Curve fitting for multivariable

2021 11 23
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更新时间：2021 11 24
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xdata = ...
[0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937
];
xdata1 = ...
[0.906307787 0.906307787 0.906307787 0.866025404 0.866025404 0.866025404 0.866025404 0.866025404 0.866025404 0.707106781 0.707106781 0.707106781 0.707106781 0.707106781 0.707106781
];
xdata2 = ...
[6 7 8 3 4 5 6 7 8 3 4 5 6 7 8
];
xdata3 = ...
[0.886554928 0.835547334 0.81144197 0.87036842 0.874342998 0.879089205 0.866834625 0.875630457 0.891094548 0.935958471 0.930808554 0.940172751 0.905018613 0.895769734 0.895561329
];
F = @(x,xdata,xdata1,xdata2,xdata3)xdata*x(1)*exp(x(2)*xdata1+x(3)*xdata2+x(4)*xdata);
Which curve fitting function can I use to solve x(1) x(2) x(3) x(4)?

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 采纳的回答

Star Strider
Star Strider 2021-11-23
Ran in:

0 个投票

Ran in:
There are several options.
I’m using fminsearch here.
xdata = ...
[0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937 0.882263937
];
xdata1 = ...
[0.906307787 0.906307787 0.906307787 0.866025404 0.866025404 0.866025404 0.866025404 0.866025404 0.866025404 0.707106781 0.707106781 0.707106781 0.707106781 0.707106781 0.707106781
];
xdata2 = ...
[6 7 8 3 4 5 6 7 8 3 4 5 6 7 8
];
xdata3 = ...
[0.886554928 0.835547334 0.81144197 0.87036842 0.874342998 0.879089205 0.866834625 0.875630457 0.891094548 0.935958471 0.930808554 0.940172751 0.905018613 0.895769734 0.895561329
];
% F = @(x,xdata,xdata1,xdata2,xdata3)xdata*x(1)*exp(x(2)*xdata1+x(3)*xdata2+x(4)*xdata);
F = @(x,xdata)xdata(:,1).*x(1).*exp(x(2).*xdata(:,2)+x(3).*xdata(:,3)+x(4).*xdata(:,4));
xdatam = [xdata(:) xdata1(:) xdata2(:) xdata3(:)];
x0 = rand(4,1);
[B,fv] = fminsearch(@(x) norm(F(x,xdatam)), x0)
B = 4×1
32.6171 329.4611 -415.3622 0.9991
fv = 0
.

5 个评论
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Hoang Khanh Le
Hoang Khanh Le 2021-11-24
Thanks for your suggestion.
Hoang Khanh Le
Hoang Khanh Le 2021-11-24
May I ask you a question? If I also do not know the exponential function in the formula, how I can find a suitable function for these data set? thanks a lot
Star Strider
Star Strider 2021-11-24
As always, my pleasure!
With respect to fitting the model, I have no idea what model correctly describes the data. I have no idea what the data are, what they represent, or the process that created them. A mathematical model of the process that created them is the best function to fit to them. Use that if it is known.
There are several different solvers available. Use whatever works best. (I chose fminserarch because it is part of base MATLAB so everyone has it.)
.
Hoang Khanh Le
Hoang Khanh Le 2021-11-24
Your proposed function works very well, thanks a lot.
Star Strider
Star Strider 2021-11-24
As always, my pleasure!
.

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