# normal_dataset

normal_dataset, a Fortran90 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))
```
where MU is the mean vector, and A is a symmetric positive definite (SPD) 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:

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 symmetric positive definite variance-covariance matrix of dimension m by m.
The data is written to the file normal_m_n.txt.

Although m, n, and seed may be entered on the command line, it probably makes more sense to enter the vector mu and the matrix a interactively.

### 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, a Fortran90 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,