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