Leap property - Class: qrandset

Interval between points

Description

Number of points to leap over and omit for each point taken from the sequence. The Leap property of a point set contains a positive integer which specifies the number of points in the sequence to leap over and omit for every point taken. The default Leap value is 0, which corresponds to taking every point from the sequence.

Leaping is a technique used to improve the quality of a point set. However, you must choose the Leap values with care; many Leap values create sequences that fail to touch on large sub-hyper-rectangles of the unit hypercube, and so fail to be a uniform quasi-random point set.

Choosing Leap Values for Halton Sets

A known rule for choosing Leap values for Halton sets is to set it to (P-1) where P is a prime number that has not been used to generate one of the dimensions, i.e. for a k-dimensional point set P would be the (k+1)th or greater prime.

Examples

Experiment with different leap values:

% No leaping produces the standard Halton sequence.
P = haltonset(5);
P(1:5,:)
 
% Set a leap of 1.  The point set now includes every other 
% point from the sequence.
P.Leap = 1;
P(1:5,:)

See Also

haltonset | net | qrandset | Skip | subsref

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