[英]Is there a performance gain of dblquad over twice quad?
From scipy reference manual, dblquad is mathematically equivalent to repeated quad twice. 从scipy参考手册中,dblquad在数学上等效于重复四次方的两次。 Initially, I thought dblquad must have performance advantage over twice quad (besides the convenience of the method).
最初,我认为dblquad必须具有超过两倍四倍的性能优势(除了方法的便利性)。 To my surprise, it seems dblquad performance is even worse.
令我惊讶的是,似乎dblquad的性能更差。 I took examples from "SciPy Reference Guide, Release 0.14.0" pages 12-13 with some modifications:
我从“SciPy参考指南,版本0.14.0”第12-13页进行了一些修改:
import scipy
import math
import timeit
def integrand(t, n, x):
return math.exp(-x*t) / t**n
def expint(n, x):
return scipy.integrate.quad(integrand, 1, scipy.Inf, args=(n, x))[0]
def I11():
res = []
for n in range(1,5):
res.append(scipy.integrate.quad(lambda x: expint(n, x), 0, scipy.Inf)[0])
return res
def I2():
res = []
for n in range(1,5):
res.append(scipy.integrate.dblquad(lambda t, x: integrand(t, n, x), 0, scipy.Inf, lambda x: 1, lambda x: scipy.Inf)[0])
return res
print('twice of quad:')
print(I11())
print(timeit.timeit('I11()', setup='from __main__ import I11', number=100))
print('dblquad:')
print(I2())
print(timeit.timeit('I2()', setup='from __main__ import I2', number=100))
My outputs look like this: 我的输出看起来像这样:
twice of quad:
[1.0000000000048965, 0.4999999999985751, 0.33333333325010883, 0.2500000000043577]
5.42371296883
dblquad:
[1.0000000000048965, 0.4999999999985751, 0.33333333325010883, 0.2500000000043577]
6.31611323357
We see the two methods produce the same results (exact results should be 1, 1/2, 1/3, 1/4). 我们看到两种方法产生相同的结果(确切的结果应该是1,1 / 2,1 / 3,1 / 4)。 But the dblquad performs worse.
但dblquad表现更差。
Does someone have some insight what is going on with dblquad? 有人对dblquad的情况有所了解吗? I also have the same question for tplquad and nquad.
我对tplquad和nquad也有同样的问题。
Have a look at the source code . 看看源代码 。 It's clear that dblquad is just a repeated integration, just like what you're doing here.
很明显,dblquad只是一个重复的集成,就像你在这里做的一样。
Re efficiency: scipy versions >0.14 might be better for multivariate functions, see https://github.com/scipy/scipy/pull/3262 效率:对于多变量函数,scipy版本> 0.14可能更好,请参阅https://github.com/scipy/scipy/pull/3262
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