python – 如何更好地使用Cython来更快地求解微分方程？

为了练习,我使用Python in scientific computations中涵盖的示例作为模板.因为odeint将函数f作为参数,所以我将此函数编写为静态类型的Cython版本并希望如此
odeint的运行时间会明显减少.

函数f包含在名为ode.pyx的文件中,如下所示：

import numpy as np
cimport numpy as np
from libc.math cimport sin,cos

def f(y,t,params):
  cdef double theta = y[0],omega = y[1]
  cdef double Q = params[0],d = params[1],Omega = params[2]
  cdef double derivs[2]
  derivs[0] = omega
  derivs[1] = -omega/Q + np.sin(theta) + d*np.cos(Omega*t)
  return derivs

def fCMath(y,double t,Omega = params[2]
  cdef double derivs[2]
  derivs[0] = omega
  derivs[1] = -omega/Q + sin(theta) + d*cos(Omega*t)
  return derivs

然后我创建一个文件setup.py来编译函数：

from distutils.core import setup
from Cython.Build import cythonize

setup(ext_modules=cythonize('ode.pyx'))

解决微分方程的脚本(也包含Python
f)的版本称为solveODE.py,其外观如下：

import ode
import numpy as np
from scipy.integrate import odeint
import time

def f(y,params):
    theta,omega = y
    Q,d,Omega = params
    derivs = [omega,-omega/Q + np.sin(theta) + d*np.cos(Omega*t)]
    return derivs

params = np.array([2.0,1.5,0.65])
y0 = np.array([0.0,0.0])
t = np.arange(0.,200.,0.05)

start_time = time.time()
odeint(f,y0,args=(params,))
print("The Python Code took: %.6s seconds" % (time.time() - start_time))

start_time = time.time()
odeint(ode.f,))
print("The Cython Code took: %.6s seconds ---" % (time.time() - start_time))

start_time = time.time()
odeint(ode.fCMath,))
print("The Cython Code incorpoarting two of DavidW_s suggestions took: %.6s seconds ---" % (time.time() - start_time))

然后我跑：

python setup.py build_ext --inplace
python solveODE.py

在终端.

python版本的时间大约是0.055秒,
而Cython版本大约需要0.04秒.

是否有人建议改进我的解决方案
微分方程,最好不用修改odeint例程本身,用Cython？

编辑

我在两个文件ode.pyx和solveODE.py中加入了DavidW的建议.使用这些建议运行代码大约需要0.015秒.