A few fixes and new continuous versions of FirstCrossing

Database/INP_mops.txt

@@ -129,8 +129,8 @@ CO_AutoCorr(x_z,37,'Fourier')	AC_37
 CO_AutoCorr(x_z,38,'Fourier')	AC_38
 CO_AutoCorr(x_z,39,'Fourier')	AC_39
 CO_AutoCorr(x_z,40,'Fourier')	AC_40
-CO_FirstZero(x_z,'ac')	CO_FirstZero_ac
-CO_f1ecac(x_z)			CO_f1ecac
+CO_FirstCrossing(x_z,'ac',0,'both')	CO_FirstCrossing_acf_0
+CO_FirstCrossing(x_z,'ac',1/exp(1),'both')	CO_FirstCrossing_acf_1e
 CO_FirstMin(x_z,'ac')	CO_FirstMin_ac
 CO_FirstMin(x_z,'mi-gaussian')	CO_FirstMin_mi-gaussian
 CO_FirstMin(x_z,'mi-kraskov1','4')  CO_FirstMin_mi-kraskov1_4
@@ -750,9 +750,9 @@ PH_ForcePotential(x_z,'dblwell',[3,0.01,0.1])	PH_ForcePotential_dblwell_3_001_01
 PH_ForcePotential(x_z,'sine',[3,0.5,1])	    PH_ForcePotential_sine_3_05_1
 PH_ForcePotential(x_z,'sine',[1,1,1])	        PH_ForcePotential_sine_1_1_1
 PH_ForcePotential(x_z,'sine',[10,0.04,10])	PH_ForcePotential_sine_10_004_10
-DN_RemovePoints(x_z,'absclose',0.1,'saturate')	DN_RemovePoints_absclose_01_saturate
-DN_RemovePoints(x_z,'absclose',0.5,'saturate')	DN_RemovePoints_absclose_05_saturate
-DN_RemovePoints(x_z,'absclose',0.8,'saturate')	DN_RemovePoints_absclose_08_saturate
+DN_RemovePoints(x_z,'absclose',0.1,'remove')	DN_RemovePoints_absclose_01_remove
+DN_RemovePoints(x_z,'absclose',0.5,'remove')	DN_RemovePoints_absclose_05_remove
+DN_RemovePoints(x_z,'absclose',0.8,'remove')	DN_RemovePoints_absclose_08_remove
 DN_RemovePoints(x_z,'absfar',0.1,'remove')	DN_RemovePoints_absfar_01_remove
 DN_RemovePoints(x_z,'absfar',0.8,'remove')	DN_RemovePoints_absfar_08_remove
 DN_RemovePoints(x_z,'absfar',0.1,'saturate')	DN_RemovePoints_absfar_01_saturate

Database/INP_ops.txt

@@ -130,9 +130,11 @@ AC_37		AC_37		correlation
 AC_38		AC_38		correlation
 AC_39		AC_39		correlation
 AC_40		AC_40		correlation
-CO_FirstZero_ac	first_zero_ac	correlation,tau
-CO_f1ecac		first_1e_ac		correlation,tau
-CO_FirstMin_ac	first_min_acf	correlation,tau
+CO_FirstCrossing_acf_0.firstCrossing	firstZero_acf_tau	correlation,timescale
+CO_FirstCrossing_acf_0.pointOfCrossing	firstZero_acf_point	correlation,timescale
+CO_FirstCrossing_acf_1e.firstCrossing	first1e_acf_tau	correlation,timescale
+CO_FirstCrossing_acf_1e.pointOfCrossing	first1e_acf_point	correlation,timescale
+CO_FirstMin_ac	firstMin_acf	correlation,timescale
 AC_nl_12		AC_nl_12		correlation,nonlinearautocorr
 AC_nl_123		AC_nl_123		correlation,nonlinearautocorr
 AC_nl_1234		AC_nl_1234		correlation,nonlinearautocorr
@@ -1683,45 +1685,45 @@ PH_ForcePotential_sine_10_004_10.ac50	PH_ForcePotential_sine_10_004_10_ac50	dyna
 PH_ForcePotential_sine_10_004_10.tau	PH_ForcePotential_sine_10_004_10_tau	dynamicalSystem
 PH_ForcePotential_sine_10_004_10.finaldev	PH_ForcePotential_sine_10_004_10_finaldev	dynamicalSystem
 PH_ForcePotential_sine_10_004_10.std	PH_ForcePotential_sine_10_004_10_std	dynamicalSystem
-DN_RemovePoints_absclose_01_saturate.fzcacrat	DN_RemovePoints_absclose_01_saturate_fzcacrat	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.ac1rat	DN_RemovePoints_absclose_01_saturate_ac1rat	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.ac1diff	DN_RemovePoints_absclose_01_saturate_ac1diff	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.ac2rat	DN_RemovePoints_absclose_01_saturate_ac2rat	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.ac2diff	DN_RemovePoints_absclose_01_saturate_ac2diff	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.ac3rat	DN_RemovePoints_absclose_01_saturate_ac3rat	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.ac3diff	DN_RemovePoints_absclose_01_saturate_ac3diff	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.sumabsacfdiff	DN_RemovePoints_absclose_01_saturate_sumabsacfdiff	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.mean	DN_RemovePoints_absclose_01_saturate_mean	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.median	DN_RemovePoints_absclose_01_saturate_median	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.std	DN_RemovePoints_absclose_01_saturate_std	correlation,outliers
-DN_RemovePoints_absclose_01_saturate.skewnessrat	DN_RemovePoints_absclose_01_saturate_skewnessrat	correlation,outliers,distribution
-DN_RemovePoints_absclose_01_saturate.kurtosisrat	DN_RemovePoints_absclose_01_saturate_kurtosisrat	correlation,outliers,distribution
-DN_RemovePoints_absclose_05_saturate.fzcacrat	DN_RemovePoints_absclose_05_saturate_fzcacrat	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.ac1rat	DN_RemovePoints_absclose_05_saturate_ac1rat	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.ac1diff	DN_RemovePoints_absclose_05_saturate_ac1diff	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.ac2rat	DN_RemovePoints_absclose_05_saturate_ac2rat	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.ac2diff	DN_RemovePoints_absclose_05_saturate_ac2diff	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.ac3rat	DN_RemovePoints_absclose_05_saturate_ac3rat	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.ac3diff	DN_RemovePoints_absclose_05_saturate_ac3diff	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.sumabsacfdiff	DN_RemovePoints_absclose_05_saturate_sumabsacfdiff	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.mean	DN_RemovePoints_absclose_05_saturate_mean	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.median	DN_RemovePoints_absclose_05_saturate_median	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.std	DN_RemovePoints_absclose_05_saturate_std	correlation,outliers
-DN_RemovePoints_absclose_05_saturate.skewnessrat	DN_RemovePoints_absclose_05_saturate_skewnessrat	correlation,outliers,distribution
-DN_RemovePoints_absclose_05_saturate.kurtosisrat	DN_RemovePoints_absclose_05_saturate_kurtosisrat	correlation,outliers,distribution
-DN_RemovePoints_absclose_08_saturate.fzcacrat	DN_RemovePoints_absclose_08_saturate_fzcacrat	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.ac1rat	DN_RemovePoints_absclose_08_saturate_ac1rat	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.ac1diff	DN_RemovePoints_absclose_08_saturate_ac1diff	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.ac2rat	DN_RemovePoints_absclose_08_saturate_ac2rat	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.ac2diff	DN_RemovePoints_absclose_08_saturate_ac2diff	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.ac3rat	DN_RemovePoints_absclose_08_saturate_ac3rat	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.ac3diff	DN_RemovePoints_absclose_08_saturate_ac3diff	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.sumabsacfdiff	DN_RemovePoints_absclose_08_saturate_sumabsacfdiff	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.mean	DN_RemovePoints_absclose_08_saturate_mean	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.median	DN_RemovePoints_absclose_08_saturate_median	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.std	DN_RemovePoints_absclose_08_saturate_std	correlation,outliers
-DN_RemovePoints_absclose_08_saturate.skewnessrat	DN_RemovePoints_absclose_08_saturate_skewnessrat	correlation,outliers,distribution
-DN_RemovePoints_absclose_08_saturate.kurtosisrat	DN_RemovePoints_absclose_08_saturate_kurtosisrat	correlation,outliers,distribution
+DN_RemovePoints_absclose_01_remove.fzcacrat	DN_RemovePoints_absclose_01_remove_fzcacrat	correlation,outliers
+DN_RemovePoints_absclose_01_remove.ac1rat	DN_RemovePoints_absclose_01_remove_ac1rat	correlation,outliers
+DN_RemovePoints_absclose_01_remove.ac1diff	DN_RemovePoints_absclose_01_remove_ac1diff	correlation,outliers
+DN_RemovePoints_absclose_01_remove.ac2rat	DN_RemovePoints_absclose_01_remove_ac2rat	correlation,outliers
+DN_RemovePoints_absclose_01_remove.ac2diff	DN_RemovePoints_absclose_01_remove_ac2diff	correlation,outliers
+DN_RemovePoints_absclose_01_remove.ac3rat	DN_RemovePoints_absclose_01_remove_ac3rat	correlation,outliers
+DN_RemovePoints_absclose_01_remove.ac3diff	DN_RemovePoints_absclose_01_remove_ac3diff	correlation,outliers
+DN_RemovePoints_absclose_01_remove.sumabsacfdiff	DN_RemovePoints_absclose_01_remove_sumabsacfdiff	correlation,outliers
+DN_RemovePoints_absclose_01_remove.mean	DN_RemovePoints_absclose_01_remove_mean	correlation,outliers
+DN_RemovePoints_absclose_01_remove.median	DN_RemovePoints_absclose_01_remove_median	correlation,outliers
+DN_RemovePoints_absclose_01_remove.std	DN_RemovePoints_absclose_01_remove_std	correlation,outliers
+DN_RemovePoints_absclose_01_remove.skewnessrat	DN_RemovePoints_absclose_01_remove_skewnessrat	correlation,outliers,distribution
+DN_RemovePoints_absclose_01_remove.kurtosisrat	DN_RemovePoints_absclose_01_remove_kurtosisrat	correlation,outliers,distribution
+DN_RemovePoints_absclose_05_remove.fzcacrat	DN_RemovePoints_absclose_05_remove_fzcacrat	correlation,outliers
+DN_RemovePoints_absclose_05_remove.ac1rat	DN_RemovePoints_absclose_05_remove_ac1rat	correlation,outliers
+DN_RemovePoints_absclose_05_remove.ac1diff	DN_RemovePoints_absclose_05_remove_ac1diff	correlation,outliers
+DN_RemovePoints_absclose_05_remove.ac2rat	DN_RemovePoints_absclose_05_remove_ac2rat	correlation,outliers
+DN_RemovePoints_absclose_05_remove.ac2diff	DN_RemovePoints_absclose_05_remove_ac2diff	correlation,outliers
+DN_RemovePoints_absclose_05_remove.ac3rat	DN_RemovePoints_absclose_05_remove_ac3rat	correlation,outliers
+DN_RemovePoints_absclose_05_remove.ac3diff	DN_RemovePoints_absclose_05_remove_ac3diff	correlation,outliers
+DN_RemovePoints_absclose_05_remove.sumabsacfdiff	DN_RemovePoints_absclose_05_remove_sumabsacfdiff	correlation,outliers
+DN_RemovePoints_absclose_05_remove.mean	DN_RemovePoints_absclose_05_remove_mean	correlation,outliers
+DN_RemovePoints_absclose_05_remove.median	DN_RemovePoints_absclose_05_remove_median	correlation,outliers
+DN_RemovePoints_absclose_05_remove.std	DN_RemovePoints_absclose_05_remove_std	correlation,outliers
+DN_RemovePoints_absclose_05_remove.skewnessrat	DN_RemovePoints_absclose_05_remove_skewnessrat	correlation,outliers,distribution
+DN_RemovePoints_absclose_05_remove.kurtosisrat	DN_RemovePoints_absclose_05_remove_kurtosisrat	correlation,outliers,distribution
+DN_RemovePoints_absclose_08_remove.fzcacrat	DN_RemovePoints_absclose_08_remove_fzcacrat	correlation,outliers
+DN_RemovePoints_absclose_08_remove.ac1rat	DN_RemovePoints_absclose_08_remove_ac1rat	correlation,outliers
+DN_RemovePoints_absclose_08_remove.ac1diff	DN_RemovePoints_absclose_08_remove_ac1diff	correlation,outliers
+DN_RemovePoints_absclose_08_remove.ac2rat	DN_RemovePoints_absclose_08_remove_ac2rat	correlation,outliers
+DN_RemovePoints_absclose_08_remove.ac2diff	DN_RemovePoints_absclose_08_remove_ac2diff	correlation,outliers
+DN_RemovePoints_absclose_08_remove.ac3rat	DN_RemovePoints_absclose_08_remove_ac3rat	correlation,outliers
+DN_RemovePoints_absclose_08_remove.ac3diff	DN_RemovePoints_absclose_08_remove_ac3diff	correlation,outliers
+DN_RemovePoints_absclose_08_remove.sumabsacfdiff	DN_RemovePoints_absclose_08_remove_sumabsacfdiff	correlation,outliers
+DN_RemovePoints_absclose_08_remove.mean	DN_RemovePoints_absclose_08_remove_mean	correlation,outliers
+DN_RemovePoints_absclose_08_remove.median	DN_RemovePoints_absclose_08_remove_median	correlation,outliers
+DN_RemovePoints_absclose_08_remove.std	DN_RemovePoints_absclose_08_remove_std	correlation,outliers
+DN_RemovePoints_absclose_08_remove.skewnessrat	DN_RemovePoints_absclose_08_remove_skewnessrat	correlation,outliers,distribution
+DN_RemovePoints_absclose_08_remove.kurtosisrat	DN_RemovePoints_absclose_08_remove_kurtosisrat	correlation,outliers,distribution
 DN_RemovePoints_absfar_01_remove.fzcacrat	DN_RemovePoints_absfar_01_remove_fzcacrat	correlation,outliers
 DN_RemovePoints_absfar_01_remove.ac1rat	DN_RemovePoints_absfar_01_remove_ac1rat	correlation,outliers
 DN_RemovePoints_absfar_01_remove.ac1diff	DN_RemovePoints_absfar_01_remove_ac1diff	correlation,outliers

Operations/CO_AddNoise.m

@@ -82,7 +82,7 @@
 end
 % Set tau to minimum of autocorrelation function
 if ~isempty(tau) && ischar(tau) && ismember(tau,{'ac','tau'})
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
 end
 if nargin < 3
     amiMethod = 'even'; % using evenly spaced bins in CO_HistogramAMI

Operations/CO_AutoCorrShape.m

@@ -155,7 +155,7 @@
     if all(acf > 0)
         out.actau = NaN;
     else
-        out.actau = CO_AutoCorr(acf,CO_FirstZero(acf,'ac'),'Fourier');
+        out.actau = CO_AutoCorr(acf,CO_FirstCrossing(acf,'ac',0,'discrete'),'Fourier');
     end
 else
     out.ac1 = NaN;

Operations/CO_Embed2.m

@@ -54,7 +54,7 @@
 
 % Set tau to the first zero-crossing of the autocorrelation function, with the 'tau' input
 if strcmp(tau,'tau'),
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
     if tau > length(y)/10
         tau = floor(length(y)/10);
     end

Operations/CO_Embed2_Basic.m

@@ -46,7 +46,7 @@
 
 if strcmp(tau,'tau')
 	% Make tau the first zero crossing of the autocorrelation function
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
 end
 
 xt = y(1:end-tau); % part of the time series

Operations/CO_Embed2_Dist.m

@@ -52,7 +52,7 @@
     tau = 'tau'; % set to the first minimum of autocorrelation function
 end
 if strcmp(tau,'tau'),
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
     if tau > N/10
         tau = floor(N/10);
     end

