In [1]:

    

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


    

In [2]:

    

x = np.linspace(0,7,10)
x


    

    
Out[2]:





array([ 0.        ,  0.77777778,  1.55555556,  2.33333333,  3.11111111,
        3.88888889,  4.66666667,  5.44444444,  6.22222222,  7.        ])

In [3]:

    

f = np.sin(x)


    

In [5]:

    

plt.plot(x,f)


    

    
Out[5]:





[<matplotlib.lines.Line2D at 0x7f1bedd65910>]






    

In [8]:

    

for i in xrange(x.shape[0]-1):
    #print f[i], f[i+1]
    if f[i]*f[i+1]<=0:
        #print x[i], x[i+1]
        a=(f[i+1]-f[i])/(x[i+1]-x[i])
        b=f[i]-a*x[i]
        x_0=-b/a
        print x_0


    

    




-0.0
3.14449096517
6.28822804578

In [9]:

    

timeit('np.zeros(1000000,dtype=np.float64)')


    

    




100000000 loops, best of 3: 7.18 ns per loop

In [10]:

    

a = np.empty(1000000,dtype=np.float64)


    

In [11]:

    

timeit('a.fill(0.0)')


    

    




100000000 loops, best of 3: 7.18 ns per loop

In [12]:

    

np.max(f)


    

    
Out[12]:





0.99988386169410237

In [13]:

    

f[np.argmax(f)]


    

    
Out[13]:





0.99988386169410237

In [14]:

    

x[np.argmax(f)]


    

    
Out[14]:





1.5555555555555556

In [15]:

    

x[np.argmin(f)]


    

    
Out[15]:





4.666666666666667

In [16]:

    

x[1:4]


    

    
Out[16]:





array([ 0.77777778,  1.55555556,  2.33333333])

In [17]:

    

x[1:6:2]


    

    
Out[17]:





array([ 0.77777778,  2.33333333,  3.88888889])

In [18]:

    

x[::2]


    

    
Out[18]:





array([ 0.        ,  1.55555556,  3.11111111,  4.66666667,  6.22222222])

In [19]:

    

x[:-1],x[-1]


    

    
Out[19]:





(array([ 0.        ,  0.77777778,  1.55555556,  2.33333333,  3.11111111,
         3.88888889,  4.66666667,  5.44444444,  6.22222222]), 7.0)

In [20]:

    

x.shape


    

    
Out[20]:





(10,)

In [21]:

    

x[1:].shape


    

    
Out[21]:





(9,)

In [22]:

    

x[:-1].shape


    

    
Out[22]:





(9,)

In [34]:

    

x = np.linspace(0,7,10)
f = np.sin(x)


    

In [35]:

    

h = x[1]-x[0]
fdiff = (f[1:]-f[:-1])/h


    

In [36]:

    

fdiff.shape, (x[:-1]+x[1:]).shape


    

    
Out[36]:





((9,), (9,))

In [38]:

    

y = np.linspace(0,7,230)
plt.plot((x[:-1]+x[1:])/2.0,fdiff, 'o-') 
plt.plot( y,np.cos(y))


    

    
Out[38]:





[<matplotlib.lines.Line2D at 0x7f1bed1180d0>]






    

In [39]:

    

f[1:]-f[:-1]


    

    
Out[39]:





array([ 0.70169788,  0.29818599, -0.27679798, -0.69260906, -0.71013478,
       -0.31929696,  0.25515281,  0.68287677,  0.71791193])

In [40]:

    

np.diff(f)


    

    
Out[40]:





array([ 0.70169788,  0.29818599, -0.27679798, -0.69260906, -0.71013478,
       -0.31929696,  0.25515281,  0.68287677,  0.71791193])

In [41]:

    

h = x[1]-x[0]
w  = h*np.ones_like(f)
w[0] = w[0]/2.0
w[-1] = w[-1]/2.0
np.sum(f*w)


    

    
Out[41]:





0.23356467160546901

In [43]:

    

# sage integrate(sin(y),(y,0,7)).n()


    

In [46]:

    

x = np.linspace(0,7,41)
h = x[1]-x[0]
f = np.sin(x)
plt.plot(x,np.cumsum(f*h))
plt.plot(y,-np.cos(y)+1)


    

    
Out[46]:





[<matplotlib.lines.Line2D at 0x7f1becfc79d0>]






    

In [33]:

    




    

    
Out[33]: