NAG Library Routine Document

F08QTF (ZTREXC)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

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

On entry: indicates whether the matrix $Q$ of Schur vectors is to be updated.

$\mathbf{COMPQ}=\text{'V'}$

The matrix $Q$ of Schur vectors is updated.

$\mathbf{COMPQ}=\text{'N'}$

No Schur vectors are updated.

Constraint: $\mathbf{COMPQ}=\text{'V'}$ or $\text{'N'}$.

2:     $\mathrm{N}$ – INTEGERInput

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

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

3:     $\mathrm{T}\left(\mathbf{LDT},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the $n$ by $n$ upper triangular matrix $T$, as returned by F08PSF (ZHSEQR).

On exit: T is overwritten by the updated matrix $\tilde{T}$.

4:     $\mathrm{LDT}$ – INTEGERInput

On entry: the first dimension of the array T as declared in the (sub)program from which F08QTF (ZTREXC) is called.

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

5:     $\mathrm{Q}\left(\mathbf{LDQ},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array Q must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{COMPQ}=\text{'V'}$ and at least $1$ if $\mathbf{COMPQ}=\text{'N'}$.

On entry: if $\mathbf{COMPQ}=\text{'V'}$, Q must contain the $n$ by $n$ unitary matrix $Q$ of Schur vectors.

On exit: if $\mathbf{COMPQ}=\text{'V'}$, Q contains the updated matrix of Schur vectors.

If $\mathbf{COMPQ}=\text{'N'}$, Q is not referenced.

6:     $\mathrm{LDQ}$ – INTEGERInput

On entry: the first dimension of the array Q as declared in the (sub)program from which F08QTF (ZTREXC) is called.

Constraints:

• if $\mathbf{COMPQ}=\text{'V'}$, $\mathbf{LDQ}\ge \max \left(1,\mathbf{N}\right)$;
• if $\mathbf{COMPQ}=\text{'N'}$, $\mathbf{LDQ}\ge 1$.

7:     $\mathrm{IFST}$ – INTEGERInput

8:     $\mathrm{ILST}$ – INTEGERInput

On entry: IFST and ILST must specify the reordering of the diagonal elements of $T$. The element with row index IFST is moved to row ILST by a sequence of exchanges between adjacent elements.

Constraint: $1\le \mathbf{IFST}\le \mathbf{N}$ and $1\le \mathbf{ILST}\le \mathbf{N}$.

9:     $\mathrm{INFO}$ – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f08qtfe.f90)

10.2  Program Data

Program Data (f08qtfe.d)

10.3  Program Results

Program Results (f08qtfe.r)