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version 1.7, 2010/12/21 13:53:45 version 1.8, 2011/11/21 20:43:11
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   *> \brief \b ZHBGST
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHBGV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgv.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgv.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgv.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
   *                         LDZ, WORK, RWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   RWORK( * ), W( * )
   *       COMPLEX*16         AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
   *      $                   Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
   *> of a complex generalized Hermitian-definite banded eigenproblem, of
   *> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
   *> and banded, and B is also positive definite.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBZ
   *> \verbatim
   *>          JOBZ is CHARACTER*1
   *>          = 'N':  Compute eigenvalues only;
   *>          = 'V':  Compute eigenvalues and eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangles of A and B are stored;
   *>          = 'L':  Lower triangles of A and B are 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'. 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 contents of AB are destroyed.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KA+1.
   *> \endverbatim
   *>
   *> \param[in,out] BB
   *> \verbatim
   *>          BB is COMPLEX*16 array, dimension (LDBB, N)
   *>          On entry, the upper or lower triangle of the Hermitian band
   *>          matrix B, stored in the first kb+1 rows of the array.  The
   *>          j-th column of B is stored in the j-th column of the array BB
   *>          as follows:
   *>          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
   *>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
   *>
   *>          On exit, the factor S from the split Cholesky factorization
   *>          B = S**H*S, as returned by ZPBSTF.
   *> \endverbatim
   *>
   *> \param[in] LDBB
   *> \verbatim
   *>          LDBB is INTEGER
   *>          The leading dimension of the array BB.  LDBB >= KB+1.
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is DOUBLE PRECISION array, dimension (N)
   *>          If INFO = 0, the eigenvalues in ascending order.
   *> \endverbatim
   *>
   *> \param[out] Z
   *> \verbatim
   *>          Z is COMPLEX*16 array, dimension (LDZ, N)
   *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
   *>          eigenvectors, with the i-th column of Z holding the
   *>          eigenvector associated with W(i). The eigenvectors are
   *>          normalized so that Z**H*B*Z = I.
   *>          If JOBZ = 'N', then Z is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is INTEGER
   *>          The leading dimension of the array Z.  LDZ >= 1, and if
   *>          JOBZ = 'V', LDZ >= N.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (3*N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  if INFO = i, and i is:
   *>             <= N:  the algorithm failed to converge:
   *>                    i off-diagonal elements of an intermediate
   *>                    tridiagonal form did not converge to zero;
   *>             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
   *>                    returned INFO = i: B is not positive definite.
   *>                    The factorization of B could not be completed and
   *>                    no eigenvalues or eigenvectors were computed.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHEReigen
   *
   *  =====================================================================
       SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,        SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
      $                  LDZ, WORK, RWORK, INFO )       $                  LDZ, WORK, RWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- LAPACK driver 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
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBZ, UPLO        CHARACTER          JOBZ, UPLO
Line 16 Line 198
      $                   Z( LDZ, * )       $                   Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHBGV computes all the eigenvalues, and optionally, the eigenvectors  
 *  of a complex generalized Hermitian-definite banded eigenproblem, of  
 *  the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian  
 *  and banded, and B is also positive definite.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBZ    (input) CHARACTER*1  
 *          = 'N':  Compute eigenvalues only;  
 *          = 'V':  Compute eigenvalues and eigenvectors.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangles of A and B are stored;  
 *          = 'L':  Lower triangles of A and B are 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'. 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 contents of AB are destroyed.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KA+1.  
 *  
 *  BB      (input/output) COMPLEX*16 array, dimension (LDBB, N)  
 *          On entry, the upper or lower triangle of the Hermitian band  
 *          matrix B, stored in the first kb+1 rows of the array.  The  
 *          j-th column of B is stored in the j-th column of the array BB  
 *          as follows:  
 *          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;  
 *          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).  
 *  
 *          On exit, the factor S from the split Cholesky factorization  
 *          B = S**H*S, as returned by ZPBSTF.  
 *  
 *  LDBB    (input) INTEGER  
 *          The leading dimension of the array BB.  LDBB >= KB+1.  
 *  
 *  W       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, the eigenvalues in ascending order.  
 *  
 *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)  
 *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of  
 *          eigenvectors, with the i-th column of Z holding the  
 *          eigenvector associated with W(i). The eigenvectors are  
 *          normalized so that Z**H*B*Z = I.  
 *          If JOBZ = 'N', then Z is not referenced.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1, and if  
 *          JOBZ = 'V', LDZ >= N.  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (N)  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (3*N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  if INFO = i, and i is:  
 *             <= N:  the algorithm failed to converge:  
 *                    i off-diagonal elements of an intermediate  
 *                    tridiagonal form did not converge to zero;  
 *             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF  
 *                    returned INFO = i: B is not positive definite.  
 *                    The factorization of B could not be completed and  
 *                    no eigenvalues or eigenvectors were computed.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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