NAG Library Routine Document

f06tqf  (zutupd)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrices $U$ and $R$.

Constraint: $\mathbf{n}\ge 0$.

2:     $\mathbf{alpha}$ – Complex (Kind=nag_wp)Input

On entry: the scalar $\alpha$.

3:     $\mathbf{x}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array x must be at least $\max \left(1,1+\left(\mathbf{n}-1\right)\times \mathbf{incx}\right)$.

On entry: the $n$-element vector $x$. $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left(1+\left(\mathit{i}-1\right)\times \mathbf{incx}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

Intermediate elements of x are not referenced.

On exit: the referenced elements are overwritten by details of the sequence of plane rotations.

4:     $\mathbf{incx}$ – IntegerInput

On entry: the increment in the subscripts of x between successive elements of $x$.

Constraint: $\mathbf{incx}>0$.

5:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array a must be at least $\mathbf{n}$.

On entry: the $n$ by $n$ upper triangular matrix $U$.

On exit: the upper triangular matrix $R$.

6:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06tqf is called.

Constraint: $\mathbf{lda}\ge \max \left(1,\mathbf{n}\right)$.

7:     $\mathbf{c}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the values $c_{\mathit{k}}$, the cosines of the rotations $Q_{\mathit{k}}$, for $\mathit{k}=1,2,\dots ,n$.

8:     $\mathbf{s}\left(\mathbf{n}\right)$ – Complex (Kind=nag_wp) arrayOutput

On exit: the values $s_{\mathit{k}}$, the sines of the rotations $Q_{\mathit{k}}$, for $\mathit{k}=1,2,\dots ,n$.

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example