How to fit with several infinite serie functions ?

Question

Chris J 2020-3-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/508421-how-to-fit-with-several-infinite-serie-functions

回答： David Hill 2020-3-2

clc
clear all
close all
syms L m n
%dbstop if error
x= [0.166666667 1.166666667 2 7.666666667 14.16666667 19.66666667 29.66666667 32.66666667 42.16666667];
y=[0.066508437 0.054771654 0.045643045 0.028689914 0.020865392 0.011736783 0 0 0];     
xx = linspace(x(1),x(end),9);
cc=xx.';
figure(1)
plot(cc,y,'bo');
hold on 
fun = @(beta,xdata) 512/(pi^6)*symsum(symsum(symsum(1./(exp(-beta(1).*x.*(((2*L+1)*pi/30.81).^2+ ((2*m+1)*pi/30.78).^2+...
     ((2*n+1)*pi/0.44).^2)).*((2*L+1).^2.*(2*m+1).^2.*(2*n+1).^2)),n,[0 10]),m,[0 10]),L,[0 10]);
betaguess = 3e-6;
betafit = nlinfit(cc,y,fun,betaguess);
plot(cc,fun(betafit,cc),'g-')
legend('Data','Fitted exponential')
title('Data and Fitted Curve')

Hi all, i am dealing with the fickian equation as follows. Try to use none linear fit. In the code, t,mt/msat is input as x,y. Using curve fitting get the best D value. However, it doesn,t work well. Is there anyway to do this in matlab?

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Answer 1

David Hill 2020-3-2

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/508421-how-to-fit-with-several-infinite-serie-functions#answer_418019

在 MATLAB Online 中打开

x=0:100;%I only went to 100 for the summations.
x0=1;%not sure what these should be
y0=1;
z0=1;
t=0.166666667;%first value of x
n=repmat(x,1,10000);
m=repmat(repelem(x,1,100),1,100);
l=repelem(x,1,10000);
Leqv2=((2*l+1)*pi/x0).^2+((2*m+1)*pi/y0).^2+((2*n+1)*pi/z0).^2;
m=@(D)1-(512/pi^6)*sum(exp(-D*t./Leqv2)./((2*l+1).^2.*(2*m+1).^2.*(2*n+1).^2));
for d=15:.1:25%whatever step you want
    if abs(m(d)-0.066508437)<.001%first value of y (whatever tolerance you want
        break;
    end
end
% you could also plot y vs. d for each value of x.
d=0:100
y=arrayfun(@(D)m(D),d);
plot(d,y);