问题
I have to use dirac delta in a complicated integral and was hoping to see how it works with a simple case but it returns the wrong answer. Any clue what I did wrong in the following?
from sympy import DiracDelta
from scipy import integrate
def f(x):
return x*DiracDelta(x-1)
b, err = integrate.quad(f, 0, 5)
print b
This returns 0.0 while it shouldn't.
回答1:
It seems sympy functions are not compatible with scipy integrate. One needs to use sympy integrate. The following gives the correct answer
from sympy import *
x = Symbol('x')
print integrate(x*DiracDelta(x-1), (x, 0, 5.0))
Although, I am not sure if sympy.integrate is as powerful and versatile as scipy.integrate.
回答2:
HuShu's answer is correct. I'll add that the Dirac δ function is a symbolic method of representing function evaluation as an integral. It's useful as a symbolic abstraction, but if you only care about numeric evaluation, just do the function evaluation. That is instead of
b
⌠
⎮ f(x)⋅DiracDelta(x - 1) dx
⌡
a
just use
f(1) if a <= 1 <= b else 0
来源：https://stackoverflow.com/questions/36755487/diracdelta-not-giving-correct-result