Saving multiple outputs from ODE45 with different dimensions?

Question

Adham Alkhaja 2020-6-21

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https://ww2.mathworks.cn/matlabcentral/answers/552190-saving-multiple-outputs-from-ode45-with-different-dimensions

回答： J. Alex Lee 2020-6-21

I have written an ODE45 function inside a for loop with an event where it stops at a zero-crossing. I have creating a variable that is three-dimensional and saves the output each iteration in the for-loop. The issue is that each iteration, the dimension of the output is different as each flags the stop condition at a different number of steps.

How can I save a changing variable size in one variable?

The code is,

counter_minus = 1;
for n=2:k
    options=odeset('RelTol',1e-13,'AbsTol',1e-22,'Events',@(t,y) Xcrossing(t,y));
    [t_out,xU_out]=ode113(@(t,y) DifferentialEquation(t,y),tspan,y0,options);
    XU_OUTPUT(:,:,counter_minus) = xU_out;
    counter_minus=counter_minus+1;
end

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Answer 1

J. Alex Lee 2020-6-21

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https://ww2.mathworks.cn/matlabcentral/answers/552190-saving-multiple-outputs-from-ode45-with-different-dimensions#answer_454990

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I would use cells...also what's with the dual indexing? options can be defined outside since nothing is changing from iteration to iteration

% define outside the loop since nothing is changing
% AbsTol = 1e-22 < eps, is this realistic?
options=odeset('RelTol',1e-13,'AbsTol',1e-22,'Events',@(t,y) Xcrossing(t,y));
% pre-allocate
XU_OUTPUT = cell(k-1,1);
for counter = 1:(k-1)
    % presumably something is changing with iterations...otherwise it's the same thing over and over again?
    [t_out,xU_out]=ode113(@(t,y) DifferentialEquation(t,y),tspan,y0,options);
    XU_OUTPUT{counter} = xU_out;
end