444 lines
14 KiB
Fortran
444 lines
14 KiB
Fortran
*> \brief \b DTRSM
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION ALPHA
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* INTEGER LDA,LDB,M,N
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* CHARACTER DIAG,SIDE,TRANSA,UPLO
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A(LDA,*),B(LDB,*)
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DTRSM solves one of the matrix equations
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*>
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*> op( A )*X = alpha*B, or X*op( A ) = alpha*B,
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*>
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*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
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*> non-unit, upper or lower triangular matrix and op( A ) is one of
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*>
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*> op( A ) = A or op( A ) = A**T.
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*>
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*> The matrix X is overwritten on B.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> On entry, SIDE specifies whether op( A ) appears on the left
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*> or right of X as follows:
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*>
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*> SIDE = 'L' or 'l' op( A )*X = alpha*B.
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*>
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*> SIDE = 'R' or 'r' X*op( A ) = alpha*B.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> On entry, UPLO specifies whether the matrix A is an upper or
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*> lower triangular matrix as follows:
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*>
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*> UPLO = 'U' or 'u' A is an upper triangular matrix.
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*>
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*> UPLO = 'L' or 'l' A is a lower triangular matrix.
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*> \endverbatim
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*>
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*> \param[in] TRANSA
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*> \verbatim
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*> TRANSA is CHARACTER*1
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*> On entry, TRANSA specifies the form of op( A ) to be used in
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*> the matrix multiplication as follows:
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*>
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*> TRANSA = 'N' or 'n' op( A ) = A.
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*>
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*> TRANSA = 'T' or 't' op( A ) = A**T.
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*>
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*> TRANSA = 'C' or 'c' op( A ) = A**T.
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> On entry, DIAG specifies whether or not A is unit triangular
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*> as follows:
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*>
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*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
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*>
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*> DIAG = 'N' or 'n' A is not assumed to be unit
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*> triangular.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> On entry, M specifies the number of rows of B. M must be at
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*> least zero.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> On entry, N specifies the number of columns of B. N must be
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*> at least zero.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is DOUBLE PRECISION.
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*> On entry, ALPHA specifies the scalar alpha. When alpha is
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*> zero then A is not referenced and B need not be set before
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*> entry.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is DOUBLE PRECISION array of DIMENSION ( LDA, k ),
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*> where k is m when SIDE = 'L' or 'l'
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*> and k is n when SIDE = 'R' or 'r'.
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*> Before entry with UPLO = 'U' or 'u', the leading k by k
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*> upper triangular part of the array A must contain the upper
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*> triangular matrix and the strictly lower triangular part of
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*> A is not referenced.
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*> Before entry with UPLO = 'L' or 'l', the leading k by k
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*> lower triangular part of the array A must contain the lower
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*> triangular matrix and the strictly upper triangular part of
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*> A is not referenced.
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*> Note that when DIAG = 'U' or 'u', the diagonal elements of
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*> A are not referenced either, but are assumed to be unity.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> On entry, LDA specifies the first dimension of A as declared
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*> in the calling (sub) program. When SIDE = 'L' or 'l' then
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*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
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*> then LDA must be at least max( 1, n ).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
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*> Before entry, the leading m by n part of the array B must
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*> contain the right-hand side matrix B, and on exit is
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*> overwritten by the solution matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> On entry, LDB specifies the first dimension of B as declared
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*> in the calling (sub) program. LDB must be at least
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*> max( 1, m ).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup double_blas_level3
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> Level 3 Blas routine.
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*>
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*>
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*> -- Written on 8-February-1989.
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*> Jack Dongarra, Argonne National Laboratory.
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*> Iain Duff, AERE Harwell.
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*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
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*> Sven Hammarling, Numerical Algorithms Group Ltd.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
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*
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* -- Reference BLAS level3 routine (version 3.4.0) --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA
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INTEGER LDA,LDB,M,N
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CHARACTER DIAG,SIDE,TRANSA,UPLO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*),B(LDB,*)
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* ..
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*
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* =====================================================================
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*
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION TEMP
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INTEGER I,INFO,J,K,NROWA
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LOGICAL LSIDE,NOUNIT,UPPER
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* ..
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* .. Parameters ..
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DOUBLE PRECISION ONE,ZERO
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PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
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* ..
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*
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* Test the input parameters.
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*
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LSIDE = LSAME(SIDE,'L')
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IF (LSIDE) THEN
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NROWA = M
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ELSE
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NROWA = N
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END IF
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NOUNIT = LSAME(DIAG,'N')
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UPPER = LSAME(UPLO,'U')
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*
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INFO = 0
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IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
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INFO = 1
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ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
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INFO = 2
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ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
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+ (.NOT.LSAME(TRANSA,'T')) .AND.
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+ (.NOT.LSAME(TRANSA,'C'))) THEN
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INFO = 3
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ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
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INFO = 4
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ELSE IF (M.LT.0) THEN
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INFO = 5
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ELSE IF (N.LT.0) THEN
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INFO = 6
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
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INFO = 9
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ELSE IF (LDB.LT.MAX(1,M)) THEN
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INFO = 11
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('DTRSM ',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF (M.EQ.0 .OR. N.EQ.0) RETURN
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*
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* And when alpha.eq.zero.
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*
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IF (ALPHA.EQ.ZERO) THEN
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DO 20 J = 1,N
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DO 10 I = 1,M
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B(I,J) = ZERO
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10 CONTINUE
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20 CONTINUE
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RETURN
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END IF
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*
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* Start the operations.