Operations/CO_Embed2_Shapes.m

@@ -66,7 +66,7 @@
 
 % Can set time lag equal to first zero crossing of the autocorrelation function with the 'tau' input
 if strcmp(tau,'tau'),
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
     % Cannot set the time delay greater than 10% the length of the time series
     if tau > length(y)/10
         tau = floor(length(y)/10);
@@ -125,7 +125,7 @@
 out.ac1 = CO_AutoCorr(counts,1,'Fourier');
 out.ac2 = CO_AutoCorr(counts,2,'Fourier');
 out.ac3 = CO_AutoCorr(counts,3,'Fourier');
-out.tau = CO_FirstZero(counts,'ac');
+out.tau = CO_FirstCrossing(counts,'ac',0,'continuous');
 out.max = max(counts);
 out.std = std(counts);
 out.median = median(counts);

Operations/CO_FirstZero.m → Operations/CO_FirstCrossing.m

@@ -1,17 +1,13 @@
-function out = CO_FirstZero(y,corrFun,maxTau)
-% CO_FirstZero      The first zero-crossing of a given autocorrelation function
+function out = CO_FirstCrossing(y,corrFun,threshold,whatOut)
+% CO_FirstCrossing  The first crossing of a given autocorrelation across a given threshold
 %
 %---INPUTS:
 %
 % y, the input time series
 % corrFun, the self-correlation function to measure:
 %         (i) 'ac': normal linear autocorrelation function. Uses CO_AutoCorr to
 %                   calculate autocorrelations.
-% maxTau, a maximum time-delay to search up to.
-%
-% In future, could add an option to return the point at which the function
-% crosses the axis, rather than the first integer lag at which it has already
-% crossed (what is currently implemented).
+% threshold, to cross: e.g., 0, 1/exp(1).
 
 % ------------------------------------------------------------------------------
 % Copyright (C) 2020, Ben D. Fulcher <ben.d.fulcher@gmail.com>,
@@ -49,34 +45,42 @@
 N = length(y); % the length of the time series
 
 if nargin < 2 || isempty(corrFun)
-    corrFun = 'ac'; % autocorrelation by default
+    corrFun = 'ac'; % linear autocorrelation function
+end
+if nargin < 3 || isempty(threshold)
+    threshold = 0;
 end
-if nargin < 3 || isempty(maxTau)
-    maxTau = N; % search up to a maximum of the length of the time series
-    % maxTau = 400; % searches up to this maximum time lag
-    % maxTau = min(maxTau,N); % searched up to the length of the time series if this is less than maxTau
+if nargin < 4 || isempty(whatOut)
+    whatOut = 'both';
 end
 
-% ------------------------------------------------------------------------------
+%-------------------------------------------------------------------------------
 % Select the self-correlation function as an inline function
 % Eventually could add additional self-correlation functions
 switch corrFun
 case 'ac'
     % Autocorrelation at all time lags
     corrs = CO_AutoCorr(y,[],'Fourier');
-    corrs = corrs(2:end); % remove the zero-lag result
 otherwise
     error('Unknown correlation function ''%s''',corrFun);
 end
 
-% Calculate autocorrelation at increasing lags, until you find a negative one
-for tau = 1:maxTau-1
-    if corrs(tau) < 0 % we know it starts positive (1), so first negative will be the zero-crossing
-        out = tau; return
-    end
+%-------------------------------------------------------------------------------
+% Calculate point of crossing:
+[firstCrossingIndex, pointOfCrossingIndex] = BF_PointOfCrossing(corrs,threshold);
+
+%-------------------------------------------------------------------------------
+% Assemble the appropriate output (structure or double):
+% Convert from index space (1,2,…) to lag space (0,1,2,…):
+switch whatOut
+case 'both'
+    out.firstCrossing = firstCrossingIndex - 1;
+    out.pointOfCrossing = pointOfCrossingIndex - 1;
+case 'discrete'
+    out = firstCrossingIndex - 1;
+case 'continuous'
+    out = pointOfCrossingIndex - 1;
 end
 
-% If haven't left yet, set output to maxTau
-out = maxTau;
 
 end

Operations/CO_FirstMin.m

@@ -11,7 +11,7 @@
 %           or 'mi-hist' (histogram-based method).
 %
 % Note that selecting 'ac' is unusual operation: standard operations are the
-% first zero-crossing of the autocorrelation (as in CO_FirstZero), or the first
+% first zero-crossing of the autocorrelation (as in CO_FirstCrossing), or the first
 % minimum of the mutual information function ('mi').
 
