Add RAD function

Feature_Analysis/Custom_features/dynamicalDistributions/RAD.m

@@ -0,0 +1,38 @@
+function f = RAD(x, centre, tau)
+% RAD Compute the rescaled auto-density, a metric for inferring the
+% distance to criticality that is insensitive to uncertainty in the noise strength
+% INPUTS
+%   x:        A vector, the input time series 
+%   centre:   Whether to centre the time series at 0 then take absolute values
+%   tau:      An integer; the embedding and differencing delay in units of the timestep
+% OUTPUTS
+%   f:        The RAD feature value
+    if nargin < 2 || isempty(centre)
+        centre = 0;
+    end
+    if nargin < 3 || isempty(tau)
+        tau = 1;
+    end
+    if isrow(x)
+        x = x';
+    end
+    if centre
+        x = x - median(x);
+        x = abs(x);
+    end
+
+    % Delay embed at interval tau, m = 2
+    y = x(tau+1:end);
+    x = x(1:end-tau); 
+
+    % Median split
+    subMedians = x < median(x);
+    superMedianSD = std(x(~subMedians));
+    subMedianSD = std(x(subMedians));
+
+    % Properties of the auto-density
+    sigma_dx = std(y - x);
+    densityDifference = 1./superMedianSD - 1./subMedianSD;
+
+    f = sigma_dx.*densityDifference;
+end