New routines to compute PDF, cumulants of order parameter
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@ -92,8 +92,16 @@ function results = analyzeFolder(options)
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bkg_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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if (isempty(atm_img) && isa(atm_img, 'double')) || ...
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(isempty(bkg_img) && isa(bkg_img, 'double')) || ...
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(isempty(dark_img) && isa(dark_img, 'double'))
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refimages = nan(size(refimages)); % fill with NaNs
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absimages = nan(size(absimages));
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else
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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end
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end
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% ===== Fringe removal =====
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@ -0,0 +1,41 @@
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function [cumulants_mean, cumulants_ci, bootstrap_samples] = bootstrapCumulants(x, maxOrder, nBoot)
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% bootstrapCumulants - compute bootstrap estimates of cumulants and confidence intervals
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%
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% Syntax:
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% [meanC, ciC, allC] = bootstrapCumulants(x, maxOrder, nBoot)
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%
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% Inputs:
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% x - Data vector (may contain NaNs)
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% maxOrder - Max cumulant order (default: 6)
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% nBoot - Number of bootstrap samples (default: 1000)
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%
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% Outputs:
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% cumulants_mean - Mean of bootstrap cumulants
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% cumulants_ci - 95% confidence intervals [2.5th; 97.5th] percentile
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% bootstrap_samples - All bootstrap cumulants (nBoot x maxOrder)
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if nargin < 2, maxOrder = 6; end
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if nargin < 3, nBoot = 1000; end
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x = x(:);
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x = x(~isnan(x)); % Remove NaNs
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if isempty(x)
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cumulants_mean = NaN(1, maxOrder);
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cumulants_ci = NaN(2, maxOrder);
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bootstrap_samples = NaN(nBoot, maxOrder);
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return;
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end
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N = numel(x);
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bootstrap_samples = zeros(nBoot, maxOrder);
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for b = 1:nBoot
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xb = x(randi(N, [N, 1])); % Resample with replacement
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bootstrap_samples(b, :) = computeCumulants(xb, maxOrder);
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end
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cumulants_mean = mean(bootstrap_samples, 1);
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cumulants_ci = prctile(bootstrap_samples, [2.5, 97.5]);
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end
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@ -8,13 +8,13 @@ format long
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font = 'Bahnschrift';
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% Load data
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Data = load('C:/Users/Karthik/Documents/GitRepositories/Calculations/Data-Analyzer/Comparison/Max_g2_DropletsToStripes.mat', 'unique_scan_parameter_values', 'mean_max_g2_values', 'std_error_g2_values');
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Data = load('C:/Users/Karthik/Documents/GitRepositories/Calculations/Data-Analyzer/StructuralPhaseTransition/SpectralAnalysisRoutines/Max_g2_DropletsToStripes.mat', 'unique_scan_parameter_values', 'mean_max_g2_values', 'std_error_g2_values');
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dts_scan_parameter_values = Data.unique_scan_parameter_values;
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dts_mean_mg2 = Data.mean_max_g2_values;
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dts_stderr_mg2 = Data.std_error_g2_values;
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Data = load('C:/Users/Karthik/Documents/GitRepositories/Calculations/Data-Analyzer/Comparison/Max_g2_StripesToDroplets.mat', 'unique_scan_parameter_values', 'mean_max_g2_values', 'std_error_g2_values');
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Data = load('C:/Users/Karthik/Documents/GitRepositories/Calculations/Data-Analyzer/StructuralPhaseTransition/SpectralAnalysisRoutines/Max_g2_StripesToDroplets.mat', 'unique_scan_parameter_values', 'mean_max_g2_values', 'std_error_g2_values');
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std_scan_parameter_values = Data.unique_scan_parameter_values;
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std_mean_mg2 = Data.mean_max_g2_values;
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@ -30,10 +30,10 @@ errorbar(std_scan_parameter_values, std_mean_mg2, std_stderr_mg2, 'o--', ...
