Working out a summation for fitting a curve

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Hashim 2022-8-19

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https://ww2.mathworks.cn/matlabcentral/answers/1782030-working-out-a-summation-for-fitting-a-curve

评论： Hashim 2022-8-20

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Hi, I want to work out a summation that goes as.

I want to fit this to a curve plotted as I on the y axis and t on the x axis using the curve fit app. My function for that goes as:

function I = CurveFitD(t, deltaQ, d)
%CurveFitD We want to fit the I(t)=f(t) to a custom function. 
%   For a bounded layer we have an expression which can yield us the
%   thickness of the polymer layer (in centimeters). We have to fit the transient to this
%   equation to calculate the layer thickness. 
D           = 1e-05; 
% deltaQ      = 4.2e-11;                                   % Couloumbs
I           = zeros(size(t));
for i    = 1:length(t)
    for k = 1:5
        I(i) = I(i) + (-(1)^(k)).*...
            (exp((-(k^2).*(d^2))))./(D*t(i));
    end
    I(i) = sqrt(1./t(i)).*(1+2.*I(i));
end
I        = sqrt(D/(pi))*(deltaQ/d).*I;
end

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Bruno Luong 2022-8-19

编辑：Bruno Luong 2022-8-19

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It looks fine to me. You can also use MATLAB vectorization instead of for-loop:

D = 1e-05; 
deltaQ = 4.7e-6;
nmax = 5;
n = (1:nmax)';
t = reshape(t,1,[]);
I = sqrt(D./(pi*t)).*deltaQ/d.*(1 + 2*sum((-1).^n.*exp(-(n*d).^2./(D*t)),1));