Generates a random table matrix

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NAG[g05qdc] NAG[nag_rngs_2_way_table] - Generates a random table matrix

Calling Sequence

g05qdc(mode, totr, totc, x, igen, iseed, r, 'nrow'=nrow, 'ncol'=ncol, 'nr'=nr, 'fail'=fail)

nag_rngs_2_way_table(. . .)

Parameters

mode - integer;

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: . .

totr - Vector(1..nrow, datatype=integer[kernelopts('wordsize')/8]);

On entry: the row totals, , for .

Constraints:

, for ;

sum(totr[i], i = 1 .. m) = sum(totc[j], j = 1 .. n) .

totc - Vector(1..ncol, datatype=integer[kernelopts('wordsize')/8]);

On entry: the column totals, , for .

Constraints:

, for ;

sum(totc[j], j = 1 .. n) = sum(totr[i], i = 1 .. m) .

x - Matrix(1..dim1, 1..ncol, datatype=integer[kernelopts('wordsize')/8], order=order);

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On exit: if or , a pseudo-random two-way by table, , with element containing the th entry in the table such that sum(x(i, j), i = 1 .. nrow) = totc[j] and sum(x(i, j), j = 1 .. ncol) = totr[i]

igen - integer;

On entry: must contain the identification number for the generator to be used to return a pseudo-random number and should remain unchanged following initialization by a prior call to one of the functions g05kbc (nag_rngs_init_repeatable) or g05kcc (nag_rngs_init_nonrepeatable).

iseed - Vector(1.., datatype=integer[kernelopts('wordsize')/8]);

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.

r - Vector(1..nr, datatype=float[8]);

On entry: if mode is set to , the reference vector from the previous call to nag_rngs_2_way_table (g05qdc).

On exit: the reference vector.

'nrow'=nrow - integer; (optional)

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

Constraint: . .

'ncol'=ncol - integer; (optional)

Default value: the first dimension of and the second dimension of the array x.

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

Constraint: . .

'nr'=nr - integer; (optional)

On entry: the dimension of the array r as declared in the function from which nag_rngs_2_way_table (g05qdc) is called.

Constraint: nr >= sum(totr[i], i = 1 .. nrow)+4 . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

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

Description

Given row totals and column totals (with sum(R[i], i = 1 .. m) = sum(C[j], j = 1 .. n) and sum(C[j], j = 1 .. n) = T , say), nag_rngs_2_way_table (g05qdc) will generate a pseudo-random 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 is large relative to the number of table entries (i.e., ). 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 g05kbc (nag_rngs_init_repeatable) (for a repeatable sequence if computed sequentially) or g05kcc (nag_rngs_init_nonrepeatable) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_2_way_table (g05qdc).

Error Indicators and Warnings

"NE_ALLOC_FAIL"

Dynamic memory allocation failed.

"NE_BAD_PARAM"

On entry, argument had an illegal value.

"NE_INT"

On entry, . Constraint: .

On entry, nr not large enough, . Minimum length required .

On entry, . Constraint: .

"NE_INT_2"

On entry, or : , .

"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 consult NAG for assistance.

"NE_PREV_CALL"

nrow or ncol is not the same as when r was set up in a previous call. Previous value of , current value of . Previous value of , current value of .

"NE_REAL_ARRAY_ELEM_CONS"

On entry, totc has at least one negative element.

On entry, totr has at least one negative element.

"NE_REAL_ARRAYS_SUM"

On entry, the arrays totr and totc do not sum to the same total: totr array total is , totc array total is .

	Accuracy
	None.

	Further Comments
	None.

Examples

mode := 2:
nrow := 4:
ncol := 3:
igen := 1:
nr := 60:
totr := Vector([9, 11, 7, 23], datatype=integer[kernelopts('wordsize')/8]):
totc := Vector([16, 17, 17], datatype=integer[kernelopts('wordsize')/8]):
x := Matrix(4, 3, datatype=integer[kernelopts('wordsize')/8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
r := Vector(60, datatype=float[8]):
NAG:-g05qdc(mode, totr, totc, x, igen, iseed, r, 'nrow' = nrow, 'ncol' = ncol, 'nr' = nr):

iseed;

	See Also
	Patefield WM (1981) An efficient method of generating tables with given row and column totals Appl. Stats. 30 91–97 g05 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.