# dspr (l) - Linux Manuals

## NAME

DSPR - performs the symmetric rank 1 operation A := alpha*x*xaq + A,

## SYNOPSIS

SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)

DOUBLE PRECISION ALPHA

INTEGER INCX,N

CHARACTER UPLO

DOUBLE PRECISION AP(*),X(*)

## PURPOSE

DSPR performs the symmetric rank 1 operation

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form.

## ARGUMENTS

UPLO - 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 = aqUaq or aquaq The upper triangular part of A is supplied in AP.

UPLO = aqLaq or aqlaq The lower triangular part of A is supplied in AP.

Unchanged on exit.

N - INTEGER.
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X - DOUBLE PRECISION array of 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 - INTEGER.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
AP - DOUBLE PRECISION array of DIMENSION at least
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = aqUaq or aquaq, 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 exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = aqLaq or aqlaq, 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. On exit, the array AP is overwritten by the lower triangular part of the updated matrix.

## FURTHER DETAILS

Level 2 Blas routine.

-- Written on 22-October-1986.

Jack Dongarra, Argonne National Lab.

Jeremy Du Croz, Nag Central Office.

Sven Hammarling, Nag Central Office.

Richard Hanson, Sandia National Labs.