# How to take 100 samples of a plot.

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Heya :) on 29 Dec 2020
Edited: Sindar on 30 Dec 2020
I have a task to take 100 samples of a plot at a fixed value of parameters a2, omega1, and omega2 and I will be changing a1 and take 100 samples. It consumes so much time so I am wondering is their a way to take a 100 samples of a plot.
clear all; close all; clc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Simulation %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%avgnum=10;
%for avg=1:avgnum
OMEGA1= 1:0.2:6.4;
OMEGA2= 6.6:0.2:12;
%Erroravg_nonzero_x1_y1=zeros([1,length(OMEGA1)]);
%Erroravg_zero_x1_y1=zeros([1,length(OMEGA1)]);
%Erroravg_nonzero_x2_y2=zeros([1,length(OMEGA2)]);
%Erroravg_zero_x2_y2=zeros([1,length(OMEGA2)]);
for num1=1:length(OMEGA1)
for num2=1:length(OMEGA2)
%value of constants
a1=0.2;a2=0.3;
%omega1=5;omega2=4;
omega1=OMEGA1(num1);
omega2=OMEGA2(num2);
%omega1= 1:0.5:10;
%omega2= 11:0.5:20;
G=1;C12=0.01;C21=0.02;
dt=0.01; %step size
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x1(1)=0.5;
y1(1)=0.5;
x2(1)=1;
y2(1)=1;
for i=2:1000
x1(i)=x1(i-1)+((a1-x1(i-1)^2-y1(i-1)^2)*x1(i-1)-omega1*y1(i-1)+G*C12*(x2(i-1)-x1(i-1)))*dt;
y1(i)=y1(i-1)+((a1-x1(i-1)^2-y1(i-1)^2)*y1(i-1)+omega1*x1(i-1)+G*C12*(y2(i-1)-y1(i-1)))*dt;
x2(i)=x2(i-1)+((a2-x2(i-1)^2-y2(i-1)^2)*x2(i-1)-omega2*y2(i-1)+G*C21*(x1(i-1)-x2(i-1)))*dt;
y2(i)=y2(i-1)+((a2-x2(i-1)^2-y2(i-1)^2)*y2(i-1)+omega2*x2(i-1)+G*C21*(y1(i-1)-y2(i-1)))*dt;
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Observation %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Ndatamin=4;Ndatamax=31;
Data=Ndatamin:1:Ndatamax;
Data=Data/Ndatamax;
Error_nonzero_x1=zeros([1,Ndatamax-Ndatamin+1]);%initialization
Error_zero_x1=zeros([1,Ndatamax-Ndatamin+1]);%initialization
Error_zero_y1=zeros([1,Ndatamax-Ndatamin+1]);%initialization
Error_nonzero_x2=zeros([1,Ndatamax-Ndatamin+1]);%initialization
Error_zero_x2=zeros([1,Ndatamax-Ndatamin+1]);%initialization
Error_nonzero_y2=zeros([1,Ndatamax-Ndatamin+1]);%initialization
Error_zero_y2=zeros([1,Ndatamax-Ndatamin+1]);%initialization
count=0;
for N_m=Ndatamin:Ndatamax
count=count+1;
N_measurements=N_m;
N_basis=31;
%index=randi([20000,30000],1,N_m);
index=randi([100,499],1,N_m);
Xdot1=zeros([1,N_measurements]);
Ydot1=zeros([1,N_measurements]);
Xdot2=zeros([1,N_measurements]);
Ydot2=zeros([1,N_measurements]);
for ni=1:N_measurements
Xdot1(ni)=(x1(index(ni)+1)-x1(index(ni)))/dt;
Ydot1(ni)=(y1(index(ni)+1)-y1(index(ni)))/dt;
Xdot2(ni)=(x2(index(ni)+1)-x2(index(ni)))/dt;
Ydot2(ni)=(y2(index(ni)+1)-y2(index(ni)))/dt;
end
M=zeros([N_measurements,N_basis]);
for i=1:N_measurements
for j=1:N_basis
if j==1
M(i,j)=1;
elseif j==2
M(i,j)=x1(index(i));
elseif j==3
M(i,j)=y1(index(i));
elseif j==4
M(i,j)=x2(index(i));
elseif j==5
M(i,j)=y2(index(i));
elseif j==6
M(i,j)=x1(index(i))^2;
elseif j==7
M(i,j)=x2(index(i))^2;
elseif j==8
M(i,j)=y1(index(i))^2;
elseif j==9
M(i,j)=y2(index(i))^2;
elseif j==10
M(i,j)=x1(index(i))*x2(index(i));
elseif j==11
M(i,j)=x1(index(i))*y1(index(i));
elseif j==12
M(i,j)=x1(index(i))*y2(index(i));
elseif j==13
M(i,j)=x2(index(i))*y1(index(i));
elseif j==14
M(i,j)=x2(index(i))*y2(index(i));
elseif j==15
M(i,j)=y1(index(i))*y2(index(i));
elseif j==16
M(i,j)=x1(index(i))^3;
elseif j==17
M(i,j)=y1(index(i))^3;
elseif j==18
M(i,j)=x2(index(i))^3;
elseif j==19
M(i,j)=y2(index(i))^3;
elseif j==20
M(i,j)=x1(index(i))^2*x2(index(i));
elseif j==21
M(i,j)=x1(index(i))^2*y1(index(i));
elseif j==22
M(i,j)=x1(index(i))^2*y2(index(i));
elseif j==23
M(i,j)=x2(index(i))^2*x1(index(i));
elseif j==24
M(i,j)=x2(index(i))^2*y1(index(i));
elseif j==25
M(i,j)=x2(index(i))^2*y2(index(i));
elseif j==26
M(i,j)=y1(index(i))^2*x1(index(i));
elseif j==27
M(i,j)=y1(index(i))^2*x2(index(i));
elseif j==28
M(i,j)=y1(index(i))^2*y2(index(i));
elseif j==29
M(i,j)=y2(index(i))^2*x1(index(i));
elseif j==30
M(i,j)=y2(index(i))^2*x2(index(i));
else
M(i,j)=y2(index(i))^2*y1(index(i));
end
end
end
end
figure
hold on
plot(x1,'r')
plot(x2,'g')
##### 2 CommentsShowHide 1 older comment
Heya :) on 29 Dec 2020
It means that I have to run the code 100 times.

Sindar on 30 Dec 2020
Edited: Sindar on 30 Dec 2020
First, what are you actually doing with M, Xdot1, etc.? Currently, the code overwrites them each N_m loop, without doing anything with the results
Try this: define sampled vectors, so you can later vectorize things:
index=randi([100,499],1,N_m);
x1_samp0 = x1(index);
x1_samp1 = x1(index+1);
...
Xdot1=(x1_samp1-x1_samp0)/dt;
...
M(:,1)=1;
M(:,2)=x1_samp0;
...
M(:,6)=x1_samp0.^2;
edit: changed my mind on other option; don't do it. Here are some general tips, though:
• if you have a set of conditions that can be expressed as variable=first, variable=second, etc. -- use a switch instead of if-elseif
• If you have a loop running over a set of conditions and operations which have nothing else in common -- just run each line individually, then fill in the "else" portion after
for j=1:N_basis
if j==1
M(i,j)=1;
elseif j==2
M(i,j)=x1(index(i));
elseif j==3
M(i,j)=y1(index(i));
end
end
does the same as the below, but cleaner and faster:
M(i,1)=1;
M(i,2)=x1(index(i));
M(i,3)=y1(index(i));
• many, many, many for loops can be replaced with vector operations. It's kinda the point of Matlab