46 lines
928 B
Mathematica
46 lines
928 B
Mathematica
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function [a,b,da,db]=fit_linear(x,y,varargin)
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%fit_linear: 1st order linear regression.
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%This function fits a dataset of x and y values to the linear equation
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%y=ax+b. it is optional for the user to insert also y error values for the
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%estimation of a and b errors.
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%
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%Yair Judkovsky, 21.8.2013
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if nargin==2 %case of no error input - assuming that all errors are equal
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dy = ones(size(y));
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else
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dy = varargin{1};
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end
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dy2=dy.^2;
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x2=x.^2;
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xy=x.*y;
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S=sum(1./dy2);
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Sx=sum(x./dy2);
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Sy=sum(y./dy2);
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Sxx=sum(x2./dy2);
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Sxy=sum(xy./dy2);
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D=S*Sxx-Sx^2;
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a=(S*Sxy-Sx*Sy)/D;
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b=(Sxx*Sy-Sxy*Sx)/D;
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if nargin==2 %no error given - need to estimate it
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Ytheo=a*x+b;
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dy2=mean((Ytheo-y).^2)*ones(size(y));
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S=sum(1./dy2);
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Sx=sum(x./dy2);
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Sxx=sum(x2./dy2);
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D=S*Sxx-Sx^2;
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da=sqrt(S/D);
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db=sqrt(Sxx/D);
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else
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da=sqrt(S/D);
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db=sqrt(Sxx/D);
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end
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return
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