F06QVF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06QVF

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

F06QVF transforms a real upper triangular matrix to an upper Hessenberg matrix by applying a given sequence of plane rotations.

2  Specification

SUBROUTINE F06QVF ( SIDE, N, K1, K2, C, S, A, LDA)
INTEGER  N, K1, K2, LDA
REAL (KIND=nag_wp)  C(*), S(*), A(LDA,*)
CHARACTER(1)  SIDE

3  Description

F06QVF transforms an n by n real upper triangular matrix U to an upper Hessenberg matrix H, by applying a given sequence of plane rotations from either the left or the right, in planes k1 to k2; H has nonzero subdiagonal elements hk+1,k, for k=k1,,k2-1 only.
If SIDE='L', the rotations are applied from the left:
H=PU ,
where P = Pk1 Pk1+1 Pk2-1 .
If SIDE='R', the rotations are applied from the right:
H = UPT ,
where P = Pk2-1 Pk1+1 Pk1 .
In either case, Pk is a rotation in the k,k+1 plane.
The 2 by 2 plane rotation part of Pk has the form
ck sk -sk ck .

4  References

None.

5  Parameters

1:     SIDE – CHARACTER(1)Input
On entry: specifies whether U is operated on from the left or the right.
SIDE='L'
U is pre-multiplied from the left.
SIDE='R'
U is post-multiplied from the right.
Constraint: SIDE='L' or 'R'.
2:     N – INTEGERInput
On entry: n, the order of the matrices U and H.
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
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.
6:     S(*) – REAL (KIND=nag_wp) arrayInput/Output
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.
On exit: Sk holds hk+1,k, the subdiagonal element of H, for k=k1,,k2-1.
7:     A(LDA,*) – REAL (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 part of the upper Hessenberg matrix H.
8:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06QVF is called.
Constraint: LDA max1,N .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06QVF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

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