Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - performs the matrix-vector operation y := alpha*A*x + beta*y,

**SYNOPSIS**

SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY ) CHARACTER UPLO INTEGER INCX, INCY, LDA, N COMPLEX*16 ALPHA, BETA COMPLEX*16 A( LDA, * ), X( * ), Y( * )

**PURPOSE**

ZSYMV performs the matrix-vector operation where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.

**ARGUMENTS**

UPLO (input) 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. N (input) INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA (input) COMPLEX*16 On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A (input) 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. LDA (input) 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. X (input) 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. INCX (input) INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. BETA (input) 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. Y (input/output) 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. INCY (input) INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. LAPACK auxiliary routine (version 3.2) April 2011 ZSYMV(3lapack)