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SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) |
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* .. Scalar Arguments .. |
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DOUBLE COMPLEX ALPHA,BETA |
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INTEGER LDA,LDB,LDC,M,N |
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CHARACTER SIDE,UPLO |
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* .. |
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* .. Array Arguments .. |
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DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* ZHEMM performs one of the matrix-matrix operations |
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* |
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* C := alpha*A*B + beta*C, |
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* |
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* or |
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* |
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* C := alpha*B*A + beta*C, |
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* |
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* where alpha and beta are scalars, A is an hermitian matrix and B and |
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* C are m by n matrices. |
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* |
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* Arguments |
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* ========== |
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* |
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* SIDE - CHARACTER*1. |
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* On entry, SIDE specifies whether the hermitian matrix A |
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* appears on the left or right in the operation as follows: |
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* |
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* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, |
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* |
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* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, |
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* |
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* Unchanged on exit. |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the upper or lower |
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* triangular part of the hermitian matrix A is to be |
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* referenced as follows: |
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* |
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* UPLO = 'U' or 'u' Only the upper triangular part of the |
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* hermitian matrix is to be referenced. |
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* |
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* UPLO = 'L' or 'l' Only the lower triangular part of the |
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* hermitian matrix is to be referenced. |
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* |
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* Unchanged on exit. |
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* |
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* M - INTEGER. |
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* On entry, M specifies the number of rows of the matrix C. |
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* M must be at least zero. |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the number of columns of the matrix C. |
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* N must be at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - COMPLEX*16 . |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is |
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* m when SIDE = 'L' or 'l' and is n otherwise. |
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* Before entry with SIDE = 'L' or 'l', the m by m part of |
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* the array A must contain the hermitian matrix, such that |
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* when UPLO = 'U' or 'u', the leading m by m upper triangular |
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* part of the array A must contain the upper triangular part |
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* of the hermitian matrix and the strictly lower triangular |
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* part of A is not referenced, and when UPLO = 'L' or 'l', |
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* the leading m by m lower triangular part of the array A |
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* must contain the lower triangular part of the hermitian |
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* matrix and the strictly upper triangular part of A is not |
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* referenced. |
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* Before entry with SIDE = 'R' or 'r', the n by n part of |
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* the array A must contain the hermitian matrix, such that |
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* when UPLO = 'U' or 'u', the leading n by n upper triangular |
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* part of the array A must contain the upper triangular part |
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* of the hermitian matrix and the strictly lower triangular |
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* part of A is not referenced, and when UPLO = 'L' or 'l', |
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* the leading n by n lower triangular part of the array A |
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* must contain the lower triangular part of the hermitian |
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* matrix and the strictly upper triangular part of A is not |
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* referenced. |
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* Note that the imaginary parts of the diagonal elements need |
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* not be set, they are assumed to be zero. |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. When SIDE = 'L' or 'l' then |
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* LDA must be at least max( 1, m ), otherwise LDA must be at |
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* least max( 1, n ). |
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* Unchanged on exit. |
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* |
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* B - COMPLEX*16 array of DIMENSION ( LDB, n ). |
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* Before entry, the leading m by n part of the array B must |
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* contain the matrix B. |
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* Unchanged on exit. |
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* |
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* LDB - INTEGER. |
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* On entry, LDB specifies the first dimension of B as declared |
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* in the calling (sub) program. LDB must be at least |
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* max( 1, m ). |
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* Unchanged on exit. |
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* |
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* BETA - COMPLEX*16 . |
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* On entry, BETA specifies the scalar beta. When BETA is |
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* supplied as zero then C need not be set on input. |
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* Unchanged on exit. |
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* |
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* C - COMPLEX*16 array of DIMENSION ( LDC, n ). |
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* Before entry, the leading m by n part of the array C must |
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* contain the matrix C, except when beta is zero, in which |
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* case C need not be set on entry. |
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* On exit, the array C is overwritten by the m by n updated |
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* matrix. |
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* |
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* LDC - INTEGER. |
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* On entry, LDC specifies the first dimension of C as declared |
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* in the calling (sub) program. LDC must be at least |
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* max( 1, m ). |
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* Unchanged on exit. |
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* |
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* |
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* Level 3 Blas routine. |
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* |
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* -- Written on 8-February-1989. |
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* Jack Dongarra, Argonne National Laboratory. |
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* Iain Duff, AERE Harwell. |
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* Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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* Sven Hammarling, Numerical Algorithms Group Ltd. |
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* |
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* |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC DBLE,DCONJG,MAX |
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* .. |
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* .. Local Scalars .. |
