How to use my numeric array results as input values for an ODE?

So I have the following code:

n = 10 ; 
result = zeros(n,5 ); 
for k=1:n ; 
A0=1;P0=29;g=rand;p=rand;B=rand ; 
result(k,:) = [A0,P0,g,p,B ]; 
end;

Which produces a 10x5 numeric array as the result.

And I'd like to use my results from there as the input values to solve this equation ten times:

tspan=[1 7];
[t,x] = ode45(@(t,x) [-g*x(1) + p*x(1); -x(1)*x(2)+ B*x(2)], tspan, [A0 P0]);

Is this possible?

Thanks in advance!

Answer 1

[Star Strider]

Try this:

n = 10 ; 
result = zeros(n,5 ); 
for k=1:n ; 
A0=1;P0=29;g=rand;p=rand;B=rand ; 
result(k,:) = [A0,P0,g,p,B ]; 
end

for k = 1:size(result,1)
    tspan=linspace(0,7,50);
    ODE = @(t,x,g,p,B) [-g*x(1) + p*x(1); -x(1)*x(2)+ B*x(2)];
    [t,x(:,:,k)] = ode45(@(t,x) ODE(t,x,result(k,3),result(k,4),result(k,5)), tspan, [result(k,1) result(k,2)]);
end

It saves the output to a 3D matrix, as previously.

[Thomas Veith]

Thank you, that is incredibly helpful!

I just have one follow up question: once I've completed this, is there any way for me to plot my x values against my t values? Can I convert the 3D matrix to 2D (bc actually previously when I solved this OD it would spit out a 2D matrix, column 1 being solved x(1), column 2 being solved x(2)) or access those x values some way?

[Star Strider]

My pleasure!

It’s likely easiest to do it in a looop:

figure
hold all
for k = 1:size(x,3)
    plot(t, x(:,:,k))
end
hold off
grid

Although you may want to plot the two values of ‘x’ separately using subplot to see the details:

figure
subplot(2,1,1)
hold all
for k = 1:size(x,3)
    plot(t, x(:,1,k))
end
title('x_1')
grid
subplot(2,1,2)
hold all
for k = 1:size(x,3)
    plot(t, x(:,2,k))
end
title('x_2')
grid
hold off

[Thomas Veith]

That is perfect, thank you so much!

[Star Strider]

As always, my pleasure!