F06TTF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06TTF

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
    10  Example

1  Purpose

F06TTF performs a QR or RQ factorization of the product of a complex upper triangular matrix and a complex matrix of plane rotations.

2  Specification

SUBROUTINE F06TTF ( SIDE, N, K1, K2, C, S, A, LDA)
INTEGER  N, K1, K2, LDA
REAL (KIND=nag_wp)  C(*)
COMPLEX (KIND=nag_wp)  S(*), A(LDA,*)
CHARACTER(1)  SIDE

3  Description

F06TTF performs one of the transformations
RPUQH   or   RQUPH ,  
where U is a given n by n complex upper triangular matrix, P is a given complex unitary matrix, and Q is a complex unitary matrix chosen to make R upper triangular. Both P and Q are represented as sequences of plane rotations in planes k1 to k2.
If SIDE='L',
RPUQH ,  
where P= Pk2-1 Pk1+1 Pk1  and Q= Qk2-1 Qk1+1 Qk1 .
If SIDE='R',
RQUPH ,  
where P=Pk1 Pk1+1 Pk2-1  and Q= Qk1 Qk1+1 Qk2-1 .
In either case Pk and Qk are rotations in the k,k+1 plane.
The 2 by 2 rotation part of Pk or Qk has the form
ck s-k -sk ck  
with ck real.

4  References

None.

5  Parameters

1:     SIDE – CHARACTER(1)Input
On entry: specifies whether P is applied from the left or the right in the transformation.
SIDE='L'
P is applied from the left.
SIDE='R'
P is applied from the right.
Constraint: SIDE='L' or 'R'.
2:     N – INTEGERInput
On entry: n, the order of the matrices U and R.
Constraint: N0.
3:     K1 – INTEGERInput
4:     K2 – INTEGERInput
On entry: the values k1 and k2.
If K1<1 or K2K1 or K2>N, an immediate return is effected.
5:     C* – REAL (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array C must be at least K2-K1.
On entry: Ck must hold the cosine of the rotation Pk, for k=k1,,k2-1.
On exit: Ck holds the cosine of the rotation Qk, for k=k1,,k2-1.
6:     S* – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array S must be at least K2-K1.
On entry: Sk must hold the sine of the rotation Pk, for k=k1,,k2-1.
On exit: Sk holds the sine of the rotation Qk, for k=k1,,k2-1.
7:     ALDA* – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least N.
On entry: the n by n upper triangular matrix U.
On exit: the upper triangular matrix R.
8:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06TTF is called.
Constraint: LDA max1,N .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

None.

10  Example

None.

F06TTF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015