I run the code below and expect to get a uniform histogram. It's not. I don't understand why not.
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% I have a two column array, the first column is time and the second column is state. I ran interp1 to observe my data at uniform time points. The results were unexpected. In trying to identify the problem, I have run this simpler code expecting the deterministic uniformly spaced points to be uniformly distributed. They are not. Can anyone explain why not? Thanks.
% Parameters
thismesh = 100; % Number of bins
deltat = 1 / thismesh;
lasttime = 1000; % Example last time
% Generate uniform time steps
xx = 0:deltat:lasttime;
% Calculate fractional times
fractime = (xx - floor(xx)).';
% Plot histogram to check uniformity
figure;
histogram(fractime, thismesh);
title('Histogram of fractional times');
xlabel('Fractional time');
ylabel('Count');
% Display counts in each bin
[counts, edges] = histcounts(fractime, thismesh);
disp('Counts per bin:');
disp(counts);
% Expected count per bin
expected_count = length(fractime) / thismesh;
disp('Expected count per bin:');
disp(expected_count);
% Plot actual counts vs expected uniform count
figure;
bar(counts);
hold on;
yline(expected_count, 'r', 'LineWidth', 2);
hold off;
title('Actual counts vs Expected uniform count');
xlabel('Bin');
ylabel('Count');
legend('Actual counts', 'Expected count');
[SL: formatted code as code and ran that code]
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the cyclist
2024-5-30
It's because of your choice of 100 bins is tuned to the periodicity of your function in a way that makes it the counts chaotic near the bin edges. Here is a better choice for binning, that gives what you expect.
% Parameters
thismesh = 100; % Number of bins
deltat = 1 / thismesh;
lasttime = 1000; % Example last time
% Generate uniform time steps
xx = 0:deltat:lasttime;
% Calculate fractional times
fractime = (xx - floor(xx)).';
%%
% Plot histogram to check uniformity
figure;
histogram(fractime, -0.005 : 0.01 : 1.005);
title('Histogram of fractional times');
xlabel('Fractional time');
ylabel('Count');
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