用于两个变量的Polyfit [英] Polyfit for two variables

问题描述

我有一种数据，想找到给定数据的方程式(poly coeff).例如，给定样本数据的方程式很简单a^2*b+10

I have a kind of data and want to find the equation(poly coeff) of given data. For example equation for given sample data is simple a^2*b+10

a\b    5    10    15
________________________
3|    55   100   145
4|    90   170   250
5|   135   260   385
6|   190   370   550

我检查了polfit，但它仅适用于一个变量.

I checked forpolfitbut It only works for one variable.

推荐答案

如达斯蒂·坎贝尔指出，您可以使用fit函数.为此，您必须使用数据构建网格

As Dusty Campbell pointed out you can use the fit function. To do this you have to build a mesh with your data

a = [3 4 5 6];
b = [5 10 15];
[A, B] = meshgrid(a, b);
C = (A.^2).*B + 10;

，然后使用自定义公式调用fit

and then call fit with a custom equation

ft = fittype('p1*a^2*b + p2', 'independent',{'a','b'}, 'dependent','c');
opts = fitoptions('Method','NonlinearLeastSquares', 'StartPoint',[0.5,1]);
[fitresult, gof] = fit([A(:), B(:)], C(:), ft, opts);

您将看到求解器收敛到正确的解决方案p1 = 1，p2 = 10.

As you'll see the solver converges to the correct solution p1 = 1, p2 = 10.

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