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set(gca, 'FontSize', 14, 'YLim', [0, 1]);
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hXLabel = xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex');
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hYLabel = ylabel('$\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', 'Interpreter', 'latex');
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hTitle = title('B = 2.42 G', 'Interpreter', 'tex');
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% hTitle = title('B = 2.42 G', 'Interpreter', 'tex');
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legend
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set([hXLabel, hYLabel], 'FontName', font)
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set([hXLabel, hYLabel], 'FontSize', 14)
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set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold'); % Set font and size for title
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% set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold'); % Set font and size for title
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grid on
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%%
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@ -0,0 +1,52 @@
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function cumulants = computeCumulants(x, maxOrder)
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% computeCumulants - compute cumulants up to specified order from data vector x
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%
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% Syntax: cumulants = computeCumulants(x, maxOrder)
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%
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% Inputs:
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% x - 1D numeric vector (may contain NaNs)
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% maxOrder - maximum order of cumulants to compute (default: 6)
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%
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% Output:
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% cumulants - vector [kappa_1, ..., kappa_maxOrder]
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if nargin < 2
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maxOrder = 6;
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end
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x = x(:);
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x = x(~isnan(x)); % Remove NaNs
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if isempty(x)
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cumulants = NaN(1, maxOrder);
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return;
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end
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mu1 = mean(x, 'omitnan');
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x_centered = x - mu1;
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cumulants = zeros(1, maxOrder);
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cumulants(1) = mu1;
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mu = zeros(1, maxOrder);
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for k = 2:maxOrder
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mu(k) = mean(x_centered.^k, 'omitnan');
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end
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if maxOrder >= 2
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cumulants(2) = mu(2);
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end
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if maxOrder >= 3
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cumulants(3) = mu(3);
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end
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if maxOrder >= 4
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cumulants(4) = mu(4) - 3 * mu(2)^2;
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end
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if maxOrder >= 5
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cumulants(5) = mu(5) - 10 * mu(3) * mu(2);
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end
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if maxOrder >= 6
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cumulants(6) = mu(6) - 15 * mu(4) * mu(2) - 10 * mu(3)^2 + 30 * mu(2)^3;
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end
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end
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@ -3,9 +3,9 @@ groupList = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1
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"/images/ODT_2_Axis_Camera/in_situ_absorption", "/images/Horizontal_Axis_Camera/in_situ_absorption", ...
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"/images/Vertical_Axis_Camera/in_situ_absorption"];
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folderPath = "//DyLabNAS/Data/TwoDGas/2025/06/23/";
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folderPath = "//DyLabNAS/Data/TwoDGas/2025/07/22/";
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run = '0300';
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run = '0021';
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folderPath = strcat(folderPath, run);
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@ -50,32 +50,32 @@ savefileName = 'DropletsToStripes';
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font = 'Bahnschrift';
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if strcmp(savefileName, 'DropletsToStripes')
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scan_groups = 0:5:45;
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scan_groups = 0:1:40;
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titleString = 'Droplets to Stripes';
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elseif strcmp(savefileName, 'StripesToDroplets')
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scan_groups = 45:-5:0;
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scan_groups = 40:-1:0;
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titleString = 'Stripes to Droplets';
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end
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% Flags
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skipNormalization = false;
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skipUnshuffling = true;
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skipNormalization = true;
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skipUnshuffling = false;
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skipPreprocessing = true;
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skipMasking = true;
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skipIntensityThresholding = true;
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skipBinarization = true;
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skipMovieRender = true;
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skipSaveFigures = false;
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skipSaveOD = false;
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skipSaveFigures = true;
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skipSaveOD = true;
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%% ===== S-D Settings =====
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groupList = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1_Axis_Camera/in_situ_absorption", ...
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"/images/ODT_2_Axis_Camera/in_situ_absorption", "/images/Horizontal_Axis_Camera/in_situ_absorption", ...
