貌似关于多元拟合的使用没有太多文章进行讲解。

首先给出数据集：数据集

目标函数：

在python中，我们使用scipy.optimize库中的curve_fit，首先给出其官方文档中一些比较重要的参数简介：Parameters

fcallable

The model function, f(x, …). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments.

xdataarray_like or object

The independent variable where the data is measured. Should usually be an M-length sequence or an (k,M)-shaped array for functions with k predictors, but can actually be any object.

ydataarray_like

The dependent data, a length M array - nominally f(xdata, ...).

p0array_like, optional

Initial guess for the parameters (length N). If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised).

bounds2-tuple of array_like, optional

Lower and upper bounds on parameters. Defaults to no bounds. Each element of the tuple must be either an array with the length equal to the number of parameters, or a scalar (in which case the bound is taken to be the same for all parameters). Use np.inf with an appropriate sign to disable bounds on all or some parameters.

method{‘lm’, ‘trf’, ‘dogbox’}, optional

Method to use for optimization. See least_squares for more details. Default is ‘lm’ for unconstrained problems and ‘trf’ if bounds are provided. The method ‘lm’ won’t work when the number of observations is less than the number of variables, use ‘trf’ or ‘dogbox’ in this case.

New in version 0.17.

Returns

poptarray

Optimal values for the parameters so that the sum of the squared residuals of f(xdata, *popt) - ydata is minimized.

pcov2-D array

The estimated covariance of popt. The diagonals provide the variance of the parameter estimate. To compute one standard deviation errors on the parameters use perr = np.sqrt(np.diag(pcov)).

How the sigma parameter affects the estimated covariance depends on absolute_sigma argument, as described above.

If the Jacobian matrix at the solution doesn’t have a full rank, then ‘lm’ method returns a matrix filled with np.inf, on the other hand ‘trf’ and ‘dogbox’ methods use Moore-Penrose pseudoinverse to compute the covariance matrix.

其中，fcallable是我们需要拟合函数原型，xdataarray是我们的输入，注意在这里，输入矩阵的形状为 k*M(k为参数个数)，ydataarray是我们的输出。

p_0array_like、bounds2-tuple of array_like、method是可选参数，分别是初始值、边界和回归算法，当我们需要设置边界时，算法只能选择为'trf'和'dogbox'。

LM是在目标函数中，加入一个阻尼项，在接近最终结果是，可以活得二次收敛速度，和高斯牛顿法类似。而dogbox算法，需要判断移动相关步长之后，是否仍在信赖域中。

最后给出，拟合之后的曲线：