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,*) ! .. ! ! Purpose ! ======= ! ! 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', ! ! 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. ! ! Arguments ! ========== ! ! TRANSA - 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'. ! ! TRANSA = 'C' or 'c', op( A ) = A'. ! ! Unchanged on exit. ! ! TRANSB - 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'. ! ! TRANSB = 'C' or 'c', op( B ) = B'. ! ! Unchanged on exit. ! ! M - 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. ! Unchanged on exit. ! ! N - 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. ! Unchanged on exit. ! ! K - 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. ! Unchanged on exit. ! ! ALPHA - DOUBLE PRECISION. ! On entry, ALPHA specifies the scalar alpha. ! Unchanged on exit. ! ! A - 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. ! Unchanged on exit. ! ! LDA - 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 ). ! Unchanged on exit. ! ! B - 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. ! Unchanged on exit. ! ! LDB - 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 ). ! Unchanged on exit. ! ! BETA - DOUBLE PRECISION. ! On entry, BETA specifies the scalar beta. When BETA is ! supplied as zero then C need not be set on input. ! Unchanged on exit. ! ! C - 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 ). ! ! LDC - 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 ). ! Unchanged on exit. ! ! ! 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. ! ! ! .. 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'*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' + 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'*B' + 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 SUBROUTINE DGEMM