NAG Toolbox: nag_lapack_ztrexc (f08qt)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{compq}$ – string (length ≥ 1)

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:     $\mathrm{t}\left(\mathit{ldt},:\right)$ – complex array

The first dimension of the array t must be at least $\max \left(1,\mathbf{n}\right)$.

The second dimension of the array t must be at least $\max \left(1,\mathbf{n}\right)$.

The $n$ by $n$ upper triangular matrix $T$, as returned by nag_lapack_zhseqr (f08ps).

3:     $\mathrm{q}\left(\mathit{ldq},:\right)$ – complex array

The first dimension, $\mathit{ldq}$, of the array q must satisfy

• if $\mathbf{compq}=\text{'V'}$, $\mathit{ldq}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{compq}=\text{'N'}$, $\mathit{ldq}\ge 1$.

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 $\mathbf{compq}=\text{'N'}$.

If $\mathbf{compq}=\text{'V'}$, q must contain the $n$ by $n$ unitary matrix $Q$ of Schur vectors.

4:     $\mathrm{ifst}$ – int64int32nag_int scalar

5:     $\mathrm{ilst}$ – int64int32nag_int scalar

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 $1\le \mathbf{ilst}\le \mathbf{n}$.

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the first dimension of the array t and the second dimension of the array t. (An error is raised if these dimensions are not equal.)

$n$, the order of the matrix $T$.

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

Output Parameters

1:     $\mathrm{t}\left(\mathit{ldt},:\right)$ – complex array

The first dimension of the array t will be $\max \left(1,\mathbf{n}\right)$.

The second dimension of the array t will be $\max \left(1,\mathbf{n}\right)$.

t stores the updated matrix $\tilde{T}$.

2:     $\mathrm{q}\left(\mathit{ldq},:\right)$ – complex array

The first dimension, $\mathit{ldq}$, of the array q will be

• if $\mathbf{compq}=\text{'V'}$, $\mathit{ldq}=\max \left(1,\mathbf{n}\right)$;
• if $\mathbf{compq}=\text{'N'}$, $\mathit{ldq}=1$.

The second dimension of the array q will be $\max \left(1,\mathbf{n}\right)$ if $\mathbf{compq}=\text{'V'}$ and at least $1$ if $\mathbf{compq}=\text{'N'}$.

If $\mathbf{compq}=\text{'V'}$, q contains the updated matrix of Schur vectors.

If $\mathbf{compq}=\text{'N'}$, q is not referenced.

3:     $\mathrm{info}$ – int64int32nag_int scalar

$\mathbf{info}=0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{info}=-i$

If $\mathbf{info}=-i$, parameter $i$ had an illegal value on entry. The parameters are numbered as follows:

1: compq, 2: n, 3: t, 4: ldt, 5: q, 6: ldq, 7: ifst, 8: ilst, 9: info.

It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f08qt_example

function f08qt_example


fprintf('f08qt example results\n\n');

% Matrix T in real Schur form
t = [-6 - 7i,  0.36 - 0.36i, -0.19 + 0.48i,  0.88 - 0.25i;
      0 + 0i, -5    + 2i,    -0.03 - 0.72i, -0.23 + 0.13i;
      0 + 0i,  0    + 0i,     8    - 1i,     0.94 + 0.53i;
      0 + 0i,  0    + 0i,     0    + 0i,     3    - 4i];

% Reorder Schure form so that the first diagonal element is moved to the last
compq = 'No update';
q    = [complex(0)];
ifst = int64(1);
ilst = int64(4);
[t, q, info] = f08qt( ...
		      compq, t, q, ifst, ilst);

mtitle = 'Reordered Schur Form';
ncols  = int64(80);
indent = int64(0);

[ifail] = x04db( ...
                 'Gen', ' ', t, 'Brac', 'F7.4', mtitle, ...
                 'Int', 'Int', ncols, indent);

f08qt example results

 Reordered Schur Form
                    1                 2                 3                 4
 1  (-5.0000, 2.0000) (-0.1574, 0.7143) ( 0.1781,-0.1913) ( 0.3950, 0.3861)
 2  ( 0.0000, 0.0000) ( 8.0000,-1.0000) ( 1.0742, 0.1447) ( 0.2515,-0.3397)
 3  ( 0.0000, 0.0000) ( 0.0000, 0.0000) ( 3.0000,-4.0000) ( 0.2264, 0.8962)
 4  ( 0.0000, 0.0000) ( 0.0000, 0.0000) ( 0.0000, 0.0000) (-6.0000,-7.0000)