# Design of ExperimentsΒΆ

The method is used in the following context: is a vector of input parameters. We want to determine a particular set of values of according to a particular design of experiments .

Different types of design of experiments can be determined:

some

*stratified*patterns: axial, composite, factorial or box patterns,some

*weighted*patterns that we can split into different categories: the random patterns, the low discrepancy sequences and the Gauss product.

**Stratified design of experiments**

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

**Weighted design of experiments**

*random patterns*, where the set of input data is generated from the joint distribution of the input random vector, according to the Monte Carlo sampling technique or the LHS one (refer to and ).

*low discrepancy sequences*. The Faure, Halton, Haselgrove, Reverse Halton and Sobol sequences are proposed.

*Gauss product*which is the set of points which components are the respective Gauss set (i.e. the roots of the orthogonal polynomials with respect to the univariate distribution).

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

**Combinatorial generators**

being a subset with elements of a set with elements, with ;

being a permutation of elements taken into a set of elements, with ;

being an element of a Cartesian product of sets with elements.

It is important to get indices and not real-valued vectors. The
distinction is made explicit by calling these design of experiments
*Combinatorial Generators*, which produce collections of indices instead
of samples.

The following figures illustrates the different patterns obtained.

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

API:

See the available design of experiments.

Examples: