NORMAL
Normal Random Number Generators

NORMAL is a Python library which computes normally distributed pseudorandom numbers.

NORMAL is based on two simple ideas:

• the use of a fairly simple uniform pseudorandom number generator, which can be implemented in software;
• the use of the Box-Muller transformation to convert pairs of uniformly distributed random values to pairs of normally distributed random values.

Using these ideas, it is not too hard to generate normal sequences of real or complex values, of single or double precision. These values can be generated as single quantities, vectors or matrices. An associated seed actually determines the sequence. Varying the seed will result in producing a different sequence.

The fundamental underlying random number generator used here is based on a simple, old, and limited linear congruential random number generator originally used in the IBM System 360.

This library makes it possible to compare certain computations that use normal random numbers, written in C, C++, FORTRAN77, FORTRAN90, MATLAB or Python.

Licensing:

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

Languages:

NORMAL 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:

HALTON, a Python library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.

HAMMERSLEY, a Python library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.

PROB, a Python library which evaluates, samples, inverts, and characterizes a number of Probability Density Functions (PDF's) and Cumulative Density Functions (CDF's), including anglit, arcsin, benford, birthday, bernoulli, beta_binomial, beta, binomial, bradford, burr, cardiod, cauchy, chi, chi squared, circular, cosine, deranged, dipole, dirichlet mixture, discrete, empirical, english sentence and word length, error, exponential, extreme values, f, fisk, folded normal, frechet, gamma, generalized logistic, geometric, gompertz, gumbel, half normal, hypergeometric, inverse gaussian, laplace, levy, logistic, log normal, log series, log uniform, lorentz, maxwell, multinomial, nakagami, negative binomial, normal, pareto, planck, poisson, power, quasigeometric, rayleigh, reciprocal, runs, sech, semicircular, student t, triangle, uniform, von mises, weibull, zipf.

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

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.

TRUNCATED_NORMAL, a Python library which works with the truncated normal distribution over [A,B], or [A,+oo) or (-oo,B], returning the probability density function (PDF), the cumulative density function (CDF), the inverse CDF, the mean, the variance, and sample values.

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. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Second Edition,
   Springer, 1987,
   ISBN: 0387964673.
2. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, December 1986, pages 362-376.
3. Donald Knuth,
   The Art of Computer Programming,
   Volume 2, Seminumerical Algorithms,
   Third Edition,
   Addison Wesley, 1997,
   ISBN: 0201896842.
4. Pierre LEcuyer,
   Random Number Generation,
   in Handbook of Simulation,
   edited by Jerry Banks,
   Wiley, 1998,
   ISBN: 0471134031,
   LC: T57.62.H37.
5. Peter Lewis, Allen Goodman, James Miller,
   A Pseudo-Random Number Generator for the System/360,
   IBM Systems Journal,
   Volume 8, 1969, pages 136-143.

Source Code:

• c8_normal_01.py, returns a unit pseudonormal dC8.
• i4_normal_ab.py, returns a scaled pseudonormal I4.
• r8_normal_01.py, returns a unit pseudonormal R8.
• r8_normal_ab.py, returns a scaled pseudonormal R8.
• r8_uniform_01.py, returns a unit pseudorandom R8.
• r8mat_normal_01.py, returns a unit pseudonormal R8MAT.
• r8mat_normal_ab.py, returns a scaled pseudonormal R8MAT.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8vec_normal_01.py, returns a unit pseudonormal R8VEC.
• r8vec_normal_ab.py, returns a scaled pseudonormal R8VEC.
• r8vec_print.py, prints an R8VEC.
• r8vec_uniform_01.py, returns a unit pseudorandom R8VEC.
• timestamp.py, prints the current YMDHMS date as a timestamp.

Examples and Tests:

• normal_test.py, a Python script that calls all the tests.
• normal_test.sh, a BASH script that runs all the tests.
• normal_test.txt, the output file.

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