*> \brief \b ZSYMV computes a matrix-vector product for a complex symmetric matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INCX, INCY, LDA, N
* COMPLEX*16 ALPHA, BETA
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYMV performs the matrix-vector operation
*>
*> y := alpha*A*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are n element vectors 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] 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.
*> 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.
*> Unchanged on exit.
*> \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
*>
*> \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] BETA
*> \verbatim
*> BETA is COMPLEX*16
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> Unchanged on exit.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is COMPLEX*16 array, dimension at least
*> ( 1 + ( N - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element vector y. On exit, Y is overwritten by the updated
*> vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> Unchanged on exit.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16SYauxiliary
*
* =====================================================================
SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INCX, INCY, LDA, N
COMPLEX*16 ALPHA, BETA
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
COMPLEX*16 TEMP1, TEMP2
* ..
* .. 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( LDA.LT.MAX( 1, N ) ) THEN
INFO = 5
ELSE IF( INCX.EQ.0 ) THEN
INFO = 7
ELSE IF( INCY.EQ.0 ) THEN
INFO = 10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSYMV ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
$ RETURN
*
* Set up the start points in X and Y.
*
IF( INCX.GT.0 ) THEN
KX = 1
ELSE
KX = 1 - ( N-1 )*INCX
END IF
IF( INCY.GT.0 ) THEN
KY = 1
ELSE
KY = 1 - ( N-1 )*INCY
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through the triangular part
* of A.
*
* First form y := beta*y.
*
IF( BETA.NE.ONE ) THEN
IF( INCY.EQ.1 ) THEN
IF( BETA.EQ.ZERO ) THEN
DO 10 I = 1, N
Y( I ) = ZERO
10 CONTINUE
ELSE
DO 20 I = 1, N
Y( I ) = BETA*Y( I )
20 CONTINUE
END IF
ELSE
IY = KY
IF( BETA.EQ.ZERO ) THEN
DO 30 I = 1, N
Y( IY ) = ZERO
IY = IY + INCY
30 CONTINUE
ELSE
DO 40 I = 1, N
Y( IY ) = BETA*Y( IY )
IY = IY + INCY
40 CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
$ RETURN
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Form y when A is stored in upper triangle.
*
IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
DO 60 J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
DO 50 I = 1, J - 1
Y( I ) = Y( I ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + A( I, J )*X( I )
50 CONTINUE
Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
60 CONTINUE
ELSE
JX = KX
JY = KY
DO 80 J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
IX = KX
IY = KY
DO 70 I = 1, J - 1
Y( IY ) = Y( IY ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + A( I, J )*X( IX )
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
80 CONTINUE
END IF
ELSE
*
* Form y when A is stored in lower triangle.
*
IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
DO 100 J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
Y( J ) = Y( J ) + TEMP1*A( J, J )
DO 90 I = J + 1, N
Y( I ) = Y( I ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + A( I, J )*X( I )
90 CONTINUE
Y( J ) = Y( J ) + ALPHA*TEMP2
100 CONTINUE
ELSE
JX = KX
JY = KY
DO 120 J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
Y( JY ) = Y( JY ) + TEMP1*A( J, J )
IX = JX
IY = JY
DO 110 I = J + 1, N
IX = IX + INCX
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + A( I, J )*X( IX )
110 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
120 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZSYMV
*
END