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*> \brief \b ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZSYR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsyr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsyr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsyr.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INCX, LDA, N
* COMPLEX*16 ALPHA
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), X( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYR performs the symmetric rank 1 operation
*>
*> A := alpha*x*x**H + A,
*>
*> where alpha is a complex scalar, x is an n element vector and A is an
*> n by n symmetric matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the upper or lower
*> triangular part of the array A is to be referenced as
*> follows:
*>
*> UPLO = 'U' or 'u' Only the upper triangular part of A
*> is to be referenced.
*>
*> UPLO = 'L' or 'l' Only the lower triangular part of A
*> is to be referenced.
*>
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is COMPLEX*16
*> On entry, ALPHA specifies the scalar alpha.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is COMPLEX*16 array, dimension at least
*> ( 1 + ( N - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the N-
*> element vector x.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension ( LDA, N )
*> Before entry, with UPLO = 'U' or 'u', the leading n by n
*> upper triangular part of the array A must contain the upper
*> triangular part of the symmetric matrix and the strictly
*> lower triangular part of A is not referenced. On exit, the
*> upper triangular part of the array A is overwritten by the
*> upper triangular part of the updated matrix.
*> Before entry, with UPLO = 'L' or 'l', the leading n by n
*> lower triangular part of the array A must contain the lower
*> triangular part of the symmetric matrix and the strictly
*> upper triangular part of A is not referenced. On exit, the
*> lower triangular part of the array A is overwritten by the
*> lower triangular part of the updated matrix.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> max( 1, N ).
*> Unchanged on exit.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16SYauxiliary
*
* =====================================================================
SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INCX, LDA, N
COMPLEX*16 ALPHA
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), X( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, IX, J, JX, KX
COMPLEX*16 TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = 1
ELSE IF( N.LT.0 ) THEN
INFO = 2
ELSE IF( INCX.EQ.0 ) THEN
INFO = 5
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = 7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSYR ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
$ RETURN
*
* Set the start point in X if the increment is not unity.
*
IF( INCX.LE.0 ) THEN
KX = 1 - ( N-1 )*INCX
ELSE IF( INCX.NE.1 ) THEN
KX = 1
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through the triangular part
* of A.
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Form A when A is stored in upper triangle.
*
IF( INCX.EQ.1 ) THEN
DO 20 J = 1, N
IF( X( J ).NE.ZERO ) THEN
TEMP = ALPHA*X( J )
DO 10 I = 1, J
A( I, J ) = A( I, J ) + X( I )*TEMP
10 CONTINUE
END IF
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1, N
IF( X( JX ).NE.ZERO ) THEN
TEMP = ALPHA*X( JX )
IX = KX
DO 30 I = 1, J
A( I, J ) = A( I, J ) + X( IX )*TEMP
IX = IX + INCX
30 CONTINUE
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
*
* Form A when A is stored in lower triangle.
*
IF( INCX.EQ.1 ) THEN
DO 60 J = 1, N
IF( X( J ).NE.ZERO ) THEN
TEMP = ALPHA*X( J )
DO 50 I = J, N
A( I, J ) = A( I, J ) + X( I )*TEMP
50 CONTINUE
END IF
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1, N
IF( X( JX ).NE.ZERO ) THEN
TEMP = ALPHA*X( JX )
IX = JX
DO 70 I = J, N
A( I, J ) = A( I, J ) + X( IX )*TEMP
IX = IX + INCX
70 CONTINUE
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZSYR
*
END
|
