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SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,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 K,LDA,LDB,LDC,M,N |
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CHARACTER TRANSA,TRANSB |
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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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* ZGEMM performs one of the matrix-matrix operations |
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* |
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* C := alpha*op( A )*op( B ) + beta*C, |
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* |
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* where op( X ) is one of |
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* |
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* op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ), |
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* |
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* alpha and beta are scalars, and A, B and C are matrices, with op( A ) |
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* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. |
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* |
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* Arguments |
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* ========== |
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* |
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* TRANSA - CHARACTER*1. |
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* On entry, TRANSA specifies the form of op( A ) to be used in |
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* the matrix multiplication as follows: |
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* |
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* TRANSA = 'N' or 'n', op( A ) = A. |
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* |
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* TRANSA = 'T' or 't', op( A ) = A'. |
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* |
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* TRANSA = 'C' or 'c', op( A ) = conjg( A' ). |
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* |
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* Unchanged on exit. |
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* |
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* TRANSB - CHARACTER*1. |
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* On entry, TRANSB specifies the form of op( B ) to be used in |
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* the matrix multiplication as follows: |
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* |
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* TRANSB = 'N' or 'n', op( B ) = B. |
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* |
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* TRANSB = 'T' or 't', op( B ) = B'. |
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* |
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* TRANSB = 'C' or 'c', op( B ) = conjg( B' ). |
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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 |
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* op( A ) and of the matrix C. 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 |
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* op( B ) and the number of columns of the matrix C. N must be |
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* at least zero. |
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* Unchanged on exit. |
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* |
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* K - INTEGER. |
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* On entry, K specifies the number of columns of the matrix |
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* op( A ) and the number of rows of the matrix op( B ). K must |
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* 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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* k when TRANSA = 'N' or 'n', and is m otherwise. |
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* Before entry with TRANSA = 'N' or 'n', the leading m by k |
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* part of the array A must contain the matrix A, otherwise |
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* the leading k by m part of the array A must contain the |
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* matrix A. |
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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 TRANSA = 'N' or 'n' 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, k ). |
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* Unchanged on exit. |
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* |
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* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is |
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* n when TRANSB = 'N' or 'n', and is k otherwise. |
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* Before entry with TRANSB = 'N' or 'n', the leading k by n |
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* part of the array B must contain the matrix B, otherwise |
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* the leading n by k part of the array B must contain the |
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* 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. When TRANSB = 'N' or 'n' then |
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* LDB must be at least max( 1, k ), otherwise LDB 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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* 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 matrix |
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* ( alpha*op( A )*op( B ) + beta*C ). |
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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 DCONJG,MAX |
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* .. |
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* .. Local Scalars .. |
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DOUBLE COMPLEX TEMP |
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INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB |
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LOGICAL CONJA,CONJB,NOTA,NOTB |
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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 NOTA and NOTB as true if A and B respectively are not |
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* conjugated or transposed, set CONJA and CONJB as true if A and |
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* B respectively are to be transposed but not conjugated and set |
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* NROWA, NCOLA and NROWB as the number of rows and columns of A |
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* and the number of rows of B respectively. |
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* |
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NOTA = LSAME(TRANSA,'N') |
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NOTB = LSAME(TRANSB,'N') |
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CONJA = LSAME(TRANSA,'C') |
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CONJB = LSAME(TRANSB,'C') |
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IF (NOTA) THEN |
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NROWA = M |
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NCOLA = K |
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ELSE |
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NROWA = K |
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NCOLA = M |
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END IF |
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IF (NOTB) THEN |
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NROWB = K |
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ELSE |
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NROWB = N |
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END IF |
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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.NOTA) .AND. (.NOT.CONJA) .AND. |
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+ (.NOT.LSAME(TRANSA,'T'))) THEN |
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INFO = 1 |
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ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND. |
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+ (.NOT.LSAME(TRANSB,'T'))) 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 (K.LT.0) THEN |
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INFO = 5 |
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN |
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INFO = 8 |
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ELSE IF (LDB.LT.MAX(1,NROWB)) THEN |
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INFO = 10 |
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ELSE IF (LDC.LT.MAX(1,M)) THEN |
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INFO = 13 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('ZGEMM ',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).OR. (K.EQ.0)).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 (NOTB) THEN |
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IF (NOTA) THEN |
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* |
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* Form C := alpha*A*B + beta*C. |
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* |
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DO 90 J = 1,N |
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IF (BETA.EQ.ZERO) THEN |
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DO 50 I = 1,M |
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C(I,J) = ZERO |
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50 CONTINUE |
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ELSE IF (BETA.NE.ONE) THEN |
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DO 60 I = 1,M |
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C(I,J) = BETA*C(I,J) |
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60 CONTINUE |
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END IF |
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DO 80 L = 1,K |
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IF (B(L,J).NE.ZERO) THEN |
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TEMP = ALPHA*B(L,J) |
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DO 70 I = 1,M |
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C(I,J) = C(I,J) + TEMP*A(I,L) |
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70 CONTINUE |
