带有多个自变量的Python curve_fit [英] Python curve_fit with multiple independent variables

问题描述

Python的 curve_fit 计算具有单个自变量的函数的最佳拟合参数，但是有一种方法可以使用 curve_fit 或其他方法来适合具有多个自变量的函数吗？例如：

Python's curve_fit calculates the best-fit parameters for a function with a single independent variable, but is there a way, using curve_fit or something else, to fit for a function with multiple independent variables? For example:

def func(x, y, a, b, c):
    return log(a) + b*log(x) + c*log(y)

其中x和y是独立的变量，我们希望适合a，b和c。

where x and y are the independent variable and we would like to fit for a, b, and c.

推荐答案

您可以传递 curve_fit 自变量的多维数组，但您的 func 必须接受相同的内容。例如，调用此数组 X 并将其解压缩为 x ， y 为清楚起见：

You can pass curve_fit a multi-dimensional array for the independent variables, but then your func must accept the same thing. For example, calling this array X and unpacking it to x, y for clarity:

import numpy as np
from scipy.optimize import curve_fit

def func(X, a, b, c):
    x,y = X
    return np.log(a) + b*np.log(x) + c*np.log(y)

# some artificially noisy data to fit
x = np.linspace(0.1,1.1,101)
y = np.linspace(1.,2., 101)
a, b, c = 10., 4., 6.
z = func((x,y), a, b, c) * 1 + np.random.random(101) / 100

# initial guesses for a,b,c:
p0 = 8., 2., 7.
print curve_fit(func, (x,y), z, p0)

给出合适的值：

(array([ 9.99933937,  3.99710083,  6.00875164]), array([[  1.75295644e-03,   9.34724308e-05,  -2.90150983e-04],
   [  9.34724308e-05,   5.09079478e-06,  -1.53939905e-05],
   [ -2.90150983e-04,  -1.53939905e-05,   4.84935731e-05]]))

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