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# Technical Reference: Base Operating System and Extensions , Volume 2

## SSPR2 or DSPR2 Subroutine

### Purpose

Performs the symmetric rank 2 operation.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE SSPR2(UPLO, N, ALPHA, X,
INCX, Y, INCY, AP)
REAL ALPHA
INTEGER INCX, INCY, N
CHARACTER*1 UPLO
REAL AP(*), X(*), Y(*)

```SUBROUTINE DSPR2(UPLO, N, ALPHA, X,
INCX, Y, INCY, AP)
DOUBLE PRECISION ALPHA
INTEGER INCX,INCY,N
CHARACTER*1 UPLO
DOUBLE PRECISION AP(*), X(*), Y(*)
```

### Description

The SSPR2 or DSPR2 subroutine performs the symmetric rank 2 operation:

A := alpha * x * y' + alpha * y * x' + 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 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 On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit. ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit. X A vector of dimension at least (1 + (N-1) * abs(INCX) ); on entry, the incremented array X must contain the N element vector x; unchanged on exit. INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit. Y A vector of dimension at least (1 + (N-1) * abs(INCY) ); on entry, the incremented array Y must contain the N element vector y; unchanged on exit. INCY On entry, INCY specifies the increment for the elements of Y; INCY must not be 0; unchanged on exit. AP A vector of dimension at least ( ( N * (N+1) )/2 ); on 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. On 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.

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