NAME

SSPR2 - performs the symmetric rank 2 operation A := alpha*x*yaq + alpha*y*xaq + A,  

SYNOPSIS

SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)

    
REAL ALPHA

    
INTEGER INCX,INCY,N

    
CHARACTER UPLO

    
REAL AP(*),X(*),Y(*)
 

PURPOSE

SSPR2 performs the symmetric rank 2 operation

where alpha is a scalar, x and y are n element vectors 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 - REAL .
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X - REAL 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.
Y - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.
AP - REAL 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.