Random Vectors with Fixed Sum

Randomly and uniformly generates vectors with a specified sum and values in a specified interval.

Description

This generates m random n-element column vectors of values, [x1;x2;...;xn], each with a fixed sum, s, and subject to a restriction a<=xi<=b. The vectors are randomly and uniformly distributed in the n-1 dimensional space of solutions. This is accomplished by decomposing that space into a number of different types of simplexes (the many-dimensional generalizations of line segments, triangles, and tetrahedra.) The 'rand' function is used to distribute vectors within each simplex uniformly, and further calls on 'rand' serve to select different types of simplexes with probabilities proportional to their respective n-1 dimensional volumes. This algorithm does not perform any rejection of solutions - all are generated so as to already fit within the prescribed hypercube.

• MATLAB release: MATLAB 5.2 (R10)
• Other Files: Theory_of_randfixedsum.doc, ; randfixedsum.m

[John D'Errico]

This took a bit of work to verify uniformity in a slice of an n-dimensional hypercube. I'm now confident that Roger has done what he claimed, having checked samplings in several different dimensions, as well as having thought through the process he used to generate the sampling.

[Mike Edwards]

very useful! beautiful code!

[Per-Anders Ekström]

Excellent!