- https://in.mathworks.com/help/matlab/ref/histcounts.html
- https://www.mathworks.com/help/matlab/ref/cumsum.html
- https://www.mathworks.com/help/matlab/ref/flip.html
- https://www.mathworks.com/help/matlab/ref/deg2rad.html

# Integrate polar histogram values about a certain value

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I have a set of directional (circular) data, and I also have the mean value of this data. I need to find out how to integrate the normlaized polar histogram to clockwise and counter-clockwise away from the mean. How could this be done, given that the data is some value X? Additionally, how could find the angle away from the mean such that I have 0.25 on eitherside of the mean? To put it in math terms, I need to determine what and are the following

Here the PMF is the normalized polar histogram for X.

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### Accepted Answer

Ayush
on 22 Aug 2023

Here is the function to integrate normalized polar histogram to clockwise & counterclockwise away from mean:

function [clockwise_cumulative_sum, counterclockwise_cumulative_sum] = integrate_polar_histogram(data, mean_value)

% Step 1: Normalize the circular data

normalized_data = deg2rad(data - mean_value);

% Step 2: Create a polar histogram

num_bins = 36; % Number of bins for the histogram

[histogram, ~] = histcounts(normalized_data, num_bins, 'BinLimits', [-pi pi]);

% Step 3: Normalize the histogram

normalized_histogram = histogram / numel(normalized_data);

% Step 4: Integrate the normalized histogram

clockwise_cumulative_sum = cumsum(normalized_histogram);

counterclockwise_cumulative_sum = flip(cumsum(flip(normalized_histogram)));

end

Refer to following documentation for further information:

Here is the function to get the angle on either side of the mean to have:

function angle_with_0_25 = find_angle_with_0_25_on_either_side(clockwise_cumulative_sum)

% Find the bin where the cumulative sum reaches 0.25

bin_index = find(clockwise_cumulative_sum >= 0.25, 1);

% Calculate the angle at the midpoint of the bin

angle_with_0_25 = (bin_index + 0.5) * (2 * pi / numel(clockwise_cumulative_sum));

angle_with_0_25 = rad2deg(angle_with_0_25);

end

An example to run the above workflow:

% Example usage

data = [10, 20, 30, 40, 350, 355, 5]; % Example circular data

mean_value = 0; % Example mean value

[clockwise_cumulative_sum, counterclockwise_cumulative_sum] = integrate_polar_histogram(data, mean_value);

angle_with_0_25 = find_angle_with_0_25_on_either_side(clockwise_cumulative_sum);

disp(['Angle away from the mean with 0.25 on either side: ' num2str(angle_with_0_25)]);

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