SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) 16,3
! .. 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