Syntax

Arguments and performed function

L = chol(X);

L is a lower-triangular matrix such that: L*L′= X

• X must be a symmetric and positive-definite matrix or dataset
• If X is not positive definite an error is produced

[v, V] = eig(X);

If X is an $M\times M$ symmetric matrix then v is an $M\times 1$ vector that contains the eigenvalues of X and V is an $M\times M$ matrix that contains the corresponding eigenvectors, such that: V*diag(v)*inv(V)= X

• X must be a symmetric matrix or dataset
• Only the lower triangular part of X is used for the decomposition. This means that if X is not symmetric, BayES will not produce a warning or error message

[x, w] = quadrature(n $[$, s$]$);

x is an n$\times 1$ vector of abscissae and w an n$\times 1$ vector of corresponding weights for a Gaussian quadrature. Depending on the value of the optional argument, the abscissae and weights could be for a Gauss-Laguerre or Gauss-Hermite quadrature.
For the Gauss-Laguerre quadrature it holds:
${\sum }_{i=1}^n$ w${}_i\cdot f($x${}_i)\approx {\int \; <!--nolimits-->}_0^{+\infty }{e}^{-x}f\left(x_i\right)\text{d}x$
For the Gauss-Hermite quadrature it holds:
${\sum }_{i=1}^n$ w${}_i\cdot f($x${}_i)\approx {\int \; <!--nolimits-->}_{-\infty }^{\infty }{e}^{-x^2}f\left(x_i\right)\text{d}x$

• i must be an integer between 2 and 300;
• s must be equal to either "laguerre" or "hermite". The default value for s is "laguerre", for which the abscissae and weights are for a Gauss-Laguerre quadrature.