This manual relates to an old release of the Library.
The documentation for the current release is also available on this site.

NAG FL Interface
f06psf (dspr2)

Settings help

FL Name Style:


FL Specification Language:


1 Purpose

f06psf computes the rank-2 update of a real symmetric matrix stored in packed form.

2 Specification

Fortran Interface
Subroutine f06psf ( uplo, n, alpha, x, incx, y, incy, ap)
Integer, Intent (In) :: n, incx, incy
Real (Kind=nag_wp), Intent (In) :: alpha, x(*), y(*)
Real (Kind=nag_wp), Intent (Inout) :: ap(*)
Character (1), Intent (In) :: uplo
C Header Interface
#include <nag.h>
void  f06psf_ (const char *uplo, const Integer *n, const double *alpha, const double x[], const Integer *incx, const double y[], const Integer *incy, double ap[], const Charlen length_uplo)
The routine may be called by the names f06psf, nagf_blas_dspr2 or its BLAS name dspr2.

3 Description

f06psf performs the symmetric rank-2 update operation
AαxyT + αyxT + A ,  
where A is an n×n real symmetric matrix, stored in packed form, x and y are n-element real vectors, and α is a real scalar.

4 References

None.

5 Arguments

1: uplo Character(1) Input
On entry: specifies whether the upper or lower triangular part of A is stored.
uplo='U'
The upper triangular part of A is stored.
uplo='L'
The lower triangular part of A is stored.
Constraint: uplo='U' or 'L'.
2: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
3: alpha Real (Kind=nag_wp) Input
On entry: the scalar α.
4: x(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array x must be at least max(1, 1+(n-1) ×|incx| ) .
On entry: the n-element vector x.
If incx>0, xi must be stored in x(1+(i-1)×incx), for i=1,2,,n.
If incx<0, xi must be stored in x(1-(n-i)×incx), for i=1,2,,n.
Intermediate elements of x are not referenced.
5: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
6: y(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array y must be at least max(1, 1+(n-1) ×|incy| ) .
On entry: the n-element vector y.
If incy>0, yi must be stored in y(1+(i-1)×incy), for i=1,2,,n.
If incy<0, yi must be stored in y(1-(n-i)×incy), for i=1,2,,n.
Intermediate elements of y are not referenced.
7: incy Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
8: ap(*) Real (Kind=nag_wp) array Input/Output
Note: the dimension of the array ap must be at least n× (n+1)/2 .
On entry: the n×n symmetric matrix A, packed by columns.
More precisely,
  • if uplo='U', the upper triangle of A must be stored with element Aij in ap(i+j(j-1)/2) for ij;
  • if uplo='L', the lower triangle of A must be stored with element Aij in ap(i+(2n-j)(j-1)/2) for ij.
On exit: the updated matrix A.

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f06psf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.