# cspmv.f - Man Page

SRC/cspmv.f

## Synopsis

### Functions/Subroutines

subroutine **cspmv** (uplo, n, alpha, ap, x, incx, beta, y, incy)**CSPMV** computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

## Function/Subroutine Documentation

### subroutine cspmv (character uplo, integer n, complex alpha, complex, dimension( * ) ap, complex, dimension( * ) x, integer incx, complex beta, complex, dimension( * ) y, integer incy)

**CSPMV** computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

**Purpose:**

CSPMV 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, supplied in packed form.

**Parameters***UPLO*UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP. Unchanged on exit.

*N*N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.

*ALPHA*ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*AP*AP is COMPLEX array, dimension at least ( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry, with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Unchanged on exit.

*X*X is COMPLEX 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*INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

*BETA*BETA is COMPLEX 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*Y is COMPLEX 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*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **150** of file **cspmv.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cspmv(3) is an alias of cspmv.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK