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version 1.8, 2011/07/22 07:38:16 version 1.9, 2011/11/21 20:43:12
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   *> \brief \b ZHPGST
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHPGVD + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgvd.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgvd.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgvd.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
   *                          LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   RWORK( * ), W( * )
   *       COMPLEX*16         AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHPGVD 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, stored in packed format, and B is also
   *> positive definite.
   *> If eigenvectors are desired, it uses a divide and conquer algorithm.
   *>
   *> The divide and conquer algorithm makes very mild assumptions about
   *> floating point arithmetic. It will work on machines with a guard
   *> digit in add/subtract, or on those binary machines without guard
   *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
   *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
   *> without guard digits, but we know of none.
   *> \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] AP
   *> \verbatim
   *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
   *>          On entry, the upper or lower triangle of the Hermitian matrix
   *>          A, packed columnwise in a linear array.  The j-th column of A
   *>          is stored in the array AP as follows:
   *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   *>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   *>
   *>          On exit, the contents of AP are destroyed.
   *> \endverbatim
   *>
   *> \param[in,out] BP
   *> \verbatim
   *>          BP is COMPLEX*16 array, dimension (N*(N+1)/2)
   *>          On entry, the upper or lower triangle of the Hermitian matrix
   *>          B, packed columnwise in a linear array.  The j-th column of B
   *>          is stored in the array BP as follows:
   *>          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
   *>          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
   *>
   *>          On exit, the triangular factor U or L from the Cholesky
   *>          factorization B = U**H*U or B = L*L**H, in the same storage
   *>          format as B.
   *> \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.  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 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 >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK.
   *>          If N <= 1,               LWORK >= 1.
   *>          If JOBZ = 'N' and N > 1, LWORK >= N.
   *>          If JOBZ = 'V' and N > 1, LWORK >= 2*N.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the required sizes of the WORK, RWORK and
   *>          IWORK arrays, returns these values as the first entries of
   *>          the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
   *>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
   *> \endverbatim
   *>
   *> \param[in] LRWORK
   *> \verbatim
   *>          LRWORK is INTEGER
   *>          The dimension of array RWORK.
   *>          If N <= 1,               LRWORK >= 1.
   *>          If JOBZ = 'N' and N > 1, LRWORK >= N.
   *>          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
   *>
   *>          If LRWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the required sizes of the WORK, RWORK
   *>          and IWORK arrays, returns these values as the first entries
   *>          of the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
   *>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
   *> \endverbatim
   *>
   *> \param[in] LIWORK
   *> \verbatim
   *>          LIWORK is INTEGER
   *>          The dimension of array IWORK.
   *>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
   *>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
   *>
   *>          If LIWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the required sizes of the WORK, RWORK
   *>          and IWORK arrays, returns these values as the first entries
   *>          of the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  ZPPTRF or ZHPEVD returned an error code:
   *>             <= N:  if INFO = i, ZHPEVD failed to converge;
   *>                    i off-diagonal elements of an intermediate
   *>                    tridiagonal form did not convergeto 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 complex16OTHEReigen
   *
   *> \par Contributors:
   *  ==================
   *>
   *>     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
   *
   *  =====================================================================
       SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,        SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
      $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )       $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, 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 16 Line 246
       COMPLEX*16         AP( * ), BP( * ), WORK( * ), Z( LDZ, * )        COMPLEX*16         AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHPGVD 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, stored in packed format, and B is also  
 *  positive definite.  
 *  If eigenvectors are desired, it uses a divide and conquer algorithm.  
 *  
 *  The divide and conquer algorithm makes very mild assumptions about  
 *  floating point arithmetic. It will work on machines with a guard  
 *  digit in add/subtract, or on those binary machines without guard  
 *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or  
 *  Cray-2. It could conceivably fail on hexadecimal or decimal machines  
 *  without guard digits, but we know of none.  
 *  
 *  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.  
 *  
 *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)  
 *          On entry, the upper or lower triangle of the Hermitian matrix  
 *          A, packed columnwise in a linear array.  The j-th column of A  
 *          is stored in the array AP as follows:  
 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;  
 *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.  
 *  
 *          On exit, the contents of AP are destroyed.  
 *  
 *  BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)  
 *          On entry, the upper or lower triangle of the Hermitian matrix  
 *          B, packed columnwise in a linear array.  The j-th column of B  
 *          is stored in the array BP as follows:  
 *          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;  
 *          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.  
 *  
 *          On exit, the triangular factor U or L from the Cholesky  
 *          factorization B = U**H*U or B = L*L**H, in the same storage  
 *          format as B.  
 *  
 *  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.  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 Z is not referenced.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1, and if  
 *          JOBZ = 'V', LDZ >= max(1,N).  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the required LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  
 *          If N <= 1,               LWORK >= 1.  
 *          If JOBZ = 'N' and N > 1, LWORK >= N.  
 *          If JOBZ = 'V' and N > 1, LWORK >= 2*N.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the required sizes of the WORK, RWORK and  
 *          IWORK arrays, returns these values as the first entries of  
 *          the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))  
 *          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.  
 *  
 *  LRWORK  (input) INTEGER  
 *          The dimension of array RWORK.  
 *          If N <= 1,               LRWORK >= 1.  
 *          If JOBZ = 'N' and N > 1, LRWORK >= N.  
 *          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.  
 *  
 *          If LRWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the required sizes of the WORK, RWORK  
 *          and IWORK arrays, returns these values as the first entries  
 *          of the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))  
 *          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.  
 *  
 *  LIWORK  (input) INTEGER  
 *          The dimension of array IWORK.  
 *          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.  
 *          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.  
 *  
 *          If LIWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the required sizes of the WORK, RWORK  
 *          and IWORK arrays, returns these values as the first entries  
 *          of the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  ZPPTRF or ZHPEVD returned an error code:  
 *             <= N:  if INFO = i, ZHPEVD failed to converge;  
 *                    i off-diagonal elements of an intermediate  
 *                    tridiagonal form did not convergeto 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.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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