F06PRF (DSYR2) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06PRF (DSYR2)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F06PRF (DSYR2) computes the rank-2 update of a real symmetric matrix.

2  Specification

SUBROUTINE F06PRF ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
INTEGER  N, INCX, INCY, LDA
REAL (KIND=nag_wp)  ALPHA, X(*), Y(*), A(LDA,*)
CHARACTER(1)  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  Parameters

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:     A(LDA,*) – 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  Further Comments

None.

9  Example

None.

F06PRF (DSYR2) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012