Numpy

Numpy provides us with multi-dimensional array objects which is useful for scientific computing. In numpy, rank refers to the number of dimensions of the array. The shape is a tuple of integers providing the size of the array in each dimension.

[1,2,3] is a numpy object of rank 1 and shape 3

[[1,2], [4,5], [7,8]] is a numpy object of rank 3 and shape 2.

Creating a numpy object

The following provides different ways of creating numpy objects.

In [1]:
import numpy as np
a = np.array([1,2,3])
print(a)
print(a.shape)

[1 2 3]
(3,)
In [2]:
b = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])
print(b)
print(b.shape)

[[ 1  2  3  4]
 [ 5  6  7  8]
 [ 9 10 11 12]]
(3, 4)
In [3]:
print("a[1]=", a[1])
print("b[2,3]=", b[2,3])

a[1]= 2
b[2,3]= 12
In [4]:
c = np.zeros((2,3))
print(c)

[[ 0.  0.  0.]
 [ 0.  0.  0.]]
In [5]:
d = np.ones((2,3))
print(d)

[[ 1.  1.  1.]
 [ 1.  1.  1.]]
In [6]:
e = np.eye(3)
print(e)

[[ 1.  0.  0.]
 [ 0.  1.  0.]
 [ 0.  0.  1.]]
In [7]:
f = np.arange(20).reshape(4,5)
print(f)

[[ 0  1  2  3  4]
 [ 5  6  7  8  9]
 [10 11 12 13 14]
 [15 16 17 18 19]]

Accessing rows and columns

In [8]:
print(f[1,:])

[5 6 7 8 9]
In [9]:
print(f[:,1])

[ 1  6 11 16]
In [10]:
print(f[1:3,:])

[[ 5  6  7  8  9]
 [10 11 12 13 14]]

Mathematical Operations

Note that in numpy, the traditional mathematical operations happen element wise and are not matrix operations like in matlab.

In [11]:
g = np.array([[1,2,3],[4,5,6],[7,8,9]])
In [12]:
h = np.array([[21,22,23],[24,25,26],[27,28,29]])
In [13]:
h+g
Out[13]:
array([[22, 24, 26],
       [28, 30, 32],
       [34, 36, 38]])
In [14]:
h-g
Out[14]:
array([[20, 20, 20],
       [20, 20, 20],
       [20, 20, 20]])
In [15]:
h*g
Out[15]:
array([[ 21,  44,  69],
       [ 96, 125, 156],
       [189, 224, 261]])
In [16]:
h/g
Out[16]:
array([[ 21.        ,  11.        ,   7.66666667],
       [  6.        ,   5.        ,   4.33333333],
       [  3.85714286,   3.5       ,   3.22222222]])

Note the difference between dot product and multiplication.

In [17]:
i = np.ones((3,3))
j = np.array([1,2,3])
print(i*j)

[[ 1.  2.  3.]
 [ 1.  2.  3.]
 [ 1.  2.  3.]]
In [18]:
print(i.dot(j))

[ 6.  6.  6.]
In [19]:
print(h)

[[21 22 23]
 [24 25 26]
 [27 28 29]]
In [20]:
print(np.sum(h))

225
In [21]:
print(np.sum(h, axis=0))

[72 75 78]
In [22]:
print(h.T)

[[21 24 27]
 [22 25 28]
 [23 26 29]]

For more on numpy, refer to the official numpy tutorial here