Python Numpy

Numpy is a numerical package used extensively in python coding. You can call the install the numpy package by

pip install numpy

When you import a module, you can choose to bound an alias to the package. In python communities, we usually import the numpy module like this:



In [1]:

    
import numpy as np

A `numpy` array

A numpy array is a grid of values, all of the same type. The number of dimensions give the rank of the array. To initilze a 1D array, we will do:



In [2]:

    
# 1D array
a = np.array([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97])



In [3]:

    
print(a.shape) # Return the ``shape`` of the array
print(a)









    



(25,)
[ 2  3  5  7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89
 97]



In [4]:

    
# 2D array
b = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])



In [5]:

    
print(b.shape) # Return the ``shape`` of the array
print(b)









    



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

To call or change the element in the array, we can apply similar operation as a list



In [6]:

    
print(a[0], a[3], a[5])



In [7]:

    
print(b[0,0],b[1,1],b[2,2])

Universal functions (ufunc)

A universal function (or ufunc for short) is a function that operates on numpy ndarrays in an element-by-element fashion that has been written in compiled C code. That is, a ufunc is a "vectorized" wrapper in high performance code.



In [8]:

    
x = range(100000)
sum(x)









    Out[8]:





4999950000



In [9]:

    
y = np.array(x)
np.sum(y)









    Out[9]:





4999950000



In [10]:

    
%timeit sum(x)









    



1.23 ms ± 10.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)



In [11]:

    
%timeit np.sum(y)









    



40.7 µs ± 193 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Initlize arrays



In [12]:

    
# Create an array of all zeros
np.zeros((5, 5))









    Out[12]:





array([[0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.]])



In [13]:

    
# Create an array of all ones
np.ones((5,5))









    Out[13]:





array([[1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.]])



In [14]:

    
# Create a constant array
np.ones((5,5)) * 7









    Out[14]:





array([[7., 7., 7., 7., 7.],
       [7., 7., 7., 7., 7.],
       [7., 7., 7., 7., 7.],
       [7., 7., 7., 7., 7.],
       [7., 7., 7., 7., 7.]])



In [15]:

    
np.full((5,5), 7)









    Out[15]:





array([[7, 7, 7, 7, 7],
       [7, 7, 7, 7, 7],
       [7, 7, 7, 7, 7],
       [7, 7, 7, 7, 7],
       [7, 7, 7, 7, 7]])



In [16]:

    
# Create a 3x3 identity matrix
np.eye(3)









    Out[16]:





array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])

Pseudo-random number generators



In [17]:

    
# Create an array filled with random values from 0 to 1
np.random.random((3,2))









    Out[17]:





array([[0.09050258, 0.20141557],
       [0.59200162, 0.58821197],
       [0.16836812, 0.55997005]])



In [18]:

    
# Create an 1D array filled with random integer from 1 to n
np.random.randint(1, 1000, 10)









    Out[18]:





array([978, 583, 984, 442, 880, 818, 627, 180, 999, 766])



In [19]:

    
# Seeding the random values will always give you the same "random" numbers on next run
# We put the answer to the Ultimate Question of Life, the Universe, and Everything to the seed integer
np.random.seed(42)



In [20]:

    
# Create an 1D array filled with random integer from 1 to n
np.random.randint(1, 1000, 10)









    Out[20]:





array([103, 436, 861, 271, 107,  72, 701,  21, 615, 122])

Array indexing



In [21]:

    
### Slicing



In [22]:

    
e = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
e









    Out[22]:





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



In [23]:

    
# Each dimensions slice similar to a list, here it means 1st dimension select all, 
# 2nd dimension select from one till end.
e[:,1:]









    Out[23]:





array([[2, 3],
       [5, 6],
       [8, 9]])



In [24]:

    
# Here it means 1st dimension and 2nd dimension select from start till 2, 
# i.e. the upper left part of the array.
e[:2,:2]









    Out[24]:





array([[1, 2],
       [4, 5]])



In [25]:

    
# An operation like numpy array > than a value return a boolean array
e > 5









    Out[25]:





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



In [26]:

    
# If we put the boolean array into the same array, it will select all element that satisfy the conditions
e[e > 5]









    Out[26]:





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

Summary

Numpy arrays are very powerful tools in numerical calculations, there are many ufuncs that has been written to optimize numerical operations with speed as close as C (because the underlying procedures are written in C).