我注意到,顺序n和参数x jv(n,x)的
scipy.special贝塞尔函数在x中被矢量化：
在[14]中：将scipy.special导入sp
在[16]中：sp.jv(1,范围(3))#n = 1,[x = 0,1,2]
Out [16]：array([0.,0.44005059,0.57672481])
但是没有相应的矢量化形式的球形贝塞尔函数,sp.sph_jn：
In [19]: sp.sph_jn(1,range(3))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-19-ea59d2f45497> in <module>()
----> 1 sp.sph_jn(1,range(3)) #n=1,3 value array
/home/glue/anaconda/envs/fibersim/lib/python2.7/site-packages/scipy/special/basic.pyc in sph_jn(n,z)
262 """
263 if not (isscalar(n) and isscalar(z)):
--> 264 raise ValueError("arguments must be scalars.")
265 if (n != floor(n)) or (n < 0):
266 raise ValueError("n must be a non-negative integer.")
ValueError: arguments must be scalars.
此外,球形贝塞尔函数在一次通过中计算N的所有阶数.因此,如果我想要参数x = 10的n = 5 Bessel函数,则返回n = 1,2,3,4,5.它实际上在一次传递中返回jn及其衍生物：
In [21]: sp.sph_jn(5,10) Out[21]: (array([-0.05440211,0.07846694,0.07794219,-0.03949584,-0.10558929,-0.05553451]),array([-0.07846694,-0.0700955,0.05508428,0.09374053,0.0132988,-0.07226858]))
为什么API中存在这种不对称性,并且有没有人知道一个库将返回矢量化的球形贝塞尔函数,或者至少更快(即在cython中)？
解决方法
你可以编写一个cython函数来加速计算,你要做的第一件事是获取fortran函数SPHJ的地址,这里是如何在Python中执行此操作：
from scipy import special as sp sphj = sp.specfun.sphj import ctypes addr = ctypes.pythonapi.PyCObject_AsVoidPtr(ctypes.py_object(sphj._cpointer))
然后你可以直接在Cython中调用fortran函数,注意我使用prange()来使用multicore来加速计算：
%%cython -c-Ofast -c-fopenmp --link-args=-fopenmp
from cpython.mem cimport PyMem_Malloc,PyMem_Free
from cython.parallel import prange
import numpy as np
import cython
from cpython cimport PyCObject_AsVoidPtr
from scipy import special
ctypedef void (*sphj_ptr) (const int *n,const double *x,const int *nm,const double *sj,const double *dj) nogil
cdef sphj_ptr _sphj=<sphj_ptr>PyCObject_AsVoidPtr(special.specfun.sphj._cpointer)
@cython.wraparound(False)
@cython.boundscheck(False)
def cython_sphj2(int n,double[::1] x):
cdef int count = x.shape[0]
cdef double * sj = <double *>PyMem_Malloc(count * sizeof(double) * (n + 1))
cdef double * dj = <double *>PyMem_Malloc(count * sizeof(double) * (n + 1))
cdef int * mn = <int *>PyMem_Malloc(count * sizeof(int))
cdef double[::1] res = np.empty(count)
cdef int i
if count < 100:
for i in range(x.shape[0]):
_sphj(&n,&x[i],mn + i,sj + i*(n+1),dj + i*(n+1))
res[i] = sj[i*(n+1) + n] #choose the element you want here
else:
for i in prange(count,nogil=True):
_sphj(&n,dj + i*(n+1))
res[i] = sj[i*(n+1) + n] #choose the element you want here
PyMem_Free(sj)
PyMem_Free(dj)
PyMem_Free(mn)
return res.base
比较一下,这是在forloop中调用sphj()的Python函数：
import numpy as np
def python_sphj(n,x):
sphj = special.specfun.sphj
res = np.array([sphj(n,v)[1][n] for v in x])
return res
以下是10个元素的％timit结果：
x = np.linspace(1,10) r1 = cython_sphj2(4,x) r2 = python_sphj(4,x) assert np.allclose(r1,r2) %timeit cython_sphj2(4,x) %timeit python_sphj(4,x)
结果：
10000 loops,best of 3: 21.5 µs per loop 10000 loops,best of 3: 28.1 µs per loop
以下是100000个元素的结果：
x = np.linspace(1,100000) r1 = cython_sphj2(4,x)
结果：
10 loops,best of 3: 44.7 ms per loop 1 loops,best of 3: 231 ms per loop