与 python 中的可变限制积分

Question

I'm trying to compute the following integral

using scipy, with the following program:

def E(z):
    result = 1/np.sqrt(Om*(1 + z)**3 + Ode + Ox*(1 + z)**2)
    return result 

def r(z, E): 
    result, error  = quad(E, 0, z) # integrate E(z) from 0 to z
    return result

z being the independent variable, while Om Ode and Ox are simply constants (previously assigned). When I then try to call the function:

z = np.linspace(1e-3, 4, 300)
plt.plot(z, r(z))

I get the error

flip, a, b = b < a, min(a, b), max(a, b)

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

What is the problem? Is scipy.quad unable to integrate up to a variable? Thank you so much for your help

Answer 1

You could use a combination of Python's map(function, iterable, ...) function,

Return an iterator that applies function to every item of iterable, yielding the results.

and functools partial(func[,*args][, **keywords]) method:

Return a new partial object which when called will behave like func called with the positional arguments args and keyword arguments keywords.

import numpy as np
from scipy.integrate import quad
import matplotlib.pyplot as plt
from functools import partial


def E(z):
    Om = 0.32
    Ode = 0.68
    Ox = 0
    result = 1/np.sqrt(Om*(1 + z)**3 + Ode + Ox*(1 + z)**2)

    return result


def r(z):
    result = np.array(
        list(map(partial(quad, E, 0), z))
    )[:, 0]  # integrate E(z) from 0 to z

    return result


z = np.linspace(1e-3, 4, 300)
fig, ax = plt.subplots()
ax.plot(z, r(z))
fig.show()