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"/images/Vertical_Axis_Camera/in_situ_absorption"];
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folderPath = "//DyLabNAS/Data/TwoDGas/2025/06/24/";
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folderPath = "//DyLabNAS/Data/TwoDGas/2025/07/23/";
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run = '0001';
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run = '0055';
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folderPath = strcat(folderPath, run);
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@ -120,10 +120,10 @@ savefileName = 'StripesToDroplets';
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font = 'Bahnschrift';
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if strcmp(savefileName, 'DropletsToStripes')
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scan_groups = 0:5:45;
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scan_groups = 0:1:40
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titleString = 'Droplets to Stripes';
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elseif strcmp(savefileName, 'StripesToDroplets')
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scan_groups = 45:-5:0;
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scan_groups = 40:-1:0;
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titleString = 'Stripes to Droplets';
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end
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@ -135,8 +135,8 @@ skipMasking = true;
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skipIntensityThresholding = true;
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skipBinarization = true;
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skipMovieRender = true;
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skipSaveFigures = false;
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skipSaveOD = false;
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skipSaveFigures = true;
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skipSaveOD = true;
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%% ===== Load and compute OD image, rotate and extract ROI for analysis =====
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% Get a list of all files in the folder with the desired file name pattern.
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@ -156,8 +156,16 @@ for k = 1 : length(files)
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bkg_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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if (isempty(atm_img) && isa(atm_img, 'double')) || ...
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(isempty(bkg_img) && isa(bkg_img, 'double')) || ...
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(isempty(dark_img) && isa(dark_img, 'double'))
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refimages = nan(size(refimages)); % fill with NaNs
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absimages = nan(size(absimages));
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else
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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end
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end
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% ===== Fringe removal =====
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@ -86,8 +86,16 @@ for k = 1 : length(files)
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bkg_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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if (isempty(atm_img) && isa(atm_img, 'double')) || ...
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(isempty(bkg_img) && isa(bkg_img, 'double')) || ...
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(isempty(dark_img) && isa(dark_img, 'double'))
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refimages = nan(size(refimages)); % fill with NaNs
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absimages = nan(size(absimages));
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else
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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end
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end
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%% ===== Fringe removal =====
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@ -209,8 +217,8 @@ for i = 1:N_params
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temp(j) = num / denom;
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end
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g2_all(i, dtheta+1) = mean(temp);
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g2_error_all(i, dtheta+1) = std(temp) / sqrt(length(group_idx)); % Standard error
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g2_all(i, dtheta+1) = mean(temp, 'omitnan');
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g2_error_all(i, dtheta+1) = std(temp, 'omitnan') / sqrt(length(group_idx)); % Standard error
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end
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end
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@ -222,7 +230,7 @@ cmap = sky(nParams); % You can also try 'jet', 'turbo', 'hot', etc.
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figure(1);
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clf;
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set(gcf,'Position',[100 100 950 750])
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set(gcf, 'Color', 'w', 'Position',[100 100 950 750])
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hold on;
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legend_entries = cell(nParams, 1);
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@ -3,9 +3,9 @@ groupList = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1
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"/images/ODT_2_Axis_Camera/in_situ_absorption", "/images/Horizontal_Axis_Camera/in_situ_absorption", ...
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"/images/Vertical_Axis_Camera/in_situ_absorption"];
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folderPath = "//DyLabNAS/Data/TwoDGas/2025/06/23/";
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folderPath = "//DyLabNAS/Data/TwoDGas/2025/07/22/";
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run = '0300';
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run = '0021';
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folderPath = strcat(folderPath, run);
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@ -86,8 +86,16 @@ for k = 1 : length(files)
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bkg_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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if (isempty(atm_img) && isa(atm_img, 'double')) || ...
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(isempty(bkg_img) && isa(bkg_img, 'double')) || ...
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(isempty(dark_img) && isa(dark_img, 'double'))
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refimages = nan(size(refimages)); % fill with NaNs
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absimages = nan(size(absimages));
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else
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refimages(:,:,k) = subtractBackgroundOffset(cropODImage(bkg_img, center, span), fraction)';
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absimages(:,:,k) = subtractBackgroundOffset(cropODImage(calculateODImage(atm_img, bkg_img, dark_img, ImagingMode, PulseDuration), center, span), fraction)';
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end
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end
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%% ===== Fringe removal =====
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@ -176,7 +184,7 @@ end
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% Group by scan parameter values (e.g., alpha, angle, etc.)
