). 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_matrix_2waytable (g05pz) 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_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_matrix_2waytable (g05pz).

References

Patefield W M (1981) An efficient method of generating

R \times C

tables with given row and column totals Appl. Stats. 30 91–97

Parameters

Compulsory Input Parameters

1: $mode$ – int64int32nag_int scalar

A code for selecting the operation to be performed by the function.

$mode = 0$: Set up reference vector only.
$mode = 1$: Generate two-way table using reference vector set up in a prior call to nag_rand_matrix_2waytable (g05pz).
$mode = 2$: Set up reference vector and generate two-way table.

Constraint:

mode = 0

1

2

2: $totr (nrow)$ – int64int32nag_int array

The

m

row totals,

R_{i}

, for

i = 1, 2, \dots, m

Constraints:

$totr (i) \geq 0$ , for $i = 1, 2, \dots, m$ ;
$\sum_{i = 1}^{m} totr (i) = \sum_{j = 1}^{n} totc (j)$ ;
$\sum_{i} totr (i) > 0$ , for $i = 1, 2, \dots, m$ .

3: $totc (ncol)$ – int64int32nag_int array

The

n

column totals,

C_{j}

, for

j = 1, 2, \dots, n

Constraints:

$totc (j) \geq 0$ , for $j = 1, 2, \dots, n$ ;
$\sum_{j = 1}^{n} totc (j) = \sum_{i = 1}^{m} totr (i)$ .

4: $r (lr)$ – double array

mode = 1

, the reference vector from the previous call to nag_rand_matrix_2waytable (g05pz).

5: $state (:)$ – int64int32nag_int array

Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

1: $nrow$ – int64int32nag_int scalar: Default: the dimension of the array totr.
$m$ , the number of rows in the table.

Constraint: $nrow \geq 2$ .
2: $ncol$ – int64int32nag_int scalar: Default: the dimension of the array totc.
$n$ , the number of columns in the table.

Constraint: $ncol \geq 2$ .
3: $lr$ – int64int32nag_int scalar: Default: the dimension of the array r.
The dimension of the array r.

Constraint: $lr \geq \sum_{i = 1}^{m} totr (i) + 5$ .

Output Parameters

1: $r (lr)$ – double array: The reference vector.
2: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
3: $x (ldx, ncol)$ – int64int32nag_int array: If $mode = 1$ or $2$ , a pseudorandom two-way $m$ by $n$ table, $X$ , with element $x (i, j)$ containing the $(i, j)$ th entry in the table such that $\sum_{i = 1}^{m} x (i, j) = totc (j)$ and $\sum_{j = 1}^{n} x (i, j) = totr (i)$
4: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: Constraint: $mode = 0$ , $1$ or $2$ .

$ifail = 2$: Constraint: $nrow \geq 2$ .

$ifail = 3$: Constraint: $ncol \geq 2$ .

$ifail = 4$: On entry, at least one element of totr is negative or totr sums to zero.

$ifail = 5$: On entry, totc has at least one negative element.

$ifail = 6$: nrow or ncol is not the same as when r was set up in a previous call.

$ifail = 7$: On entry, lr is not large enough, $lr =_$ : minimum length required .

$ifail = 8$: On entry, state vector has been corrupted or not initialized.

$ifail = 10$: Constraint: $ldx \geq nrow$ .

$ifail = 15$: On entry, the arrays totr and totc do not sum to the same total.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

None.

Further Comments

None.

Example

Following initialization of the pseudorandom number generator by a call to nag_rand_init_repeat (g05kf), this example generates and prints a

4

3

two-way table, with row totals of

9

11

7

and

23

respectively, and column totals of

16

17

and

17

respectively.

Open in the MATLAB editor: g05pz_example

function g05pz_example


fprintf('g05pz example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% row and column totals
totr = [int64( 9); 11;  7; 23];
totc = [int64(16); 17; 17];

% Set up and generate in one go
mode = int64(2);

% Generate the random table with given totals
lr = sum(totr) + 5;
r = zeros(lr, 1);
[r, state, x, ifail] = g05pz( ...
                              mode, totr, totc, r, state);

disp('Random Table')
disp(double(x));
disp('Supplied row totals:');
disp(double(totr)');
disp('Supplied column totals:')
disp(double(totc)');

g05pz example results

Random Table
     2     4     3
     6     1     4
     2     4     1
     6     8     9

Supplied row totals:
     9    11     7    23

Supplied column totals:
    16    17    17

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox