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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채택된 답변
Torsten
2016년 11월 17일
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.
댓글 수: 5
Walter Roberson
2016년 11월 21일
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
2016년 11월 21일
You don't get statistics from lsqnonlin.
You will have to use tools like nlinfit in combination with nlparci and nlpredci.
Best wishes
Torsten.
추가 답변 (1개)
Walter Roberson
2016년 11월 18일
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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