g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_2_way_table (g05pzc)

## 1  Purpose

nag_rand_2_way_table (g05pzc) generates a random two-way table.

## 2  Specification

 #include #include
 void nag_rand_2_way_table (Nag_ModeRNG mode, Integer nrow, Integer ncol, const Integer totr[], const Integer totc[], double r[], Integer lr, Integer state[], Integer x[], Integer pdx, NagError *fail)

## 3  Description

Given $m$ row totals ${R}_{i}$ and $n$ column totals ${C}_{j}$ (with $\sum _{i=1}^{m}{R}_{i}=\sum _{j=1}^{n}{C}_{j}=T$, say), nag_rand_2_way_table (g05pzc) will generate a pseudorandom two-way table of integers such that the row and column totals are satisfied.
The method used is based on that described by Patefield (1981) which is most efficient when $T$ is large relative to the number of table entries $m×n$ (i.e., $T>2mn$). Entries are generated one row at a time and one entry at a time within a row. Each entry is generated using the conditional probability distribution for that entry given the entries in the previous rows and the previous entries in the same row.
A reference vector is used to store computed values that can be reused in the generation of new tables with the same row and column totals. nag_rand_2_way_table (g05pzc) can be called to simply set up the reference vector, or to generate a two-way table using a reference vector set up in a previous call, or it can combine both functions in a single call.
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_2_way_table (g05pzc).

## 4  References

Patefield W M (1981) An efficient method of generating $R×C$ tables with given row and column totals Appl. Stats. 30 91–97

## 5  Arguments

1:     modeNag_ModeRNGInput
On entry: a code for selecting the operation to be performed by the function.
${\mathbf{mode}}=\mathrm{Nag_InitializeReference}$
Set up reference vector only.
${\mathbf{mode}}=\mathrm{Nag_GenerateFromReference}$
Generate two-way table using reference vector set up in a prior call to nag_rand_2_way_table (g05pzc).
${\mathbf{mode}}=\mathrm{Nag_InitializeAndGenerate}$
Set up reference vector and generate two-way table.
Constraint: ${\mathbf{mode}}=\mathrm{Nag_InitializeReference}$, $\mathrm{Nag_GenerateFromReference}$ or $\mathrm{Nag_InitializeAndGenerate}$.
2:     nrowIntegerInput
On entry: $m$, the number of rows in the table.
Constraint: ${\mathbf{nrow}}\ge 2$.
3:     ncolIntegerInput
On entry: $n$, the number of columns in the table.
Constraint: ${\mathbf{ncol}}\ge 2$.
4:     totr[nrow]const IntegerInput
On entry: the $m$ row totals, ${R}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,m$.
Constraints:
• ${\mathbf{totr}}\left[\mathit{i}-1\right]\ge 0$, for $\mathit{i}=1,2,\dots ,m$;
• $\sum _{i=1}^{m}{\mathbf{totr}}\left[i-1\right]=\sum _{j=1}^{n}{\mathbf{totc}}\left[j-1\right]$;
• ${\sum }_{\mathit{i}}{\mathbf{totr}}\left[\mathit{i}-1\right]>0$, for $\mathit{i}=1,2,\dots ,m$.
5:     totc[ncol]const IntegerInput
On entry: the $n$ column totals, ${C}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,n$.
Constraints:
• ${\mathbf{totc}}\left[\mathit{j}-1\right]\ge 0$, for $\mathit{j}=1,2,\dots ,n$;
• $\sum _{j=1}^{n}{\mathbf{totc}}\left[j-1\right]=\sum _{i=1}^{m}{\mathbf{totr}}\left[i-1\right]$.
6:     r[lr]doubleCommunication Array
On entry: if ${\mathbf{mode}}=\mathrm{Nag_GenerateFromReference}$, the reference vector from the previous call to nag_rand_2_way_table (g05pzc).
On exit: the reference vector.
7:     lrIntegerInput
On entry: the dimension of the array r.
Constraint: ${\mathbf{lr}}\ge \sum _{i=1}^{m}{\mathbf{totr}}\left[i-1\right]+5$.
8:     state[$\mathit{dim}$]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
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:     x[${\mathbf{nrow}}×{\mathbf{pdx}}$]IntegerOutput
On exit: if ${\mathbf{mode}}=\mathrm{Nag_GenerateFromReference}$ or $\mathrm{Nag_InitializeAndGenerate}$, a pseudorandom two-way $m$ by $n$ table, $X$, with element ${\mathbf{x}}\left[\left(i-1\right)×{\mathbf{pdx}}+j-1\right]$ containing the $\left(i,j\right)$th entry in the table such that $\sum _{\mathit{i}=1}^{m}{\mathbf{x}}\left[\left(i-1\right)×{\mathbf{pdx}}+j-1\right]={\mathbf{totc}}\left[j-1\right]$ and $\sum _{\mathit{j}=1}^{n}{\mathbf{x}}\left[\left(i-1\right)×{\mathbf{pdx}}+j-1\right]={\mathbf{totr}}\left[i-1\right]$
10:   pdxIntegerInput
On entry: the stride separating matrix column elements in the array x.
Constraint: ${\mathbf{pdx}}\ge {\mathbf{ncol}}$.
11:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, lr is not large enough, ${\mathbf{lr}}=〈\mathit{\text{value}}〉$: minimum length required $\text{}=〈\mathit{\text{value}}〉$.
On entry, ${\mathbf{ncol}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{ncol}}\ge 2$.
On entry, ${\mathbf{nrow}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nrow}}\ge 2$.
NE_INT_2
On entry, ${\mathbf{pdx}}=〈\mathit{\text{value}}〉$ and ${\mathbf{ncol}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{pdx}}\ge {\mathbf{ncol}}$.
NE_INT_ARRAY
On entry, at least one element of totr is negative or totr sums to zero.
On entry, totc has at least one negative element.
NE_INT_ARRAY_2
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 $〈\mathit{\text{value}}〉$.
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.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_PREV_CALL
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 ${\mathbf{ncol}}=〈\mathit{\text{value}}〉$.

None.

None.

## 9  Example

Following initialization of the pseudorandom number generator by a call to nag_rand_init_repeatable (g05kfc), this example generates and prints a $4$ by $3$ two-way table, with row totals of $9$, $11$, $7$ and $23$ respectively, and column totals of $16$, $17$ and $17$ respectively.

### 9.1  Program Text

Program Text (g05pzce.c)

None.

### 9.3  Program Results

Program Results (g05pzce.r)