NAG Library Routine Document

F06QMF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{UPLO}$ – CHARACTER(1)Input

On entry: specifies whether the upper or lower triangular part of $A$ is stored.

$\mathbf{UPLO}=\text{'U'}$

The upper triangular part of $A$ is stored.

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

The lower triangular part of $A$ is stored.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

2:     $\mathrm{PIVOT}$ – 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:     $\mathrm{DIRECT}$ – 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:     $\mathrm{N}$ – INTEGERInput

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

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

5:     $\mathrm{K1}$ – INTEGERInput

6:     $\mathrm{K2}$ – 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.

7:     $\mathrm{C}\left(*\right)$ – 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 $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

8:     $\mathrm{S}\left(*\right)$ – REAL (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 $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

9:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the $n$ by $n$ symmetric matrix $A$.

• If $\mathbf{UPLO}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: the transformed matrix $A$.

10:   $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06QMF is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example