# Latin HyperCube

A square grid containing sample positions is a Latin square if, and only if, there is only one sample in each row and each column. A Latin HyperCube DOE, categorized as a space filling DOE, is the generalization of this concept to an arbitrary number of dimensions.

When sampling a design space of N variables, the range of each variable is divided into M equally probable intervals. M sample points are then placed to satisfy the Latin HyperCube requirements. As a result, all experiments have unique levels for each input variable and the number of sample points, M, is not a function of the number of input variables.

## Usability Characteristics

• To get a good quality fitting function, a minimum number of runs should be evaluated. (N+1)(N+2)/2 runs are needed to fit a second order polynomial, assuming that most output responses are close to a second order polynomial within the commonly used input variable ranges of -+10%. An additional number of runs equal to 10% is recommended to provide redundancy, which results in more reliable post-processing. As a result, this equation is recommend to calculate the number of runs needed or a minimum of 1.1*(N+1)(N+2)/2 runs.
• The structure of a Latin HyperCube run matrix ensures that the runs are orthogonal. Orthogonality is desirable because it is less likely to result in singularities when creating Least Squares Regression fits.
• Any data in the inclusion matrix is combined with the run data for post-processing. Any run matrix point which is already part of the inclusion data will not be rerun.

## Settings

In the Specifications step, Settings tab, change method settings.
Parameter Default Range Description
Number of Runs $\frac{1.1\left(N+1\right)\left(N+2\right)}{2}$ > 0 integer Number of new designs to be evaluated.
Random Seed 1 Integer

0 to 10000

Controlling repeatability of runs depending on the way the sequence of random numbers is generated.
0
Random (non-repeatable).
>0
Triggers a new sequence of pseudo-random numbers, repeatable if the same number is specified.
Use Inclusion Matrix Off Off or On Concatenation without duplication between the inclusion and the generated run matrix.