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DOUBLE COMPLEX TEMP1,TEMP2 |
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INTEGER I,INFO,J,K,NROWA |
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LOGICAL UPPER |
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* .. |
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* .. Parameters .. |
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DOUBLE COMPLEX ONE |
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PARAMETER (ONE= (1.0D+0,0.0D+0)) |
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DOUBLE COMPLEX ZERO |
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PARAMETER (ZERO= (0.0D+0,0.0D+0)) |
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* .. |
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* |
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* Set NROWA as the number of rows of A. |
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* |
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IF (LSAME(SIDE,'L')) THEN |
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NROWA = M |
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ELSE |
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NROWA = N |
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END IF |
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UPPER = LSAME(UPLO,'U') |
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* |
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* Test the input parameters. |
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* |
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INFO = 0 |
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IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN |
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INFO = 1 |
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ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN |
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INFO = 2 |
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ELSE IF (M.LT.0) THEN |
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INFO = 3 |
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ELSE IF (N.LT.0) THEN |
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INFO = 4 |
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN |
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INFO = 7 |
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ELSE IF (LDB.LT.MAX(1,M)) THEN |
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INFO = 9 |
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ELSE IF (LDC.LT.MAX(1,M)) THEN |
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INFO = 12 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('ZHEMM ',INFO)
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RETURN |
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END IF |
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* |
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* Quick return if possible. |
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* |
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IF ((M.EQ.0) .OR. (N.EQ.0) .OR. |
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+ ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN |
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* |
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* And when alpha.eq.zero. |
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* |
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IF (ALPHA.EQ.ZERO) THEN |
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IF (BETA.EQ.ZERO) THEN |
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DO 20 J = 1,N |
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DO 10 I = 1,M |
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C(I,J) = ZERO |
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10 CONTINUE |
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20 CONTINUE |
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ELSE |
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DO 40 J = 1,N |
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DO 30 I = 1,M |
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C(I,J) = BETA*C(I,J) |
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30 CONTINUE |
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40 CONTINUE |
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END IF |
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RETURN |
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END IF |
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* |
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* Start the operations. |
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* |
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IF (LSAME(SIDE,'L')) THEN |
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* |
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* Form C := alpha*A*B + beta*C. |
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* |
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IF (UPPER) THEN |
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DO 70 J = 1,N |
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DO 60 I = 1,M |
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TEMP1 = ALPHA*B(I,J) |
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TEMP2 = ZERO |
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DO 50 K = 1,I - 1 |
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C(K,J) = C(K,J) + TEMP1*A(K,I) |
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TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I)) |
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50 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2 |
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ELSE |
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C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) + |
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+ ALPHA*TEMP2 |
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END IF |
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60 CONTINUE |
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70 CONTINUE |
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ELSE |
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DO 100 J = 1,N |
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DO 90 I = M,1,-1 |
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TEMP1 = ALPHA*B(I,J) |
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TEMP2 = ZERO |
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DO 80 K = I + 1,M |
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C(K,J) = C(K,J) + TEMP1*A(K,I) |
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TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I)) |
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80 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2 |
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ELSE |
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C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) + |
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+ ALPHA*TEMP2 |
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END IF |
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90 CONTINUE |
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100 CONTINUE |
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END IF |
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ELSE |
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* |
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* Form C := alpha*B*A + beta*C. |
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* |
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DO 170 J = 1,N |
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TEMP1 = ALPHA*DBLE(A(J,J)) |
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IF (BETA.EQ.ZERO) THEN |
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DO 110 I = 1,M |
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C(I,J) = TEMP1*B(I,J) |
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110 CONTINUE |
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ELSE |
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DO 120 I = 1,M |
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C(I,J) = BETA*C(I,J) + TEMP1*B(I,J) |
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120 CONTINUE |
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END IF |
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DO 140 K = 1,J - 1 |
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IF (UPPER) THEN |
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TEMP1 = ALPHA*A(K,J) |
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ELSE |
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TEMP1 = ALPHA*DCONJG(A(J,K)) |
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END IF |
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DO 130 I = 1,M |
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C(I,J) = C(I,J) + TEMP1*B(I,K) |
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130 CONTINUE |
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140 CONTINUE |
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DO 160 K = J + 1,N |
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IF (UPPER) THEN |
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TEMP1 = ALPHA*DCONJG(A(J,K)) |
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ELSE |
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TEMP1 = ALPHA*A(K,J) |
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END IF |
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DO 150 I = 1,M |
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C(I,J) = C(I,J) + TEMP1*B(I,K) |
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150 CONTINUE |
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160 CONTINUE |
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170 CONTINUE |
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END IF |
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* |
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RETURN |
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* |
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* End of ZHEMM . |
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* |
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END |