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Diff for /rpl/lapack/blas/dtrsv.f between versions 1.5 and 1.13

version 1.5, 2010/08/13 21:03:40 version 1.13, 2017/06/17 10:53:44
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       SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)  *> \brief \b DTRSV
 *     .. Scalar Arguments ..  
       INTEGER INCX,LDA,N  
       CHARACTER DIAG,TRANS,UPLO  
 *     ..  
 *     .. Array Arguments ..  
       DOUBLE PRECISION A(LDA,*),X(*)  
 *     ..  
 *  
 *  Purpose  
 *  =======  
 *  *
 *  DTRSV  solves one of the systems of equations  *  =========== DOCUMENTATION ===========
 *  *
 *     A*x = b,   or   A'*x = b,  * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
 *  *
 *  where b and x are n element vectors and A is an n by n unit, or  *  Definition:
 *  non-unit, upper or lower triangular matrix.  *  ===========
   *
   *       SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
   *
   *       .. Scalar Arguments ..
   *       INTEGER INCX,LDA,N
   *       CHARACTER DIAG,TRANS,UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION A(LDA,*),X(*)
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DTRSV  solves one of the systems of equations
   *>
   *>    A*x = b,   or   A**T*x = b,
   *>
   *> where b and x are n element vectors and A is an n by n unit, or
   *> non-unit, upper or lower triangular matrix.
   *>
   *> No test for singularity or near-singularity is included in this
   *> routine. Such tests must be performed before calling this routine.
   *> \endverbatim
 *  *
 *  No test for singularity or near-singularity is included in this  *  Arguments:
 *  routine. Such tests must be performed before calling this routine.  
 *  
 *  Arguments  
 *  ==========  *  ==========
 *  *
 *  UPLO   - CHARACTER*1.  *> \param[in] UPLO
 *           On entry, UPLO specifies whether the matrix is an upper or  *> \verbatim
 *           lower triangular matrix as follows:  *>          UPLO is CHARACTER*1
 *  *>           On entry, UPLO specifies whether the matrix is an upper or
 *              UPLO = 'U' or 'u'   A is an upper triangular matrix.  *>           lower triangular matrix as follows:
 *  *>
 *              UPLO = 'L' or 'l'   A is a lower triangular matrix.  *>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
 *  *>
 *           Unchanged on exit.  *>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
 *  *> \endverbatim
 *  TRANS  - CHARACTER*1.  *>
 *           On entry, TRANS specifies the equations to be solved as  *> \param[in] TRANS
 *           follows:  *> \verbatim
 *  *>          TRANS is CHARACTER*1
 *              TRANS = 'N' or 'n'   A*x = b.  *>           On entry, TRANS specifies the equations to be solved as
 *  *>           follows:
 *              TRANS = 'T' or 't'   A'*x = b.  *>
 *  *>              TRANS = 'N' or 'n'   A*x = b.
 *              TRANS = 'C' or 'c'   A'*x = b.  *>
   *>              TRANS = 'T' or 't'   A**T*x = b.
   *>
   *>              TRANS = 'C' or 'c'   A**T*x = b.
   *> \endverbatim
   *>
   *> \param[in] DIAG
   *> \verbatim
   *>          DIAG is CHARACTER*1
   *>           On entry, DIAG specifies whether or not A is unit
   *>           triangular as follows:
   *>
   *>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
   *>
   *>              DIAG = 'N' or 'n'   A is not assumed to be unit
   *>                                  triangular.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix A.
   *>           N must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
   *>           Before entry with  UPLO = 'U' or 'u', the leading n by n
   *>           upper triangular part of the array A must contain the upper
   *>           triangular matrix and the strictly lower triangular part of
   *>           A is not referenced.
   *>           Before entry with UPLO = 'L' or 'l', the leading n by n
   *>           lower triangular part of the array A must contain the lower
   *>           triangular matrix and the strictly upper triangular part of
   *>           A is not referenced.
