NAME

dspr - perform the symmetric rank 1 operation   A := alpha∗x∗x’ + A

SYNOPSIS

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

void dspr(char uplo, long int n, double alpha,
double ∗dx, long int incx, double ∗ap)

DOUBLE PRECISION ALPHA

INTEGER INCX, N

CHARACTER∗1 UPLO

DOUBLE PRECISION AP( ∗ ), X( ∗ )

PURPOSE

DSPR    performs the symmetric rank 1 operation A := alpha∗x∗x’ + A 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. 
 

PARAMETERS

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.

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.

Sun, Inc.  —  Last change: 20 Sep 1996