NAG Library Routine Document

f06prf (dsyr2)

1
Purpose

f06prf (dsyr2) computes the rank-2 update of a real symmetric matrix.

2
Specification

Fortran Interface
Subroutine f06prf ( uplo, n, alpha, x, incx, y, incy, a, lda)
Integer, Intent (In):: n, incx, incy, lda
Real (Kind=nag_wp), Intent (In):: alpha, x(*), y(*)
Real (Kind=nag_wp), Intent (Inout):: a(lda,*)
Character (1), Intent (In):: uplo
C Header Interface
#include <nagmk26.h>
void  f06prf_ (const char *uplo, const Integer *n, const double *alpha, const double x[], const Integer *incx, const double y[], const Integer *incy, double a[], const Integer *lda, const Charlen length_uplo)
The routine may be called by its BLAS name dsyr2.

3
Description

f06prf (dsyr2) performs the symmetric rank-2 update operation
AαxyT + αyxT + A ,  
where A is an n by n real symmetric matrix, 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 – IntegerInput
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) arrayInput
Note: the dimension of the array x must be at least max1, 1+n-1 ×incx .
On entry: the n-element vector x.
If incx>0, xi must be stored in x1+i-1×incx, for i=1,2,,n.
If incx<0, xi must be stored in x1-n-i×incx, for i=1,2,,n.
Intermediate elements of x are not referenced.
5:     incx – IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
6:     y* – Real (Kind=nag_wp) arrayInput
Note: the dimension of the array y must be at least max1, 1+n-1 ×incy .
On entry: the n-element vector y.
If incy>0, yi must be stored in y1+i-1×incy, for i=1,2,,n.
If incy<0, yi must be stored in y1-n-i×incy, for i=1,2,,n.
Intermediate elements of y are not referenced.
7:     incy – IntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
8:     alda* – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a must be at least max1,n.
On entry: the n by n symmetric matrix A.
  • If uplo='U', the upper triangular part of A must be stored and the elements of the array below the diagonal are not referenced.
  • If uplo='L', the lower triangular part of A must be stored and the elements of the array above the diagonal are not referenced.
On exit: the updated matrix A.
9:     lda – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06prf (dsyr2) is called.
Constraint: lda max1,n .

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06prf (dsyr2) is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.