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version 1.7, 2010/12/21 13:53:39 version 1.16, 2017/06/17 11:06:36
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   *> \brief \b DSYTRS
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DSYTRS + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, LDA, LDB, N, NRHS
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSYTRS solves a system of linear equations A*X = B with a real
   *> symmetric matrix A using the factorization A = U*D*U**T or
   *> A = L*D*L**T computed by DSYTRF.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          Specifies whether the details of the factorization are stored
   *>          as an upper or lower triangular matrix.
   *>          = 'U':  Upper triangular, form is A = U*D*U**T;
   *>          = 'L':  Lower triangular, form is A = L*D*L**T.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] NRHS
   *> \verbatim
   *>          NRHS is INTEGER
   *>          The number of right hand sides, i.e., the number of columns
   *>          of the matrix B.  NRHS >= 0.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   *>          The block diagonal matrix D and the multipliers used to
   *>          obtain the factor U or L as computed by DSYTRF.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>          Details of the interchanges and the block structure of D
   *>          as determined by DSYTRF.
   *> \endverbatim
   *>
   *> \param[in,out] B
   *> \verbatim
   *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
   *>          On entry, the right hand side matrix B.
   *>          On exit, the solution matrix X.
   *> \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 December 2016
   *
   *> \ingroup doubleSYcomputational
   *
   *  =====================================================================
       SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )        SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.7.0) --
 *  -- 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  *     December 2016
 *  *
 *     .. 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  
 *  =======  
 *  
 *  DSYTRS solves a system of linear equations A*X = B with a real  
 *  symmetric matrix A using the factorization A = U*D*U**T or  
 *  A = L*D*L**T computed by DSYTRF.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          Specifies whether the details of the factorization are stored  
 *          as an upper or lower triangular matrix.  
 *          = 'U':  Upper triangular, form is A = U*D*U**T;  
 *          = 'L':  Lower triangular, form is A = L*D*L**T.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  NRHS    (input) INTEGER  
 *          The number of right hand sides, i.e., the number of columns  
 *          of the matrix B.  NRHS >= 0.  
 *  
 *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)  
 *          The block diagonal matrix D and the multipliers used to  
 *          obtain the factor U or L as computed by DSYTRF.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  IPIV    (input) INTEGER array, dimension (N)  
 *          Details of the interchanges and the block structure of D  
 *          as determined by DSYTRF.  
 *  
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)  
 *          On entry, the right hand side matrix B.  
 *          On exit, the solution matrix X.  
 *  
 *  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 ..
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 *  *
       IF( UPPER ) THEN        IF( UPPER ) THEN
 *  *
 *        Solve A*X = B, where A = U*D*U'.  *        Solve A*X = B, where A = U*D*U**T.
 *  *
 *        First solve U*D*X = B, overwriting B with X.  *        First solve U*D*X = B, overwriting B with X.
 *  *
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          GO TO 10           GO TO 10
    30    CONTINUE     30    CONTINUE
 *  *
 *        Next solve U'*X = B, overwriting B with X.  *        Next solve U**T *X = B, overwriting B with X.
 *  *
 *        K is the main loop index, increasing from 1 to N in steps of  *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.  *        1 or 2, depending on the size of the diagonal blocks.
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 *  *
 *           1 x 1 diagonal block  *           1 x 1 diagonal block
 *  *
 *           Multiply by inv(U'(K)), where U(K) is the transformation  *           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.  *           stored in column K of A.
 *  *
             CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),              CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
Line 211 Line 286
 *  *
 *           2 x 2 diagonal block  *           2 x 2 diagonal block
 *  *
 *           Multiply by inv(U'(K+1)), where U(K+1) is the transformation  *           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.  *           stored in columns K and K+1 of A.
 *  *
             CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),              CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
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 *  *
       ELSE        ELSE
 *  *
 *        Solve A*X = B, where A = L*D*L'.  *        Solve A*X = B, where A = L*D*L**T.
 *  *
 *        First solve L*D*X = B, overwriting B with X.  *        First solve L*D*X = B, overwriting B with X.
 *  *
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          GO TO 60           GO TO 60
    80    CONTINUE     80    CONTINUE
 *  *
 *        Next solve L'*X = B, overwriting B with X.  *        Next solve L**T *X = B, overwriting B with X.
 *  *
 *        K is the main loop index, decreasing from N to 1 in steps of  *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.  *        1 or 2, depending on the size of the diagonal blocks.
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 *  *
 *           1 x 1 diagonal block  *           1 x 1 diagonal block
 *  *
 *           Multiply by inv(L'(K)), where L(K) is the transformation  *           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.  *           stored in column K of A.
 *  *
             IF( K.LT.N )              IF( K.LT.N )
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 *  *
 *           2 x 2 diagonal block  *           2 x 2 diagonal block
 *  *
 *           Multiply by inv(L'(K-1)), where L(K-1) is the transformation  *           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.  *           stored in columns K-1 and K of A.
 *  *
             IF( K.LT.N ) THEN              IF( K.LT.N ) THEN
Removed from v.1.7  
changed lines
  Added in v.1.16

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