python – 在Cython中优化代码的技巧

我有一个相对简单的问题(我认为).我正在研究一段Cython代码,当给定应变和特定方向时(即,对于一定量的应变,平行于给定方向的半径),计算应变椭圆的半径.在每个程序运行期间,此函数被称为几百万次,并且分析显示该功能是性能方面的限制因素.这是代码：

# importing math functions from a C-library (faster than numpy)
from libc.math cimport sin,cos,acos,exp,sqrt,fabs,M_PI

cdef class funcs:

    cdef inline double get_r(self,double g,double omega):
        # amount of strain: g,angle: omega
        cdef double l1,l2,A,r,g2,gs   # defining some variables
        if g == 0: return 1   # no strain means the strain ellipse is a circle
        omega = omega*M_PI/180   # converting angle omega to radians
        g2 = g*g
        gs = g*sqrt(4 + g2)
        l1 = 0.5*(2 + g2 + gs)   # l1 and l2: eigenvalues of the Cauchy strain tensor
        l2 = 0.5*(2 + g2 - gs)
        A = acos(g/sqrt(g2 + (1 - l2)**2))   # orientation of the long axis of the ellipse
        r = 1./sqrt(sqrt(l2)*(cos(omega - A)**2) + sqrt(l1)*(sin(omega - A)**2))   # the radius parallel to omega
        return r   # return of the jedi

运行此代码每次调用大约需要0.18微秒,我认为这对于这样一个简单的函数来说有点长.另外,math.h有一个square(x)函数,但是我不能从libc.math库中导入它,谁知道怎么做？有什么其他建议可以进一步改善这段小代码的性能吗？

更新2013/09/04：

似乎有更多的在发挥,而不是满足眼睛.当我分析一个调用get_r 10万次的函数时,我获得的性能与调用另一个函数不同.我添加了部分代码的更新版本.当我使用get_r_profile进行性能分析时,每次调用get_r得到0.073微秒,而MC_criterion_profile给我约0.164微秒/ get_r调用,50％的差异似乎与返回r的开销成本有关.

from libc.math cimport sin,M_PI

cdef class thesis_funcs:

    cdef inline double get_r(self,double omega):
        cdef double l1,gs,cos_oa2,sin_oa2
        if g == 0: return 1
        omega = omega*SCALEDPI
        g2 = g*g
        gs = g*sqrt(4 + g2)
        l1 = 0.5*(2 + g2 + gs)
        l2 = l1 - gs
        A = acos(g/sqrt(g2 + square(1 - l2)))
        cos_oa2 = square(cos(omega - A))
        sin_oa2 = 1 - cos_oa2
        r = 1.0/sqrt(sqrt(l2)*cos_oa2 + sqrt(l1)*sin_oa2)
        return r

    @cython.profile(False)
    cdef inline double get_mu(self,double r,double mu0,double mu1):
        return mu0*exp(-mu1*(r - 1))

    def get_r_profile(self): # Profiling through this guy gives me 0.073 microsec/call
        cdef unsigned int i
        for i from 0 <= i < 10000000:
            self.get_r(3.0,165)

    def MC_criterion(self,double omega,double mu1,double C = 0.0):
        cdef double r,mu,theta,res
        r = self.get_r(g,omega)
        mu = self.get_mu(r,mu0,mu1)
        theta = 45 - omega
        theta = theta*SCALEDPI
        res = fabs(g*sin(2.0*theta)) - mu*(1 + g*cos(2.0*theta)) - C
        return res

    def MC_criterion_profile(self): # Profiling through this one gives 0.164 microsec/call
        cdef double g,omega,mu1
        cdef unsigned int i
        omega = 165
        mu0 = 0.6
        mu1 = 2.0
        g = 3.0
        for i from 1 <= i < 10000000:
            self.MC_criterion(g,mu1)

我认为get_r_profile和MC_criterion之间可能存在根本区别,这会导致额外的开销成本.你能发现它吗？

cos_oa2 = cos(omega - A)**2
sin_oa2 = 1 - cos_oa2
r = 1. / sqrt(sqrt(l2) * cos_oa2 + sqrt(l1) * sin_oa2)