nag_rngs_2_way_table (g05qdc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rngs_2_way_table (g05qdc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_2_way_table (g05qdc) generates a random two-way table.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_2_way_table (Nag_OrderType order, Integer mode, Integer nrow, Integer ncol, const Integer totr[], const Integer totc[], Integer x[], Integer pdx, Integer igen, Integer iseed[], double r[], Integer nr, NagError *fail)

3  Description

Given m row totals Ri and n column totals Cj (with i=1m Ri=j=1n Cj=T, say), nag_rngs_2_way_table (g05qdc) 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_rngs_2_way_table (g05qdc) 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_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_2_way_table (g05qdc).

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:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     modeIntegerInput
On entry: a code for selecting the operation to be performed by the function.
Set up reference vector only.
Generate two-way table using reference vector set up in a prior call to nag_rngs_2_way_table (g05qdc).
Set up reference vector and generate two-way table.
Constraint: mode=0, 1 or 2.
3:     nrowIntegerInput
On entry: m, the number of rows in the table.
Constraint: nrow2.
4:     ncolIntegerInput
On entry: n, the number of columns in the table.
Constraint: ncol2.
5:     totr[nrow]const IntegerInput
On entry: the m row totals, Ri, for i=1,2,,m.
  • totr[i-1]0, for i=1,2,,m;
  • i=1mtotr[i-1]=j=1ntotc[j-1].
6:     totc[ncol]const IntegerInput
On entry: the n column totals, Cj, for j=1,2,,n.
  • totc[j-1]0, for j=1,2,,n;
  • j=1ntotc[j-1]=i=1mtotr[i-1].
7:     x[dim]IntegerOutput
Note: the dimension, dim, of the array x must be at least
  • max1,pdx×ncol when order=Nag_ColMajor;
  • max1,nrow×pdx when order=Nag_RowMajor.
Where Xi,j appears in this document, it refers to the array element
  • x[j-1×pdx+i-1] when order=Nag_ColMajor;
  • x[i-1×pdx+j-1] when order=Nag_RowMajor.
On exit: if mode=1 or 2, a pseudorandom two-way m by n table, X, with element Xi,j containing the i,jth entry in the table such that i=1nrowXi,j=totc[j-1] and j=1ncolXi,j=totr[i-1]
8:     pdxIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array x.
  • if order=Nag_ColMajor, pdxnrow;
  • if order=Nag_RowMajor, pdxncol.
9:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
10:   iseed[4]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
11:   r[nr]doubleCommunication Array
On entry: if mode=1, the reference vector from the previous call to nag_rngs_2_way_table (g05qdc).
On exit: the reference vector.
12:   nrIntegerInput
On entry: the dimension of the array r.
Constraint: nri=1nrowtotr[i-1]+4.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, mode=value.
Constraint: mode=0, 1 or 2.
On entry, ncol=value.
Constraint: ncol2.
On entry, nr not large enough, nr=value. Minimum length required =value.
On entry, nrow=value.
Constraint: nrow2.
On entry, pdx=value.
Constraint: pdx>0.
On entry, nrow<2 or ncol<2: nrow=value and ncol=value.
On entry, pdx=value and ncol=value.
Constraint: pdxncol.
On entry, pdx=value and nrow=value.
Constraint: pdxnrow.
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.
nrow or ncol is not the same as when r was set up in a previous call. Previous value of nrow=value, current value of nrow=value. Previous value of ncol=value, current value of ncol=value.
On entry, totc has at least one negative element.
On entry, totr has at least one negative element.
On entry, the arrays totr and totc do not sum to the same total: totr array total is value, totc array total is value.

7  Accuracy


8  Further Comments


9  Example

Following initialization of the pseudorandom number generator by a call to nag_rngs_init_repeatable (g05kbc), 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 (g05qdce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05qdce.r)

nag_rngs_2_way_table (g05qdc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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