   *>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
   *>           A are not referenced either, but are assumed to be unity.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>           On entry, LDA specifies the first dimension of A as declared
   *>           in the calling (sub) program. LDA must be at least
   *>           max( 1, n ).
   *> \endverbatim
   *>
   *> \param[in,out] X
   *> \verbatim
   *>          X is DOUBLE PRECISION array of dimension at least
   *>           ( 1 + ( n - 1 )*abs( INCX ) ).
   *>           Before entry, the incremented array X must contain the n
   *>           element right-hand side vector b. On exit, X is overwritten
   *>           with the solution vector x.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *>
   *>  Level 2 Blas routine.
   *>
   *>  -- Written on 22-October-1986.
   *>     Jack Dongarra, Argonne National Lab.
   *>     Jeremy Du Croz, Nag Central Office.
   *>     Sven Hammarling, Nag Central Office.
   *>     Richard Hanson, Sandia National Labs.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
 *  *
 *           Unchanged on exit.  *> \date December 2016
 *  *
 *  DIAG   - CHARACTER*1.  *> \ingroup double_blas_level1
 *           On entry, DIAG specifies whether or not A is unit  
 *           triangular as follows:  
 *  
 *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.  
 *  
 *              DIAG = 'N' or 'n'   A is not assumed to be unit  
 *                                  triangular.  
 *  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry, N specifies the order of the matrix A.  
 *           N must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).  
 *           Before entry with  UPLO = 'U' or 'u', the leading n by n  
 *           upper triangular part of the array A must contain the upper  
 *           triangular matrix and the strictly lower triangular part of  
 *           A is not referenced.  
 *           Before entry with UPLO = 'L' or 'l', the leading n by n  
 *           lower triangular part of the array A must contain the lower  
 *           triangular matrix and the strictly upper triangular part of  
 *           A is not referenced.  
 *           Note that when  DIAG = 'U' or 'u', the diagonal elements of  
 *           A are not referenced either, but are assumed to be unity.  
 *           Unchanged on exit.  
 *  
 *  LDA    - INTEGER.  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in the calling (sub) program. LDA must be at least  
 *           max( 1, n ).  
 *           Unchanged on exit.  
 *  
 *  X      - DOUBLE PRECISION array of dimension at least  
 *           ( 1 + ( n - 1 )*abs( INCX ) ).  
 *           Before entry, the incremented array X must contain the n  
 *           element right-hand side vector b. On exit, X is overwritten  
 *           with the solution vector x.  
 *  
 *  INCX   - INTEGER.  
 *           On entry, INCX specifies the increment for the elements of  
 *           X. INCX must not be zero.  
 *           Unchanged on exit.  
 *  *
   *  =====================================================================
         SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
 *  *
 *  Level 2 Blas routine.  *  -- Reference BLAS level1 routine (version 3.7.0) --
   *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     December 2016
 *  *
 *  -- Written on 22-October-1986.  *     .. Scalar Arguments ..
 *     Jack Dongarra, Argonne National Lab.        INTEGER INCX,LDA,N
 *     Jeremy Du Croz, Nag Central Office.        CHARACTER DIAG,TRANS,UPLO
 *     Sven Hammarling, Nag Central Office.  *     ..
 *     Richard Hanson, Sandia National Labs.  *     .. Array Arguments ..
         DOUBLE PRECISION A(LDA,*),X(*)
   *     ..
 *  *
 *  =====================================================================  *  =====================================================================
 *  *
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           END IF            END IF
       ELSE        ELSE
 *  *
 *        Form  x := inv( A' )*x.  *        Form  x := inv( A**T )*x.
 *  *
           IF (LSAME(UPLO,'U')) THEN            IF (LSAME(UPLO,'U')) THEN
               IF (INCX.EQ.1) THEN                IF (INCX.EQ.1) THEN
Removed from v.1.5  
changed lines
  Added in v.1.13

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