F06QMF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06QMF

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

F06QMF performs an orthogonal similarity transformation (as a sequence of plane rotations) of a real symmetric matrix.

2  Specification

SUBROUTINE F06QMF ( UPLO, PIVOT, DIRECT, N, K1, K2, C, S, A, LDA)
INTEGER  N, K1, K2, LDA
REAL (KIND=nag_wp)  C(*), S(*), A(LDA,*)
CHARACTER(1)  UPLO, PIVOT, DIRECT

3  Description

F06QMF performs the transformation
APAPT
where A is an n by n real symmetric matrix, and P is a real orthogonal matrix defined as a sequence of plane rotations, Pk, applied in planes k1 to k2.
The 2 by 2 plane rotation part of Pk is assumed to have the form
ck sk -sk ck .

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:     PIVOT – CHARACTER(1)Input
On entry: specifies the plane rotated by Pk.
PIVOT='V' (variable pivot)
Pk rotates the k,k+1  plane.
PIVOT='T' (top pivot)
Pk rotates the k1,k+1  plane.
PIVOT='B' (bottom pivot)
Pk rotates the k,k2  plane.
Constraint: PIVOT='V', 'T' or 'B'.
3:     DIRECT – CHARACTER(1)Input
On entry: specifies the sequence direction.
DIRECT='F' (forward sequence)
P=Pk2-1Pk1+1Pk1.
DIRECT='B' (backward sequence)
P=Pk1Pk1+1Pk2-1.
Constraint: DIRECT='F' or 'B'.
4:     N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint: N0.
5:     K1 – INTEGERInput
6:     K2 – INTEGERInput
On entry: the values k1 and k2.
If K1<1 or K2K1 or K2>N, an immediate return is effected.
7:     C(*) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array C must be at least K2-K1.
On entry: Ck must hold ck, the cosine of the rotation Pk, for k=k1,,k2-1.
8:     S(*) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array S must be at least K2-K1.
On entry: Sk must hold sk, the sine of the rotation Pk, for k=k1,,k2-1.
9:     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 transformed matrix A.
10:   LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06QMF is called.
Constraint: LDA max1,N .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06QMF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

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