NAG Library Function Document

nag_trans_hessenberg_controller (g13exc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

On entry: the actual state dimension, $n$, i.e., the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 1$.

2:    $\mathbf{m}$ – IntegerInput

On entry: the actual input dimension, $m$.

Constraint: $\mathbf{m}\ge 1$.

3:    $\mathbf{reduceto}$ – Nag_ControllerFormInput

On entry: indicates whether the matrix pair $\left(B,A\right)$ is to be reduced to upper or lower controller Hessenberg form as follows:

$\mathbf{reduceto}=\mathrm{Nag\_UH\_Controller}$

Upper controller Hessenberg form).

$\mathbf{reduceto}=\mathrm{Nag\_LH\_Controller}$

Lower controller Hessenberg form).

Constraint: $\mathbf{reduceto}=\mathrm{Nag\_UH\_Controller}$ or $\mathrm{Nag\_LH\_Controller}$.

4:    $\mathbf{a}\left[\mathbf{n}\times \mathbf{tda}\right]$ – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix $A$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{tda}+j-1\right]$.

On entry: the leading $n$ by $n$ part of this array must contain the state transition matrix $A$ to be transformed.

On exit: the leading $n$ by $n$ part of this array contains the transformed state transition matrix $UA{U}^{\mathrm{T}}$.

5:    $\mathbf{tda}$ – IntegerInput

On entry: the stride separating matrix column elements in the array a.

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

6:    $\mathbf{b}\left[\mathbf{n}\times \mathbf{tdb}\right]$ – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix $B$ is stored in $\mathbf{b}\left[\left(i-1\right)\times \mathbf{tdb}+j-1\right]$.

On entry: the leading $n$ by $m$ part of this array must contain the input matrix $B$ to be transformed.

On exit: the leading $n$ by $m$ part of this array contains the transformed input matrix $UB$.

7:    $\mathbf{tdb}$ – IntegerInput

On entry: the stride separating matrix column elements in the array b.

Constraint: $\mathbf{tdb}\ge \mathbf{m}$.

8:    $\mathbf{u}\left[\mathbf{n}\times \mathbf{tdu}\right]$ – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix $U$ is stored in $\mathbf{u}\left[\left(i-1\right)\times \mathbf{tdu}+j-1\right]$.

On entry: if u is not NULL, then the leading $n$ by $n$ part of this array must contain either a transformation matrix (e.g., from a previous call to this function) or be initialized as the identity matrix. If this information is not to be input then u must be set to NULL.

On exit: if u is not NULL, then the leading $n$ by $n$ part of this array contains the product of the input matrix $U$ and the state-space transformation matrix which reduces the given pair to observer Hessenberg form.

9:    $\mathbf{tdu}$ – IntegerInput

On entry: the stride separating matrix column elements in the array u.

Constraint: $\mathbf{tdu}\ge \mathbf{n}$ if u is defined.

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{tda}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tda}\ge \mathbf{n}$. On entry $\mathbf{tdb}=〈\mathit{\text{value}}〉$ while $\mathbf{m}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdb}\ge \mathbf{m}$. On entry $\mathbf{tdu}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdu}\ge \mathbf{n}$.

NE_BAD_PARAM

On entry, argument reduceto had an illegal value.

NE_INT_ARG_LT

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 1$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g13exce.c)

10.2

Program Data

Program Data (g13exce.d)

10.3

Program Results

Program Results (g13exce.r)