我正在处理二重积分，内部积分有可变边界。我写了一个函数，使用SciPy的四次积分，可以计算这个积分。然而，我想要的只是计算内部积分，这样我只剩下一个关于某个变量的单一的、未计算的积分。然后，我想画出这个"中途"评估的二重积分与该变量的范围，这样我就可以看到一些趋势。然而，当我输入该变量的数组(它只是0-10000，但增量为1(时，它会提供以下错误消息：
"ValueError:包含多个元素的数组的真值不明确。请使用.any((或.all((">
我以前定义过允许我输入数组的函数(无论数组中有多少点，它都会输出该函数(，所以我不确定为什么现在会出现这个消息。我认为这与我在定义函数时使用SciPy的"quad"集成有关。我该如何绕过它以便输入数组？
import numpy as np
from scipy import integrate
from scipy.integrate import quad
import matplotlib.pyplot as plt
#This is the array of values of the variable I ultimately want to have the function plotted
against
timearray = np.arange(0,10000,1)
#This below defines the general function, that is with respect to two variables (p and t)
def thomtest(p,t):
d = 3.086e22
c = 2.998e10
return (3*((np.cos(p + (2*t/(d*p))))**2))/(8*(t+((p**2)*d/(2*c))))
#The function below evaluates just the inner-integral
def phib(t):
d = 3.086e22
c = 2.998e10
return quad(thomtest,0.00001*(c*t)/d,np.pi, args=(t))[0]
#This evaluates the outer-integral, giving me the complete numerical answer
doubleintegral = quad(phib,0,((3.086e22)/(2.998e10)))
#This below is what gives me the error message: "ValueError: The truth
#value of an array with more than one element is ambiguous.
#Use a.any() or a.all()". Apparently I cannot input an array
print(phib(timearray))
附件是完整错误信息的图片
In [2]: doubleintegral
Out[2]: (0.9892936902920587, 1.3643899787751934e-08)
In [3]: phib(0)
Out[3]: 6.377997354641736e-10
In [4]: phib(np.arange(0,5))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-4-89b7b858c2f5> in <module>
----> 1 phib(np.arange(0,5))
<ipython-input-1-4c64e69e4f62> in phib(t)
10 d = 3.086e22
11 c = 2.998e10
---> 12 return quad(thomtest,0.00001*(c*t)/d,np.pi, args=(t))[0]
13
14 doubleintegral = quad(phib,0,((3.086e22)/(2.998e10)))
/usr/local/lib/python3.6/dist-packages/scipy/integrate/quadpack.py in quad(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)
336
337 # check the limits of integration: int_a^b, expect a < b
--> 338 flip, a, b = b < a, min(a, b), max(a, b)
339
340 if weight is None:
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
In [5]:
当它测试积分边界，确保第一个小于第二个时，就会出现错误。
但是对于数组t，该测试是多值的，不能使用：
In [6]: d = 3.086e22
...: c = 2.998e10
In [7]: 0.00001*(c*np.arange(5))/d
Out[7]:
array([0.00000000e+00, 9.71484122e-18, 1.94296824e-17, 2.91445237e-17,
3.88593649e-17])
对于quad，您必须为t的每个元素运行一次代码phib和doubleintegral。在numpy中，我们试图避免迭代，但quad仅适用于标量边界。所以需要好的旧迭代。