normal

normal, an Octave code 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 MIT license

Languages:

normal is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

normal_test

octave_random_test, an Octave code which uses MATLAB's random number generators.

random_sorted, an Octave code which generates vectors of random values which are already sorted.

ranlib, an Octave code which produces random samples from Probability Density Functions (PDF's), including Beta, Chi-square Exponential, F, Gamma, Multivariate normal, Noncentral chi-square, Noncentral F, Univariate normal, random permutations, Real uniform, Binomial, Negative Binomial, Multinomial, Poisson and Integer uniform, by Barry Brown and James Lovato.

rnglib, an Octave code which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

truncated_normal, an Octave code 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, an Octave code which computes a sequence of uniformly distributed pseudorandom values.

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:

• c4_normal_01.m, returns a unit pseudonormal C4.
• c8_normal_01.m, returns a unit pseudonormal dC8.
• i4_normal_ab.m, returns a scaled pseudonormal I4.
• r4_normal_01.m, returns a unit pseudonormal R4.
• r4_normal_ab.m, returns a scaled pseudonormal R4.
• r4_uniform_01.m, returns a unit pseudorandom R4.
• r8_normal_01.m, returns a unit pseudonormal R8.
• r8_normal_ab.m, returns a scaled pseudonormal R8.
• r8mat_normal_01.m, returns a unit pseudonormal R8MAT.
• r8mat_normal_ab.m, returns a scaled pseudonormal R8MAT.
• r8mat_print.m, prints an R8MAT.
• r8mat_print_some.m, prints some of an R8MAT.
• r8vec_normal_01.m, returns a unit pseudonormal R8VEC.
• r8vec_normal_ab.m, returns a scaled pseudonormal R8VEC.
• r8vec_print.m, prints an R8VEC.