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[unique_scan_parameter_values, ~, idx] = unique(scan_parameter_values);
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N_params = length(unique_scan_parameter_values);
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N_params = length(unique_scan_parameter_values);
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% Define angular range and conversion
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angle_range = 180;
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@ -189,22 +197,23 @@ window_size = 10;
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angle_threshold = 100;
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% Initialize containers for final results
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mean_max_g2_values = zeros(1, N_params);
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mean_max_g2_angle_values = zeros(1, N_params);
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var_max_g2_values = zeros(1, N_params);
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var_max_g2_angle_values = zeros(1, N_params);
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mean_max_g2_values = zeros(1, N_params);
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skew_max_g2_angle_values = zeros(1, N_params);
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var_max_g2_values = zeros(1, N_params);
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kurt_max_g2_angle_values = zeros(1, N_params);
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fifth_order_cumulant_max_g2_angle_values = zeros(1, N_params);
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sixth_order_cumulant_max_g2_angle_values = zeros(1, N_params);
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% Also store raw data per group
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g2_all_per_group = cell(1, N_params);
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angle_all_per_group = cell(1, N_params);
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max_g2_all_per_group = cell(1, N_params);
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std_error_g2_values = zeros(1, N_params);
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for i = 1:N_params
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group_idx = find(idx == i);
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group_data = delta_nkr_all(group_idx, :);
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N_reps = size(group_data, 1);
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group_idx = find(idx == i);
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group_data = delta_nkr_all(group_idx, :);
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N_reps = size(group_data, 1);
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g2_values = zeros(1, N_reps);
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angle_at_max_g2 = zeros(1, N_reps);
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g2_values = zeros(1, N_reps);
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for j = 1:N_reps
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profile = group_data(j, :);
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@ -225,7 +234,6 @@ for i = 1:N_params
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ref = profile(ref_window);
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correlations = zeros(size(offsets));
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angles = zeros(size(offsets));
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for k = 1:length(offsets)
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shifted_idx = mod(peak_idx + offsets(k) - 1, N_angular_bins) + 1;
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@ -237,36 +245,191 @@ for i = 1:N_params
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g2 = num / denom;
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correlations(k) = g2;
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angles(k) = mod((peak_idx - 1 + offsets(k)) * angle_per_bin, angle_range);
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end
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[max_corr, max_idx] = max(correlations);
