fit a curve to data without using curve fitting toolbox

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Anqi Li 2014-12-12

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https://ww2.mathworks.cn/matlabcentral/answers/166373-fit-a-curve-to-data-without-using-curve-fitting-toolbox

评论： Andreas Goser 2014-12-12

采纳的回答： Mohammad Abouali

I have a set of data=[x1 x2] which looks periodical. I want to fit them into this Fourier transform equation:

x2 = A1 + A2.*sin(x1) + A3.*cos(x1) + A4.*sin(2*x1) + A5.*cos(2*x1)

by using least squares optimisation to know the optimum A = [A1;A2;A3;A4;A5]

I don't have curve fitting toolbox. please let me know how to do it without using toolbox.

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Andreas Goser 2014-12-12

I see you already have answers, but I wonder why you do not have the Curve Fitting Toolbox. Is the information about the university you work at current (your profile)?

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Mohammad Abouali 2014-12-12

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https://ww2.mathworks.cn/matlabcentral/answers/166373-fit-a-curve-to-data-without-using-curve-fitting-toolbox#answer_162103

编辑：Mohammad Abouali 2014-12-12

在 MATLAB Online 中打开

Assuming your X1 and X2 are vector, i.e. size(x1)=size(x2)=[N 1] and N>=5 (since there are 5 coefficients, A1 to A5); then

C=[ones(numel(x1),1) sin(x1(:)) cos(x1(:)) sin(2*x1(:)) cos(2*x1(:))];
A=(C'*C)\(C'*x2(:));

or even:

A=C\x2(:);

so x2(:) makes sure that your data is a column vector data, i.e. size(x2(:))=[N 1]. I just wanted to be sure that it is not a row data but a vertical column vector. If it is already a column vector you can just replace it with X2 and drop (:).

A=C\x2 conceptually is pretty much solving C*A=x2; Your system of equations can be written as matrix C (the one with sine and cosine functions) multiplied by the unknown column vector, and x2 is your known variable vectors. once you do A=C\x2 pretty much you are solving the system of linear-equations. This operation is known as mldivide. If you want to know more about it go to mldivide help section, there you can find more information on how to use this.

Anqi Li 2014-12-12