NORMAL_DATASET Generate Multivariate Normal Random Datasets

NORMAL_DATASET is a MATLAB program 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))
```
where MU is the mean vector, and A is a positive definite symmetric matrix called the variance-covariance matrix.

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
where
• 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.
The data is written to the file normal_m_n.txt.

Languages:

NORMAL_DATASET is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CVT_DATASET, a MATLAB program which computes a Centroidal Voronoi Tessellation and writes it to a file.

FAURE_DATASET, a MATLAB program which creates a Faure quasirandom dataset;

GRID_DATASET, a MATLAB program which creates a grid sequence and writes it to a file.

HALTON_DATASET, a MATLAB program which creates a Halton sequence and writes it to a file.

HAMMERSLEY_DATASET, a MATLAB program which creates a Hammersley sequence and writes it to a file.

HEX_GRID_DATASET, a MATLAB program which creates a hexagonal grid dataset and writes it to a file.

IHS_DATASET, a MATLAB program which creates an improved distributed Latin hypercube dataset and writes it to a file.

LATIN_CENTER_DATASET, a MATLAB program which creates a Latin Center Hypercube dataset;

LATIN_EDGE_DATASET, a MATLAB program which creates a Latin Edge Hypercube dataset;

LATIN_RANDOM_DATASET, a MATLAB program which creates a Latin Random Hypercube dataset;

LCVT_DATASET, a MATLAB program which computes a latinized Centroidal Voronoi Tessellation and writes it to a file.

NIEDERREITER2_DATASET, a MATLAB program which creates a Niederreiter quasirandom dataset with base 2;

NORMAL, a MATLAB library which computes normally distributed pseudorandom values.

SOBOL_DATASET, a MATLAB program which computes a Sobol quasirandom sequence and writes it to a file.

UNIFORM_DATASET, a MATLAB program which generates a dataset of uniform pseudorandom values and write them to a file.

VAN_DER_CORPUT_DATASET, a MATLAB program which creates a van der Corput quasirandom sequence and writes it to a file.

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,
```          "normal_dataset ( 2, 25, 123456789, [ 1 2 ],  [ 1 0; 0 3] )".