NAG Library Routine Document

f06twf (zutsrs)

1
Purpose

f06twf transforms a complex upper triangular matrix to an upper spiked matrix by applying a given sequence of plane rotations.

2
Specification

Fortran Interface
Subroutine f06twf ( side, n, k1, k2, c, s, a, lda)
Integer, Intent (In):: n, k1, k2, lda
Real (Kind=nag_wp), Intent (In):: c(*)
Complex (Kind=nag_wp), Intent (Inout):: s(*), a(lda,*)
Character (1), Intent (In):: side
C Header Interface
#include <nagmk26.h>
void  f06twf_ (const char *side, const Integer *n, const Integer *k1, const Integer *k2, const double c[], Complex s[], Complex a[], const Integer *lda, const Charlen length_side)

3
Description

f06twf transforms an n by n complex upper triangular matrix U with real diagonal elements, to an upper spiked matrix H, by applying a given sequence of plane rotations from either the left or the right, in planes k1 to k2. H has real diagonal elements except where the spike joins the diagonal.
If side='L', H has a row spike, with nonzero elements h k2,k , for k = k1 , k1+1, , k2-1 . The rotations are applied from the left:
H=PU ,  
where P = Pk1 Pk1+1 Pk2-1  and Pk is a rotation in the k,k2 plane.
If side='R', H has a column spike, with nonzero elements h k+1, k1 , for k= k1, k1+1, , k2-1 . The rotations are applied from the right:
HPH = R ,  
where P = Pk2-1 Pk1+1 Pk1  and Pk is a rotation in the k1,k+1 plane.
The 2 by 2 plane rotation part of Pk has the form
ck s-k -sk ck  
with ck real.

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* – Complex (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 a nonzero element of the spike of H: hk2,k if side='L', or hk+1,k1 if side='R', 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. The imaginary parts of the diagonal elements must be zero.
On exit: the upper triangular part of the upper spiked matrix H. The imaginary parts of the diagonal elements are set to zero except for the k2,k2  element if side='L', or the k1,k1  element if side='R'.
8:     lda – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06twf is called.
Constraint: lda max1,n .

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06twf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.