VAN_DER_CORPUT
van der Corput Datasets

VAN_DER_CORPUT is a dataset directory which contains points generated by the 1-dimensional van der Corput sequence.

The arguments that the user may set include:

• BASE, the base of the computation, which might be 2, or any prime, or any integer greater than 1.
• SEED, the index of the first element, which might be 0 or 1;
• N, the number of elements to compute.

Licensing:

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

Related Data and Programs:

HALTON, a dataset directory which contains examples of the Halton sequence, a multi-dimensional generalization of the van der Corput sequence.

HAMMERSLEY, a dataset directory which contains examples of the Hammersley sequence, a multi-dimensional generalization of the van der Corput sequence.

SEQUENCE_STREAK_DISPLAY, a MATLAB program which can make a "streak plot" of a sequence.

TABLE, a file format which is used to store these datasets.

VAN_DER_CORPUT, a C++ library which computes elements of a 1D van der Corput quasirandom sequence.

VAN_DER_CORPUT_DATASET, a C++ program which creates a van der Corput quasirandom sequence and writes it to a file.

Example dataset:

A typical (but small) dataset looks like this:

#  van_der_corput_2_0_10.txt
#  created by VAN_DER_CORPUT_WRITE.F90
#
#  File generated on March 20 2005   3:04:35.796 PM
#
#  N =              10
#  SEED =            0
#  BASE =            2
#  EPSILON (unit roundoff ) =   0.222045E-15
#
     0.00000    
    0.500000    
    0.250000    
    0.750000    
    0.125000    
    0.625000    
    0.375000    
    0.875000    
    0.625000E-01
    0.562500    
      

Reference:

1. J G van der Corput,
   Verteilungsfunktionen I & II,
   Nederl. Akad. Wetensch. Proc.,
   Volume 38, 1935, pages 813-820, pages 1058-1066.

Datasets:

van_der_corput_2_0_* uses BASE = 2, SEED = 0, and N = 10, 20, 40, 80, 100.

• van_der_corput_2_0_10.txt, the dataset of 10 points.
• van_der_corput_2_0_20.txt, the dataset of 20 points.
• van_der_corput_2_0_40.txt, the dataset of 40 points.
• van_der_corput_2_0_80.txt, the dataset of 80 points.
• van_der_corput_2_0_100.txt, the dataset of 100 points.
• van_der_corput_2_0_100.png, a PNG image of a "streak plot" of the sequence, created by SEQUENCE_STREAK.

van_der_corput_2_5_10 uses BASE = 2, SEED = 5, N = 10.

• van_der_corput_2_5_10.txt, the dataset.

van_der_corput_3_0_10 uses BASE = 3, SEED = 0, N = 10.

• van_der_corput_3_0_10.txt, the dataset.

van_der_corput_10_0_10 uses BASE = 10, SEED = 0, N = 10.

• van_der_corput_10_0_10.txt, the dataset.

You can go up one level to the DATASETS directory.