NAG Library Routine Document

F06TMF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     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:     N – INTEGERInput

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

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

5:     K1 – INTEGERInput

6:     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:     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 $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

8:     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 $\mathit{k}={\mathit{k}}_1,\dots ,{\mathit{k}}_2-1$.

9:     A(LDA,$*$) – COMPLEX (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 $n$ Hermitian 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 $A$. The imaginary parts of the diagonal elements are set to zero.

10:   LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06TMF is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example