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# Technical Reference: Base Operating System and Extensions , Volume 2

## SSYMV or DSYMV Subroutine

### Purpose

Performs matrix-vector operations using a symmetric matrix.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE SSYMV(UPLO, N, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
REAL ALPHA, BETA
INTEGER INCX, INCY, LDA, N
CHARACTER*1 UPLO
REAL A(LDA,*), X(*), Y(*)

```SUBROUTINE DSYMV(UPLO, N, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
DOUBLE PRECISION ALPHA,BETA
INTEGER INCX,INCY,LDA,N
CHARACTER*1 UPLO
DOUBLE PRECISION A(LDA,*), X(*), Y(*)
```

### Description

The SSYMV or DSYMV 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.

### Parameters

 UPLO 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 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. A An array of dimension ( LDA, N ); on 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; the strictly lower triangular part of A is not referenced; on 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; the strictly upper triangular part of A is not referenced; unchanged on exit. LDA 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 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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