NAG Library Routine Document

F06TXF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     SIDE – CHARACTER(1)Input

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

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

$A$ is pre-multiplied from the left.

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

$A$ is post-multiplied from the right.

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

2:     PIVOT – CHARACTER(1)Input

On entry: specifies the plane rotated by $P_k$.

$\mathbf{PIVOT}=\text{'V'}$ (variable pivot)

$P_k$ rotates the $\left(k,k+1\right)$ plane.

$\mathbf{PIVOT}=\text{'T'}$ (top pivot)

$P_k$ rotates the $\left(k_1,k+1\right)$ plane.

$\mathbf{PIVOT}=\text{'B'}$ (bottom pivot)

$P_k$ rotates the $\left(k,k_2\right)$ plane.

Constraint: $\mathbf{PIVOT}=\text{'V'}$, $\text{'T'}$ or $\text{'B'}$.

3:     DIRECT – CHARACTER(1)Input

On entry: specifies the sequence direction.

$\mathbf{DIRECT}=\text{'F'}$ (forward sequence)

$P=P_{k_2-1}\cdots P_{k_1+1}{P}_{k_1}$.

$\mathbf{DIRECT}=\text{'B'}$ (backward sequence)

$P=P_{k_1}{P}_{k_1+1}\cdots P_{k_2-1}$.

Constraint: $\mathbf{DIRECT}=\text{'F'}$ or $\text{'B'}$.

4:     M – INTEGERInput

On entry: $m$, the number of rows of the matrix $A$.

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

5:     N – INTEGERInput

On entry: $n$, the number of columns of the matrix $A$.

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

6:     K1 – INTEGERInput

7:     K2 – INTEGERInput

On entry: the values $k_1$ and $k_2$.

If $\mathbf{K1}<1$ or $\mathbf{K2}\le \mathbf{K1}$, or $\mathbf{SIDE}=\text{'L'}$ and $\mathbf{K2}>\mathbf{M}$, or $\mathbf{SIDE}=\text{'R'}$ and $\mathbf{K2}>\mathbf{N}$, an immediate return is effected.

8:     C($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array C must be at least $\mathbf{K2}-\mathbf{K1}$.

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

9:     S($*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the dimension of the array S must be at least $\mathbf{K2}-\mathbf{K1}$.

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

10:   A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the $m$ by $n$ matrix $A$.

On exit: the transformed matrix $A$.

11:   LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06TXF is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example