385 lines
11 KiB
FortranFixed
385 lines
11 KiB
FortranFixed
|
*> \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, 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, 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, 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 December 2016
|
||
|
|
*
|
||
|
|
*> \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 3.7.0) --
|
||
|
|
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
* December 2016
|
||
|
|
*
|
||
|
|
* .. 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
|
||
|
|
TEMP = ALPHA*B(L,J)
|
||
|
|
DO 70 I = 1,M
|
||
|
|
C(I,J) = C(I,J) + TEMP*A(I,L)
|
||
|
|
70 CONTINUE
|
||
|
|
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
|
||
|
|
TEMP = ALPHA*B(J,L)
|
||
|
|
DO 150 I = 1,M
|
||
|
|
C(I,J) = C(I,J) + TEMP*A(I,L)
|
||
|
|
150 CONTINUE
|
||
|
|
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
|