van_der_corput, a Python code which computes the van der Corput Quasi Monte Carlo (QMC) sequence, using a simple interface.
The van der Corput sequence generates a sequence of points in [0,1] which never repeats. For positive index I, the elements of the van der Corput sequence are strictly between 0 and 1.
The I-th element of the van der Corput sequence is computed by writing I in the base B (usually 2) and then reflecting its digits about the decimal point. For example, if we start with I = 11, its binary expansion is 1011, and so its reflected binary expansion is 0.1101 which is 1/2+1/4+1/16=0.8125.
The generation is quite simple. Given an index I, the expansion of I in base B is generated. Then, essentially, the result R is generated by writing a decimal point followed by the digits of the expansion of I, in reverse order. This decimal value is actually still in base B, so it must be properly interpreted to generate a usable value.
Here is an example in base 2:
I (decimal) | I (binary) | R (binary) | R (decimal) |
---|---|---|---|
0 | 0 | .0 | 0.0 |
1 | 1 | .1 | 0.5 |
2 | 10 | .01 | 0.25 |
3 | 11 | .11 | 0.75 |
4 | 100 | .001 | 0.125 |
5 | 101 | .101 | 0.625 |
6 | 110 | .011 | 0.375 |
7 | 111 | .111 | 0.875 |
8 | 1000 | .0001 | 0.0625 |
The computer code and data files described and made available on this web page are distributed under the MIT license
van_der_corput is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
halton, a Python code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
hammersley, a python code which computes elements of a hammersley quasi monte carlo (qmc) sequence, using a simple interface.
latin_random, a python code which computes elements of a latin hypercube dataset, choosing points at random.
normal, a python code which computes elements of a sequence of pseudorandom normally distributed values.
randlc, a python code which generates a sequence of pseudorandom numbers, used by the nas benchmark programs.
rnglib, a python code which implements a random number generator (rng) with splitting facilities, allowing multiple independent streams to be computed, by l'ecuyer and cote.
uniform, a python code which computes elements of a uniform pseudorandom sequence.