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

Question

ramin asadi 2017-11-22

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https://ww2.mathworks.cn/matlabcentral/answers/368542-can-anyone-explain-the-types-of-the-code-poincare-section-including-cut-max-min-and-period-wh

编辑： Walter Roberson 2018-9-23

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

2 个评论
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John D'Errico 2017-11-22

You want us to read through some poorly documented code, figuring out what this variable does, then give you an explanation? CONTACT THE AUTHOR. You got it from them. So ask them.

ramin asadi 2017-11-24