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version 1.8, 2011/07/22 07:38:10 version 1.9, 2011/11/21 20:43:03
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   *> \brief \b DSPGST
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSPGV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgv.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgv.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgv.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
   *                         INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, ITYPE, LDZ, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AP( * ), BP( * ), W( * ), WORK( * ),
   *      $                   Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSPGV computes all the eigenvalues and, optionally, the eigenvectors
   *> of a real generalized symmetric-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 symmetric, stored in packed format,
   *> 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] AP
   *> \verbatim
   *>          AP is DOUBLE PRECISION array, dimension
   *>                            (N*(N+1)/2)
   *>          On entry, the upper or lower triangle of the symmetric 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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
   *>          On entry, the upper or lower triangle of the symmetric 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**T*U or B = L*L**T, 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 DOUBLE PRECISION 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**T*B*Z = I;
   *>          if ITYPE = 3, Z**T*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 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:  DPPTRF or DSPEV returned an error code:
   *>             <= N:  if INFO = i, DSPEV 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 doubleOTHEReigen
   *
   *  =====================================================================
       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,        SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
      $                  INFO )       $                  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
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      $                   Z( LDZ, * )       $                   Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSPGV computes all the eigenvalues and, optionally, the eigenvectors  
 *  of a real generalized symmetric-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 symmetric, stored in packed format,  
 *  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.  
 *  
 *  AP      (input/output) DOUBLE PRECISION array, dimension  
 *                            (N*(N+1)/2)  
 *          On entry, the upper or lower triangle of the symmetric 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)  
 *          On entry, the upper or lower triangle of the symmetric 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**T*U or B = L*L**T, in the same storage  
 *          format as B.  
 *  
 *  W       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, the eigenvalues in ascending order.  
 *  
 *  Z       (output) DOUBLE PRECISION 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**T*B*Z = I;  
 *          if ITYPE = 3, Z**T*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) 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:  DPPTRF or DSPEV returned an error code:  
 *             <= N:  if INFO = i, DSPEV 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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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