#include "ESMF_LapackBlas.inc" !> \brief \b DGEMM ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! ! Definition: ! =========== ! ! SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) ! ! .. Scalar Arguments .. ! DOUBLE PRECISION ALPHA,BETA ! INTEGER K,LDA,LDB,LDC,M,N ! CHARACTER TRANSA,TRANSB ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DGEMM performs one of the matrix-matrix operations !> !> C := alpha*op( A )*op( B ) + beta*C, !> !> where op( X ) is one of !> !> op( X ) = X or op( X ) = X**T, !> !> alpha and beta are scalars, and A, B and C are matrices, with op( A ) !> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. !> \endverbatim ! ! Arguments: ! ========== ! !> \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] TRANSB !> \verbatim !> TRANSB is CHARACTER*1 !> On entry, TRANSB specifies the form of op( B ) to be used in !> the matrix multiplication as follows: !> !> TRANSB = 'N' or 'n', op( B ) = B. !> !> TRANSB = 'T' or 't', op( B ) = B**T. !> !> TRANSB = 'C' or 'c', op( B ) = B**T. !> \endverbatim !> !> \param[in] M !> \verbatim !> M is INTEGER !> On entry, M specifies the number of rows of the matrix !> op( A ) and of the matrix C. M must be at least zero. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> On entry, N specifies the number of columns of the matrix !> op( B ) and the number of columns of the matrix C. N must be !> at least zero. !> \endverbatim !> !> \param[in] K !> \verbatim !> K is INTEGER !> On entry, K specifies the number of columns of the matrix !> op( A ) and the number of rows of the matrix op( B ). K must !> be at least zero. !> \endverbatim !> !> \param[in] ALPHA !> \verbatim !> ALPHA is DOUBLE PRECISION. !> On entry, ALPHA specifies the scalar alpha. !> \endverbatim !> !> \param[in] A !> \verbatim !> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is !> k when TRANSA = 'N' or 'n', and is m otherwise. !> Before entry with TRANSA = 'N' or 'n', the leading m by k !> part of the array A must contain the matrix A, otherwise !> the leading k by m part of the array A must contain the !> matrix A. !> \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 TRANSA = 'N' or 'n' then !> LDA must be at least max( 1, m ), otherwise LDA must be at !> least max( 1, k ). !> \endverbatim !> !> \param[in] B !> \verbatim !> B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is !> n when TRANSB = 'N' or 'n', and is k otherwise. !> Before entry with TRANSB = 'N' or 'n', the leading k by n !> part of the array B must contain the matrix B, otherwise !> the leading n by k part of the array B must contain the !> matrix B. !> \endverbatim !> !> \param[in] LDB !> \verbatim !> LDB is INTEGER !> On entry, LDB specifies the first dimension of B as declared !> in the calling (sub) program. When TRANSB = 'N' or 'n' then !> LDB must be at least max( 1, k ), otherwise LDB must be at !> least max( 1, n ). !> \endverbatim !> !> \param[in] BETA !> \verbatim !> BETA is DOUBLE PRECISION. !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then C need not be set on input. !> \endverbatim !> !> \param[in,out] C !> \verbatim !> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). !> Before entry, the leading m by n part of the array C must !> contain the matrix C, except when beta is zero, in which !> case C need not be set on entry. !> On exit, the array C is overwritten by the m by n matrix !> ( alpha*op( A )*op( B ) + beta*C ). !> \endverbatim !> !> \param[in] LDC !> \verbatim !> LDC is INTEGER !> On entry, LDC specifies the first dimension of C as declared !> in the calling (sub) program. LDC 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 DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) ! ! -- 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,BETA INTEGER K,LDA,LDB,LDC,M,N CHARACTER TRANSA,TRANSB ! .. ! .. Array Arguments .. DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) ! .. ! ! ===================================================================== ! ! .. External Functions .. LOGICAL LSAME EXTERNAL LSAME ! .. ! .. External Subroutines .. EXTERNAL XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX ! .. ! .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB LOGICAL NOTA,NOTB ! .. ! .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) ! .. ! ! Set NOTA and NOTB as true if A and B respectively are not ! transposed and set NROWA, NCOLA and NROWB as the number of rows ! and columns of A and the number of rows of B respectively. ! NOTA = LSAME(TRANSA,'N') NOTB = LSAME(TRANSB,'N') IF (NOTA) THEN NROWA = M NCOLA = K ELSE NROWA = K NCOLA = M END IF IF (NOTB) THEN NROWB = K ELSE NROWB = N END IF ! ! Test the input parameters. ! INFO = 0 IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. & & (.NOT.LSAME(TRANSA,'T'))) THEN INFO = 1 ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. & & (.NOT.LSAME(TRANSB,'T'))) THEN INFO = 2 ELSE IF (M.LT.0) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (K.LT.0) THEN INFO = 5 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 8 ELSE IF (LDB.LT.MAX(1,NROWB)) THEN INFO = 10 ELSE IF (LDC.LT.MAX(1,M)) THEN INFO = 13 END IF IF (INFO.NE.0) THEN CALL XERBLA('DGEMM ',INFO) RETURN END IF ! ! Quick return if possible. ! IF ((M.EQ.0) .OR. (N.EQ.0) .OR. & & (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN ! ! And if alpha.eq.zero. ! IF (ALPHA.EQ.ZERO) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,M C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF RETURN END IF ! ! Start the operations. ! IF (NOTB) THEN IF (NOTA) THEN ! ! Form C := alpha*A*B + beta*C. ! DO 90 J = 1,N IF (BETA.EQ.ZERO) THEN DO 50 I = 1,M C(I,J) = ZERO 50 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 60 I = 1,M C(I,J) = BETA*C(I,J) 60 CONTINUE END IF DO 80 L = 1,K IF (B(L,J).NE.ZERO) THEN TEMP = ALPHA*B(L,J) DO 70 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 70 CONTINUE END IF 80 CONTINUE 90 CONTINUE ELSE ! ! Form C := alpha*A**T*B + beta*C ! DO 120 J = 1,N DO 110 I = 1,M TEMP = ZERO DO 100 L = 1,K TEMP = TEMP + A(L,I)*B(L,J) 100 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 110 CONTINUE 120 CONTINUE END IF ELSE IF (NOTA) THEN ! ! Form C := alpha*A*B**T + beta*C ! DO 170 J = 1,N IF (BETA.EQ.ZERO) THEN DO 130 I = 1,M C(I,J) = ZERO 130 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 140 I = 1,M C(I,J) = BETA*C(I,J) 140 CONTINUE END IF DO 160 L = 1,K IF (B(J,L).NE.ZERO) THEN TEMP = ALPHA*B(J,L) DO 150 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 150 CONTINUE END IF 160 CONTINUE 170 CONTINUE ELSE ! ! Form C := alpha*A**T*B**T + beta*C ! DO 200 J = 1,N DO 190 I = 1,M TEMP = ZERO DO 180 L = 1,K TEMP = TEMP + A(L,I)*B(J,L) 180 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 190 CONTINUE 200 CONTINUE END IF END IF ! RETURN ! ! End of DGEMM . ! END