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g2_values(j) = max_corr;
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angle_at_max_g2(j) = angles(max_idx);
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end
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% Store raw values
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g2_all_per_group{i} = g2_values;
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angle_all_per_group{i} = angle_at_max_g2;
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max_g2_all_per_group{i} = g2_values;
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% Compute cumulants
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kappa = computeCumulants(g2_values(:), 6);
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% Final stats
|
||||
mean_max_g2_values(i) = mean(g2_values, 'omitnan');
|
||||
var_max_g2_values(i) = var(g2_values, 0, 'omitnan');
|
||||
mean_max_g2_angle_values(i)= mean(angle_at_max_g2, 'omitnan');
|
||||
var_max_g2_angle_values(i) = var(angle_at_max_g2, 0, 'omitnan');
|
||||
mean_max_g2_values(i) = kappa(1);
|
||||
var_max_g2_values(i) = kappa(2);
|
||||
|
||||
N_eff = sum(~isnan(g2_values));
|
||||
std_error_g2_values(i) = sqrt(kappa(2)) / sqrt(N_eff);
|
||||
|
||||
skew_max_g2_angle_values(i) = kappa(3);
|
||||
kurt_max_g2_angle_values(i) = kappa(4);
|
||||
fifth_order_cumulant_max_g2_angle_values(i) = kappa(5);
|
||||
sixth_order_cumulant_max_g2_angle_values(i) = kappa(6);
|
||||
|
||||
end
|
||||
|
||||
%% ── Mean ± Std vs. scan parameter ──────────────────────────────────────
|
||||
% Compute standard error instead of standard deviation
|
||||
std_error_g2_values = zeros(1, N_params);
|
||||
for i = 1:N_params
|
||||
n_i = numel(g2_all_per_group{i}); % Number of repetitions for this param
|
||||
std_error_g2_values(i) = sqrt(var_max_g2_values(i) / n_i);
|
||||
%% Plot PDF of order parameter
|
||||
|
||||
if ~skipSaveFigures
|
||||
% Define folder for saving images
|
||||
saveFolder = [savefileName '_SavedFigures'];
|
||||
if ~exist(saveFolder, 'dir')
|
||||
mkdir(saveFolder);
|
||||
end
|
||||
end
|
||||
|
||||
figure(2); % one persistent figure
|
||||
set(gcf, 'Color', 'w', 'Position', [100 100 950 750])
|
||||
|
||||
for val = scan_groups
|
||||
% Find the index i that matches this scan parameter value
|
||||
i = find(unique_scan_parameter_values == val, 1);
|
||||
|
||||
% Skip if not found (sanity check)
|
||||
if isempty(i)
|
||||
continue;
|
||||
end
|
||||
|
||||
g2_vals = g2_all_per_group{i};
|
||||
g2_vals = g2_vals(~isnan(g2_vals));
|
||||
|
||||
if isempty(g2_vals)
|
||||
continue;
|
||||
end
|
||||
|
||||
% KDE estimation
|
||||
[f, xi] = ksdensity(g2_vals, 'NumPoints', 200);
|
||||
|
||||
clf;
|
||||
histogram(g2_vals, 'Normalization', 'pdf', ...
|
||||
'NumBins', 10, ...
|
||||
'FaceAlpha', 0.3, ...
|
||||
'EdgeColor', 'none', ...
|
||||
'FaceColor', [0.3 0.5 0.8]);
|
||||
|
||||
hold on;
|
||||
plot(xi, f, 'LineWidth', 2, 'Color', [0 0.2 0.6]);
|
||||
|
||||
set(gca, 'FontSize', 16);
|
||||
title(sprintf('%s: \\boldmath$\\alpha = %.1f^{\\circ}$', titleString, val), ...
|
||||
'FontSize', 16, 'Interpreter', 'latex');
|
||||
|
||||
xlabel('$\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', 'Interpreter', 'latex', 'FontSize', 14);
|
||||
ylabel('PDF', 'FontSize', 14);
|
||||
xlim([0.0, 1.5]);
|
||||
grid on;
|
||||
|
||||
drawnow;
|
||||
|
||||
% ==== Save Figure ====
|
||||
if ~skipSaveFigures
|
||||
% Create a filename for each averaged plot
|
||||
fileNamePNG = fullfile(saveFolder, sprintf('max_g2_analysis_param_%03d.png', val));
|
||||
|
||||
% Save current figure as PNG with high resolution
|
||||
print(gcf, fileNamePNG, '-dpng', '-r300'); % 300 dpi for high quality
|
||||
else
|
||||
pause(0.5)
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%% Plot all cumulants
|
||||
figure(3)
|
||||
set(gcf, 'Color', 'w', 'Position', [100 100 950 750])
|
||||
|
||||
scan_vals = unique_scan_parameter_values;
|
||||
|
||||
% Define font style for consistency
|
||||
axis_fontsize = 14;
|
||||
label_fontsize = 16;
|
||||
title_fontsize = 16;
|
||||
|
||||
% 1. Mean with error bars
|
||||
subplot(3,2,1);
|
||||
errorbar(scan_vals, mean_max_g2_values, std_error_g2_values, 'o-', ...
