2013-05-31 23:35:54 +08:00
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*> \brief \b DTRMM
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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 DTRMM(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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*> DTRMM performs one of the matrix-matrix operations
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*>
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*> B := alpha*op( A )*B, or B := alpha*B*op( A ),
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*>
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*> where alpha is a scalar, B is an m by n matrix, 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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*> \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 ) multiplies B from
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*> the left or right as follows:
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*>
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*> SIDE = 'L' or 'l' B := alpha*op( A )*B.
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*>
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*> SIDE = 'R' or 'r' B := alpha*B*op( A ).
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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 ), where k is m
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*> when SIDE = 'L' or 'l' and 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 matrix B, and on exit is overwritten by the
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*> transformed matrix.
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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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*> -- 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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2012-01-07 01:41:26 +08:00
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SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
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2013-05-31 23:35:54 +08:00
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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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2012-01-07 01:41:26 +08:00
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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('DTRMM ',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*A*B.
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*
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IF (UPPER) THEN
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DO 50 J = 1,N
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DO 40 K = 1,M
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IF (B(K,J).NE.ZERO) THEN
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TEMP = ALPHA*B(K,J)
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DO 30 I = 1,K - 1
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B(I,J) = B(I,J) + TEMP*A(I,K)
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30 CONTINUE
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IF (NOUNIT) TEMP = TEMP*A(K,K)
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B(K,J) = TEMP
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END IF
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40 CONTINUE
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50 CONTINUE
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ELSE
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DO 80 J = 1,N
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DO 70 K = M,1,-1
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IF (B(K,J).NE.ZERO) THEN
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TEMP = ALPHA*B(K,J)
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B(K,J) = TEMP
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IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
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DO 60 I = K + 1,M
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B(I,J) = B(I,J) + TEMP*A(I,K)
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60 CONTINUE
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END IF
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70 CONTINUE
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80 CONTINUE
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END IF
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ELSE
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*
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2013-05-31 23:35:54 +08:00
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* Form B := alpha*A**T*B.
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2012-01-07 01:41:26 +08:00
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*
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IF (UPPER) THEN
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DO 110 J = 1,N
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DO 100 I = M,1,-1
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TEMP = B(I,J)
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IF (NOUNIT) TEMP = TEMP*A(I,I)
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DO 90 K = 1,I - 1
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TEMP = TEMP + A(K,I)*B(K,J)
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90 CONTINUE
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B(I,J) = ALPHA*TEMP
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100 CONTINUE
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110 CONTINUE
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ELSE
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DO 140 J = 1,N
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DO 130 I = 1,M
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TEMP = B(I,J)
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IF (NOUNIT) TEMP = TEMP*A(I,I)
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DO 120 K = I + 1,M
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TEMP = TEMP + A(K,I)*B(K,J)
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120 CONTINUE
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B(I,J) = ALPHA*TEMP
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130 CONTINUE
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140 CONTINUE
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END IF
|
|
|
|
|
END IF
|
|
|
|
|
ELSE
|
|
|
|
|
IF (LSAME(TRANSA,'N')) THEN
|
|
|
|
|
*
|
|
|
|
|
* Form B := alpha*B*A.
|
|
|
|
|
*
|
|
|
|
|
IF (UPPER) THEN
|
|
|
|
|
DO 180 J = N,1,-1
|
|
|
|
|
TEMP = ALPHA
|
|
|
|
|
IF (NOUNIT) TEMP = TEMP*A(J,J)
|
|
|
|
|
DO 150 I = 1,M
|
|
|
|
|
B(I,J) = TEMP*B(I,J)
|
|
|
|
|
150 CONTINUE
|
|
|
|
|
DO 170 K = 1,J - 1
|
|
|
|
|
IF (A(K,J).NE.ZERO) THEN
|
|
|
|
|
TEMP = ALPHA*A(K,J)
|
|
|
|
|
DO 160 I = 1,M
|
|
|
|
|
B(I,J) = B(I,J) + TEMP*B(I,K)
|
|
|
|
|
160 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
170 CONTINUE
|
|
|
|
|
180 CONTINUE
|
|
|
|
|
ELSE
|
|
|
|
|
DO 220 J = 1,N
|
|
|
|
|
TEMP = ALPHA
|
|
|
|
|
IF (NOUNIT) TEMP = TEMP*A(J,J)
|
|
|
|
|
DO 190 I = 1,M
|
|
|
|
|
B(I,J) = TEMP*B(I,J)
|
|
|
|
|
190 CONTINUE
|
|
|
|
|
DO 210 K = J + 1,N
|
|
|
|
|
IF (A(K,J).NE.ZERO) THEN
|
|
|
|
|
TEMP = ALPHA*A(K,J)
|
|
|
|
|
DO 200 I = 1,M
|
|
|
|
|
B(I,J) = B(I,J) + TEMP*B(I,K)
|
|
|
|
|
200 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
210 CONTINUE
|
|
|
|
|
220 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
ELSE
|
|
|
|
|
*
|
2013-05-31 23:35:54 +08:00
|
|
|
* Form B := alpha*B*A**T.
|
2012-01-07 01:41:26 +08:00
|
|
|
*
|
|
|
|
|
IF (UPPER) THEN
|
|
|
|
|
DO 260 K = 1,N
|
|
|
|
|
DO 240 J = 1,K - 1
|
|
|
|
|
IF (A(J,K).NE.ZERO) THEN
|
|
|
|
|
TEMP = ALPHA*A(J,K)
|
|
|
|
|
DO 230 I = 1,M
|
|
|
|
|
B(I,J) = B(I,J) + TEMP*B(I,K)
|
|
|
|
|
230 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
240 CONTINUE
|
|
|
|
|
TEMP = ALPHA
|
|
|
|
|
IF (NOUNIT) TEMP = TEMP*A(K,K)
|
|
|
|
|
IF (TEMP.NE.ONE) THEN
|
|
|
|
|
DO 250 I = 1,M
|
|
|
|
|
B(I,K) = TEMP*B(I,K)
|
|
|
|
|
250 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
260 CONTINUE
|
|
|
|
|
ELSE
|
|
|
|
|
DO 300 K = N,1,-1
|
|
|
|
|
DO 280 J = K + 1,N
|
|
|
|
|
IF (A(J,K).NE.ZERO) THEN
|
|
|
|
|
TEMP = ALPHA*A(J,K)
|
|
|
|
|
DO 270 I = 1,M
|
|
|
|
|
B(I,J) = B(I,J) + TEMP*B(I,K)
|
|
|
|
|
270 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
280 CONTINUE
|
|
|
|
|
TEMP = ALPHA
|
|
|
|
|
IF (NOUNIT) TEMP = TEMP*A(K,K)
|
|
|
|
|
IF (TEMP.NE.ONE) THEN
|
|
|
|
|
DO 290 I = 1,M
|
|
|
|
|
B(I,K) = TEMP*B(I,K)
|
|
|
|
|
290 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
300 CONTINUE
|
|
|
|
|
END IF
|
|
|
|
|
END IF
|
|
|
|
|
END IF
|
|
|
|
|
*
|
|
|
|
|
RETURN
|
|
|
|
|
*
|
|
|
|
|
* End of DTRMM .
|
|
|
|
|
*
|
|
|
|
|
END
|
