Christian Elsasser (che@physik.uzh.ch)
The content of this lecture might be distributed under CC by-sa.
Plain python version
def fib0(n):
a,b = 1,1
for i in range(n):
a,b=a+b,a
return a
fib0(5)
13
fib0(6)
21
%timeit fib0(10000)
1.86 ms ± 11.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
import cython
cython.__version__
'0.29.19'
%load_ext Cython
Hello, Cython
%%cython
def helloWorld():
print("Hello, Cython!")
helloWorld
<function _cython_magic_d55d0d78aaf5722976e35d5b029bdf83.helloWorld>
helloWorld()
Hello, Cython!
Pure python in Cython
%%cython
def fib1(n):
a,b = 1,1
for i in range(n):
a,b=a+b,a
return a
fib1
<function _cython_magic_c7b2b79161369470b419d69e14fd8c7f.fib1>
fib1(5)
13
%timeit fib1(10000)
1.69 ms ± 36.8 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
C-code enhanced Python
%%cython
def fib2(int n):
cdef int i,a,b
a,b = 1,1
for i in range(n):
a,b = a+b,a
return a
fib2
<function _cython_magic_e7de6ac7b507cb5c9be41b44460ce6fa.fib2>
fib2(5)
13
%timeit fib2(10000)
2.69 µs ± 189 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
First try to integrate a function
%%cython -a
from math import sin,exp
def f0(double x):
return sin(x)*exp(-x)
def integrate0(double a,double b,int N):
cdef double s,dx
cdef int i
s = 0
dx = (b-a)/N
for i in range(N):
s += f0(a+(i+0.5)*dx)
return s*dx
Generated by Cython 0.29.19
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
" to see the C code that Cython generated for it.
01:
+02: from math import sin,exp
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03:
+04: def f0(double x):
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+05: return sin(x)*exp(-x)
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06:
+07: def integrate0(double a,double b,int N):
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08: cdef double s,dx
09: cdef int i
+10: s = 0
__pyx_v_s = 0.0;
+11: dx = (b-a)/N
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from math import pi
integrate0(0.0,pi,1000000)
0.5216069591323289
%timeit integrate0(0.0,pi,1000000)
110 ms ± 2.53 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
Improvement iteration 1
%%cython -a
from math import sin,exp
cdef double f1(double x):
return sin(x)*exp(-x)
def integrate1(double a,double b,int N):
cdef double dx,s
cdef int i
dx = (b-a)/N
s = 0.0
for i in range(N):
s+=f1(a+(i+0.5)*dx)
return s*dx
Generated by Cython 0.29.19
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
" to see the C code that Cython generated for it.
01:
+02: from math import sin,exp
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08: cdef double dx,s
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%timeit integrate1(0.0,pi,1000000)
79.3 ms ± 1.15 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
f1(5)
--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-27-c5ed7dd0edc1> in <module> ----> 1 f1(5) NameError: name 'f1' is not defined
%%cython -a
from math import sin,exp
cpdef double f2(double x):
return sin(x)*exp(-x)
def integrate2(double a,double b,int N):
cdef double dx,s
cdef int i
dx = (b-a)/N
s = 0.0
for i in range(N):
s+=f2(a+(i+0.5)*dx)
return s*dx
Generated by Cython 0.29.19
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
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01:
+02: from math import sin,exp
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08: cdef double dx,s
09: cdef int i
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f2(5)
-0.006461180938816702
Improvement iteration 2
%%cython
from libc.math cimport sin,exp
cpdef double f3(double x):
return sin(x)*exp(-x)
def integrate3(double a,double b,int N):
cdef double dx,s
cdef int i
dx = (b-a)/N
s = 0.0
for i in range(N):
s+=f3(a+(i+0.5)*dx)
return s*dx
f3(5)
-0.006461180938816702
%timeit integrate3(0.0,pi,1000000)
13.7 ms ± 160 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
import numpy as np
def f4(x):
return np.sin(x)*np.exp(-x)
def integrate4(a,b,N):
dx = (b-a)/N
x = (np.arange(N)+0.5)*dx+a
return np.sum(f4(x))*dx
%timeit integrate4(0.0,pi,1000000)
28.3 ms ± 284 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
%%cython -+
#distutils: language = c++
from libcpp.vector cimport vector
def manipulateVector(vector[double] v):
v.push_back(42.0) # Equivalent to append for list in python
return v
manipulateVector([1,2,3,4])
[1.0, 2.0, 3.0, 4.0, 42.0]
Python Errors in Cython
%%cython
cpdef int raiseError():
raise RuntimeError("A problem!")
return 1
warning: /Users/che/.ipython/cython/_cython_magic_14462e3e19cc337c50c4347922e844d0.pyx:3:4: Unreachable code
raiseError()
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) RuntimeError: A problem!
Exception ignored in: '_cython_magic_14462e3e19cc337c50c4347922e844d0.raiseError' RuntimeError: A problem!
0
%%cython
cpdef int raiseErrorBetter() except *:
raise RuntimeError("A problem!")
return 1
warning: /Users/che/.ipython/cython/_cython_magic_870d2bad77c520fa5a606110565cf636.pyx:3:4: Unreachable code
raiseErrorBetter()
--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) <ipython-input-48-9e77aa258386> in <module> ----> 1 raiseErrorBetter() _cython_magic_870d2bad77c520fa5a606110565cf636.pyx in _cython_magic_870d2bad77c520fa5a606110565cf636.raiseErrorBetter() _cython_magic_870d2bad77c520fa5a606110565cf636.pyx in _cython_magic_870d2bad77c520fa5a606110565cf636.raiseErrorBetter() RuntimeError: A problem!
try:
raiseErrorBetter()
except RuntimeError:
print("Error caught")
Error caught
C Error codes in Cython
%%cython
cpdef int raiseException(int n) except -1:
# Assuming C function returning an integer; if -1 --> Error appeared
return n
raiseException(1)
1
raiseException(-1)
--------------------------------------------------------------------------- SystemError Traceback (most recent call last) <ipython-input-52-f1e17eec89ff> in <module> ----> 1 raiseException(-1) SystemError: <built-in function raiseException> returned NULL without setting an error
%%cython
from libc.math cimport sin,exp
cdef class Integrand(object):
cpdef double evaluate(self,double x):
raise NotImplementedError()
cdef class SinExpFunction(Integrand):
cpdef double evaluate(self,double x):
return sin(x)*exp(-x)
def integrate(Integrand f, double a, double b, int N):
cdef int i
cdef double dx,s
dx = (b-a)/N
s = 0.0
for i in range(N):
s += f.evaluate(a+(i+0.5)*dx)
return s*dx
f = SinExpFunction()
import math
%timeit integrate(f,0,math.pi,1000000)
16.8 ms ± 147 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
class Poly(Integrand):
def evaluate(self,x):
return 3*x-x**3
g = Poly()
integrate(g,0,math.pi,10000)
-9.5478660351052
%timeit integrate(g,0,math.pi,1000000)
185 ms ± 4.46 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)