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AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2

## SSPMV or DSPMV Subroutine

### Purpose

Performs matrix-vector operations using a packed symmetric matrix.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

```SUBROUTINE SSPMV(UPLO, N, ALPHA, AP, X,
INCX, BETA, Y, INCY)
REAL ALPHA,BETA
INTEGER INCX,INCY,N
CHARACTER*1 UPLO
REAL AP(*), X(*), Y(*)```
```SUBROUTINE DSPMV(UPLO, N, ALPHA, AP, X,
INCX, BETA, Y, INCY)
DOUBLE PRECISION ALPHA,BETA
INTEGER INCX,INCY,N
CHARACTER*1 UPLO
DOUBLE PRECISION AP(*), X(*), Y(*)```

### Description

The SSPMV or DSPMV 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 symmetric 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 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; on 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 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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