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version 1.8, 2011/07/22 07:38:15 version 1.9, 2011/11/21 20:43:11
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   *> \brief \b ZHEGST
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHEGV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegv.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegv.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegv.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
   *                         LWORK, RWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   RWORK( * ), W( * )
   *       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
   *> of a complex generalized Hermitian-definite eigenproblem, of the form
   *> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
   *> Here A and B are assumed to be Hermitian and B is also
   *> positive definite.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] ITYPE
   *> \verbatim
   *>          ITYPE is INTEGER
   *>          Specifies the problem type to be solved:
   *>          = 1:  A*x = (lambda)*B*x
   *>          = 2:  A*B*x = (lambda)*x
   *>          = 3:  B*A*x = (lambda)*x
   *> \endverbatim
   *>
   *> \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,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA, N)
   *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
   *>          leading N-by-N upper triangular part of A contains the
   *>          upper triangular part of the matrix A.  If UPLO = 'L',
   *>          the leading N-by-N lower triangular part of A contains
   *>          the lower triangular part of the matrix A.
   *>
   *>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
   *>          matrix Z of eigenvectors.  The eigenvectors are normalized
   *>          as follows:
   *>          if ITYPE = 1 or 2, Z**H*B*Z = I;
   *>          if ITYPE = 3, Z**H*inv(B)*Z = I.
   *>          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
   *>          or the lower triangle (if UPLO='L') of A, including the
   *>          diagonal, is destroyed.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in,out] B
   *> \verbatim
   *>          B is COMPLEX*16 array, dimension (LDB, N)
   *>          On entry, the Hermitian positive definite matrix B.
   *>          If UPLO = 'U', the leading N-by-N upper triangular part of B
   *>          contains the upper triangular part of the matrix B.
   *>          If UPLO = 'L', the leading N-by-N lower triangular part of B
   *>          contains the lower triangular part of the matrix B.
   *>
   *>          On exit, if INFO <= N, the part of B containing the matrix is
   *>          overwritten by the triangular factor U or L from the Cholesky
   *>          factorization B = U**H*U or B = L*L**H.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of the array B.  LDB >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is DOUBLE PRECISION array, dimension (N)
   *>          If INFO = 0, the eigenvalues in ascending order.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The length of the array WORK.  LWORK >= max(1,2*N-1).
   *>          For optimal efficiency, LWORK >= (NB+1)*N,
   *>          where NB is the blocksize for ZHETRD returned by ILAENV.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal size of the WORK array, returns
   *>          this value as the first entry of the WORK array, and no error
   *>          message related to LWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  ZPOTRF or ZHEEV returned an error code:
   *>             <= N:  if INFO = i, ZHEEV 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 the leading
   *>                    minor of order i of 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 complex16HEeigen
   *
   *  =====================================================================
       SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,        SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
      $                  LWORK, RWORK, INFO )       $                  LWORK, RWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.3.1) --  *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBZ, UPLO        CHARACTER          JOBZ, UPLO
Line 15 Line 195
       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )        COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHEGV computes all the eigenvalues, and optionally, the eigenvectors  
 *  of a complex generalized Hermitian-definite eigenproblem, of the form  
 *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  
 *  Here A and B are assumed to be Hermitian and B is also  
 *  positive definite.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  ITYPE   (input) INTEGER  
 *          Specifies the problem type to be solved:  
 *          = 1:  A*x = (lambda)*B*x  
 *          = 2:  A*B*x = (lambda)*x  
 *          = 3:  B*A*x = (lambda)*x  
 *  
 *  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.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)  
 *          On entry, the Hermitian matrix A.  If UPLO = 'U', the  
 *          leading N-by-N upper triangular part of A contains the  
 *          upper triangular part of the matrix A.  If UPLO = 'L',  
 *          the leading N-by-N lower triangular part of A contains  
 *          the lower triangular part of the matrix A.  
 *  
 *          On exit, if JOBZ = 'V', then if INFO = 0, A contains the  
 *          matrix Z of eigenvectors.  The eigenvectors are normalized  
 *          as follows:  
 *          if ITYPE = 1 or 2, Z**H*B*Z = I;  
 *          if ITYPE = 3, Z**H*inv(B)*Z = I.  
 *          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')  
 *          or the lower triangle (if UPLO='L') of A, including the  
 *          diagonal, is destroyed.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  B       (input/output) COMPLEX*16 array, dimension (LDB, N)  
 *          On entry, the Hermitian positive definite matrix B.  
 *          If UPLO = 'U', the leading N-by-N upper triangular part of B  
 *          contains the upper triangular part of the matrix B.  
 *          If UPLO = 'L', the leading N-by-N lower triangular part of B  
 *          contains the lower triangular part of the matrix B.  
 *  
 *          On exit, if INFO <= N, the part of B containing the matrix is  
 *          overwritten by the triangular factor U or L from the Cholesky  
 *          factorization B = U**H*U or B = L*L**H.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= max(1,N).  
 *  
 *  W       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, the eigenvalues in ascending order.  
 *  
 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The length of the array WORK.  LWORK >= max(1,2*N-1).  
 *          For optimal efficiency, LWORK >= (NB+1)*N,  
 *          where NB is the blocksize for ZHETRD returned by ILAENV.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal size of the WORK array, returns  
 *          this value as the first entry of the WORK array, and no error  
 *          message related to LWORK is issued by XERBLA.  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  ZPOTRF or ZHEEV returned an error code:  
 *             <= N:  if INFO = i, ZHEEV 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 the leading  
 *                    minor of order i of B is not positive definite.  
 *                    The factorization of B could not be completed and  
 *                    no eigenvalues or eigenvectors were computed.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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