
   *>          X is COMPLEX*16 array, dimension (LDX,N)
   *>          If VECT = 'V', the n-by-n matrix X.
   *>          If VECT = 'N', the array X is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDX
   *> \verbatim
   *>          LDX is INTEGER
   *>          The leading dimension of the array X.
   *>          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (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.
   *
   *> \ingroup complex16OTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE ZHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,        SUBROUTINE ZHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
      $                   LDX, WORK, RWORK, INFO )       $                   LDX, WORK, RWORK, 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  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO, VECT        CHARACTER          UPLO, VECT
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      $                   X( LDX, * )       $                   X( LDX, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHBGST reduces a complex Hermitian-definite banded generalized  
 *  eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,  
 *  such that C has the same bandwidth as A.  
 *  
 *  B must have been previously factorized as S**H*S by ZPBSTF, using a  
 *  split Cholesky factorization. A is overwritten by C = X**H*A*X, where  
 *  X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the  
 *  bandwidth of A.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  VECT    (input) CHARACTER*1  
 *          = 'N':  do not form the transformation matrix X;  
 *          = 'V':  form X.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices A and B.  N >= 0.  
 *  
 *  KA      (input) INTEGER  
 *          The number of superdiagonals of the matrix A if UPLO = 'U',  
 *          or the number of subdiagonals if UPLO = 'L'.  KA >= 0.  
 *  
 *  KB      (input) INTEGER  
 *          The number of superdiagonals of the matrix B if UPLO = 'U',  
 *          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.  
 *  
 *  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)  
 *          On entry, the upper or lower triangle of the Hermitian band  
 *          matrix A, stored in the first ka+1 rows of the array.  The  
 *          j-th column of A is stored in the j-th column of the array AB  
 *          as follows:  
 *          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;  
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).  
 *  
 *          On exit, the transformed matrix X**H*A*X, stored in the same  
 *          format as A.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KA+1.  
 *  
 *  BB      (input) COMPLEX*16 array, dimension (LDBB,N)  
 *          The banded factor S from the split Cholesky factorization of  
 *          B, as returned by ZPBSTF, stored in the first kb+1 rows of  
 *          the array.  
 *  
 *  LDBB    (input) INTEGER  
 *          The leading dimension of the array BB.  LDBB >= KB+1.  
 *  
 *  X       (output) COMPLEX*16 array, dimension (LDX,N)  
 *          If VECT = 'V', the n-by-n matrix X.  
 *          If VECT = 'N', the array X is not referenced.  
 *  
 *  LDX     (input) INTEGER  
 *          The leading dimension of the array X.  
 *          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (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 ..
Line 507 Line 596
   230    CONTINUE    230    CONTINUE
 *  *
          IF( KB.GT.1 ) THEN           IF( KB.GT.1 ) THEN
             DO 240 J = N - 1, I2 + KA, -1              DO 240 J = N - 1, J2 + KA, -1
                RWORK( J-M ) = RWORK( J-KA-M )                 RWORK( J-M ) = RWORK( J-KA-M )
                WORK( J-M ) = WORK( J-KA-M )                 WORK( J-M ) = WORK( J-KA-M )
   240       CONTINUE    240       CONTINUE
Line 771 Line 860
   460    CONTINUE    460    CONTINUE
 *  *
          IF( KB.GT.1 ) THEN           IF( KB.GT.1 ) THEN
             DO 470 J = N - 1, I2 + KA, -1              DO 470 J = N - 1, J2 + KA, -1
                RWORK( J-M ) = RWORK( J-KA-M )                 RWORK( J-M ) = RWORK( J-KA-M )
                WORK( J-M ) = WORK( J-KA-M )                 WORK( J-M ) = WORK( J-KA-M )
   470       CONTINUE    470       CONTINUE
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  Added in v.1.18

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