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END IF |
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80 CONTINUE |
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90 CONTINUE |
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ELSE IF (CONJA) THEN |
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* |
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* Form C := alpha*conjg( A' )*B + beta*C. |
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* |
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DO 120 J = 1,N |
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DO 110 I = 1,M |
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TEMP = ZERO |
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DO 100 L = 1,K |
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TEMP = TEMP + DCONJG(A(L,I))*B(L,J) |
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100 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = ALPHA*TEMP |
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ELSE |
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C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
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END IF |
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110 CONTINUE |
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120 CONTINUE |
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ELSE |
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* |
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* Form C := alpha*A'*B + beta*C |
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* |
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DO 150 J = 1,N |
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DO 140 I = 1,M |
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TEMP = ZERO |
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DO 130 L = 1,K |
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TEMP = TEMP + A(L,I)*B(L,J) |
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130 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = ALPHA*TEMP |
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ELSE |
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C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
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END IF |
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140 CONTINUE |
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150 CONTINUE |
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END IF |
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ELSE IF (NOTA) THEN |
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IF (CONJB) THEN |
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* |
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* Form C := alpha*A*conjg( B' ) + beta*C. |
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* |
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DO 200 J = 1,N |
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IF (BETA.EQ.ZERO) THEN |
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DO 160 I = 1,M |
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C(I,J) = ZERO |
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160 CONTINUE |
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ELSE IF (BETA.NE.ONE) THEN |
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DO 170 I = 1,M |
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C(I,J) = BETA*C(I,J) |
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170 CONTINUE |
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END IF |
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DO 190 L = 1,K |
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IF (B(J,L).NE.ZERO) THEN |
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TEMP = ALPHA*DCONJG(B(J,L)) |
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DO 180 I = 1,M |
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C(I,J) = C(I,J) + TEMP*A(I,L) |
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180 CONTINUE |
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END IF |
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190 CONTINUE |
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200 CONTINUE |
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ELSE |
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* |
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* Form C := alpha*A*B' + beta*C |
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* |
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DO 250 J = 1,N |
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IF (BETA.EQ.ZERO) THEN |
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DO 210 I = 1,M |
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C(I,J) = ZERO |
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210 CONTINUE |
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ELSE IF (BETA.NE.ONE) THEN |
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DO 220 I = 1,M |
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C(I,J) = BETA*C(I,J) |
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220 CONTINUE |
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END IF |
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DO 240 L = 1,K |
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IF (B(J,L).NE.ZERO) THEN |
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TEMP = ALPHA*B(J,L) |
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DO 230 I = 1,M |
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C(I,J) = C(I,J) + TEMP*A(I,L) |
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230 CONTINUE |
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END IF |
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240 CONTINUE |
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250 CONTINUE |
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END IF |
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ELSE IF (CONJA) THEN |
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IF (CONJB) THEN |
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* |
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* Form C := alpha*conjg( A' )*conjg( B' ) + beta*C. |
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* |
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DO 280 J = 1,N |
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DO 270 I = 1,M |
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TEMP = ZERO |
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DO 260 L = 1,K |
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TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L)) |
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260 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = ALPHA*TEMP |
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ELSE |
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C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
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END IF |
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270 CONTINUE |
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280 CONTINUE |
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ELSE |
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* |
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* Form C := alpha*conjg( A' )*B' + beta*C |
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* |
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DO 310 J = 1,N |
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DO 300 I = 1,M |
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TEMP = ZERO |
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DO 290 L = 1,K |
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TEMP = TEMP + DCONJG(A(L,I))*B(J,L) |
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290 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = ALPHA*TEMP |
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ELSE |
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C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
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END IF |
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300 CONTINUE |
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310 CONTINUE |
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END IF |
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ELSE |
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IF (CONJB) THEN |
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* |
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* Form C := alpha*A'*conjg( B' ) + beta*C |
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* |
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DO 340 J = 1,N |
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DO 330 I = 1,M |
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TEMP = ZERO |
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DO 320 L = 1,K |
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TEMP = TEMP + A(L,I)*DCONJG(B(J,L)) |
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320 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = ALPHA*TEMP |
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ELSE |
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C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
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END IF |
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330 CONTINUE |
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340 CONTINUE |
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ELSE |
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* |
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* Form C := alpha*A'*B' + beta*C |
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* |
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DO 370 J = 1,N |
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DO 360 I = 1,M |
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TEMP = ZERO |
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DO 350 L = 1,K |
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TEMP = TEMP + A(L,I)*B(J,L) |
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350 CONTINUE |
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IF (BETA.EQ.ZERO) THEN |
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C(I,J) = ALPHA*TEMP |
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ELSE |
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C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
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END IF |
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360 CONTINUE |
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370 CONTINUE |
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END IF |
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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 ZGEMM . |
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* |
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END |