# dspr2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dspr2** (UPLO, **N**, ALPHA, X, INCX, Y, INCY, AP)**DSPR2**

## Function/Subroutine Documentation

### subroutine dspr2 (character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) Y, integer INCY, double precision, dimension(*) AP)

**DSPR2**

**Purpose:**

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

**Parameters:***UPLO*UPLO is 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.

*N*N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.

*ALPHA*ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.

*X*X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.

*INCX*INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

*Y*Y is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y.

*INCY*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

*AP*AP is DOUBLE PRECISION array, 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.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**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.

Definition at line 144 of file dspr2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dspr2(3) is an alias of dspr2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK