351 lines
9.2 KiB
Fortran
351 lines
9.2 KiB
Fortran
*> \brief \b ZGEMV
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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 ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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*
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* .. Scalar Arguments ..
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* COMPLEX*16 ALPHA,BETA
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* INTEGER INCX,INCY,LDA,M,N
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* CHARACTER TRANS
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A(LDA,*),X(*),Y(*)
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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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*> ZGEMV performs one of the matrix-vector operations
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*>
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*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
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*>
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*> y := alpha*A**H*x + beta*y,
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*>
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*> where alpha and beta are scalars, x and y are vectors and A is an
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*> 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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> On entry, TRANS specifies the operation to be performed as
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*> follows:
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*>
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*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
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*>
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*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
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*>
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*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
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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 A.
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*> 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 A.
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*> N must 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 of DIMENSION ( LDA, n ).
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*> Before entry, the leading m by n part of the array A must
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*> contain the matrix of coefficients.
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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. LDA must be at least
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*> max( 1, m ).
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is COMPLEX*16 array of DIMENSION at least
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*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
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*> and at least
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*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
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*> Before entry, the incremented array X must contain the
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*> vector x.
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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is INTEGER
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*> On entry, INCX specifies the increment for the elements of
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*> X. INCX must not be zero.
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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 Y need not be set on input.
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*> \endverbatim
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*>
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*> \param[in,out] Y
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*> \verbatim
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*> Y is COMPLEX*16 array of DIMENSION at least
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*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
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*> and at least
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*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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*> Before entry with BETA non-zero, the incremented array Y
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*> must contain the vector y. On exit, Y is overwritten by the
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*> updated vector y.
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*> \endverbatim
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*>
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*> \param[in] INCY
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*> \verbatim
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*> INCY is INTEGER
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*> On entry, INCY specifies the increment for the elements of
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*> Y. INCY must not be zero.
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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 November 2015
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*
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*> \ingroup complex16_blas_level2
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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 2 Blas routine.
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*> The vector and matrix arguments are not referenced when N = 0, or M = 0
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*>
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*> -- Written on 22-October-1986.
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*> Jack Dongarra, Argonne National Lab.
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*> Jeremy Du Croz, Nag Central Office.
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*> Sven Hammarling, Nag Central Office.
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*> Richard Hanson, Sandia National Labs.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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*
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* -- Reference BLAS level2 routine (version 3.6.0) --
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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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* November 2015
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*
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* .. Scalar Arguments ..
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COMPLEX*16 ALPHA,BETA
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INTEGER INCX,INCY,LDA,M,N
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CHARACTER TRANS
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A(LDA,*),X(*),Y(*)
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* ..
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*
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* =====================================================================
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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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* .. Local Scalars ..
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COMPLEX*16 TEMP
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INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
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LOGICAL NOCONJ
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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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*
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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(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
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+ .NOT.LSAME(TRANS,'C')) THEN
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INFO = 1
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ELSE IF (M.LT.0) THEN
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INFO = 2
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ELSE IF (N.LT.0) THEN
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INFO = 3
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ELSE IF (LDA.LT.MAX(1,M)) THEN
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INFO = 6
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ELSE IF (INCX.EQ.0) THEN
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INFO = 8
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ELSE IF (INCY.EQ.0) THEN
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INFO = 11
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('ZGEMV ',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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NOCONJ = LSAME(TRANS,'T')
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*
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* Set LENX and LENY, the lengths of the vectors x and y, and set
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* up the start points in X and Y.
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*
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IF (LSAME(TRANS,'N')) THEN
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LENX = N
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LENY = M
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ELSE
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LENX = M
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LENY = N
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END IF
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IF (INCX.GT.0) THEN
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KX = 1
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ELSE
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KX = 1 - (LENX-1)*INCX
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END IF
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IF (INCY.GT.0) THEN
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KY = 1
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ELSE
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KY = 1 - (LENY-1)*INCY
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END IF
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*
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* Start the operations. In this version the elements of A are
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* accessed sequentially with one pass through A.
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*
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* First form y := beta*y.
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*
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IF (BETA.NE.ONE) THEN
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IF (INCY.EQ.1) THEN
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IF (BETA.EQ.ZERO) THEN
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DO 10 I = 1,LENY
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Y(I) = ZERO
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10 CONTINUE
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ELSE
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DO 20 I = 1,LENY
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Y(I) = BETA*Y(I)
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20 CONTINUE
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END IF
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ELSE
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IY = KY
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IF (BETA.EQ.ZERO) THEN
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DO 30 I = 1,LENY
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Y(IY) = ZERO
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IY = IY + INCY
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30 CONTINUE
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ELSE
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DO 40 I = 1,LENY
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Y(IY) = BETA*Y(IY)
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IY = IY + INCY
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40 CONTINUE
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END IF
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END IF
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END IF
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IF (ALPHA.EQ.ZERO) RETURN
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form y := alpha*A*x + y.
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*
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JX = KX
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IF (INCY.EQ.1) THEN
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DO 60 J = 1,N
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TEMP = ALPHA*X(JX)
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DO 50 I = 1,M
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Y(I) = Y(I) + TEMP*A(I,J)
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50 CONTINUE
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JX = JX + INCX
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60 CONTINUE
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ELSE
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DO 80 J = 1,N
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TEMP = ALPHA*X(JX)
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IY = KY
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DO 70 I = 1,M
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Y(IY) = Y(IY) + TEMP*A(I,J)
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IY = IY + INCY
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70 CONTINUE
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JX = JX + INCX
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80 CONTINUE
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END IF
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ELSE
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*
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* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
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*
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JY = KY
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IF (INCX.EQ.1) THEN
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DO 110 J = 1,N
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TEMP = ZERO
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IF (NOCONJ) THEN
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DO 90 I = 1,M
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TEMP = TEMP + A(I,J)*X(I)
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90 CONTINUE
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ELSE
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DO 100 I = 1,M
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TEMP = TEMP + DCONJG(A(I,J))*X(I)
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100 CONTINUE
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END IF
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Y(JY) = Y(JY) + ALPHA*TEMP
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JY = JY + INCY
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110 CONTINUE
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ELSE
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DO 140 J = 1,N
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TEMP = ZERO
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IX = KX
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IF (NOCONJ) THEN
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DO 120 I = 1,M
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TEMP = TEMP + A(I,J)*X(IX)
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IX = IX + INCX
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120 CONTINUE
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ELSE
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DO 130 I = 1,M
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TEMP = TEMP + DCONJG(A(I,J))*X(IX)
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IX = IX + INCX
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130 CONTINUE
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END IF
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Y(JY) = Y(JY) + ALPHA*TEMP
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JY = JY + INCY
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140 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 ZGEMV .
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*
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END
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