generate confidence intervals for mrdivide in matlab

To generate confidence intervals for the mrdivide function in MATLAB, we can use bootstrapping. Bootstrapping is a resampling technique used to estimate the sampling distribution of a statistic.

Here's how you can generate confidence intervals for mrdivide in MATLAB:

1. First, you'll need a dataset on which you'll perform the mrdivide operation. Let's assume you have two matrices A and B:

main.m
A = [1 2 3; 4 5 6; 7 8 9];
B = [1 2 3; 4 5 6; 7 8 9];
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2. Next, define a function that performs mrdivide operation on random samples from your dataset. This function will be used to generate bootstrap samples:

main.m
mrdivide_bootstrap = @(A, B) mrdivide(A(randi(numel(A), size(A))), B(randi(numel(B), size(B))));
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3. Now, you can generate bootstrap samples by resampling your dataset and applying the mrdivide operation on each sample. Let's say you want to generate 1000 bootstrap samples:

main.m
num_samples = 1000;
bootstrap_samples = arrayfun(@(i) mrdivide_bootstrap(A, B), 1:num_samples, 'UniformOutput', false);
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4. Once you have the bootstrap samples, you can calculate the mean of each sample:

main.m
bootstrap_means = cellfun(@(sample) mean(sample(:)), bootstrap_samples);
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5. Finally, you can calculate the confidence interval for mrdivide using the percentiles of the bootstrap means. For example, to calculate a 95% confidence interval:

main.m
confidence_level = 0.95;
lower_bound = prctile(bootstrap_means, 100 * (1 - confidence_level) / 2);
upper_bound = prctile(bootstrap_means, 100 * (1 + confidence_level) / 2);

fprintf('Confidence interval for mrdivide: [%f, %f]\n', lower_bound, upper_bound);
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This will give you the confidence interval estimate for the mrdivide operation.

Note: Bootstrapping assumes that your dataset is a representative sample from the population of interest. If your dataset violates this assumption, bootstrapping may not be appropriate.