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341 lines
9.7 KiB
341 lines
9.7 KiB
2 years ago
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*> \brief \b CSYMV computes a matrix-vector product for a complex symmetric matrix.
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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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*> \htmlonly
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*> Download CSYMV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csymv.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csymv.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csymv.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INCX, INCY, LDA, N
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* COMPLEX ALPHA, BETA
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* ..
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* .. Array Arguments ..
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* COMPLEX 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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*> CSYMV performs the matrix-vector operation
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*>
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*> y := alpha*A*x + beta*y,
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*>
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*> where alpha and beta are scalars, x and y are n element vectors and
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*> A is an n by n symmetric 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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> On entry, UPLO specifies whether the upper or lower
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*> triangular part of the array A is to be referenced as
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*> follows:
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*>
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*> UPLO = 'U' or 'u' Only the upper triangular part of A
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*> is to be referenced.
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*>
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*> UPLO = 'L' or 'l' Only the lower triangular part of A
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*> is to be referenced.
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*>
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*> Unchanged on exit.
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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 order of the matrix A.
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*> N must be at least zero.
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*> Unchanged on exit.
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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
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*> On entry, ALPHA specifies the scalar alpha.
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*> Unchanged on exit.
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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 array, dimension ( LDA, N )
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*> Before entry, with UPLO = 'U' or 'u', the leading n by n
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*> upper triangular part of the array A must contain the upper
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*> triangular part of the symmetric matrix and the strictly
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*> lower triangular part of A is not referenced.
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*> Before entry, with UPLO = 'L' or 'l', the leading n by n
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*> lower triangular part of the array A must contain the lower
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*> triangular part of the symmetric matrix and the strictly
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*> upper triangular part of A is not referenced.
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*> Unchanged on exit.
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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, N ).
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*> Unchanged on exit.
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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 array, dimension at least
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*> ( 1 + ( N - 1 )*abs( INCX ) ).
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*> Before entry, the incremented array X must contain the N-
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*> element vector x.
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*> Unchanged on exit.
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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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*> Unchanged on exit.
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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
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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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*> Unchanged on exit.
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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 array, dimension at least
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*> ( 1 + ( N - 1 )*abs( INCY ) ).
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*> Before entry, the incremented array Y must contain the n
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*> element vector y. On exit, Y is overwritten by the updated
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*> 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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*> Unchanged on exit.
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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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*> \ingroup complexSYauxiliary
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*
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* =====================================================================
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SUBROUTINE CSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK 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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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INCX, INCY, LDA, N
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COMPLEX ALPHA, BETA
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* ..
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* .. Array Arguments ..
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COMPLEX 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 ONE
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PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
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COMPLEX ZERO
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PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
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COMPLEX TEMP1, TEMP2
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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 MAX
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* ..
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* .. Executable Statements ..
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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( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = 1
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ELSE IF( N.LT.0 ) THEN
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INFO = 2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = 5
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ELSE IF( INCX.EQ.0 ) THEN
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INFO = 7
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ELSE IF( INCY.EQ.0 ) THEN
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INFO = 10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CSYMV ', 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( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
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$ RETURN
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*
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* Set up the start points in X and Y.
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*
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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 - ( N-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 - ( N-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 the triangular part
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* of 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, N
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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, N
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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, N
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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, N
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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 )
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$ RETURN
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Form y when A is stored in upper triangle.
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*
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IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
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DO 60 J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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DO 50 I = 1, J - 1
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Y( I ) = Y( I ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + A( I, J )*X( I )
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50 CONTINUE
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Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
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60 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 80 J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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IX = KX
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IY = KY
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DO 70 I = 1, J - 1
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Y( IY ) = Y( IY ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + A( I, J )*X( IX )
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IX = IX + INCX
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IY = IY + INCY
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70 CONTINUE
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Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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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 when A is stored in lower triangle.
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*
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IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
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DO 100 J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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Y( J ) = Y( J ) + TEMP1*A( J, J )
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DO 90 I = J + 1, N
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Y( I ) = Y( I ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + A( I, J )*X( I )
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90 CONTINUE
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Y( J ) = Y( J ) + ALPHA*TEMP2
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100 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 120 J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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Y( JY ) = Y( JY ) + TEMP1*A( J, J )
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IX = JX
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IY = JY
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DO 110 I = J + 1, N
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IX = IX + INCX
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IY = IY + INCY
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Y( IY ) = Y( IY ) + TEMP1*A( I, J )
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TEMP2 = TEMP2 + A( I, J )*X( IX )
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110 CONTINUE
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Y( JY ) = Y( JY ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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120 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 CSYMV
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*
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END
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