Create a logarithmic Latin Hypercube Sampling distribution (with lhsdesign).

Hi,

i want to get a logarithmic sample distribution with lhsdesign and fix boundaries. Heres my code:

num_samples = 40; % number of samples
num_parameters = 2; % number of parameters

variableBounds = [1e-14 1e-12; 1e-14 1e-12]; % defines the boundaries

lhsMatrix = lhsdesign(num_samples, num_parameters);

% Scale the LHS samples to the desired parameter ranges
params = zeros(num_samples, num_parameters);
    
        for j = 1:num_parameters
            params(:, j) = lhsMatrix(:, j) * (variableBounds(j, 2) - variableBounds(j, 1)) + variableBounds(j, 1);
        end
       
scatter(params(:,1), params(:,2),'filled', 'MarkerFaceAlpha',0.3, 'SizeData',90,'MarkerFaceColor', 'blue');
xlabel('$Parameter 1$', 'Interpreter', 'latex');
ylabel('$Parameter 2$', 'Interpreter', 'latex');
title('Sample distribution');
% set(gca, 'XScale', 'log');
% set(gca, 'YScale', 'log');
grid on

If i create the lhsMatrix with lhsdesign, the samples will get distributed perfectly with no log axes.

What i desire is a proper sample distribution with log axes.

num_samples = 40; % number of samples
num_parameters = 2; % number of parameters

variableBounds = [1e-14 1e-12; 1e-14 1e-12]; % defines the boundaries

lhsMatrix = lhsdesign(num_samples, num_parameters);

% Scale the LHS samples to the desired parameter ranges
params = zeros(num_samples, num_parameters);
    
        for j = 1:num_parameters
            params(:, j) = lhsMatrix(:, j) * (variableBounds(j, 2) - variableBounds(j, 1)) + variableBounds(j, 1);
        end
       
scatter(params(:,1), params(:,2),'filled', 'MarkerFaceAlpha',0.3, 'SizeData',90,'MarkerFaceColor', 'blue');
xlabel('$Parameter 1$', 'Interpreter', 'latex');
ylabel('$Parameter 2$', 'Interpreter', 'latex');
title('Sample distribution');
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'log');
grid on

As you can see the distribution with log axes is really bad. So i need to create a lhsMatrix with log values to get a proper distribution on my log scales. Can someone help me out with this problem?

Thanks in advance :)

Answer 1

[Harald]

Hi Lorenz,

I am not sure whether this is legitimate from the statistics point of view, but you could get a nice distribution by taking the log of the bounds and then the exponential of params. For better readability, you could use base 10 for both.

variableBounds = log10([1e-14 1e-12; 1e-14 1e-12]); % or log
%...
params = 10.^(params); % or exp    

Best wishes,

Harald

[Lorenz]

thanks harald, that will do it :)