484 lines
14 KiB
Fortran
484 lines
14 KiB
Fortran
*> \brief \b ZGEMM
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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*
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* .. Scalar Arguments ..
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* COMPLEX*16 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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* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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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**T or op( X ) = X**H,
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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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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] TRANSA
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*> \verbatim
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*> TRANSA is 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**T.
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*>
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*> TRANSA = 'C' or 'c', op( A ) = A**H.
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*> \endverbatim
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*>
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*> \param[in] TRANSB
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*> \verbatim
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*> TRANSB is 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**T.
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*>
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*> TRANSB = 'C' or 'c', op( B ) = B**H.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is 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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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is 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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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is 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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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is COMPLEX*16
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*> On entry, ALPHA specifies the scalar alpha.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, 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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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is 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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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is COMPLEX*16 array, 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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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is 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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*> \endverbatim
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*>
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*> \param[in] BETA
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*> \verbatim
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*> BETA is 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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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is COMPLEX*16 array, 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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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is 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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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup complex16_blas_level3
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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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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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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*
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* -- Reference BLAS level3 routine (version 3.7.0) --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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COMPLEX*16 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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COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
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* ..
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*
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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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COMPLEX*16 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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COMPLEX*16 ONE
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PARAMETER (ONE= (1.0D+0,0.0D+0))
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COMPLEX*16 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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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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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*A**H*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**T*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*B**H + 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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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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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**T + 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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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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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*A**H*B**H + 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*A**H*B**T + 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**T*B**H + 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**T*B**T + 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
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