DSPR(1)

NAME
LAPACK-3 - performs the symmetric rank 1 operation A := alpha*x*x**T + 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 = '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.

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.