NAG Library Routine Document

f06qmf (dsysrc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{uplo}$ – 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:     $\mathbf{pivot}$ – 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:     $\mathbf{direct}$ – 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:     $\mathbf{n}$ – IntegerInput

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

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

5:     $\mathbf{k1}$ – IntegerInput

6:     $\mathbf{k2}$ – 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:     $\mathbf{c}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array c must be at least $\mathbf{k2}-1$.

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:     $\mathbf{s}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array s must be at least $\mathbf{k2}-1$.

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:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – 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:   $\mathbf{lda}$ – 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

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Accuracy

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Parallelism and Performance

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Further Comments

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Example