NAG Library Routine Document

g05pzf  (matrix_2waytable)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{mode}$ – IntegerInput

On entry: a code for selecting the operation to be performed by the routine.

$\mathbf{mode}=0$

Set up reference vector only.

$\mathbf{mode}=1$

Generate two-way table using reference vector set up in a prior call to g05pzf.

$\mathbf{mode}=2$

Set up reference vector and generate two-way table.

Constraint: $\mathbf{mode}=0$, $1$ or $2$.

2:     $\mathbf{nrow}$ – IntegerInput

On entry: $m$, the number of rows in the table.

Constraint: $\mathbf{nrow}\ge 2$.

3:     $\mathbf{ncol}$ – IntegerInput

On entry: $n$, the number of columns in the table.

Constraint: $\mathbf{ncol}\ge 2$.

4:     $\mathbf{totr}\left(\mathbf{nrow}\right)$ – Integer arrayInput

On entry: the $m$ row totals, $R_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,m$.

Constraints:

• $\mathbf{totr}\left(\mathit{i}\right)\ge 0$, for $\mathit{i}=1,2,\dots ,m$;
• ${\displaystyle \sum _{i=1}^m}\mathbf{totr}\left(i\right)={\displaystyle \sum _{j=1}^n}\mathbf{totc}\left(j\right)$;
• ${\sum }_{\mathit{i}}\mathbf{totr}\left(\mathit{i}\right)>0$, for $\mathit{i}=1,2,\dots ,m$.

5:     $\mathbf{totc}\left(\mathbf{ncol}\right)$ – Integer arrayInput

On entry: the $n$ column totals, $C_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,n$.

Constraints:

• $\mathbf{totc}\left(\mathit{j}\right)\ge 0$, for $\mathit{j}=1,2,\dots ,n$;
• ${\displaystyle \sum _{j=1}^n}\mathbf{totc}\left(j\right)={\displaystyle \sum _{i=1}^m}\mathbf{totr}\left(i\right)$.

6:     $\mathbf{r}\left(\mathbf{lr}\right)$ – Real (Kind=nag_wp) arrayCommunication Array

On entry: if $\mathbf{mode}=1$, the reference vector from the previous call to g05pzf.

On exit: the reference vector.

7:     $\mathbf{lr}$ – IntegerInput

On entry: the dimension of the array r as declared in the (sub)program from which g05pzf is called.

Constraint: $\mathbf{lr}\ge {\displaystyle \sum _{i=1}^m}\mathbf{totr}\left(i\right)+5$.

8:     $\mathbf{state}\left(*\right)$ – Integer arrayCommunication Array

Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

9:     $\mathbf{x}\left(\mathbf{ldx},\mathbf{ncol}\right)$ – Integer arrayOutput

On exit: if $\mathbf{mode}=1$ or $2$, a pseudorandom two-way $m$ by $n$ table, $X$, with element $\mathbf{x}\left(i,j\right)$ containing the $\left(i,j\right)$th entry in the table such that ${\displaystyle \sum _{\mathit{i}=1}^m}\mathbf{x}\left(i,j\right)=\mathbf{totc}\left(j\right)$ and ${\displaystyle \sum _{\mathit{j}=1}^n}\mathbf{x}\left(i,j\right)=\mathbf{totr}\left(i\right)$

10:   $\mathbf{ldx}$ – IntegerInput

On entry: the first dimension of the array x as declared in the (sub)program from which g05pzf is called.

Constraint: $\mathbf{ldx}\ge \mathbf{nrow}$.

11:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{mode}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mode}=0$, $1$ or $2$.

$\mathbf{ifail}=2$

On entry, $\mathbf{nrow}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrow}\ge 2$.

$\mathbf{ifail}=3$

On entry, $\mathbf{ncol}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ncol}\ge 2$.

$\mathbf{ifail}=4$

On entry, at least one element of totr is negative or totr sums to zero.

$\mathbf{ifail}=5$

On entry, totc has at least one negative element.

$\mathbf{ifail}=6$

nrow or ncol is not the same as when r was set up in a previous call.
Previous value of $\mathbf{nrow}=〈\mathit{\text{value}}〉$ and $\mathbf{nrow}=〈\mathit{\text{value}}〉$.
Previous value of $\mathbf{ncol}=〈\mathit{\text{value}}〉$ and $\mathbf{ncol}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=7$

On entry, lr is not large enough, $\mathbf{lr}=〈\mathit{\text{value}}〉$: minimum length required $=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=8$

On entry, state vector has been corrupted or not initialized.

$\mathbf{ifail}=10$

On entry, $\mathbf{ldx}=〈\mathit{\text{value}}〉$ and $\mathbf{nrow}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldx}\ge \mathbf{nrow}$.

$\mathbf{ifail}=15$

On entry, the arrays totr and totc do not sum to the same total: totr array total is $〈\mathit{\text{value}}〉$, totc array total is $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 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 (g05pzfe.f90)

10.2

Program Data

Program Data (g05pzfe.d)

10.3

Program Results

Program Results (g05pzfe.r)