|
||||
'LineWidth', 1.5, 'MarkerSize', 6);
|
||||
title('Mean of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
|
||||
'Interpreter', 'latex', 'FontSize', title_fontsize);
|
||||
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
ylabel('$\kappa_1$', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
set(gca, 'FontSize', axis_fontsize);
|
||||
grid on;
|
||||
|
||||
% 2. Variance
|
||||
subplot(3,2,2);
|
||||
plot(scan_vals, var_max_g2_values, 's-', 'LineWidth', 1.5, 'MarkerSize', 6);
|
||||
title('Variance of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
|
||||
'Interpreter', 'latex', 'FontSize', title_fontsize);
|
||||
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
ylabel('$\kappa_2$', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
set(gca, 'FontSize', axis_fontsize);
|
||||
grid on;
|
||||
|
||||
% 3. Skewness
|
||||
subplot(3,2,3);
|
||||
plot(scan_vals, skew_max_g2_angle_values, 'd-', 'LineWidth', 1.5, 'MarkerSize', 6);
|
||||
title('Skewness of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
|
||||
'Interpreter', 'latex', 'FontSize', title_fontsize);
|
||||
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
ylabel('$\kappa_3$', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
set(gca, 'FontSize', axis_fontsize);
|
||||
grid on;
|
||||
|
||||
% 4. Kurtosis
|
||||
subplot(3,2,4);
|
||||
plot(scan_vals, kurt_max_g2_angle_values, '^-', 'LineWidth', 1.5, 'MarkerSize', 6);
|
||||
title('Kurtosis of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
|
||||
'Interpreter', 'latex', 'FontSize', title_fontsize);
|
||||
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
ylabel('$\kappa_4$', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
set(gca, 'FontSize', axis_fontsize);
|
||||
grid on;
|
||||
|
||||
% 5. 5th-order cumulant
|
||||
subplot(3,2,5);
|
||||
plot(scan_vals, fifth_order_cumulant_max_g2_angle_values, 'v-', 'LineWidth', 1.5, 'MarkerSize', 6);
|
||||
title('Fifth-order cumulant of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
|
||||
'Interpreter', 'latex', 'FontSize', title_fontsize);
|
||||
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
ylabel('$\kappa_5$', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
set(gca, 'FontSize', axis_fontsize);
|
||||
grid on;
|
||||
|
||||
% 6. 6th-order cumulant
|
||||
subplot(3,2,6);
|
||||
plot(scan_vals, sixth_order_cumulant_max_g2_angle_values, '>-', 'LineWidth', 1.5, 'MarkerSize', 6);
|
||||
title('Sixth-order cumulant of $\mathrm{max}[g^{(2)}_{[50,70]}(\delta\theta)]$', ...
|
||||
'Interpreter', 'latex', 'FontSize', title_fontsize);
|
||||
xlabel('$\alpha$ (degrees)', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
ylabel('$\kappa_6$', 'Interpreter', 'latex', ...
|
||||
'FontSize', label_fontsize);
|
||||
set(gca, 'FontSize', axis_fontsize);
|
||||
grid on;
|
||||
|
||||
% Super title
|
||||
sgtitle(sprintf('Cumulants of Peak Offset Angular Correlation - %s', titleString), ...
|
||||
'FontWeight', 'bold', 'FontSize', 16, 'Interpreter', 'latex');
|
||||
|
||||
%% ── Mean ± Std vs. scan parameter ──────────────────────────────────────
|
||||
|
||||
% Plot mean ± SEM
|
||||
figure(1);
|
||||
set(gcf,'Position',[100 100 950 750])
|
||||
set(gcf, 'Color', 'w', 'Position',[100 100 950 750])
|
||||
set(gca, 'FontSize', 14); % For tick labels only
|
||||
errorbar(unique_scan_parameter_values, ... % x-axis
|
||||
mean_max_g2_values, ... % y-axis (mean)
|
||||
@ -289,75 +452,6 @@ if ~exist(saveFolder, 'dir')
|
||||
end
|
||||
save([saveFolder savefileName '.mat'], 'unique_scan_parameter_values', 'mean_max_g2_values', 'std_error_g2_values');
|
||||
|
||||
%{
|
||||
%% Plot histograms within 0-180 degrees only
|
||||
figure(1);
|
||||
hold on;
|
||||
|
||||
bin_edges = 0:10:180;
|
||||
|
||||
h1 = histogram(ref_peak_angles, 'BinEdges', bin_edges, ...
