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version 1.8, 2011/07/22 07:38:11 version 1.9, 2011/11/21 20:43:04
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   *> \brief \b DSYGST
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSYGST + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygst.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygst.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygst.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, ITYPE, LDA, LDB, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSYGST reduces a real symmetric-definite generalized eigenproblem
   *> to standard form.
   *>
   *> If ITYPE = 1, the problem is A*x = lambda*B*x,
   *> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
   *>
   *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
   *> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
   *>
   *> B must have been previously factorized as U**T*U or L*L**T by DPOTRF.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] ITYPE
   *> \verbatim
   *>          ITYPE is INTEGER
   *>          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
   *>          = 2 or 3: compute U*A*U**T or L**T*A*L.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangle of A is stored and B is factored as
   *>                  U**T*U;
   *>          = 'L':  Lower triangle of A is stored and B is factored as
   *>                  L*L**T.
   *> \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 DOUBLE PRECISION array, dimension (LDA,N)
   *>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
   *>          N-by-N upper triangular part of A contains the upper
   *>          triangular part of the matrix A, and the strictly lower
   *>          triangular part of A is not referenced.  If UPLO = 'L', the
   *>          leading N-by-N lower triangular part of A contains the lower
   *>          triangular part of the matrix A, and the strictly upper
   *>          triangular part of A is not referenced.
   *>
   *>          On exit, if INFO = 0, the transformed matrix, stored in the
   *>          same format as A.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] B
   *> \verbatim
   *>          B is DOUBLE PRECISION array, dimension (LDB,N)
   *>          The triangular factor from the Cholesky factorization of B,
   *>          as returned by DPOTRF.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of the array B.  LDB >= max(1,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. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleSYcomputational
   *
   *  =====================================================================
       SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )        SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational 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          UPLO        CHARACTER          UPLO
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       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )        DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSYGST reduces a real symmetric-definite generalized eigenproblem  
 *  to standard form.  
 *  
 *  If ITYPE = 1, the problem is A*x = lambda*B*x,  
 *  and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)  
 *  
 *  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or  
 *  B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.  
 *  
 *  B must have been previously factorized as U**T*U or L*L**T by DPOTRF.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  ITYPE   (input) INTEGER  
 *          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);  
 *          = 2 or 3: compute U*A*U**T or L**T*A*L.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored and B is factored as  
 *                  U**T*U;  
 *          = 'L':  Lower triangle of A is stored and B is factored as  
 *                  L*L**T.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices A and B.  N >= 0.  
 *  
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)  
 *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading  
 *          N-by-N upper triangular part of A contains the upper  
 *          triangular part of the matrix A, and the strictly lower  
 *          triangular part of A is not referenced.  If UPLO = 'L', the  
 *          leading N-by-N lower triangular part of A contains the lower  
 *          triangular part of the matrix A, and the strictly upper  
 *          triangular part of A is not referenced.  
 *  
 *          On exit, if INFO = 0, the transformed matrix, stored in the  
 *          same format as A.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  B       (input) DOUBLE PRECISION array, dimension (LDB,N)  
 *          The triangular factor from the Cholesky factorization of B,  
 *          as returned by DPOTRF.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= max(1,N).  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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