In [1]:

    

%matplotlib inline

import matplotlib
import numpy as np
import matplotlib.pyplot as plt


    

In [2]:

    

#import setuptools
%load_ext Cython


    

In [3]:

    

%%cython
cdef f1(int x):
    return x*x

cpdef f2(int x):
    return x*x

cpdef f3(int x):
    return f1(x)


    

In [4]:

    

#dir()


    

In [5]:

    

f2(3)


    

    
Out[5]:





9

In [7]:

    

f1(3)


    

    




---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-7-a636accabfae> in <module>()
----> 1 f1(3)

NameError: name 'f1' is not defined

In [8]:

    

f3(3)


    

    
Out[8]:





9

In [9]:

    

%%cython
cpdef fibseq(float[:] x):
    cdef int n
    cdef int i
    n = len(x)
    
    x[0] = 1.
    x[1] = 1.
    for i in range(2,n):
        x[i] = x[i-1]+x[i-2]


    

In [11]:

    

x = np.zeros((43,), np.float32)


    

In [12]:

    

fibseq(x)


    

In [13]:

    

x


    

    
Out[13]:





array([  1.00000000e+00,   1.00000000e+00,   2.00000000e+00,
         3.00000000e+00,   5.00000000e+00,   8.00000000e+00,
         1.30000000e+01,   2.10000000e+01,   3.40000000e+01,
         5.50000000e+01,   8.90000000e+01,   1.44000000e+02,
         2.33000000e+02,   3.77000000e+02,   6.10000000e+02,
         9.87000000e+02,   1.59700000e+03,   2.58400000e+03,
         4.18100000e+03,   6.76500000e+03,   1.09460000e+04,
         1.77110000e+04,   2.86570000e+04,   4.63680000e+04,
         7.50250000e+04,   1.21393000e+05,   1.96418000e+05,
         3.17811000e+05,   5.14229000e+05,   8.32040000e+05,
         1.34626900e+06,   2.17830900e+06,   3.52457800e+06,
         5.70288700e+06,   9.22746500e+06,   1.49303520e+07,
         2.41578160e+07,   3.90881680e+07,   6.32459840e+07,
         1.02334152e+08,   1.65580128e+08,   2.67914272e+08,
         4.33494400e+08], dtype=float32)

In [14]:

    

ratio = x[0:-1]/x[1:]


    

In [16]:

    

plt.plot(ratio,'.');


    

In [17]:

    

(np.sqrt(5)-1)/2.


    

    
Out[17]:





0.6180339887498949

In [18]:

    

plt.semilogy(ratio-(np.sqrt(5)-1)/2,'.');


    

In [19]:

    

ratio


    

    
Out[19]:





array([ 1.        ,  0.5       ,  0.66666669,  0.60000002,  0.625     ,
        0.61538464,  0.61904764,  0.61764705,  0.61818182,  0.6179775 ,
        0.61805558,  0.61802578,  0.61803716,  0.61803281,  0.61803442,
        0.61803383,  0.61803406,  0.61803395,  0.61803401,  0.61803401,
        0.61803401,  0.61803401,  0.61803401,  0.61803401,  0.61803401,
        0.61803401,  0.61803401,  0.61803401,  0.61803401,  0.61803401,
        0.61803401,  0.61803401,  0.61803401,  0.61803401,  0.61803401,
        0.61803401,  0.61803401,  0.61803401,  0.61803401,  0.61803401,
        0.61803401,  0.61803401], dtype=float32)

In [20]:

    

import seaborn as sbs


    

In [21]:

    

sbs.plt.plot(ratio)


    

    
Out[21]:





[<matplotlib.lines.Line2D at 0x7f9ccec88210>]






    

In [22]:

    

def pyfib(n):
    a,b = 1,1
    for i in range(n):
        a,b = a+b, a
    return a


    

In [23]:

    

pyfib(5)


    

    
Out[23]:





13

In [24]:

    

%%cython
def fib(int n):
    cdef int i,a,b
    a,b = 1,1
    for i in range(n):
        a,b = a+b, a
    return a


    

In [25]:

    

fib(10)


    

    
Out[25]:





144

In [26]:

    

[fib(i) for i in range(10)]


    

    
Out[26]:





[1, 2, 3, 5, 8, 13, 21, 34, 55, 89]

In [27]:

    

pyfib(10)


    

    
Out[27]:





144

In [28]:

    

%timeit fib(10)
%timeit pyfib(10)


    

    




The slowest run took 28.11 times longer than the fastest. This could mean that an intermediate result is being cached.
10000000 loops, best of 3: 67.9 ns per loop
The slowest run took 4.74 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 1.06 µs per loop

In [29]:

    

%%cython
cpdef float distance(float[:] x, float[:] y):
    cdef int i
    cdef int n = x.shape[0]
    cdef float d = 0.0
    for i in range(n):
        d += (x[i]-y[i])**2
    return d


    

In [30]:

    

import numpy as np
x = np.array([1,2,3], np.float32)
y = np.array([7,6,5], np.float32)
dist = distance(x,y)
print dist


    

    




56.0

In [31]:

    

def pydistance(x, y, n):
    d = 0.0
    for i in range(n):
        d += (x[i]-y[i])**2
    return d


    

In [32]:

    

%timeit distance(x,y)
%timeit pydistance(x,y,3)


    

    




The slowest run took 15.03 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 1.33 µs per loop
100000 loops, best of 3: 16.8 µs per loop

In [ ]: