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266 lines
7.5 KiB
266 lines
7.5 KiB
2 years ago
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*> \brief \b CSYR performs the symmetric rank-1 update of 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 CSYR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csyr.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/csyr.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/csyr.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 CSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INCX, LDA, N
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* COMPLEX ALPHA
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* ..
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* .. Array Arguments ..
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* COMPLEX A( LDA, * ), X( * )
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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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*> CSYR performs the symmetric rank 1 operation
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*>
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*> A := alpha*x*x**H + A,
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*>
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*> where alpha is a complex scalar, x is an n element vector and A is an
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*> 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] 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,out] 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. On exit, the
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*> upper triangular part of the array A is overwritten by the
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*> upper triangular part of the updated matrix.
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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. On exit, the
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*> lower triangular part of the array A is overwritten by the
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*> lower triangular part of the updated matrix.
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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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* 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 CSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
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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, LDA, N
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COMPLEX ALPHA
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* ..
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* .. Array Arguments ..
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COMPLEX A( LDA, * ), X( * )
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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 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, J, JX, KX
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COMPLEX TEMP
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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( INCX.EQ.0 ) THEN
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INFO = 5
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = 7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CSYR ', 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 ) )
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$ RETURN
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*
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* Set the start point in X if the increment is not unity.
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*
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IF( INCX.LE.0 ) THEN
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KX = 1 - ( N-1 )*INCX
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ELSE IF( INCX.NE.1 ) THEN
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KX = 1
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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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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Form A when A is stored in upper triangle.
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*
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IF( INCX.EQ.1 ) THEN
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DO 20 J = 1, N
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IF( X( J ).NE.ZERO ) THEN
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TEMP = ALPHA*X( J )
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DO 10 I = 1, J
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A( I, J ) = A( I, J ) + X( I )*TEMP
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10 CONTINUE
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END IF
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20 CONTINUE
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ELSE
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JX = KX
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DO 40 J = 1, N
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IF( X( JX ).NE.ZERO ) THEN
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TEMP = ALPHA*X( JX )
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IX = KX
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DO 30 I = 1, J
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A( I, J ) = A( I, J ) + X( IX )*TEMP
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IX = IX + INCX
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30 CONTINUE
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END IF
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JX = JX + INCX
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40 CONTINUE
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END IF
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ELSE
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*
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* Form A when A is stored in lower triangle.
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*
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IF( INCX.EQ.1 ) THEN
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DO 60 J = 1, N
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IF( X( J ).NE.ZERO ) THEN
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TEMP = ALPHA*X( J )
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DO 50 I = J, N
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A( I, J ) = A( I, J ) + X( I )*TEMP
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50 CONTINUE
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END IF
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60 CONTINUE
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ELSE
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JX = KX
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DO 80 J = 1, N
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IF( X( JX ).NE.ZERO ) THEN
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TEMP = ALPHA*X( JX )
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IX = JX
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DO 70 I = J, N
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A( I, J ) = A( I, J ) + X( IX )*TEMP
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IX = IX + INCX
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70 CONTINUE
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END IF
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JX = JX + INCX
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80 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 CSYR
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*
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END
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