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Technical Reference: Base Operating System and Extensions , Volume 2
Performs the symmetric rank 2
operation.
BLAS Library
(libblas.a)
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(*)
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.
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 + (N1) *
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 + (N1) *
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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