Working out a summation for fitting a curve
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Hi, I want to work out a summation that goes as.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1101895/image.png)
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
9 件のコメント
Bruno Luong
2022 年 8 月 19 日
編集済み: Bruno Luong
2022 年 8 月 19 日
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));
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