How do I get some sampling points from a 4 dimentional function at LHS(Latin Hypercube Sampling)?

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민제 강
민제 강 2021-7-12
回答： Zuber Khan 2024-5-9
function scores = rosenbrockfcn(x)
scores = 0;
n = size(x, 2);
assert(n >= 1, 'Given input X cannot be empty');
a = 1;
b = 100;
for i = 1 : (n-1)
scores = scores + (b * ((x(:, i+1) - (x(:, i).^2)) .^ 2)) + ((a - x(:, i)) .^ 2);
end
This is Rosenbrock function.
I want to get some samples from a 4 dimentional rosenbrock function.
like [x1 x2 x3 x4] and f(x)
Boundary conditions are [-10 10]
Please let me know. Thank you!

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回答（1 个）

Zuber Khan
Zuber Khan 2024-5-9
Hi,
To obtain Latin Hypercube Sampling (LHS) points from a 4-dimensional Rosenbrock function, you can use the "lhsdesign" function in MATLAB. The function as used below,
X = lhsdesign(n,p)
returns a Latin hypercube sample matrix of size n-by-p. For each column of 'X', the 'n' values are randomly distributed with one from each interval (0,1/n), (1/n,2/n), ..., (1 - 1/n,1), and randomly permuted.
You can generate LHS samples and evaluate the Rosenbrock function at sampled points as follows:
numSamples = 10; % Assuming there are 10 sample points
numDims = 4; % Number of dimensions
% Generate Latin Hypercube Samples in the range [0, 1]
lhsSamples = lhsdesign(numSamples, numDims);
% Scale samples to the range [-10, 10]
lowerBound = -10;
upperBound = 10;
scaledPoints = lowerBound + (upperBound - lowerBound) * lhsSamples; % Transform [0, 1] to [-10, 10]
% Evaluate the Rosenbrock function at the LHS points
scores = rosenbrockfcn(scaledPoints);
% Combine the sampled points and corresponding function values if you want
% better visibility
sampledData = [scaledPoints, scores];
I hope this will resolve your query.
Regards,
Zuber

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