numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/BLAS/SRC/chemm.f | 11275B | -rw-r--r-- |
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*> \brief \b CHEMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * COMPLEX ALPHA,BETA * INTEGER LDA,LDB,LDC,M,N * CHARACTER SIDE,UPLO * .. * .. Array Arguments .. * COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CHEMM performs one of the matrix-matrix operations *> *> C := alpha*A*B + beta*C, *> *> or *> *> C := alpha*B*A + beta*C, *> *> where alpha and beta are scalars, A is an hermitian matrix and B and *> C are m by n matrices. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether the hermitian matrix A *> appears on the left or right in the operation as follows: *> *> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, *> *> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the hermitian matrix A is to be *> referenced as follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of the *> hermitian matrix is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of the *> hermitian matrix is to be referenced. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows 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 C. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension ( LDA, ka ), where ka is *> m when SIDE = 'L' or 'l' and is n otherwise. *> Before entry with SIDE = 'L' or 'l', the m by m part of *> the array A must contain the hermitian matrix, such that *> when UPLO = 'U' or 'u', the leading m by m upper triangular *> part of the array A must contain the upper triangular part *> of the hermitian matrix and the strictly lower triangular *> part of A is not referenced, and when UPLO = 'L' or 'l', *> the leading m by m lower triangular part of the array A *> must contain the lower triangular part of the hermitian *> matrix and the strictly upper triangular part of A is not *> referenced. *> Before entry with SIDE = 'R' or 'r', the n by n part of *> the array A must contain the hermitian matrix, such that *> when UPLO = 'U' or 'u', the leading n by n upper triangular *> part of the array A must contain the upper triangular part *> of the hermitian matrix and the strictly lower triangular *> part of A is not referenced, and when UPLO = 'L' or 'l', *> the leading n by n lower triangular part of the array A *> must contain the lower triangular part of the hermitian *> matrix and the strictly upper triangular part of A is not *> referenced. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero. *> \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 SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), otherwise LDA must be at *> least max( 1, n ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is COMPLEX array, dimension ( LDB, N ) *> Before entry, the leading m by n 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. LDB must be at least *> max( 1, m ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX *> 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 COMPLEX 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 updated *> matrix. *> \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 hemm * *> \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 CHEMM(SIDE,UPLO,M,N,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 .. COMPLEX ALPHA,BETA INTEGER LDA,LDB,LDC,M,N CHARACTER SIDE,UPLO * .. * .. Array Arguments .. COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG,MAX,REAL * .. * .. Local Scalars .. COMPLEX TEMP1,TEMP2 INTEGER I,INFO,J,K,NROWA LOGICAL UPPER * .. * .. Parameters .. COMPLEX ONE PARAMETER (ONE= (1.0E+0,0.0E+0)) COMPLEX ZERO PARAMETER (ZERO= (0.0E+0,0.0E+0)) * .. * * Set NROWA as the number of rows of A. * IF (LSAME(SIDE,'L')) THEN NROWA = M ELSE NROWA = N END IF UPPER = LSAME(UPLO,'U') * * Test the input parameters. * INFO = 0 IF ((.NOT.LSAME(SIDE,'L')) .AND. + (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. + (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF (M.LT.0) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 9 ELSE IF (LDC.LT.MAX(1,M)) THEN INFO = 12 END IF IF (INFO.NE.0) THEN CALL XERBLA('CHEMM ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * And when 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 (LSAME(SIDE,'L')) THEN * * Form C := alpha*A*B + beta*C. * IF (UPPER) THEN DO 70 J = 1,N DO 60 I = 1,M TEMP1 = ALPHA*B(I,J) TEMP2 = ZERO DO 50 K = 1,I - 1 C(K,J) = C(K,J) + TEMP1*A(K,I) TEMP2 = TEMP2 + B(K,J)*CONJG(A(K,I)) 50 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*REAL(A(I,I)) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*REAL(A(I,I)) + + ALPHA*TEMP2 END IF 60 CONTINUE 70 CONTINUE ELSE DO 100 J = 1,N DO 90 I = M,1,-1 TEMP1 = ALPHA*B(I,J) TEMP2 = ZERO DO 80 K = I + 1,M C(K,J) = C(K,J) + TEMP1*A(K,I) TEMP2 = TEMP2 + B(K,J)*CONJG(A(K,I)) 80 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*REAL(A(I,I)) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*REAL(A(I,I)) + + ALPHA*TEMP2 END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form C := alpha*B*A + beta*C. * DO 170 J = 1,N TEMP1 = ALPHA*REAL(A(J,J)) IF (BETA.EQ.ZERO) THEN DO 110 I = 1,M C(I,J) = TEMP1*B(I,J) 110 CONTINUE ELSE DO 120 I = 1,M C(I,J) = BETA*C(I,J) + TEMP1*B(I,J) 120 CONTINUE END IF DO 140 K = 1,J - 1 IF (UPPER) THEN TEMP1 = ALPHA*A(K,J) ELSE TEMP1 = ALPHA*CONJG(A(J,K)) END IF DO 130 I = 1,M C(I,J) = C(I,J) + TEMP1*B(I,K) 130 CONTINUE 140 CONTINUE DO 160 K = J + 1,N IF (UPPER) THEN TEMP1 = ALPHA*CONJG(A(J,K)) ELSE TEMP1 = ALPHA*A(K,J) END IF DO 150 I = 1,M C(I,J) = C(I,J) + TEMP1*B(I,K) 150 CONTINUE 160 CONTINUE 170 CONTINUE END IF * RETURN * * End of CHEMM * END