jburkardt

DIAPHONY\ the “Diaphony” (dispersion)\ of an M-dimensional Pointset {#diaphony-the-diaphony-dispersion-of-an-m-dimensional-pointset align=”center”} ============================


DIAPHONY is a C++ program which computes the “diaphony” of an M-dimensional pointset.

The “diaphony” of an M-dimensional pointset is a numeric measure of the uniformity of the dispersion of the points throughout the unit hypercube.

Regarded as a random variable itself, the diaphony of a set of N points has an expected value of 1/sqrt(N).

For the Halton datasets in 2D, 7D and 16D, here is the table of the number of points versus the diaphony:

Diaphony(M,N) M=2D M=7D M=16D 1/Sqrt(N) ————— ——- ——- ——- ———– N=10 0.246 0.316 0.316 0.316 N=100 0.043 0.099 0.099 0.100 N=1000 0.006 0.031 0.031 0.031 N=10000 0.001 0.009 0.009 0.010

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

DIAPHONY is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

STAR_DISCREPANCY, a C++ program which reads a TABLE file of points (presumed to lie in the unit hypercube) and computes bounds on the star discrepancy, a measure of dispersion, by Eric Thiemard.

TABLE_LATINIZE, a C++ program which reads a file of points and creates a “latinized” version by adjusting the data.

TABLE_QUALITY, a C++ program which reads a file of points and computes the quality of dispersion.

Reference: {#reference align=”center”}

  1. Peter Heelekalek,\ On Correlation Analysis of Pseudorandom Numbers, in Monte Carlo and Quasi-Monte Carlo Methods 1996,\ edited by Harald Niederreiter, Peter Hellekalek, Gerhard Larcher, and Peter Zinterhof,\ Volume 127 of Lecture Notes in Statistics,\ Springer Verlag, 1997, pages 251-265.
  2. Peter Heelekalek, Harald Niederreiter,\ The Weighted Spectral Test: Diaphony,\ ACM Transactions on Modeling and Computer Simulation,\ Volume 8, Number 1, January 1998, pages 43-60.
  3. Peter Heelekalek, Hannes Leeb,\ Dyadic Diaphony,\ Acta Arithmetica,\ Volume 80, Number 2, 1997, pages 187-196.

Source Code: {#source-code align=”center”}

List of Routines: {#list-of-routines align=”center”}

You can go up one level to the C++ source codes.


Last revised on 25 January 2012.