NAG Library Function Document

nag_ztrexc (f08qtc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 2.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{compq}$ – Nag_ComputeQTypeInput

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

$\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$

The matrix $Q$ of Schur vectors is updated.

$\mathbf{compq}=\mathrm{Nag\_NotQ}$

No Schur vectors are updated.

Constraint: $\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$ or $\mathrm{Nag\_NotQ}$.

3:    $\mathbf{n}$ – IntegerInput

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

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

4:    $\mathbf{t}\left[\mathit{dim}\right]$ – ComplexInput/Output

Note: the dimension, dim, of the array t must be at least $\max \left(1,\mathbf{pdt}\times \mathbf{n}\right)$.

The $\left(i,j\right)$th element of the matrix $T$ is stored in

• $\mathbf{t}\left[\left(j-1\right)\times \mathbf{pdt}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{t}\left[\left(i-1\right)\times \mathbf{pdt}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $n$ upper triangular matrix $T$, as returned by nag_zhseqr (f08psc).

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

5:    $\mathbf{pdt}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array t.

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

6:    $\mathbf{q}\left[\mathit{dim}\right]$ – ComplexInput/Output

Note: the dimension, dim, of the array q must be at least

• $\max \left(1,\mathbf{pdq}\times \mathbf{n}\right)$ when $\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$;
• $1$ when $\mathbf{compq}=\mathrm{Nag\_NotQ}$.

The $\left(i,j\right)$th element of the matrix $Q$ is stored in

• $\mathbf{q}\left[\left(j-1\right)\times \mathbf{pdq}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{q}\left[\left(i-1\right)\times \mathbf{pdq}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: if $\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$, q must contain the $n$ by $n$ unitary matrix $Q$ of Schur vectors.

On exit: if $\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$, q contains the updated matrix of Schur vectors.

If $\mathbf{compq}=\mathrm{Nag\_NotQ}$, q is not referenced.

7:    $\mathbf{pdq}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array q.

Constraints:

• if $\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$, $\mathbf{pdq}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{compq}=\mathrm{Nag\_NotQ}$, $\mathbf{pdq}\ge 1$.

8:    $\mathbf{ifst}$ – IntegerInput

9:    $\mathbf{ilst}$ – 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 $1\le \mathbf{ilst}\le \mathbf{n}$.

10:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_INT_2

On entry, $\mathbf{compq}=〈\mathit{\text{value}}〉$, $\mathbf{pdq}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{compq}=\mathrm{Nag\_UpdateSchur}$, $\mathbf{pdq}\ge \max \left(1,\mathbf{n}\right)$;
if $\mathbf{compq}=\mathrm{Nag\_NotQ}$, $\mathbf{pdq}\ge 1$.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{pdq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdq}>0$.

On entry, $\mathbf{pdt}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdt}>0$.

NE_INT_2

On entry, $\mathbf{pdt}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdt}\ge \max \left(1,\mathbf{n}\right)$.

NE_INT_3

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{ifst}=〈\mathit{\text{value}}〉$ and $\mathbf{ilst}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{ifst}\le \mathbf{n}$ and $1\le \mathbf{ilst}\le \mathbf{n}$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f08qtce.c)

10.2  Program Data

Program Data (f08qtce.d)

10.3  Program Results

Program Results (f08qtce.r)