NAME¶

DSPR2 - performs the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A,

SYNOPSIS¶

SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)

DOUBLE PRECISION ALPHA INTEGER INCX,INCY,N CHARACTER UPLO DOUBLE PRECISION AP(*),X(*),Y(*)

PURPOSE¶

DSPR2 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 = '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 - 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.

Y - DOUBLE PRECISION 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 - DOUBLE PRECISION array of DIMENSION at least

( ( n*( n + 1 ) )/2 ). Before 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 exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before 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. 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.