numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/BLAS/SRC/sgemmtr.f | 12449B | -rw-r--r-- |
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*> \brief \b SGEMMTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGEMMTR(UPLO,TRANSA,TRANSB,N,K,ALPHA,A,LDA,B,LDB,BETA, * C,LDC) * * .. Scalar Arguments .. * REAL ALPHA,BETA * INTEGER K,LDA,LDB,LDC,N * CHARACTER TRANSA,TRANSB, UPLO * .. * .. Array Arguments .. * REAL A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGEMMTR 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 n by k matrix, op( B ) a k by n matrix and C an n by n matrix. *> Thereby, the routine only accesses and updates the upper or lower *> triangular part of the result matrix C. This behaviour can be used if *> the resulting matrix C is known to be symmetric. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the lower or the upper *> triangular part of C is access and updated. *> *> UPLO = 'L' or 'l', the lower tringular part of C is used. *> *> UPLO = 'U' or 'u', the upper tringular part of C is used. *> \endverbatim * *> \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] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of rows and columns of *> the matrix C, the number of columns of op(B) and the number *> of rows of op(A). 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 n otherwise. *> Before entry with TRANSA = 'N' or 'n', the leading n 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, n ), 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 n 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 upper or lower trinangular part of the matrix *> C is overwritten by the n 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, n ). *> \endverbatim * * Authors: * ======== * *> \author Martin Koehler * *> \ingroup gemmtr * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 19-July-2023. *> Martin Koehler, MPI Magdeburg *> \endverbatim *> * ===================================================================== SUBROUTINE SGEMMTR(UPLO,TRANSA,TRANSB,N,K,ALPHA,A,LDA,B,LDB, + BETA,C,LDC) IMPLICIT NONE * * -- 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,N CHARACTER TRANSA,TRANSB,UPLO * .. * .. 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, ISTART, ISTOP LOGICAL NOTA,NOTB, UPPER * .. * .. Parameters .. REAL 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 and NROWB as the number of rows of A * and B respectively. * NOTA = LSAME(TRANSA,'N') NOTB = LSAME(TRANSB,'N') IF (NOTA) THEN NROWA = N ELSE NROWA = K END IF IF (NOTB) THEN NROWB = K ELSE NROWB = N END IF UPPER = LSAME(UPLO, 'U') * * Test the input parameters. * INFO = 0 IF ((.NOT. UPPER) .AND. (.NOT. LSAME(UPLO, 'L'))) THEN INFO = 1 ELSE IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. + (.NOT.LSAME(TRANSA,'T'))) THEN INFO = 2 ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. + (.NOT.LSAME(TRANSB,'T'))) 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,N)) THEN INFO = 13 END IF IF (INFO.NE.0) THEN CALL XERBLA('SGEMMTR',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * * And if alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N IF (UPPER) THEN ISTART = 1 ISTOP = J ELSE ISTART = J ISTOP = N END IF DO 10 I = ISTART, ISTOP C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N IF (UPPER) THEN ISTART = 1 ISTOP = J ELSE ISTART = J ISTOP = N END IF DO 30 I = ISTART, ISTOP 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 (UPPER) THEN ISTART = 1 ISTOP = J ELSE ISTART = J ISTOP = N END IF IF (BETA.EQ.ZERO) THEN DO 50 I = ISTART, ISTOP C(I,J) = ZERO 50 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 60 I = ISTART, ISTOP C(I,J) = BETA*C(I,J) 60 CONTINUE END IF DO 80 L = 1,K TEMP = ALPHA*B(L,J) DO 70 I = ISTART, ISTOP 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 IF (UPPER) THEN ISTART = 1 ISTOP = J ELSE ISTART = J ISTOP = N END IF DO 110 I = ISTART, ISTOP 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 (UPPER) THEN ISTART = 1 ISTOP = J ELSE ISTART = J ISTOP = N END IF IF (BETA.EQ.ZERO) THEN DO 130 I = ISTART,ISTOP C(I,J) = ZERO 130 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 140 I = ISTART,ISTOP C(I,J) = BETA*C(I,J) 140 CONTINUE END IF DO 160 L = 1,K TEMP = ALPHA*B(J,L) DO 150 I = ISTART,ISTOP 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 IF (UPPER) THEN ISTART = 1 ISTOP = J ELSE ISTART = J ISTOP = N END IF DO 190 I = ISTART, ISTOP 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 SGEMMTR * END