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Diff for /rpl/lapack/lapack/dsytrs2.f between versions 1.2 and 1.15

version 1.2, 2010/12/21 13:53:40 version 1.15, 2023/08/07 08:39:11
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       SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,   *> \brief \b DSYTRS2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DSYTRS2 + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs2.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs2.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs2.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
   *                           WORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, LDA, LDB, N, NRHS
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSYTRS2 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 and converted by DSYCONV.
   *> \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,out] 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.
   *>          Note that A is input / output. This might be counter-intuitive,
   *>          and one may think that A is input only. A is input / output. This
   *>          is because, at the start of the subroutine, we permute A in a
   *>          "better" form and then we permute A back to its original form at
   *>          the end.
   *> \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] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (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.
   *
   *> \ingroup doubleSYcomputational
   *
   *  =====================================================================
         SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
      $                    WORK, INFO )       $                    WORK, INFO )
 *  *
 *  -- LAPACK PROTOTYPE routine (version 3.3.0) --  *  -- LAPACK computational routine --
 *  -- 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 2010  
 *  
 *  -- Written by Julie Langou of the Univ. of TN    --  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )        DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSYTRS2 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 and converted by DSYCONV.  
 *  
 *  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).  
 *  
 *  WORK    (workspace) REAL array, dimension (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.
 *  *
 *       P' * B    *       P**T * B
         K=N          K=N
         DO WHILE ( K .GE. 1 )          DO WHILE ( K .GE. 1 )
          IF( IPIV( K ).GT.0 ) THEN           IF( IPIV( K ).GT.0 ) THEN
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          END IF           END IF
         END DO          END DO
 *  *
 *  Compute (U \P' * B) -> B    [ (U \P' * B) ]  *  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
   *
           CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *  *
         CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N)  *  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *  *
 *  Compute D \ B -> B   [ D \ (U \P' * B) ]  
 *         
          I=N           I=N
          DO WHILE ( I .GE. 1 )           DO WHILE ( I .GE. 1 )
             IF( IPIV(I) .GT. 0 ) THEN              IF( IPIV(I) .GT. 0 ) THEN
               CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )                CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
             ELSEIF ( I .GT. 1) THEN              ELSEIF ( I .GT. 1) THEN
                IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN                 IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
                   AKM1K = WORK(I)                    AKM1K = WORK(I)
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             I = I - 1              I = I - 1
          END DO           END DO
 *  *
 *      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]  *      Compute (U**T \ B) -> B   [ U**T \ (D \ (U \P**T * B) ) ]
 *  *
          CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,N,B,N)           CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *  *
 *       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]  *       P * B  [ P * (U**T \ (D \ (U \P**T * B) )) ]
 *  *
         K=1          K=1
         DO WHILE ( K .LE. N )          DO WHILE ( K .LE. N )
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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.
 *  *
 *       P' * B    *       P**T * B
         K=1          K=1
         DO WHILE ( K .LE. N )          DO WHILE ( K .LE. N )
          IF( IPIV( K ).GT.0 ) THEN           IF( IPIV( K ).GT.0 ) THEN
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          ENDIF           ENDIF
         END DO          END DO
 *  *
 *  Compute (L \P' * B) -> B    [ (L \P' * B) ]  *  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *  *
         CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N)          CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
   *
   *  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *  *
 *  Compute D \ B -> B   [ D \ (L \P' * B) ]  
 *         
          I=1           I=1
          DO WHILE ( I .LE. N )           DO WHILE ( I .LE. N )
             IF( IPIV(I) .GT. 0 ) THEN              IF( IPIV(I) .GT. 0 ) THEN
               CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )                CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB )
             ELSE              ELSE
                   AKM1K = WORK(I)                    AKM1K = WORK(I)
                   AKM1 = A( I, I ) / AKM1K                    AKM1 = A( I, I ) / AKM1K
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             I = I + 1              I = I + 1
          END DO           END DO
 *  *
 *  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]  *  Compute (L**T \ B) -> B   [ L**T \ (D \ (L \P**T * B) ) ]
 *   *
         CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,N,B,N)          CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *  *
 *       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]  *       P * B  [ P * (L**T \ (D \ (L \P**T * B) )) ]
 *  *
         K=N          K=N
         DO WHILE ( K .GE. 1 )          DO WHILE ( K .GE. 1 )
Removed from v.1.2  
changed lines
  Added in v.1.15

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