Create pair_corr.m

A function to calculate the density-density correlation function. Uses Monte Carlo sampling over a vector v.

+tools/pair_corr.m

@@ -0,0 +1,71 @@
+
+% PAIR_CORR  Compute the pair correlation function for a binary image. 
+%  
+%  AUTHOR: Timothy Sipkens, 2023-12-13
+
+function [g, v] = pair_corr(img_binary, v, ns)
+
+if ~exist('v', 'var'); v = []; end
+
+if ~exist('ns', 'var'); ns = []; end
+if isempty(ns); ns = 1e5; end
+
+
+% Vector of distances.
+if or(isempty(v), numel(v) == 1)
+
+    if numel(v) == 1  % then radius of gyration (in px) or similar, use to generate v
+        R = v;
+        maxd = R * 2 * 2;
+    else  % otherwise, use size of the image
+        maxd = min(size(img_binary)) / 4;
+    end
+
+    % v = linspace(1, maxd, 50)';
+    v = logspace(0, log10(maxd), 50)';
+end
+
+
+[row, col] = find(img_binary); % starting row/col in aggregate
+g = zeros(size(v));
+
+for ii=1:length(v)
+
+    ri = randi(length(row), [ns,1]);
+
+    rthe = 2*pi .* rand([ns,1]);  % random angle
+    rx = round(v(ii) .* sin(rthe));  % random x dir.
+    ry = round(v(ii) .* cos(rthe));  % random y dir.
+
+    row_new = row(ri) + ry; % new row
+    col_new = col(ri) + rx;  % new col
+
+    % Catch out-of-bounds cases.
+    out_of_bounds = or( ...
+        or(row_new < 1, row_new > size(img_binary,1)), ... 
+        or(col_new < 1, col_new > size(img_binary,2)));
+    nout = sum(out_of_bounds);
+    row_new(out_of_bounds) = [];
+    col_new(out_of_bounds) = [];
+
+    % Get new pixels. 
+    in = img_binary(sub2ind(size(img_binary), row_new, col_new));
+
+    % Pad with removed cases. 
+    g(ii) = sum(in) ./ (length(in) + nout);
+
+end
+
+%{
+% Diagnostic plotting.
+if exist('R', 'var')
+    plot(v ./ R, g);
+    xlabel('Pixel distance / R [px/px]');
+else
+    plot(v, g);
+    xlabel('Pixel distance [px]');
+end
+set(gca, 'XScale', 'log');
+%}
+
+end