NAG Library Function Document

nag_trans_hessenberg_observer (g13ewc)

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:    $\mathbf{p}$ – IntegerInput

On entry: the actual output dimension, $p$.

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

3:    $\mathbf{reduceto}$ – Nag_ObserverFormInput

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

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

Upper observer Hessenberg form).

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

Lower observer Hessenberg form).

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

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:    $\mathbf{c}\left[\mathbf{p}\times \mathbf{tdc}\right]$ – doubleInput/Output

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

On entry: the leading $p$ by $n$ part of this array must contain the output matrix $C$ to be transformed.

On exit: the leading $p$ by $n$ part of this array contains the transformed output matrix $C{U}^{\mathrm{T}}$.

7:    $\mathbf{tdc}$ – IntegerInput

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

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

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 $\mathbf{tdc}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdc}\ge \mathbf{n}$.
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, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

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

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g13ewce.c)

10.2

Program Data

Program Data (g13ewce.d)

10.3

Program Results

Program Results (g13ewce.r)