VAN_DER_CORPUT
The van der Corput
Quasirandom Sequence

VAN_DER_CORPUT is a set of MATLAB routines that compute the van der Corput quasirandom sequence.

It also 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 disttinct prime) bases for each dimension, and the Hammersley sequence is derived in almost the same way.

Related Data and Programs:

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

VAN_DER_CORPUT is also available in a C++ version and a FORTRAN90 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. J G van der Corput,
   Verteilungsfunktionen I & II,
   Nederl. Akad. Wetensch. Proc.,
   Volume 38, 1935, pages 813-820, pages 1058-1066.

Source Code:

• i4_to_van_der_corput.m, computes the SEED-th element of the van der Corput sequence in base BASE.
• i4_to_van_der_corput_sequence.m, computes the next N elements, starting at SEED, of the van der Corput sequence in base BASE.
• r8_epsilon.m, returns the machine precision for R8's.
• timestamp.m, prints the current YMDHMS date as a timestamp.
• timestring.m, returns the current YMDHMS date as a string.
• van_der_corput.m, computes the next element of the van der Corput sequence in the current base.
• van_der_corput_base_get.m, returns the current base.
• van_der_corput_base_set.m, sets the current base.
• van_der_corput_seed_get.m, returns the current seed.
• van_der_corput_seed_set.m, sets the current seed.
• van_der_corput_sequence.m, computes the next N elements of the van der Corput sequence, starting at the current seed, in the current base.
• van_der_corput_write.m, writes a van der Corput sequence to a file.

Examples and Tests:

• van_der_corput_test.m, runs all the tests.
• van_der_corput_test01.m, tests van_der_corput.
• van_der_corput_test02.m, tests van_der_corput_sequence.
• van_der_corput_test03.m, tests van_der_corput_seed_get and van_der_corput_seed_set.
• van_der_corput_test04.m, tests van_der_corput_base_get and van_der_corput_base_set.
• van_der_corput_test045.m, tests van_der_corput_seed_get and van_der_corput_seed_set.
• van_der_corput_test05.m, tests i_to_van_der_corput.
• van_der_corput_test06.m, tests i_to_van_der_corput_sequence.
• van_der_corput_test.out, output from the tests.

You can go up one level to the MATLAB source codes.