cocomice / matlab-lhsdesigncon

Latin hypercube sample with constraints.

lhsdesigncon (MATLAB)

MATLAB function to generate an NxP latin hypercube sample with bounds and linear constraints and optional exponential distribution.

Getting the lhsdesigncon MATLAB function

To use the lhsdesigncon function:

1. Download the zip file from either:

• MATLAB Central File Exchange, or
• GitHub.

2. Unzip the files and place them on your MATLAB path (e.g. your My Documents/MATLAB folder on Windows).
3. Use the function (see examples below).

This GitHub repo is a development library. To contribute fork this repo and submit pull requests.

MATLAB Function Description and Examples

Generate an NxP latin hypercube sample with bounds and linear constraints and optional exponential distribution.

X=LHSDESIGNCON(N,P,LB,UB,ISEXP) generates a latin hypercube sample X containing N values on each of P variables. For each column, if ISEXP is FALSE the N values are randomly distributed with one from each of N intervals, between LB and UB, of identical widths (UB-LB)/N, and they are randomly permuted. For columns with ISEXP=TRUE, the logarithm of the intervals have identical widths.

X=LHSDESIGNCON(...,A,b) generates a latin hypercube sample subject to the linear inequalities A*x ? b.

X=LHSDESIGNCON(...,'PARAM1',val1,'PARAM2',val2,...) specifies parameter name/value pairs to control the sample generation. See LHSDESIGN for valid parameters.

Latin hypercube designs are useful when you need a sample that is random but that is guaranteed to be relatively uniformly/exponentially distributed over each dimension.

Example: The following command generates a latin hypercube sample X containing 10000 values for each of 2 variables. The first variable is uniformly sampled between -100 and +100, the second is exponentially sampled between 10^-1 and 10^2 (ie. the exponent is uniformly sampled between -1 and 2). Additionally, the samples satisfy the constraints X(1) + X(2) <= 50 and X(2) - X(1) >= 25.

A = [1, 1; 1, -1]; b = [50; -25]; % A x <= b
x = lhsdesigncon(10000,2,[-100 1e-1],[100 1e2],[false true],A,b);
% Show samples are well distributed within constraints.
figure;
semilogy(x(:,1),x(:,2),'.');

Limitations

• The constraints are not checked for consistency. If they are inconsistent the function will loop forever, with just a warning "None of ... samples fit constraints."

License

The MATLAB Central File Exchange and this source code are distributed under the BSD-2 License.