scipy curve_fit不喜欢数学模块

Question

在尝试创建一个示例时，scipy.optimize curve_fit我发现scipy似乎与Python的math模块不兼容。虽然功能f1正常，但f2会引发错误消息。

from scipy.optimize import curve_fit
from math import sin, pi, log, exp, floor, fabs, pow

x_axis = np.asarray([pi * i / 6 for i in range(-6, 7)])  
y_axis = np.asarray([sin(i) for i in x_axis])

def f1(x, m, n):
    return m * x + n

coeff1, mat = curve_fit(f1, x_axis, y_axis)    
print(coeff1)

def f2(x, m, n):
    return m * sin(x) + n

coeff2, mat = curve_fit(f2, x_axis, y_axis)  
print(coeff2)

完整的追溯是

Traceback (most recent call last):
  File "/Documents/Programming/Eclipse/PythonDevFiles/so_test.py", line 49, in <module>
    coeff2, mat = curve_fit(f2, x_axis, y_axis)
  File "/usr/local/lib/python3.5/dist-packages/scipy/optimize/minpack.py", line 742, in curve_fit
    res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
  File "/usr/local/lib/python3.5/dist-packages/scipy/optimize/minpack.py", line 377, in leastsq
    shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
  File "/usr/local/lib/python3.5/dist-packages/scipy/optimize/minpack.py", line 26, in _check_func
    res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
  File "/usr/local/lib/python3.5/dist-packages/scipy/optimize/minpack.py", line 454, in func_wrapped
    return func(xdata, *params) - ydata
  File "/Documents/Programming/Eclipse/PythonDevFiles/so_test.py", line 47, in f2
    return m * sin(x) + n 
TypeError: only length-1 arrays can be converted to Python scalars

出现错误消息，并带有列表和numpy数组作为输入。它会影响math我测试过的所有功能（请参阅导入中的功能），并且必须与数学模块如何处理输入数据有关。这对于pow()函数最为明显-
如果我不从中导入该函数math，则curve_fit可以与之正常工作pow()。

显而易见的问题-为什么会发生这种情况？如何math与函数一起使用curve_fit？

PS：请不要讨论，不应以线性拟合来拟合样本数据。选择它只是为了说明问题。

Answer 1

小心numpy-arrays，对数组进行操作和对标量进行操作！

Scipy
Optimizer假定输入（初始点）是一维数组，在其他情况下通常会出错（例如，列表变成数组，如果您假设要处理列表，则事情会变得很混乱；这类问题是这在StackOverflow上很常见，调试起来并不是一件容易的事；代码交互很有帮助！）。

import numpy as np
import math

x = np.ones(1)

np.sin(x)
> array([0.84147098])

math.sin(x)
> 0.8414709848078965                     # this only works as numpy has dedicated support
                                         # as indicated by the error-msg below!
x = np.ones(2)

np.sin(x)
> array([0.84147098, 0.84147098])

math.sin(x)
> TypeError: only size-1 arrays can be converted to Python scalars

老实说：这是对numpy的非常基本的了解的一部分，在使用scipy的某些敏感函数时应该理解。