Data fitting by non linear discrete equation.
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xdata=[5.0 4.2 4.3 4.3 4.3 4.1 3.7 3.6 3.9 5.9 6.7 5.4 5.1 5.5 6.2 6.7 6.9 6.2 6.1 6.3 5.9 5.5 5.5 5.5 5.5];
ydata=[2.0 2.5 1.9 2.1 2.0 2.1 2.7 4.0 3.8 3.9 3.6 3.2 3.2 3.1 3.2 3.7 3.7 3.2 3.2 3.5 3.5 3.2 3.1 3.3 3.1];
I want to fit the following equations to this data: I want to estimate all the parameter. (alpha and beta lie between 0 and 1, a lies between 0 and alpha, b lies between 0 and beta and c can be any value from 0 to infinity.) Thanks in advance.
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Rik
2020-11-24
What did you try so far?
采纳的回答
The code below uses fminsearch, which means you don't need the optimization toolbox. The downside is that it is sensitive to a local minimum, depending on your initial parameter estimate.
xdata=[5.0 4.2 4.3 4.3 4.3 4.1 3.7 3.6 3.9 5.9 6.7 5.4 5.1 5.5 6.2 6.7 6.9 6.2 6.1 6.3 5.9 5.5 5.5 5.5 5.5];
ydata=[2.0 2.5 1.9 2.1 2.0 2.1 2.7 4.0 3.8 3.9 3.6 3.2 3.2 3.1 3.2 3.7 3.7 3.2 3.2 3.5 3.5 3.2 3.1 3.3 3.1];
initial_guess=0.5*ones(1,5);
fitted_params=fminsearch(@(fit_vals) costfun(fit_vals,xdata,ydata),initial_guess);
[alpha,beta,a,b,c]=deal(fitted_params(1),fitted_params(2),fitted_params(3),fitted_params(4),fitted_params(5));
x0=xdata(1);y0=ydata(1);elems=numel(xdata);
[x_fitted,y_fitted]=f_g(fitted_params,x0,y0,elems);
disp([x_fitted;y_fitted])
function cost=costfun(fit_vals,xdata,ydata)
x0=xdata(1);y0=ydata(1);elems=numel(xdata);
[x,y]=f_g(fit_vals,x0,y0,elems);
cost= sum((x-xdata).^2) + sum((y-ydata).^2);
[alpha,beta,a,b,c]=deal(fit_vals(1),fit_vals(2),fit_vals(3),fit_vals(4),fit_vals(5));
if ( alpha<0 || alpha>1 ) || ...
( a<0 || a>alpha ) || ...
( beta<0 || beta>1 ) || ...
( b<0 || b>beta ) || ...
c<0
cost=inf;
end
end
function [x,y]=f_g(params,x0,y0,elems)
[alpha,beta,a,b,c]=deal(params(1),params(2),params(3),params(4),params(5));
x=zeros(1,elems);x(1)=x0;
y=zeros(1,elems);y(1)=y0;
for n=2:elems
x(n)=(1-alpha)*x(n-1) + a/(1+exp(-c*(x(n-1)-y(n-1))));
y(n)=(1-beta )*y(n-1) + b/(1+exp(-c*(x(n-1)-y(n-1))));
end
end
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