nag_rand_2_way_table (g05pzc) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_2_way_table (g05pzc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

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

2  Specification

#include <nag.h>
#include <nagg05.h>
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 Ri and n column totals Cj (with i=1m Ri=j=1n Cj=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.
mode=Nag_InitializeReference
Set up reference vector only.
mode=Nag_GenerateFromReference
Generate two-way table using reference vector set up in a prior call to nag_rand_2_way_table (g05pzc).
mode=Nag_InitializeAndGenerate
Set up reference vector and generate two-way table.
Constraint: mode=Nag_InitializeReference, Nag_GenerateFromReference or Nag_InitializeAndGenerate.
2:     nrowIntegerInput
On entry: m, the number of rows in the table.
Constraint: nrow2.
3:     ncolIntegerInput
On entry: n, the number of columns in the table.
Constraint: ncol2.
4:     totr[nrow]const IntegerInput
On entry: the m row totals, Ri, for i=1,2,,m.
Constraints:
  • totr[i-1]0, for i=1,2,,m;
  • i=1mtotr[i-1]=j=1ntotc[j-1];
  • i totr[i-1]>0, for i=1,2,,m.
5:     totc[ncol]const IntegerInput
On entry: the n column totals, Cj, for j=1,2,,n.
Constraints:
  • totc[j-1]0, for j=1,2,,n;
  • j=1ntotc[j-1]=i=1mtotr[i-1].
6:     r[lr]doubleCommunication Array
On entry: if mode=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: lri=1mtotr[i-1]+5.
8:     state[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[nrow×pdx]IntegerOutput
On exit: if mode=Nag_GenerateFromReference or Nag_InitializeAndGenerate, a pseudorandom two-way m by n table, X, with element x[i-1×pdx+j-1] containing the i,jth entry in the table such that i=1 m x[i-1×pdx+j-1]=totc[j-1] and j=1 n x[i-1×pdx+j-1]=totr[i-1]
10:   pdxIntegerInput
On entry: the stride separating matrix column elements in the array x.
Constraint: pdxncol.
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.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, lr is not large enough, lr=value: minimum length required =value.
On entry, ncol=value.
Constraint: ncol2.
On entry, nrow=value.
Constraint: nrow2.
NE_INT_2
On entry, pdx=value and ncol=value.
Constraint: pdxncol.
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 value, totc array total is 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 nrow=value and nrow=value.
Previous value of ncol=value and ncol=value.

7  Accuracy

None.

8  Further Comments

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)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05pzce.r)


nag_rand_2_way_table (g05pzc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012