# Plotting different datasets from looped ode45 using subplots.

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Frederik Bjerregaard on 9 Dec 2021
Commented: Star Strider on 9 Dec 2021
Hi. I have a script where I'm solving and ode for different values of a parameter. I want to plot each of these cases on a seperate subplot as plotting them all on the same plot is messy. So far i have managed to get the result for the first iteration onto every subplot using:
clc; clear;close all;
% Defining parameters and initial conditions
f = 0.35+[0.1:0.1:0.4];
r = 0.3;
zeta = 0.25;
eps = -1/6;
Theta0 = [0.30, 0];
tspan = [0 100];
% Solver options
opts = odeset('RelTol',1e-6,'AbsTol',[1e-9 1e-9]);
% Solver
for i = 1:length(f)
[t,theta] = ode45(@(t,theta) odefcn(t,theta,f(i),r,zeta), tspan,Theta0);
eqn=@(A) f(i)^2-(-r^2*A+A+(3*eps*A^3)/4)^2-(2*zeta*r*A)^2;
Amp(:,i)=fzero(eqn,0.1);
thetaHB=Amp(i).*sin(r.*t);
theta_HB=Amp(i).*r.*cos(r.*t);
subplot(2,2,1);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title('f=0.35+0.1');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');
subplot(2,2,2);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([2 2 1])
title('f=0.35+0.2');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');
subplot(2,2,3);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title('f=0.35+0.3');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');
subplot(2,2,4);
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title('f=0.35+0.4');
xlabel ('\theta');
ylabel('d\theta/dt');
legend('Numerical','Harmonic Balance');
sgtitle('Phase Planes r=0.3','FontSize',20)
end
The underlying function for odefcn is
end

Star Strider on 9 Dec 2021
I assume that the intended result is to have different plots representing the function with different values of ‘f’ in each subplot. The code needs to be tweaked dlightly to get there —
% Defining parameters and initial conditions
f0 = 0.35;
fv = [0.1:0.1:0.4];
r = 0.3;
zeta = 0.25;
eps = -1/6;
Theta0 = [0.30, 0];
tspan = [0 100];
% Solver options
opts = odeset('RelTol',1e-6,'AbsTol',[1e-9 1e-9]);
% Solver
for i = 1:numel(fv)
f = f0 + fv(i); % Create New 'f' For Each Iteration
[t,theta] = ode45(@(t,theta) odefcn(t,theta,f,r,zeta), tspan,Theta0);
eqn=@(A) f^2-(-r^2*A+A+(3*eps*A^3)/4)^2-(2*zeta*r*A)^2;
Amp(:,i)=fzero(eqn,0.1);
thetaHB=Amp(i).*sin(r.*t);
theta_HB=Amp(i).*r.*cos(r.*t);
subplot(3,2,i); % Iterate Through 'subplot' Array
plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
pbaspect([1 1 1])
title(sprintf('f=0.35+%.1f',fv(i)));
xlabel ('\theta');
ylabel('d\theta/dt');
hl = legend('Numerical','Harmonic Balance');
hl.Visible = 'off';
% subplot(2,2,2);
% plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
% pbaspect([2 2 1])
% title('f=0.35+0.2');
% xlabel ('\theta');
% ylabel('d\theta/dt');
% legend('Numerical','Harmonic Balance');
%
% subplot(2,2,3);
% plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
% pbaspect([1 1 1])
% title('f=0.35+0.3');
% xlabel ('\theta');
% ylabel('d\theta/dt');
% legend('Numerical','Harmonic Balance');
%
% subplot(2,2,4);
% plot(theta(:,1),theta(:,2),thetaHB,theta_HB);
% pbaspect([1 1 1])
% title('f=0.35+0.4');
% xlabel ('\theta');
% ylabel('d\theta/dt');
% legend('Numerical','Harmonic Balance');
% sgtitle('Phase Planes r=0.3','FontSize',20)
end
subplot(3,2,[5 6])
ax = gca;
pos = ax.Position;
hl.Position = pos + [0.1 0.15 -0.2 -0.2];
hl.Visible = 'on';
ax.Visible = 'off';
sgtitle('Phase Planes r=0.3','FontSize',20)
end
I re-positioned the legend so that it would not cover the plots, since it was common to all of them.
.
##### 2 CommentsShowHide 1 older comment
Star Strider on 9 Dec 2021
As always, my pleasure!
.

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