NAG Library Routine Document

f06qvf  (dutsrh)

 Contents

    1  Purpose
    7  Accuracy
    10  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

Fortran Interface
Subroutine f06qvf ( side, n, k1, k2, c, s, a, lda)
Integer, Intent (In):: n, k1, k2, lda
Real (Kind=nag_wp), Intent (In):: c(*)
Real (Kind=nag_wp), Intent (Inout):: s(*), a(lda,*)
Character (1), Intent (In):: side
C Header Interface
#include nagmk26.h
void  f06qvf_ ( const char *side, const Integer *n, const Integer *k1, const Integer *k2, const double c[], double s[], double a[], const Integer *lda, const Charlen length_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
Arguments

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 k2-1.
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 k2-1.
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:     alda* – 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
Parallelism and Performance

f06qvf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017