Fitting an equation with x,y variables and b, d constant.
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Hi,
I have an equation.
x=[10,50,100,300,500,1000,1500,2000,3000];
y=[0.11,0.17,0.2,0.24,0.29,0.3,0.31,0.35,0.38];
I want to fit this equation and get b and d values.
I tried with lsqcurvefit command, but I can not convert this equation to y=function(x).
Anybody has a suggestion.
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Risposta accettata
Torsten
il 17 Nov 2016
Use lsqnonlin and define the functions f_i as
f_i = 1/a*(b-ydata(i)).^1.5-log(d./xdata(i))+0.5*log(1-ydata(i)/b)
Best wishes
Torsten.
5 Commenti
Walter Roberson
il 21 Nov 2016
lsqnonlin does not calculate Chi-Square or any other probability measure. It does not create any hypotheses about how well the model fits: it only searches for a minimum.
Torsten
il 21 Nov 2016
You don't get statistics from lsqnonlin.
You will have to use tools like nlinfit in combination with nlparci and nlpredci.
Best wishes
Torsten.
Più risposte (1)
Walter Roberson
il 18 Nov 2016
a = some value
y1 = @(b, d, x) -b .* (exp(-(2/3) .* lambertw(-3 .* (b.^3 ./ a.^2).^(1/2) .* d.^3 ./ x.^3)) .* d.^2 - x.^2) ./ x.^2
y2 = @(b, d, x) -b .* (exp(-(2/3) .* lambertw(3 .* (b.^3 ./ a.^2).^(1/2) .* d.^3 ./ x.^3)) .* d.^2 - x.^2) ./ x.^2;
guessbd = rand(1,2);
fit1 = fittype(y1, 'coefficients', {'b', 'd'}, 'dependent', 'y', 'independent', x);
fit2 = fittype(y2, 'coefficients', {'b', 'd'}, 'dependent', 'y', 'independent', x);
[bd1, gof1] = fit( x, y, fit1, 'startpoint', guessbd );
[bd2, gof2] = fit( x, y, fit2, 'startpoint', guessbd );
The pair of fits is due to there being two solutions when y is expressed in terms of x, almost identical but differing in sign of the LambertW expression. You would need to check the goodness of fit results to see which was better.
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