Numpy¶

In [1]:

import numpy as np

import numpy as np

In [2]:

x = np.arange(10)

x = np.arange(10)

In [3]:

x

x

Out[3]:

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

In [4]:

x + 1

x + 1

Out[4]:

array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])

In [5]:

(x + 1)**2

(x + 1)**2

Out[5]:

array([  1,   4,   9,  16,  25,  36,  49,  64,  81, 100])

In [6]:

np.sin(x)

np.sin(x)

Out[6]:

array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ,
       -0.95892427, -0.2794155 ,  0.6569866 ,  0.98935825,  0.41211849])

In [7]:

np.sin(x).dtype

np.sin(x).dtype

Out[7]:

dtype('float64')

In [8]:

x > 3

x > 3

Out[8]:

array([False, False, False, False,  True,  True,  True,  True,  True,
        True])

In [9]:

x[:4]

x[:4]

Out[9]:

array([0, 1, 2, 3])

In [10]:

x[7:]

x[7:]

Out[10]:

array([7, 8, 9])

In [11]:

x[x > 3]

x[x > 3]

Out[11]:

array([4, 5, 6, 7, 8, 9])

In [12]:

x[(x > 3) & (x < 7)]

x[(x > 3) & (x < 7)]

Out[12]:

array([4, 5, 6])

In [13]:

x[(x > 7) | (x < 3)]

x[(x > 7) | (x < 3)]

Out[13]:

array([0, 1, 2, 8, 9])

In [14]:

np.arange(50)

np.arange(50)

Out[14]:

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49])

In [15]:

np.arange(50).reshape(10,5)

np.arange(50).reshape(10,5)

Out[15]:

array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24],
       [25, 26, 27, 28, 29],
       [30, 31, 32, 33, 34],
       [35, 36, 37, 38, 39],
       [40, 41, 42, 43, 44],
       [45, 46, 47, 48, 49]])

In [16]:

table = _

table = _

In [17]:

table

table

Out[17]:

array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24],
       [25, 26, 27, 28, 29],
       [30, 31, 32, 33, 34],
       [35, 36, 37, 38, 39],
       [40, 41, 42, 43, 44],
       [45, 46, 47, 48, 49]])

In [18]:

table**2

table**2

Out[18]:

array([[   0,    1,    4,    9,   16],
       [  25,   36,   49,   64,   81],
       [ 100,  121,  144,  169,  196],
       [ 225,  256,  289,  324,  361],
       [ 400,  441,  484,  529,  576],
       [ 625,  676,  729,  784,  841],
       [ 900,  961, 1024, 1089, 1156],
       [1225, 1296, 1369, 1444, 1521],
       [1600, 1681, 1764, 1849, 1936],
       [2025, 2116, 2209, 2304, 2401]])

In [19]:

(table**2)[2:4]

(table**2)[2:4]

Out[19]:

array([[100, 121, 144, 169, 196],
       [225, 256, 289, 324, 361]])

In [20]:

(table**2)[:,2:4]

(table**2)[:,2:4]

Out[20]:

array([[   4,    9],
       [  49,   64],
       [ 144,  169],
       [ 289,  324],
       [ 484,  529],
       [ 729,  784],
       [1024, 1089],
       [1369, 1444],
       [1764, 1849],
       [2209, 2304]])

In [21]:

(table**2)[5:7, 2:4]

(table**2)[5:7, 2:4]

Out[21]:

array([[ 729,  784],
       [1024, 1089]])

In [22]:

table ** 2 == 1089

table ** 2 == 1089

Out[22]:

array([[False, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False,  True, False],
       [False, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False]])

In [23]:

[index for (index, value) in np.ndenumerate(table**2) if value == 1089]

[index for (index, value) in np.ndenumerate(table**2) if value == 1089]

Out[23]:

[(6, 3)]

In [24]:

l = list(range(10))

l = list(range(10))

In [25]:

l

l

Out[25]:

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

In [26]:

[i * 2 for i in l if i < 5]

[i * 2 for i in l if i < 5]

Out[26]:

[0, 2, 4, 6, 8]

In [27]:

table**100

table**100

Out[27]:

array([[                   0,                    1,                    0,
        -2984622845537545263,                    0],
       [-3842938066129721103,                    0,  3728452490685454945,
                           0,  6627890308811632801],
       [                   0, -5485011738861510223,                    0,
        -8267457965844590319,                    0],
       [ 6813754833676406721,                    0, -1895149777787118527,
                           0,  8207815121025376913],
       [                   0,  1178643571979107377,                    0,
         5958518545374539809,                    0],
       [-7817535966050405663,                    0,  4157753088978724465,
                           0,  3054346751387081297],
       [                   0,  6365139678740040577,                    0,
        -8877898876394183551,                    0],
       [ 8170176069297290577,                    0, -1901415581956121743,
                           0,  2024094702548431329],
       [                   0,  6476859561917718817,                    0,
         5633018509028505393,                    0],
       [ 3548161959473065873,                    0, -2387541571489615039,
                           0,  1459632558914132161]])

In [28]:

a = np.mat('4 3; 2 1')

a = np.mat('4 3; 2 1')

In [29]:

b = np.mat('1 2; 3 4')

b = np.mat('1 2; 3 4')

In [30]:

a**2

a**2

Out[30]:

matrix([[22, 15],
        [10,  7]])

In [31]:

a

a

Out[31]:

matrix([[4, 3],
        [2, 1]])

In [32]:

a*b

a*b

Out[32]:

matrix([[13, 20],
        [ 5,  8]])

In [33]:

(np.arange(4)+1).reshape(2,2)

(np.arange(4)+1).reshape(2,2)

Out[33]:

array([[1, 2],
       [3, 4]])

In [34]:

np.mat(_)

np.mat(_)

Out[34]:

matrix([[1, 2],
        [3, 4]])