RANDOM COMPOSITION

RANDOM COMPOSITION (LET)

Let Subcommand

Generate a random composition.

Given positive integers n and k, a composition of n into k parts is defined as
n = r₁ + r₂ + ... + r_k             (r_i ≥ 0, i = 1, k)

The number of compositions is given by

This command generates a single random composition.

The output is an array of size k.

LET <y> = RANDOM COMPOSITION             FOR I = 1 1 <k>
where <k> is a number or parameter that specifies the size of the composition;
and     <y> is a variable where the random composition is saved.

This command must be preceeded with the command

LET N = <value>

LET N = 5
LET K = 3
LET Y = RANDOM COMPOSITION FOR I = 1 1 K

Dataplot implements this command using the RANCOM algorithm described in Nijenhuis and Wilf (see Reference section below).

Dataplot supports a number of different random number generators. Enter HELP RANDOM NUMBER GENERATOR for details.

The SEED command can be used to specify a seed for the random number generator.

None

None

LET	= Generate data transformations.
RANDOM PERMUTATION	= Generate a random permutation.
RANDOM K-SET OF N-SET	= Generate a random k-set of n-set.
RANDOM PARTITION	= Generate a random partition.
RANDOM SUBSET	= Generate a random subset.
RANDOM EQUIVALENCE RELATION	= Generate a random equivalence relation.
NEXT SUBSET	= Generate the next subset of a set.
NEXT PERMUTATION	= Generate the next permutation.
NEXT K-SET OF N-SET	= Generate the next k-set of n-set.
NEXT COMPOSITION	= Generate the next composition.
NEXT PARTITION	= Generate the next partition.
NEXT EQUIVALENCE RELATION	= Generate the next composition.

Nijenhuis and Wilf (1978), "Combinatorial Algorithms", Second Edition, Academic Press, Chapter 6.

Combinatorial Analysis

2008/4

 
LET N = 8
LET K = 3
LET Y = RANDOM COMPOSITION FOR I =  1  1  K
PRINT Y