Pseudo-random permutation of an integer vector

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NAG[g05ehc] NAG[nag_ran_permut_vec] - Pseudo-random permutation of an integer vector

Calling Sequence

g05ehc(index_vector, 'n'=n, 'fail'=fail)

nag_ran_permut_vec(. . .)

Parameters

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

On entry: the integer values to be permuted.

On exit: the permuted integer values.

'n'=n - integer; (optional)

Default value: the first dimension of the array index_vector.

On entry: the number of values to be permuted.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_ran_permut_vec (g05ehc) performs a pseudo-random permutation of a vector of integers.

	Description
	nag_ran_permut_vec (g05ehc) generates a single pseudo-random permutation of the elements of index_vector without inspecting their values. Each of the ! possible permutations of the values may be regarded as being equiprobable.

	Error Indicators and Warnings
	"NE_INT_ARG_LT" On entry, n must not be less than 1: .

	Accuracy
	Not applicable.

Further Comments

It should be noted that if is 20 or more it is theoretically impossible to generate all ! permutations as ! exceeds the cycle length of the internal random number generator. The time taken by the function is of order . In order to permute other kinds of objects (i.e., vectors, or matrices of higher dimensions), the following technique may be used:

a. Set , for (where is the number of objects)

b. Use nag_ran_permut_vec (g05ehc) to permute index_vector

c. Use the contents of index_vector as a set of indices to access the relevant object.

In order to divide pseudo-randomly an array of objects (obj_array) into subgroups of chosen sizes a similar procedure may be used. For the first , elements of index_vector set , for the next elements of index_vector set , for size set etc. Permute index_vector using nag_ran_permut_vec (g05ehc) and then, if , obj_array is to be included in the th subgroup.

Examples

>	n := 8: index_vector := Vector([0, 1, 2, 3, 4, 5, 6, 7], datatype=integer[kernelopts('wordsize')/8]): NAG:-g05cbc(0): NAG:-g05ehc(index_vector, 'n' = n):

>	index_vector;

	See Also
	Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley g05 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.