GP-EIGEN: Find eigenvalues/vectors of a Gaussian process's covariance. GP-eigen prints the eigenvalues and/or eigenvectors of the covariance matrix for a Gaussian process, as constructed at a specified set of input points. The ratio of the largest to the smallest eigenvalue is a measure of the "conditioning" of the matrix; a large ratio indicates that computational problems may arise. The eigenvalues and eigenvectors are also of theoretical interest. Usage: gp-eigen [ -values ] [ -vectors ] log-file index [ extra ] [ / test-inputs ] Computes the eigenvalues and/or eigenvectors for the Gaussian process stored at the specified iteration in the log file. If no extra argument is given, the covariance matrix for latent values is used, without the noise variance being added to the diagonal. If the extra argument is the string "+noise", the noise is added. This is valid only for a regression model, and only if the noise variances do not vary on a case-by-case basis. If the extra argument is a positive number, that number is added to the diagonal. If there is more than one output/target, the covariance and added noise is for the first. By default, the covariance matrix is for the set of training inputs, but this can be overridden by specifying a file of inputs at the end of the command line. By default, or if only the "-values" option is specified, the eigenvalues are printed on per line, in descending order of magnitude. If both "-values" and "-vectors" are specified, the eigenvalues are followed, on the same line, by their eigenvectors. If only "-vectors" is specified, only the eigenvectors are printed, but they are still ordered according to decreasing eigenvalue. The eigenvalues and eigenvectors are computed by Jacobi iteration, stopping when all off-diagonal elements are less than 1e-10. If the matrix is poorly conditioned, it is possible for some of the eigenvalues found to be negative, even though these cannot be correct, since the covariance matrix is supposed to be positive semi-definite. Copyright (c) 1995-2004 by Radford M. Neal