SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * .. Scalar Arguments .. DOUBLE COMPLEX ALPHA,BETA INTEGER LDA,LDB,LDC,M,N CHARACTER SIDE,UPLO * .. * .. Array Arguments .. DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) * .. * * Purpose * ======= * * ZHEMM 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. * * Arguments * ========== * * SIDE - 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, * * Unchanged on exit. * * UPLO - 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. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows 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 C. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX*16 array of 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. * Unchanged on exit. * * LDA - 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 ). * Unchanged on exit. * * B - COMPLEX*16 array of DIMENSION ( LDB, n ). * Before entry, the leading m by n 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. LDB must be at least * max( 1, m ). * Unchanged on exit. * * BETA - COMPLEX*16 . * 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 - COMPLEX*16 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 updated * matrix. * * 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 DBLE,DCONJG,MAX * .. * .. Local Scalars .. DOUBLE COMPLEX TEMP1,TEMP2 INTEGER I,INFO,J,K,NROWA LOGICAL UPPER * .. * .. Parameters .. DOUBLE COMPLEX ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) DOUBLE COMPLEX ZERO PARAMETER (ZERO= (0.0D+0,0.0D+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('ZHEMM ',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)*DCONJG(A(K,I)) 50 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*DBLE(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)*DCONJG(A(K,I)) 80 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*DBLE(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*DBLE(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*DCONJG(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*DCONJG(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 ZHEMM . * END