The Vandermonde object

Every sample has a Vandermonde object. The importance of the Vandermonde matrix is explained in Appendix C of the thesis. It is essential to the algorithms that work on the sample: least square fitting, calculating the Fisher information and taking the mean squared error. Building the Vandermonde matrix and especially putting it in triangular form are time expensive operations. The time complexity of putting it into triangular form is O(n³). A Vandermonde matrix of size n x n is useful for polynomials of degree n-1 or lower. But, at least with the algorithms known to the author of this application, for a higher degree polynomial a bigger Vandermonde matrix has to be built from the sample and again put into triangular form. The attributes of the Vandermonde object specify the dimension of the matrix and whether it has already been built and put into triangular form.

Normally you shouldn't use this object. Selecting a sample for a polynomial and fitting an n-degree polynomial on it will build the n+1 degree Vandermonde matrix for you. The matrix is preserved and will be reused whenever needed. It is saved and loaded together with the project. But remember that first fitting a low degree polynomial on a sample and than fitting a high degree polynomial will result in the expensive recalculation of the Vandermonde matrix.