NORMAL
Normal Random Number Generators

NORMAL is a MATLAB 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 or MATLAB.

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:

ASA183 is a MATLAB library which implements the Wichman-Hill pseudorandom number generator.

CVT is a MATLAB library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a MATLAB library which computes elements of a Faure quasirandom sequence.

GRID is a MATLAB library which computes elements of a grid dataset.

HALTON is a MATLAB library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a MATLAB library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is a MATLAB library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE is a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS is a MATLAB library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a MATLAB librarys which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a MATLAB library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a MATLAB library which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a MATLAB library which computes a latinized Centroidal Voronoi Tessellation.

MATLAB includes the randn function, which can produce a single value, vector or array of normally distributed random numbers.

NIEDERREITER2 is a MATLAB library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version

SOBOL is a MATLAB library which computes elements of a Sobol quasirandom sequence.

UNIFORM is a MATLAB library which computes a sequence of uniformly distributed pseudorandom values.

VAN_DER_CORPUT is a MATLAB library which computes elements of a van der Corput quasirandom sequence.

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_huge.m, returns a huge I4.
• i4_normal.m, returns a scaled pseudonormal I4.
• i8_normal.m, returns a scaled pseudonormal I8.
• r4_normal.m, returns a scaled pseudonormal R4.
• r4_normal_01.m, returns a unit pseudonormal R4.
• r4_uniform_01.m, returns a unit pseudorandom R4.
• r8_normal.m, returns a scaled pseudonormal R8.
• r8_normal_01.m, returns a unit pseudonormal R8.
• r8_uniform_01.m, returns a unit pseudorandom R8.
• r8mat_normal.m, returns a scaled pseudonormal R8MAT.
• r8mat_normal_01.m, returns a unit pseudonormal R8MAT.
• r8vec_normal.m, returns a scaled pseudonormal R8VEC.
• r8vec_normal_01.m, returns a unit pseudonormal R8VEC.
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• timestamp.m, prints the current YMDHMS date as a timestamp.

Examples and Tests:

• normal_test.m, a script that runs all the tests.
• normal_test_output.txt, the output file.
• normal_test01.m, tests C4_NORMAL_01.
• normal_test02.m, tests C8_NORMAL_01.
• normal_test03.m, tests I4_NORMAL.
• normal_test04.m, tests I8_NORMAL.
• normal_test05.m, tests R4_NORMAL.
• normal_test06.m, tests R4_NORMAL_01.
• normal_test07.m, tests R8_NORMAL.
• normal_test08.m, tests R8_NORMAL_01.
• normal_test09.m, tests R8_NORMAL_01.
• normal_test10.m, tests R8_NORMAL_01.
• normal_test11.m, tests R8_NORMAL_01 and R8MAT_NORMAL_01.
• normal_test12.m, tests R8_NORMAL_01 and R8VEC_NORMAL_01.

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