 % ------------------------------------------------------------------------------
@@ -92,7 +92,8 @@
     % Hit a NaN before got to a minimum -- there is no minimum
     if isnan(autoCorr(i))
         warning('No minimum in %s [[time series too short to find it?]]',minWhat)
-        out = NaN; return
+        out = NaN;
+        return
     end
 
     % We're at a minimum:

Operations/CO_HistogramAMI.m

@@ -62,7 +62,7 @@
     tau = 1;  % time-lag of 1
 end
 if ischar(tau) && ismember(tau,{'ac','tau'})
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
 end
 
 if nargin < 3 || isempty(meth)

Operations/CO_StickAngles.m

@@ -235,22 +235,22 @@
 
 %% correlations?
 if ~isempty(zangles{1});
-    out.tau_p = CO_FirstZero(zangles{1},'ac');
+    out.tau_p = CO_FirstCrossing(zangles{1},'ac',0,'continuous');
     out.ac1_p = CO_AutoCorr(zangles{1},1,'Fourier');
     out.ac2_p = CO_AutoCorr(zangles{1},2,'Fourier');
 else
     out.tau_p = NaN; out.ac1_p = NaN; out.ac2_p = NaN;
 end
 
 if ~isempty(zangles{2});
-    out.tau_n = CO_FirstZero(zangles{2},'ac');
+    out.tau_n = CO_FirstCrossing(zangles{2},'ac',0,'continuous');
     out.ac1_n = CO_AutoCorr(zangles{2},1,'Fourier');
     out.ac2_n = CO_AutoCorr(zangles{2},2,'Fourier');
 else
     out.tau_n=NaN; out.ac1_n = NaN; out.ac2_n = NaN;
 end
 
-out.tau_all = CO_FirstZero(zallAngles,'ac');
+out.tau_all = CO_FirstCrossing(zallAngles,'ac',0,'continuous');
 out.ac1_all = CO_AutoCorr(zallAngles,1,'Fourier');
 out.ac2_all = CO_AutoCorr(zallAngles,2,'Fourier');
 
@@ -292,9 +292,8 @@
 out.skewness_all = skewness(allAngles);
 out.kurtosis_all = kurtosis(allAngles);
 
-%% Outliers?
-% forget about this, I think.
 
+%-------------------------------------------------------------------------------
 function [statavmean, statavstd] = SUB_statav(x,n)
     % Does a n-partition statav.
     % Require 2*n points (i.e., minimum of 2 in each partition) to do a
@@ -306,7 +305,10 @@
     end
 
     x_buff = buffer(x,floor(NN/n));
-    if size(x_buff,2) > n, x_buff = x_buff(:,1:n); end % lose last point
+    if size(x_buff,2) > n
+        % Remove final point
+        x_buff = x_buff(:,1:n);
+    end
     statavmean = std(mean(x_buff))/std(x);
     statavstd = std(std(x_buff))/std(x);
 end

Operations/CO_glscf.m

@@ -56,7 +56,7 @@
 
 % Set tau to first zero-crossing of the autocorrelation function with the input 'tau'
 if strcmp(tau,'tau')
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
 end
 
 % Take magnitudes of time-delayed versions of the time series:

Operations/CO_tc3.m

@@ -60,7 +60,7 @@
 % ------------------------------------------------------------------------------
 % Can set the time lag, tau, to be 'ac' or 'mi'
 if strcmp(tau,'ac')
-    tau = CO_FirstZero(y,'ac');
+    tau = CO_FirstCrossing(y,'ac',0,'discrete');
     % tau is first zero crossing of the autocorrelation function
 elseif strcmp(tau,'mi')
     tau = CO_FirstMin(y,'mi');