Question

If i read the doc of how to construct a Halton quasi-random point set and it mentions that it’s possible to ‘skip’ the first values and then retain the ‘leap’ values.

Don’t understand what the ‘skip’ and ‘leap’ really mean.

Have tried the following:

>> p = haltonset(1,'Skip',50,'Leap',10); d = haltonset(1,'Skip',51,'Leap',9);
>> p(2:10), d(1:9)
ans =
0.7344
0.0703
0.7891
0.4766
0.5859
0.1797
0.9922
0.3164
0.6602

ans =
0.7969
0.7344
0.8828
0.5391
0.8516
0.6484
0.9609
0.6172
0.7539

>> p(2:10) == d(1:9)
ans =

 0
 0
 0
 0
 0
 0
 0
 0
 0

Thought that it might be that that this would save 10 values to p and 9 to d. Also thought that d would have the same values as p. But this was not the case.

I then tested if the ‘leap’ would be the same as a normal way to make a vector
– ex: (1:leap:10)

>> p = haltonset(1,'Skip',50,'Leap',1); d = haltonset(1,'Skip',50,'Leap',2);
>> p(1:2:10)==d(1:5)
ans =
 1
 0
 0
 0
 0

>> p = haltonset(1,'Skip',0,'Leap',1); d = haltonset(1,'Skip',0,'Leap',2);
>> p(1:2:10)==d(1:5)
ans =
 1
 0
 0
 0
 0

but this seemed not to be the case..

Can anybody give a plain English explanation of how to interpreted the ‘skip’ and ‘leap’ variables.

Answer 1

I find the following description to be very clear [quoting this documentation page]:

Imagine a simple 1-D sequence that produces the integers from 1 to 10.
This is the basic sequence and the first three points are [1,2,3]:

Now look at how Scramble, Leap, and Skip work together:

• Scramble: Scrambling shuffles the points in one of several
  different ways. In this example, assume a scramble turns the sequence
  into 1,3,5,7,9,2,4,6,8,10. The first three points are now [1,3,5]:

• Skip: A Skip value specifies the number of initial points to
  ignore. In this example, set the Skip value to 2. The sequence is now
  5,7,9,2,4,6,8,10 and the first three points are [5,7,9]:

• Leap: A Leap value specifies the number of points to ignore for
  each one you take. Continuing the example with the Skip set to 2, if
  you set the Leap to 1, the sequence uses every other point. In this
  example, the sequence is now 5,9,4,8 and the first three points are
  [5,9,4]:

EDIT:

Let me show with an example:

%# create 1D sequences (x: picked, .: ignored)
p00 = haltonset(1,'Skip',0,'Leap',0);   %# xxxxxxxxxxxxxxx
p50 = haltonset(1,'Skip',5,'Leap',0);   %# .....xxxxxxxxxx
p02 = haltonset(1,'Skip',0,'Leap',2);   %# x..x..x..x..x..
p52 = haltonset(1,'Skip',5,'Leap',2);   %# .....x..x..x..x

%# each pair of these are equal
[p50(1:10) p00(6:15)]     %# skip vs. noskip
[p02(1:5) p00(1:3:13)]    %# leap vs. noleap
[p52(1:4) p00(6:3:15)]    %# skip+leap vs. noskip+noleap

In general:

skip = 50;
leap = 10;
p00 = haltonset(1,'Skip',0,'Leap',0);
p = haltonset(1,'Skip',skip,'Leap',leap);

num = 9;
[p(1:num) p00(skip+1:leap+1:num*leap+num-leap+skip)]