RANDOM_SORTED
Generate Sorted Random Vectors

RANDOM_SORTED is a Python library which generates vectors of random values which are already sorted.

Since the computation of the spacing between the values requires some additional arithmetic, it is not immediately obvious when this procedure will be faster than simply generating a vector of random values and then sorting it.

Because the library can generate a sorted random vector of values between 0 and 1, it is possible to generate sorted data samples from any distribution for which the inverse Cumulative Density Function (CDF) is known. For instance, to generate sorted normal data, simply generate sorted uniform data, and then apply the inverse of the normal CDF, as in the example code listed below.

Licensing:

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

Languages:

RANDOM_SORTED is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

NORMAL, a Python library which computes a sequence of pseudorandom normally distributed values.

RANDLC, a Python library which generates a sequence of pseudorandom numbers, used by the NAS Benchmark programs.

RNGLIB, a Python library which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

TOMS515, a Python library which can select subsets of size K from a set of size N. This is a version of ACM TOMS Algorithm 515, by Bill Buckles, Matthew Lybanon.

UNIFORM, a Python library which computes a sequence of uniformly distributed pseudorandom values.

VAN_DER_CORPUT, a Python library which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.

Reference:

1. Jon Bentley, James Saxe,
   Generating sorted lists of random numbers,
   ACM Transactions on Mathematical Software,
   Volume 6, Number 3, September 1980, pages 359-364.

Source Code:

• normal_01.py the Normal 01 distribution.
• r8_uniform_01.py returns a uniform random value in [0,1].
• r8poly_print.py prints a polynomial.
• r8poly_value_horner.py uses Horner's method to evaluate a polynomial.
• r8vec_normal_01_sorted.py returns a random sorted vector of normal values.
• r8vec_print.py, prints an R8VEC.
• r8vec_transpose_print.py, prints the "transpose" of an R8VEC.
• r8vec_uniform_01.py, returns a unit pseudorandom R8VEC.
• r8vec_uniform_01_sorted1.py returns a random sorted vector of uniform values.
• r8vec_uniform_01_sorted2.py returns a random sorted vector of uniform values.
• timestamp.py prints the current YMDHMS date as a time stamp.

Examples and Tests:

• random_sorted_test.py, calls all the tests.
• random_sorted_test.sh, runs all the tests.
• random_sorted_test.txt, the output file.

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