ODE45 using array input

I am trying to solve a set of differential equations in which some parameters are random generated arrays. However when I run the code I get an following error. Does ode45 take the complete array for each iteration causing the error, if so how do I resolve it.

Unable to perform assignment because the left and right sides have a different number of elements.

Error in PDE_Backstepping>deq (line 21)

x(2) = -e + r_prime;

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in PDE_Backstepping (line 8)

[t,x] = ode45(@deq, ts, Xin, options);

Here's the code I am using:

Xin = [0, 0];
ts = [0:0.00001:10];
k = 1e-6;
r = rand(1,1000001);
r_prime = [0 diff(r)];

options = odeset('RelTol',1e-10,'AbsTol',1e-10);
[t,x] = ode45(@deq, ts, Xin, options);
  
function f = deq(t,x)
k = 1e-6;
w = 212.28;
zeta  = 0.1;
BLE = -1.4099e-08;
BTE = -1.375e-08

r = rand(1,1000001);
r_prime = [0 diff(r)];
 
e = x(1) - r;
x(2) = -e + r_prime;
 
u = x(2) - (x(2) - r_prime) - k*(x(2) - r_prime + e);
f(1,1) = x(2);
f(2,1) = -2*zeta*w*x(2) - w^2*x(1) + (BLE+BTE)*u;
end

Answer 1

[darova]

Can you explain what you are trying to do?

[Amit Bhayadia]

The r here is the reference input to the set of ode. e is the error defined such that the output of the ode (x(1)) is teh same as r. Usually r is afunction that iterates with time but here I am using an array which I dont have the defibing function for. Using an pre determined array leads to a dimensionality problem when using ode45, So I am looking for a way to work around it.

[darova]

try this

% r = rand(1,1000001);
r = rand;

[Amit Bhayadia]

That would work since now r is a single number but in actuality the r I am using is a saved array. I just used a random array here as an example. So if r were a predetermined array how do I make it work. Is there a way too use a for loop in the function to make it work.

[darova]

I understand, here is an example:

function main
r = (your_array);
time = (appropriate_time_array);
    function du = f(t,u)
        r1 = interp1(time,r,t);     % extract current r
        du = (ode_equation);
    end
end

[Amit Bhayadia]

Can you explain the purpose of having a function within function? Also in my ode do I use the r1 value?

[darova]

You should try. My typing skills are poor. Don't want to explain that