Question

我有以下代码：

import numpy as np
import scipy.integrate as spi
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import math as mh

def GUFunction(z, Omega_Lambda):
    integral = spi.quad(lambda zvar: AuxIntegrandum(zvar, Omega_Lambda), 0.0, z)[0]
    DL = (1+z) * c/H0 * integral *1000000
    return (5*(mh.log(DL,10)-1))

def AuxIntegrandum(z, Omega_Lambda):
    Omega_m = 1 - Omega_Lambda

    return 1 / mh.sqrt(Omega_m*(1+z)**3 + Omega_Lambda)

def DataFit(filename):
    print curve_fit(GUFunction, ComputeData(filename)[0], ComputeData(filename)[1])

DataFit("data.dat")

data.dat在第一列中有z值，在第二列中有GUF（z）值。

执行此代码时，编译器告诉我将数组与值（+ inf或-inf）进行比较是不明确的。
我认为这是指集成边界，它看起来是否要集成到无穷大。由于某种原因，它显然将数据文件中的所有z值放入集成边界是否有一些技巧我不知道哪个允许你将曲线拟合到数值积分函数中？

这是确切的错误：

Traceback (most recent call last):
  File "plot.py", line 83, in <module>
    DataFit("data.dat")
  File "plot.py", line 67, in DataFit
    print curve_fit(GUFunction, ComputeData(filename)[0], ComputeData(filename)[1])
  File "/home/joshua/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 736, in curve_fit
    res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
  File "/home/joshua/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 377, in leastsq
    shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
  File "/home/joshua/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 26, in _check_func
    res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
  File "/home/joshua/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 454, in func_wrapped
    return func(xdata, *params) - ydata
  File "plot.py", line 57, in GUFunction
    integral = spi.quad(lambda zvar: AuxIntegrandum(zvar, Omega_Lambda), 0.0, z)[0]
  File "/home/joshua/anaconda2/lib/python2.7/site-packages/scipy/integrate/quadpack.py", line 323, in quad
    points)
  File "/home/joshua/anaconda2/lib/python2.7/site-packages/scipy/integrate/quadpack.py", line 372, in _quad
    if (b != Inf and a != -Inf):
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

Answer 1

简答：curve_fit尝试评估xdata数组上的目标函数，但quad不能接受vector参数。您需要通过以下方式定义目标函数：对输入数组的列表理解。

让我们做一个可重复的最小例子：

In [33]: xdata = np.linspace(0, 3, 11)

In [34]: ydata = xdata**3

In [35]: def integr(x):
    ...:     return quad(lambda t: t**2, 0, x)[0]
    ...: 

In [36]: def func(x, a):
    ...:     return integr(x) * a
    ...: 

In [37]: curve_fit(func, xdata, ydata)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-37-4660c65f85a2> in <module>()
----> 1 curve_fit(func, xdata, ydata)

 [... removed for clarity ...]

~/virtualenvs/py35/lib/python3.5/site-packages/scipy/integrate/quadpack.py in _quad(func, a, b, args, full_output, epsabs, epsrel, limit, points)
    370 def _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points):
    371     infbounds = 0
--> 372     if (b != Inf and a != -Inf):
    373         pass   # standard integration
    374     elif (b == Inf and a != -Inf):

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

这正是您所看到的错误。好的，错误来自quad，它会尝试评估func(xdata, a)，其归结为integr(xdata)，但不起作用。（我是如何找到它的？我将import pdb; pdf.set_trace()置于func函数内并在调试器中调试。）

然后，让我们使目标函数处理数组参数：

In [38]: def func2(x, a):
    ...:     return np.asarray([integr(xx) for xx in x]) * a
    ...: 

In [39]: curve_fit(func2, xdata, ydata)
Out[39]: (array([ 3.]), array([[  3.44663413e-32]]))

Python - 如何将曲线拟合到包含数值计算积分的函数？

1 个答案: