HALTON Procedure

%HALTON (a function) generates an n-vector of the Halton(1964) sequence for the given base (which should be a prime number). Halton sequences are deterministic "low-discrepancy" sequences which fill the unit cube relatively uniformly (with a different base for each dimension) allowing numerical integrals to be estimated more accurately for a given number of function evaluations than would be possible with truly random numbers.

outputVECTOR = %Halton(n,base)

Parameters

n	size of the vector to be generated
base	(INTEGER) prime number which chooses the sequence
outputVECTOR	n-VECTOR. This is deterministic given n and base.

Example

source halton.src

compute r=100

compute uu=%Halton(r,7)

dec vect u(r)

ewise u(i)=%invnormal(uu(i))

generates a Halton sequence of length 100, which would be used like uniform 0,1 values. These are transformed to the equivalent N(0,1) deviates using %INVNORMAL to produce U.