MATLAB Examples

## Contents

clear all;close all;clc;

## EXAMPLE 1

Example 1: Bendat and piersol, Random data, 2010, page 99 Example 4.4

data = [5.2,6.2,3.7,6.4,3.9,4.0,3.9,5.3,4,4.6,5.9,6.5,4.3,5.7,3.1,5.6,5.2,3.9,6.2,5.0];
[ResultTest,A,Ainf,Asup] = RA_test(data,1)
ResultTest =

1

A =

86

Ainf =

65

Asup =

125

## EXAMPLE 2

White noise - stationnary - method 1

N = 1000; % number of data points
data = randn(1,N);
[ResultTest,A,Ainf,Asup] = RA_test(data,1)

% plot the reverse arrangement as a function of the sample size
% Inspired from:
% -------------------------------------------------------------------------
% Analysis of trends between solar wind velocity and energetic electron
% fluxes at geostationary orbit using the reverse arrangement test
% H Aryan - ?2013
% -------------------------------------------------------------------------
clear Res A Ainf Asup
rng(1)
jj=1;
Ndata = 50:50:N;
for ii=1:numel(Ndata),
dummy =  data(1:Ndata(ii));
[Res(jj),A(jj),Ainf(jj),Asup(jj)] = RA_test(dummy,1);
jj=jj+1;
end
figure
plot(Ndata,A,'r',Ndata,Ainf,'k--',Ndata,Asup,'k:')
xlabel('Number of data')
ylabel('reverse arrangements');
legend('Measured','lower boundary','upper boundary','location','NorthWest')
set(gcf,'color','w')
% The red curve falls between the upper and lower boundary: The signal is
% stationnary
ResultTest =

1

A =

253666

Ainf =

239412

Asup =

260088

## EXAMPLE 3

White noise - stationnary - method 2

clear Res A Ainf Asup
jj=1;
Ndata = [50:50:N];
for ii=1:numel(Ndata),
dummy =  data(1:Ndata(ii));
[Res(jj),A(jj),Ainf(jj),Asup(jj)] = RA_test(dummy,2);
jj=jj+1;
end

figure
plot(Ndata,A,'r',Ndata,Ainf,'k--',Ndata,Asup,'k:')
xlabel('Number of data')
ylabel('reverse arrangements');
legend('Measured','lower boundary','upper boundary','location','NorthWest')
set(gcf,'color','w')
ylim([-5,5])
% The red curve falls between the upper and lower boundary: The signal is
% stationnary

## EXAMPLE 3

White noise - non stationnary (trend) - method 1 plot the reverse arrangement as a function of the sample size

rng(1)
myTrend =-0.003.*linspace(0,N,N);
t = linspace(0,12,N); % time
data = randn(1,N)+myTrend;

% Let's have a look of the time serie generated.
figure
hold on;box on
plot(t,data);
plot(t,myTrend,'r'); % a significativ trend is visible
legend('measured','trend')
xlabel('time (months)');
ylabel('popularity among girls')
set(gcf,'color','w')
clear Res A Ainf Asup
jj=1;
Ndata = 50:50:N;
for ii=1:numel(Ndata),
dummy =  data(1:Ndata(ii));
[Res(jj),A(jj),Ainf(jj),Asup(jj)] = RA_test(dummy,1);
jj=jj+1;
end

clf;close all
figure
plot(Ndata,A,'r',Ndata,Ainf,'k--',Ndata,Asup,'k:')
xlabel('Number of data')
ylabel('reverse arrangements');
legend('Measured','lower boundary','upper boundary','location','NorthWest')
set(gcf,'color','w')
% The red curve falls outside the upper and lower boundary: The signal is
% non-stationnary

## EXAMPLE 4

White noise - non stationnary (trend) - method 2 plot the reverse arrangement as a function of the sample size

clear Res A Ainf Asup
jj=1;
for ii=1:numel(Ndata),
dummy =  data(1:Ndata(ii));
[Res(jj),A(jj),Ainf(jj),Asup(jj)] = RA_test(dummy,2);
jj=jj+1;
end
figure
plot(Ndata,A,'r',Ndata,Ainf,'k--',Ndata,Asup,'k:')
xlabel('Number of data')
ylabel('reverse arrangements');
legend('Measured','lower boundary','upper boundary','location','NorthWest')
ylim([-10,10])
% The red curve falls outside the upper and lower boundary: The signal is
% non-stationnary

## EXAMPLE 5

White noise - non stationnary (sinusoid) - method 1 plot the reverse arrangement as a function of the sample size

% White noise  - non stationnary (trend) - method 1
% plot the reverse arrangement as a function of the sample size
rng(1)
t = linspace(0,12,N); % time
myAverage =sin(0.5.*t);
data = randn(1,N)+myAverage;

% Let's have a look of the time serie generated.
figure
hold on;box on
plot(t,data);
plot(t,myAverage,'r'); % a significativ trend is visible
legend('measured','sinusoid')
xlabel('time (s)');
ylabel('popularity among girls')
set(gcf,'color','w')

Reverse arrangement calculation

clear Res A Ainf Asup
jj=1;
Ndata = 50:50:N;
for ii=1:numel(Ndata),
dummy =  data(1:Ndata(ii));
[Res(jj),A(jj),Ainf(jj),Asup(jj)] = RA_test(dummy,1);
jj=jj+1;
end

figure
plot(Ndata,A,'r',Ndata,Ainf,'k--',Ndata,Asup,'k:')
xlabel('Number of data')
ylabel('reverse arrangements');
legend('Measured','lower boundary','upper boundary','location','NorthWest')
set(gcf,'color','w')
% The red curve falls outside the upper and lower boundary: The signal is
% non-stationnary

## EXAMPLE 6

White noise - non stationnary (step function) - method 2 plot the reverse arrangement as a function of the sample size

% White noise  - non stationnary (trend) - method 1
% plot the reverse arrangement as a function of the sample size
rng(1)
t = linspace(0,4,N); % time
myStep =10.*[ones(1,round(2/4*N)),zeros(1,round(2/4*N))];
data = 10+randn(1,N)+myStep;

% Let's have a look of the time serie generated.
figure
hold on;box on
plot(t,data);
plot(t,10+myStep,'r'); % a significativ trend is visible
legend('measured','step function')
xlabel('rounds');
ylabel('Ronda Roussey dignity')
set(gcf,'color','w')

Reverse arrangement calculation

clear Res A Ainf Asup
jj=1;
Ndata = 50:50:N;
for ii=1:numel(Ndata),
dummy =  data(1:Ndata(ii));
[Res(jj),A(jj),Ainf(jj),Asup(jj)] = RA_test(dummy,2);
jj=jj+1;
end

figure
plot(Ndata,A,'r',Ndata,Ainf,'k--',Ndata,Asup,'k:')
xlabel('Number of data')
ylabel('reverse arrangements');
legend('Measured','lower boundary','upper boundary','location','NorthWest')
set(gcf,'color','w')
% The red curve falls outside the upper and lower boundary after the step function: The signal is
% non-stationnary
ylim([-10,10])