numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/BLAS/SRC/sgemm.f | 10831B | -rw-r--r-- |
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*> \brief \b SGEMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * REAL ALPHA,BETA * INTEGER K,LDA,LDB,LDC,M,N * CHARACTER TRANSA,TRANSB * .. * .. Array Arguments .. * REAL A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGEMM 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 REAL *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL 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 REAL 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 REAL *> 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 REAL 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. * *> \ingroup gemm * *> \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 SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB, + BETA,C,LDC) * * -- Reference BLAS level3 routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. REAL ALPHA,BETA INTEGER K,LDA,LDB,LDC,M,N CHARACTER TRANSA,TRANSB * .. * .. Array Arguments .. REAL A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. REAL TEMP INTEGER I,INFO,J,L,NROWA,NROWB LOGICAL NOTA,NOTB * .. * .. Parameters .. REAL ONE,ZERO PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) * .. * * Set NOTA and NOTB as true if A and B respectively are not * transposed and set NROWA and NROWB as the number of rows of A * and B respectively. * NOTA = LSAME(TRANSA,'N') NOTB = LSAME(TRANSB,'N') IF (NOTA) THEN NROWA = M ELSE NROWA = K 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('SGEMM ',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 SGEMM * END