can anyone explain the types of the code "poincare section" (including cut, max, min and period)? what is the difference of them?

function poincare

%%% Compute Poincare section or First return map from a time series. %%% Author: Didier Gonze %%% Created 8/3/2011 %%% Updated 22/3/2011

clear; clc;

% ------------------------------------------------------------ % Data & parameters % ------------------------------------------------------------

D=load('myfile.dat'); % Read data

type='max'; % 'cut', 'max', 'min', 'period', 'mean' var=2; % variable used for the cut/first return map (column of D)

cut=2; % to be used with type = 'cut' (value for the cut) dir=1; % to be used with type = 'cut' (1=upwards;-1=downwards;0=both)

varo1=3; % output variable 1 used with 'cut' or 'mean' (column of D) varo2=4; % output variable 2 used with 'cut' or 'mean' (column of D)

% ------------------------------------------------------------ % Compute First return map for max % Return max_n as a function of max_(n-1) % ------------------------------------------------------------

if strcmp(type,'max')

x=D(:,var); % extract time series for variable var

xt=x(2:end-1); % variable xp=x(1:end-2); % variable shifted to left xm=x(3:end); % variable shifted to right

kmax=find((xt>xp) & (xt>=xm)); % index of maxima

xmax=xt(kmax); % maxima

R=[]; for i=2:length(kmax) R=[R; xmax(i-1) xmax(i)]; end

figure(1) clf; plot(R(:,1),R(:,2),'b.') xlabel('Max_n','fontsize',18) ylabel('Max_n_+_1','fontsize',18) title('Return map of the maxima','fontsize',18)

end

% ------------------------------------------------------------ % Compute First return map for min % Return min_n as a function of min_(n-1) % ------------------------------------------------------------

if strcmp(type,'min')

x=D(:,var); % extract time series for variable var

xt=x(2:end-1); % variable xp=x(1:end-2); % variable shifted to left xm=x(3:end); % variable shifted to right

kmin=find((xt<xp) & (xt<=xm)); % index of minima

xmin=xt(kmin); % minima

R=[]; for i=2:length(kmin) R=[R; xmin(i-1) xmin(i)]; end

figure(1) clf; plot(R(:,1),R(:,2),'b.') xlabel('Min_n','fontsize',18) ylabel('Min_n_+_1','fontsize',18) title('Return map of the minima','fontsize',18)

end

% ------------------------------------------------------------ % Compute First return map for period % Return period_n as a function of period_(n-1) % ------------------------------------------------------------

if strcmp(type,'period')

x=D(:,var); % extract time series for variable var t=D(:,1); % extract time series for time (1st column)

xt=x(2:end-1); % variable xp=x(1:end-2); % variable shifted to left xm=x(3:end); % variable shifted to right

k=find((xt>xp) & (xt>=xm)); % index of maxima

tp=t(k); % time of max x

R=[]; pold=tp(2)-tp(1); for i=3:length(k) p=tp(i)-tp(i-1); R=[R; pold p]; pold=p; end

figure(1) clf; plot(R(:,1),R(:,2),'b.') xlabel('Period_n','fontsize',18) ylabel('Period_n_+_1','fontsize',18) title('Return map of the period','fontsize',18)

end

% ------------------------------------------------------------ % Compute Poicare section for cut % Return values of all variables at cut(var) = cut % ------------------------------------------------------------

if strcmp(type,'cut')

x=D(:,var); % extract time series for variable var

xt=x(2:end-1); % variable xp=x(1:end-2); % variable shifted to left xm=x(3:end); % variable shifted to right

if (dir==1) k=find((xp<cut) & (xt>=cut)); % index of cut points (cross upwards) elseif (dir==-1) k=find((xp>cut) & (xm<=cut)); % index of cut points (cross downwards) elseif (dir==0) k=find(((xp<cut) & (xt>=cut)) | ((xp>cut) & (xm<=cut))); % index of cut points (cross up- or downwards) end

R=[]; for i=1:length(k) R=[R; D(k(i),:)]; end

figure(1) clf; plot(R(:,varo1),R(:,varo2),'b.') % specify the two variables to be plotted xlabel('Var (1)','fontsize',18) ylabel('Var (2)','fontsize',18) title(sprintf('Poincare section (cut=%g)',cut),'fontsize',18)

end

% ------------------------------------------------------------ % Compute Poicare section for mean % Return values of all variables at cut(var) = mean(var) % ------------------------------------------------------------

if strcmp(type,'mean')

x=D(:,var); % extract time series for variable var cut=mean(x); % cut at mean(x)

xt=x(2:end-1); % variable xp=x(1:end-2); % variable shifted to left xm=x(3:end); % variable shifted to right

if (dir==1) k=find((xp<cut) & (xt>=cut)); % index of cut points (cross upwards) elseif (dir==-1) k=find((xp>cut) & (xm<=cut)); % index of cut points (cross downwards) elseif (dir==0) k=find(((xp<cut) & (xt>=cut)) | ((xp>cut) & (xm<=cut))); % index of cut points (cross up- or downwards) end

R=[]; for i=1:length(k) R=[R; D(k(i),:)]; end

figure(1) clf; plot(R(:,varo1),R(:,varo2),'b.') % specify the two variables to be plotted xlabel('Var (1)','fontsize',18) ylabel('Var (2)','fontsize',18) title(sprintf('Poincare section (cut at mean=%g)',cut),'fontsize',18)

end