MATLAB function to generate an NxP latin hypercube sample with bounds and linear constraints and optional exponential distribution.
To use the lhsdesigncon function:
- Download the zip file from either:
- Unzip the files and place them on your MATLAB path
(e.g. your
My Documents/MATLABfolder on Windows). - Use the function (see examples below).
This GitHub repo is a development library. To contribute fork this repo and submit pull requests.
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),'.');- 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."
The MATLAB Central File Exchange and this source code are distributed under the BSD-2 License.