Curve fitting for multivariable

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)?

Answer 1

[Star Strider]

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

.

[Hoang Khanh Le]

Thanks for your suggestion.

[Hoang Khanh Le]

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]

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]

Your proposed function works very well, thanks a lot.

[Star Strider]

As always, my pleasure!

.