NAG FL Interface
f06tvf (zutsrh)

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1 Purpose

f06tvf transforms a complex upper triangular matrix to an upper Hessenberg matrix by applying a given sequence of plane rotations.

2 Specification

Fortran Interface
Subroutine f06tvf ( side, n, k1, k2, c, s, a, lda)
Integer, Intent (In) :: n, k1, k2, lda
Real (Kind=nag_wp), Intent (Inout) :: s(*)
Complex (Kind=nag_wp), Intent (In) :: c(*)
Complex (Kind=nag_wp), Intent (Inout) :: a(lda,*)
Character (1), Intent (In) :: side
C Header Interface
#include <nag.h>
void  f06tvf_ (const char *side, const Integer *n, const Integer *k1, const Integer *k2, const Complex c[], double s[], Complex a[], const Integer *lda, const Charlen length_side)
The routine may be called by the names f06tvf or nagf_blas_zutsrh.

3 Description

f06tvf transforms an n×n complex upper triangular matrix U with real diagonal elements, 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 real 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 = UPH ,  
where P = Pk2-1 Pk1+1 Pk1 .
In either case, Pk is a rotation in the (k,k+1) plane.
The 2×2 plane rotation part of Pk has the form
( c¯k sk -sk ck )  
with sk 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 Integer Input
On entry: n, the order of the matrices U and H.
Constraint: n0.
3: k1 Integer Input
4: k2 Integer Input
On entry: the values k1 and k2.
If k1<1 or k2k1 or k2>n, an immediate return is effected.
5: c(*) Complex (Kind=nag_wp) array Input
Note: the dimension of the array c must be at least k2-1.
On entry: c(k) must hold ck, the cosine of the rotation Pk, for k=k1,,k2-1.
6: s(*) Real (Kind=nag_wp) array Input/Output
Note: the dimension of the array s must be at least k2-1.
On entry: s(k) must hold sk, the sine of the rotation Pk, for k=k1,,k2-1.
On exit: s(k) holds hk+1,k, the subdiagonal element of H, for k=k1,,k2-1.
7: a(lda,*) Complex (Kind=nag_wp) array Input/Output
Note: the second dimension of the array a must be at least n.
On entry: the n×n upper triangular matrix U. The imaginary parts of the diagonal elements must be zero.
On exit: the upper triangular part of the upper Hessenberg matrix H.
8: lda Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f06tvf is called.
Constraint: lda max(1,n) .

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f06tvf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.