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Technical Reference: Base Operating System and Extensions , Volume 2

CHPMV or ZHPMV Subroutine

Purpose

Performs matrix-vector operations using a packed Hermitian matrix.

Library

BLAS Library (libblas.a)

FORTRAN Syntax

SUBROUTINE CHPMV(UPLO, N, ALPHA, AP, X,
INCX, BETA, Y, INCY)
COMPLEX ALPHA, BETA
INTEGER INCX, INCY, N
CHARACTER*1 UPLO
COMPLEX AP(*), X(*), Y(*)

```SUBROUTINE ZHPMV
COMPLEX*16 ALPHA,BETA
INTEGER INCX,INCY,N
CHARACTER*1 UPLO
COMPLEX*16 AP(*), X(*), Y(*)
```

Description

The CHPMV or ZHPMV subroutine 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 Hermitian matrix, supplied in packed form.

Parameters

 UPLO 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 On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit. ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit. AP A vector of dimension at least ( ( N * (N+1) )/2 ); on entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the Hermitian 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; on entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the Hermitian 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. The imaginary parts of the diagonal elements need not be set and are assumed to be 0; unchanged on exit. X A vector of dimension at least (1 + (N-1) * abs( INCX ) ); on entry, the incremented array X must contain the N element vector x; unchanged on exit. INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit. BETA On entry, BETA specifies the scalar beta; when BETA is supplied as 0 then Y need not be set on input; unchanged on exit. Y A vector of dimension at least (1 + (N-1) * abs( INCY ) ); on entry, the incremented array Y must contain the N element vector y; on exit, Y is overwritten by the updated vector y. INCY On entry, INCY specifies the increment for the elements of Y; INCY must not be 0; unchanged on exit.

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