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*
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IF (LSIDE) THEN
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IF (LSAME(TRANSA,'N')) THEN
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*
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* Form B := alpha*inv( A )*B.
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*
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IF (UPPER) THEN
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DO 60 J = 1,N
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IF (ALPHA.NE.ONE) THEN
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DO 30 I = 1,M
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B(I,J) = ALPHA*B(I,J)
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30 CONTINUE
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END IF
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DO 50 K = M,1,-1
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IF (B(K,J).NE.ZERO) THEN
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IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
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DO 40 I = 1,K - 1
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B(I,J) = B(I,J) - B(K,J)*A(I,K)
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40 CONTINUE
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END IF
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50 CONTINUE
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60 CONTINUE
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ELSE
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DO 100 J = 1,N
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IF (ALPHA.NE.ONE) THEN
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DO 70 I = 1,M
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B(I,J) = ALPHA*B(I,J)
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70 CONTINUE
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END IF
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DO 90 K = 1,M
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IF (B(K,J).NE.ZERO) THEN
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IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
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DO 80 I = K + 1,M
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B(I,J) = B(I,J) - B(K,J)*A(I,K)
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80 CONTINUE
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END IF
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90 CONTINUE
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100 CONTINUE
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END IF
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ELSE
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*
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* Form B := alpha*inv( A**T )*B.
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*
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IF (UPPER) THEN
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DO 130 J = 1,N
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DO 120 I = 1,M
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TEMP = ALPHA*B(I,J)
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DO 110 K = 1,I - 1
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TEMP = TEMP - A(K,I)*B(K,J)
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110 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(I,I)
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B(I,J) = TEMP
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120 CONTINUE
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130 CONTINUE
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ELSE
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DO 160 J = 1,N
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DO 150 I = M,1,-1
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TEMP = ALPHA*B(I,J)
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DO 140 K = I + 1,M
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TEMP = TEMP - A(K,I)*B(K,J)
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140 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(I,I)
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B(I,J) = TEMP
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150 CONTINUE
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160 CONTINUE
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END IF
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END IF
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ELSE
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IF (LSAME(TRANSA,'N')) THEN
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*
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* Form B := alpha*B*inv( A ).
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*
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IF (UPPER) THEN
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DO 210 J = 1,N
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IF (ALPHA.NE.ONE) THEN
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DO 170 I = 1,M
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B(I,J) = ALPHA*B(I,J)
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170 CONTINUE
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END IF
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DO 190 K = 1,J - 1
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IF (A(K,J).NE.ZERO) THEN
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DO 180 I = 1,M
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B(I,J) = B(I,J) - A(K,J)*B(I,K)
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180 CONTINUE
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END IF
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190 CONTINUE
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IF (NOUNIT) THEN
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TEMP = ONE/A(J,J)
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DO 200 I = 1,M
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B(I,J) = TEMP*B(I,J)
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200 CONTINUE
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END IF
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210 CONTINUE
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ELSE
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DO 260 J = N,1,-1
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IF (ALPHA.NE.ONE) THEN
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DO 220 I = 1,M
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B(I,J) = ALPHA*B(I,J)
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220 CONTINUE
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END IF
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DO 240 K = J + 1,N
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IF (A(K,J).NE.ZERO) THEN
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DO 230 I = 1,M
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B(I,J) = B(I,J) - A(K,J)*B(I,K)
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230 CONTINUE
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END IF
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240 CONTINUE
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IF (NOUNIT) THEN
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TEMP = ONE/A(J,J)
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DO 250 I = 1,M
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B(I,J) = TEMP*B(I,J)
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250 CONTINUE
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END IF
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260 CONTINUE
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END IF
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ELSE
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*
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* Form B := alpha*B*inv( A**T ).
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*
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IF (UPPER) THEN
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DO 310 K = N,1,-1
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IF (NOUNIT) THEN
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TEMP = ONE/A(K,K)
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DO 270 I = 1,M
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B(I,K) = TEMP*B(I,K)
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270 CONTINUE
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END IF
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DO 290 J = 1,K - 1
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IF (A(J,K).NE.ZERO) THEN
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TEMP = A(J,K)
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DO 280 I = 1,M
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B(I,J) = B(I,J) - TEMP*B(I,K)
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280 CONTINUE
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END IF
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290 CONTINUE
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IF (ALPHA.NE.ONE) THEN
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DO 300 I = 1,M
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B(I,K) = ALPHA*B(I,K)
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300 CONTINUE
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END IF
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310 CONTINUE
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ELSE
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DO 360 K = 1,N
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IF (NOUNIT) THEN
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TEMP = ONE/A(K,K)
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DO 320 I = 1,M
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B(I,K) = TEMP*B(I,K)
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320 CONTINUE
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END IF
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DO 340 J = K + 1,N
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IF (A(J,K).NE.ZERO) THEN
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TEMP = A(J,K)
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DO 330 I = 1,M
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B(I,J) = B(I,J) - TEMP*B(I,K)
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330 CONTINUE
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END IF
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340 CONTINUE
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IF (ALPHA.NE.ONE) THEN
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DO 350 I = 1,M
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B(I,K) = ALPHA*B(I,K)
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350 CONTINUE
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END IF
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360 CONTINUE
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END IF
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END IF
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END IF
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*
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RETURN
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*
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* End of DTRSM .
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*
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END
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