dspr2 (l)  Linux Manuals
dspr2: performs the symmetric rank 2 operation A := alpha*x*yaq + alpha*y*xaq + A,
NAME
DSPR2  performs the symmetric rank 2 operation A := alpha*x*yaq + alpha*y*xaq + 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 = 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.
 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 = 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 22October1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.