Fit data with a given equation for 3 variables

Question

Tesla 2022-5-24

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1726005-fit-data-with-a-given-equation-for-3-variables

评论： Tesla 2022-5-24

I want to fit my data to the following equation, but I dont know how to force the program to take the b values which i have, instead of calculating them automatically, I attached here my code which i wrote

fy = @(a,b,x) ((1-(x/a)).^(-a*b));
x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001,	0.00111499,	0.0011926,	0.0013699,	0.00161633,	0.00192075,	0.00274991,	0.00357156]; 
b = [0,	1.1499,	0.963,	1.233,	1.540825,	2.001630435,	3.181654545,	4.285933333];
B = fmincon(@(c) norm(y - fy(c(1),c(2),x)), [1; 1], [],[],[],[], [0 0],[1 90]);
fprintf('PhiMax  = %.15f\nVisco = %.15f\n', B)
xv = linspace(min(x), max(x));
figure(1)
plot(x, y, 'pg')
hold on
plot(xv, fy(B(1),B(2),xv), '-r')
hold off
grid

2 个评论
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Torsten 2022-5-24

How should it be possible to have the value for b if you don't know the value for a ?

Tesla 2022-5-24

Indeed i am looking for the value of a

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Answer 1

Torsten 2022-5-24

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https://ww2.mathworks.cn/matlabcentral/answers/1726005-fit-data-with-a-given-equation-for-3-variables#answer_970485

编辑：Torsten 2022-5-24

在 MATLAB Online 中打开

Your function is not suited to reflect your data.

x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001,	0.00111499,	0.0011926,	0.0013699,	0.00161633,	0.00192075,	0.00274991,	0.00357156]; 
b = [0,	1.1499,	0.963,	1.233,	1.540825,	2.001630435,	3.181654545,	4.285933333];
p0 = 1;
B = lsqnonlin(@(a)fy(a,x,y,b),p0,max(x),Inf)
fprintf('PhiMax  = %.15f\nVisco = %.15f\n', B)
figure(1)
plot(x, y, 'pg')
hold on
plot(x, fy(B(1),x,y,b)+y, '-r')
hold off
grid
function res = fy(a,x,y,b)
  res = ((1-(x/a)).^a).^b - y;
end

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显示 -1更早的评论隐藏 -1更早的评论

Tesla 2022-5-24

在 MATLAB Online 中打开

Thanks a lot, it works, I just need to multipy the function by 0.001.

function res = fy(a,x,y,b)
res = 0.001*((1-(x/a)).^a).^b - y;
end

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Answer 2

Hiro Yoshino 2022-5-24

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https://ww2.mathworks.cn/matlabcentral/answers/1726005-fit-data-with-a-given-equation-for-3-variables#answer_970470

在 MATLAB Online 中打开

How about this?

You only need to think about c as follows:

fy = @(a,b,x) ((1-(x/a)).^(-a*b));
x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001,	0.00111499,	0.0011926,	0.0013699,	0.00161633,	0.00192075,	0.00274991,	0.00357156]; 
b = [0,	1.1499,	0.963,	1.233,	1.540825,	2.001630435,	3.181654545,	4.285933333];
B = fmincon(@(c) norm(y - fy(c,b,x)),1,[],[],0,1)
Converged to an infeasible point.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance but constraints are not
satisfied to within the value of the constraint tolerance.


Consider enabling the interior point method feasibility mode.
B = 6.6511e+03