NAG Library Routine Document

F06QRF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     SIDE – CHARACTER(1)Input

On entry: specifies whether $H$ is operated on from the left or the right.

$\mathbf{SIDE}=\text{'L'}$

$H$ is pre-multiplied from the left.

$\mathbf{SIDE}=\text{'R'}$

$H$ is post-multiplied from the right.

Constraint: $\mathbf{SIDE}=\text{'L'}$ or $\text{'R'}$.

2:     N – INTEGERInput

On entry: $n$, the order of the matrix $H$.

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

3:     K1 – INTEGERInput

4:     K2 – INTEGERInput

On entry: the values $k_1$ and $k_2$.

If $\mathbf{K1}<1$ or $\mathbf{K2}\le \mathbf{K1}$ or $\mathbf{K2}>\mathbf{N}$, an immediate return is effected.

5:     C($\mathbf{K2}-1$) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{C}\left(\mathit{k}\right)$ holds $c_{\mathit{k}}$, the cosine of the rotation $P_{\mathit{k}}$, for $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

6:     S($\mathbf{K2}-1$) – REAL (KIND=nag_wp) arrayInput/Output

On entry: the nonzero subdiagonal elements of $H$: $\mathbf{S}\left(\mathit{k}\right)$ must hold $h_{\mathit{k}+1,\mathit{k}}$, for $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

On exit: $\mathbf{S}\left(\mathit{k}\right)$ holds $s_{\mathit{k}}$, the sine of the rotation $P_{\mathit{k}}$, for $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

7:     A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput/Output

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

On entry: the upper triangular part of the $n$ by $n$ upper Hessenberg matrix $H$.

On exit: the upper triangular matrix $R$.

8:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06QRF is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example