curve fit toolbox help system ODE and excel?

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Renee 2014-10-23

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评论： Renee 2014-10-30

Hi, I am trying to curve fit using the toolbox to a function which is a system of ODE. my data corresponds to one equation of the function. how can i specify this? Also, the tutorial seems to say you should put your data into the command line, but mine is in excel, is there some easier way? Thanks!

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Matt Tearle 2014-10-23

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If I interpret your problem correctly, you have a system of ODEs with a parameter -- y' = f(t,y;c) -- and an Excel spreadsheet that has data for t and y3 (or whatever -- one of the components of y). You're trying to do a curve fit to determine c.

That's fun!

Here's an example that does that with the classic mass-spring system. I'm making some t and y data; you could read this from Excel with xlsread. You need to do this only once at the beginning, then you have the data to fit to.

% ---------------------------------------------------------------
% Make some data -- replace all this with a call to XLSREAD
m = 0.1*rand;
k = 4*rand;
w = 0.5*sqrt(4*k-m*m);
t = linspace(0,2*pi)';
y = exp(m*t/2).*cos(w*t) + 0.02*randn(size(t));
% ---------------------------------------------------------------
% Do curvefitting
cfit = lsqcurvefit(@myode,rand(2,1),t,y)
% See results
plot(t,y,'o',t,myode(cfit,t))

And here's the curve-fitting function:

function y = myode(c,x)
% Define ODE system with parameter c
f = @(t,y,c) [y(2);-c(1)*y(1)+c(2)*y(2)];
% Solve ODE system with given initial condition
[~,z] = ode45(@(t,y) f(t,y,c),x,[1;0]);
% Extract desired solution component
y = z(:,1);

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Renee 2014-10-23

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Thanks! That solved one of the errors I was getting. Now it says "Dimensions of matrices being concatenated are not consistent." Do you happen to know what its referring to? There's 9 ODEs, and I have one initial condition for each ODE. Beyond that I am lost as to what dimensions its talking about.

    function y = splitodes(c,x)
% Define ODE system with parameter c
f = @(t,y,c) [-c(1) .*y(1) .*y(2) + c(2) .* y(6); - c(1) .* y(1) .*y(2) + c(2) .* y(6);-c(3) .*y(6).*y(3) + c(4) .*y(7) - c(5).*y(3).*y(8) + c(6) .*y(9);-c(7) .*y(4).*y(6) + c(8) .*y(8) - c(9) .*y(4).*y(7) + c(10) .*y(9);c(11) *c(12)*c(13) .* y(9) - y(5);c(1).*y(1).*y(2) - c(2).*y(6) -c(7) .*y(6).*y(4)+c(8).*y(8)-c(3).*y(3).*y(6) + c(4).*y(8) + c(11).*y(9);c(3).*y(6).*y(3)- c(4).*y(7)-c(9).*y(4).*y(7) + c(10).*y(9);-c(5).*y(8).*y(3)+c(6).*y(9) + c(7).*y(4).*y(6)-c(8).*y(8);c(5).*y(8).*y(3)-c(6).*y(9) + c(9).*y(4).*y(7)-c(10).*y(9) -c(11).*y(9)];
%error
options = odeset('RelTol',1e-6);
%init conditions
init = [1;0;0;0;0;0;0;0;0;];
%solve
[~,z] = ode45(@(t,y) f(t,y,c),x,init,options);
% Extract desired solution component
y = z(:,5);