VAN_DER_CORPUT
The van der Corput
Quasirandom Sequence

VAN_DER_CORPUT is a library of C++ routines, using double precision arithmetic, that compute the van der Corput quasirandom sequence.

VAN_DER_CORPUT includes several subroutines to make it easy to manipulate this computation, to compute the next N entries, to compute a particular entry, or to restart the sequence at a particular point.

The NDIM-dimensional Halton sequence is derived from the 1-dimensional van der Corput sequence by using a set of different (usually distinct prime) bases for each dimension, and the Hammersley sequence is derived in almost the same way.

Related Data and Programs:

CVT is a C++ library of routines for computing points in a Centroidal Voronoi Tessellation.

FAURE is a C++ library of routines for computing Faure sequences.

GRID is a C++ library of routines for computing points on a grid.

HALTON is a C++ library of routines for computing Halton sequences.

HAMMERSLEY is a C++ library of routines for computing Hammersley sequences.

HEX_GRID is a C++ library of routines for computing sets of points in a 2D hexagonal grid.

IHS is a C++ library of routines for computing improved Latin Hypercube datasets.

LATIN_CENTER is a C++ library of routines for computing Latin square data choosing the center value.

LATIN_EDGE is a C++ library of routines for computing Latin square data choosing the edge value.

LATIN_RANDOM is a C++ library of routines for computing Latin square data choosing a random value in the square.

NIEDERREITER2 is a C++ library of routines for computing Niederreiter sequences with base 2.

NORMAL is a C++ library which computes elements of a sequence of pseudorandom normally distributed values.

SEQUENCE_STREAK_DISPLAY is a MATLAB program that can make a "streak file" of a van der Corput sequence.

SOBOL is a C++ library of routines for computing Sobol sequences.

UNIFORM is a C++ library of routines for computing uniform random values.

VAN_DER_CORPUT is also available in a FORTRAN90 version and a MATLAB version.

VAN_DER_CORPUT is a dataset directory which contains datasets of van der Corput sequences.

Reference:

1. John Halton,
   On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,
   Numerische Mathematik,
   Volume 2, pages 84-90, 1960.
2. John Hammersley,
   Monte Carlo methods for solving multivariable problems,
   Proceedings of the New York Academy of Science,
   Volume 86, pages 844-874, 1960.
3. Johannes van der Corput,
   Verteilungsfunktionen I & II,
   Nederl. Akad. Wetensch. Proc.,
   Volume 38, 1935, pages 813-820, pages 1058-1066.

Source Code:

• van_der_corput.C, the source code.
• van_der_corput.H, the include file.
• van_der_corput.csh, commands to compile the source code.

Examples and Tests:

• van_der_corput_prb.C, a sample problem.
• van_der_corput_prb.csh, commands to compile, link and run the sample problem.
• van_der_corput_prb.out, sample problem output.

List of Routines:

• DIGIT_TO_CH returns the base 10 digit character corresponding to a digit.
• GET_SEED returns a random seed for the random number generator.
• I4_LOG_10 returns the whole part of the logarithm base 10 of an integer.
• I4_TO_S converts an integer to a string.
• I4_TO_VAN_DER_CORPUT computes an element of a van der Corput sequence.
• I4_TO_VAN_DER_CORPUT_SEQUENCE: next N elements of a van der Corput sequence.
• R8_EPSILON returns the R8 round off unit.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING returns the current YMDHMS date as a string.
• VAN_DER_CORPUT computes the next element in the van der Corput sequence.
• VAN_DER_CORPUT_BASE_GET gets the base for a van der Corput sequence.
• VAN_DER_CORPUT_BASE_SET sets the base for a van der Corput sequence.
• VAN_DER_CORPUT_SEED_GET gets the "seed" for the van der Corput sequence.
• VAN_DER_CORPUT_SEED_SET sets the "seed" for the van der Corput sequence.
• VAN_DER_CORPUT_SEQUENCE: next N elements in the van der Corput sequence.
• VAN_DER_CORPUT_WRITE writes a van der Corput dataset to a file.

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