VDC

Pure JS implementation of van der Corput low-discrepancy sequences.

Installation

With npm:

$ npm install vdc

In the browser:

<script src="vdc.js"></script>

The browser exposes a variable VDC

Usage

The exported function VDC accepts a opts object with the following fields:

• b (default 2) base for the sequence.
• n (default 0) starting index for the sequence.

Calling without arguments will default to the aforementioned values.

The object returned by VDC exposes a next() method to get the next element.

The field last holds the most recently generated value (accessing the field does not trigger a recalculation)

For example:

//var VDC = require('vdc') // uncomment this line if in node
 
var opts = {'n':0, 'b':2};
var generator = VDC(opts);
for(var i = 0; i != 10; ++i) console.log(generator.next());

The expected output is

0       (0/1)
0.5     (1/2)
0.25    (1/4)
0.75    (3/4)
0.125   (1/8)
0.625   (5/8)
0.375   (3/8)
0.875   (7/8)
0.0625  (1/16)
0.5625  (9/16)

Testing

make test will run the nodejs-based test.

make baseline will generate the test baselines using Mathematica by explicitly extracting and reversing the digits. The implementation is based off a tutorial http://reference.wolfram.com/mathematica/CUDALink/tutorial/Applications.html

VanDerCorput[base_][len_] := Table[
  With[{digits = Reverse@IntegerDigits[n, base]},
   Sum[2^(-ii)*digits[[ii]], {ii, Length[digits]}]
   ], {n, len}]

Notes

0 is the first value. Some sources (notably Wikipedia) start the sequence at 1/2, but others (Glasserman "Monte Carlo Methods in Financial Engineering") claim that the original sequence definition started at 0.

License

Please consult the attached LICENSE file for details. All rights not explicitly granted by the Apache 2.0 license are reserved by the Original Author.

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