>

Continuous built-in kernels

Unless otherwise stated in this section we denote by $\Omega=\{X_1,X_2,...,X_n\}$ a variable set with $n$ unidimensional continuous variables $X_i=[x_i^{min},x_i^{max}]$. $\Omega_o=\{X_1^o,X_2^o,...,X_n^o\}$ denotes a half-open variable set of $\Omega$ with $X_i^o=[x_i^{omin},x_i^{omax})$ being a half-open continuous subinterval on $X_i \in \Omega$. Particularly, we denote by $\Omega _o^\ast$ the half-open variable set of $\Omega$ such that $x_i^{min}=x_i^{omin}$ and $x_i^{max}=x_i^{omax}$.

To depict the built-in kernels main functionalities, we will use the following program framework:

1. Define the variable types, set and values.
2. Print the variable sets and types
3. Construct the kernel.
4. Print the kernel.
5. Plot the kernel.
6. Execute and print $n$ draw tests.
7. Execute and print $n$ best tests.
8. Execute and print $m$ compute tests.

Program 8 is one instance of this framework and illustrates the case for a plCUniform. In this section, we use the same framework for all the program examples. Consequently, we don not show the full program for each of the build-in kernel examples, just a few lines of the program and the resulting output are shown.