|
||||
'FaceColor', [0.3 0.7 0.9], 'EdgeColor', 'none', 'FaceAlpha', 0.6);
|
||||
|
||||
h2 = histogram(angle_at_max_g2, 'BinEdges', bin_edges, ...
|
||||
'FaceColor', [0.9 0.4 0.4], 'EdgeColor', 'none', 'FaceAlpha', 0.6);
|
||||
|
||||
h1.Normalization = 'probability';
|
||||
h2.Normalization = 'probability';
|
||||
|
||||
xlabel('Angle (degrees)', 'FontSize', 12);
|
||||
ylabel('Probability', 'FontSize', 12);
|
||||
legend({'Reference Peak Angle', 'Angle at Max g₂'}, 'FontSize', 12);
|
||||
title('Comparison of Reference Peak and Max g₂ Angles', 'FontSize', 14);
|
||||
grid on;
|
||||
xlim([0 180]);
|
||||
hold off;
|
||||
|
||||
% Assume ref_peak_angles and angle_at_max_g2 are row or column vectors of angles in [0,180]
|
||||
|
||||
% Define fine angle grid for KDE evaluation
|
||||
angle_grid = linspace(0, 180, 1000);
|
||||
|
||||
% KDE for reference peak angles
|
||||
[f_ref, xi_ref] = ksdensity(ref_peak_angles, angle_grid, 'Bandwidth', 5);
|
||||
|
||||
% KDE for max g2 angles
|
||||
[f_g2, xi_g2] = ksdensity(angle_at_max_g2, angle_grid, 'Bandwidth', 5);
|
||||
|
||||
% Plot KDEs
|
||||
figure(2);
|
||||
plot(xi_ref, f_ref, 'LineWidth', 2, 'DisplayName', 'Reference Peak Angles');
|
||||
hold on;
|
||||
plot(xi_g2, f_g2, 'LineWidth', 2, 'DisplayName', 'Max g_2 Angles');
|
||||
xlabel('Angle (degrees)');
|
||||
ylabel('Probability Density');
|
||||
title('KDE of Angle Distributions');
|
||||
legend;
|
||||
grid on;
|
||||
|
||||
% Find modes (angle at max KDE value)
|
||||
[~, mode_idx_ref] = max(f_ref);
|
||||
mode_ref = xi_ref(mode_idx_ref);
|
||||
|
||||
[~, mode_idx_g2] = max(f_g2);
|
||||
mode_g2 = xi_g2(mode_idx_g2);
|
||||
|
||||
% Calculate difference in mode
|
||||
mode_diff = abs(mode_ref - mode_g2);
|
||||
fprintf('Mode difference between distributions: %.2f degrees\n', mode_diff);
|
||||
|
||||
% Add vertical dashed lines at mode positions
|
||||
yl = ylim; % get y-axis limits for text positioning
|
||||
|
||||
% Reference peak mode line and label
|
||||
xline(mode_ref, 'k--', 'LineWidth', 1.5, 'DisplayName', sprintf('Ref Mode: %.1f°', mode_ref));
|
||||
text(mode_ref, yl(2)*0.9, sprintf('%.1f°', mode_ref), 'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom', 'FontSize', 12, 'Color', 'k');
|
||||
|
||||
% Max g2 mode line and label
|
||||
xline(mode_g2, 'r--', 'LineWidth', 1.5, 'DisplayName', sprintf('g_2 Mode: %.1f°', mode_g2));
|
||||
text(mode_g2, yl(2)*0.75, sprintf('%.1f°', mode_g2), 'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom', 'FontSize', 12, 'Color', 'r');
|
||||
%}
|
||||
|
||||
%% Helper Functions
|
||||
function [IMGFFT, IMGPR] = computeFourierTransform(I, skipPreprocessing, skipMasking, skipIntensityThresholding, skipBinarization)
|
||||
% computeFourierSpectrum - Computes the 2D Fourier power spectrum
|
||||
|
||||
Loading…
Reference in New Issue
Block a user