具有两个参数的方程的曲线拟合 [英] Curve Fitting for equation with two parameters

问题描述

我有两个数组:

E= [6656400;
    13322500;
    19980900;
    26625600;
    33292900;
    39942400;
    46648900;
    53290000]

和

J=[0.0000000021;
    0.0000000047;
    0.0000000128;
    0.0000000201;
    0.0000000659;
    0.0000000748;
    0.0000001143;
    0.0000001397]

我想通过应用以下等式为上述数据找到合适的曲线拟合:

I want to find the appropriate curve fitting for the above data by applying this equation:

J=A0.*(298).^2.*exp(-(W-((((1.6e-19)^3)/(4*pi*2.3*8.854e-12))^0.5).*E.^0.5)./((1.38e-23).*298))

我想从1e-19中选择W的起始值

I want to select the starting value of W from 1e-19

我已经尝试过曲线拟合工具，但是并不能帮助我解决问题！

I have tried the curve fitting tools but it is not helping me to solve it!

然后，我选择了一些随机值A0 = 1.2e9和W = 2.243e-19，这给了我更好的结果.但是我想通过使用代码(而不是曲线拟合应用程序)找到正确的值

Then, I selected some random values of A0=1.2e9 and W=2.243e-19, it gave me a better results. But I want to find the right values by using the code (not the curve fitting Apps)

你能帮我吗?

推荐答案

一种快速(且可能很简单)的解决方法是将曲线拟合作为最小化问题.

A quick (and potentially easy) solution method would be to pose the curve fit as a minimization problem.

定义一个以fit参数作为参数的相关函数:

Define a correlation function that takes the fit parameters as an argument:

% x(1) == A0; x(2) == W
Jfunc = @(x) x(1).*(298).^2.*exp(-(x(2)-((((1.6e-19)^3)/(4*pi*2.3*8.854e-12))^0.5).*E.^0.5)./((1.38e-23).*298));

然后将目标函数最小化.由于您有数据J，因此我们将数据和相关性之间的差异的平方和最小化:

Then a objective function to minimize. Since you have data J we'll minimize the sum-of-squares of the difference between the data and the correlation:

Objective = @(x) sum((Jfunc(x) - J).^2);

，然后尝试使用 fminsearch 最小化目标:

And then attempt to minimize the objective using fminsearch:

x0  = [1.2E9;2.243E-19];
sol = fminsearch(Objective,x0);

我用了你的猜测.对于非线性解决方案，良好的初步猜测通常对于收敛至关重要.

I used the guesses you gave. For nonlinear solutions, a good first guess is often important for convergence.

如果您有优化工具箱，也可以尝试 lsqcurvefit 或 lsqnonlin (fminsearch是香草MATLAB).

If you have the Optimization Toolbox, you can also try lsqcurvefit or lsqnonlin (fminsearch is vanilla MATLAB).

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