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

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!

Answer 1

[Zuber Khan]

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