normal_dataset

normal_dataset, an Octave code which creates a multivariate normal random dataset and writes it to a file.

The multivariate normal distribution for the M dimensional vector X has the form:

        pdf(X) = (2*pi*det(A))**(-M/2) * exp(-0.5*(X-MU)'*inverse(A)*(X-MU))
      

To create X, an MxN matrix containing N samples from this distribution, it is only necessary to

1. create an MxN vector Y, each of whose elements is a sample of the 1-dimensional normal distribution with mean 0 and variance 1;
2. determine the upper triangular Cholesky factor R of the matrix A, so that A = R' * R;
3. compute X = MU + R' * Y.

Usage:

r = normal_dataset m n seed mu a

• m is the spatial dimension;
• n is the number of points to generate;
• seed is the initial seed value;
• mu is the mean vector, of length m;
• a is the positive definite symmetric variance-covariance matrix of dimension m by m.
• r is the computed m by n sequence.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

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

Related Data and Programs:

normal_dataset_test

normal, an Octave code which computes normally distributed pseudorandom values.

Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Springer Verlag, pages 201-202, 1983.
2. Donald Knuth,
   The Art of Computer Programming,
   Volume 2: Seminumerical Algorithms,
   Addison Wesley, 1969.

Source Code:

• normal_dataset.m, the source code.