Basics of Numpy
Before you start this tutorial you should know a bit about Python. If you dont have any background in Python head over to my Introduction to Python post.
Numpy
Numpy or Numerical Python is the core library for scientific computing in Python. It provides a high-performance multidimensional array object, and tools for working with these arrays.
Arrays
A numpy array is a grid of values, all of the same type. The number of dimensions is the rank of the array; the shape of an array is a tuple of integers giving the size of the array along each dimension.
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import numpy as np
my_list = [1,2,3]
a = np.array(my_list) # Creates a rank 1 array
my_mat = [[1,2,3][4,5,6][7,8,9]]
b = np.array(my_mat) # Creates a rank 2 array
print(a.shape) # Prints (3,)
print(b.shape) # Prints (3,3)
Numpy internally provides many functions to create arrays.
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np.random.rand(5,5) # Creates a 5x5 matrix of random numbers
# from a uniform distribution over [0,1]
np.random.randn(3,2) # Creates a 3x2 matrix of random numbers
# from a standard normal distribution
np.zeros((3,4)) # Creates a 3x4 matrix of all zeros
np.ones((2,2)) # Creats a 2x2 matrix of all ones
np.eye(4) # Creates a 4x4 Identity matrix
Array Indexing
One Dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences.
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a = np.arange(0,11)
print(a) #Prints array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
print(a[8]) # Prints 8
print(a[0:5]) # Prints array([0, 1, 2, 3, 4])
print(a[6:]) # Prints array([ 6, 7, 8, 9, 10])
Multi Dimensional have one index per axis. These indices are given as a tuple.
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a_2d = np.array([[5,10,15],[20,25,30],[35,40,45]])
print(a_2d)
# Prints array([[ 5, 10, 15],
# [20, 25, 30],
# [35, 40, 45]])
print(a_2d[0][0]) # Bracket notation. Prints 5
print(a_2d[1,2]) # Comma notation. Prints 30
print(a_2d[:2, 1:])
# Prints [[10 15]
# [25 30]]
To know more about numpy array indexing you should read the documentation
Numpy operations
Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result.
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arr = np.arange(1,6)
print(arr) # Prints [1 2 3 4 5]
#Elementwise Addition
#Prints [ 2 4 6 8 10]
print(arr + arr)
#Elementwise Subtraction
#Prints [0 0 0 0 0]
print(arr - arr)
#Element wise multiplication
#Prints [ 1 4 9 16 25]
print(arr * arr)
* is elementwise multiplication, not matrix
multiplication. We instead use the dot function to compute inner
products of vectors, to multiply a vector by a matrix, and to
multiply matrices.
dot is available both as a function in the numpy
module and as an instance method of array objects
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a = np.array([1,2])
b = np.array([3,4])
#Inner product of vectors. Both prints 11
print(np.dot(a,b))
print(a.dot(b))
x = np.array([[1,2], [3,4]])
y = np.array([[5,6], [7,8]])
#Dot product of the matrices.
#Prints [[19 22]
# [43 50]]
print(np.dot(x, y))
print(x.dot(y))
This brief overview has touched on many of the important topics that you need to know about numpy. Check out the documentation to know more about numpy.