Numpy

Learning Objectives

• Python basics.
• Numpy arrays.
• Chapter 2 of Python Data Science Handbook.

Python Overview

In R I Want	In Python I Use
Base R	numpy
dplyr/tidyr	pandas
ggplot2	matplotlib/seaborn

Numpy Arrays

• Let’s import the numpy package:

  Python

  import numpy as np

• In Python, we assign variables with =, not <-

  Python

  x = 10
  x

  10

• The arithmetic operations (+, -, *, /) are the exact same

  Python

  x * 2
  x + 2
  x / 2
  x - 2
  x ** 2 # square
  x % 2 # remainder

• Comments also begin with a #:

  Python

  # This is a comment

• Help files are called the same way

  Python

  help(min)
  ?min

• Python lists are like R lists, in that they can have the different types. You create Python lists with brackets []

  Python

  x = ["hello", 1, True]
  x

  ['hello', 1, True]

• Numpy Arrays are the Python equivalent to R vectors (where each element is the same type). You use the array() method of the numpy package to create a numpy array (note that you give it a list as input)

  Python

  vec = np.array([2, 3, 5, 1])
  vec

  array([2, 3, 5, 1])

• You can do vectorized operations on NumPy arrays

  Python

  vec + 2
  vec - 2
  vec * 2
  vec / 2
  2 / vec

• Two vectors of the same size can be added/subtracted/multiplied/divided:

  Python

  x = np.array([1, 2, 3, 4])
  y = np.array([5, 6, 7, 8])
  x + y
  x - y
  x / y
  x * y
  x ** y

• You extract individual elements just like in R, using brackets []

  Python

  vec[0]
  vec[0:2]

• Extract arbitrary elements by passing an index array:

  Python

  ind = np.array([0, 2])
  vec[ind]
  # or
  vec[np.array([0, 2])]

• Key Difference: Python starts counting from 0, not 1. So the first element of a vector is vec[0], not vec[1].

• Combine two arrays via np.concatenate() (notice the use of brackets here)

  Python

  x = np.array([1, 2, 3, 4])
  y = np.array([5, 6, 7, 8])
  np.concatenate([x, y])

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

Useful functions over vectors

• In R, we have functions operate on objects (e.g. log(x), sort(x), etc).

• Python also has functions that operate on objects. But objects usually have functions associated with them directly. You access these functions by a period after the object name. These functions are called “methods”. Use tab completion to scroll through the available methods of an object.

  Python

  vec.sort() # sort
  vec.min() # minimum
  vec.max() # maximum
  vec.mean() # mean
  vec.sum() # sum
  vec.var() # variance

• But there are still loads of useful functions that operate on objects.

  Python

  np.sort(vec)
  np.min(vec)
  np.max(vec)
  np.mean(vec)
  np.sum(vec)
  np.var(vec)
  np.size(vec)
  np.exp(vec)
  np.log(vec)

Booleans (Python’s logicals)

• Python uses True and False. It uses the same comparison operators as R

  Python

  vec > 3
  vec < 3
  vec == 3
  vec != 3
  vec <= 3
  vec >= 3

• The logical operators are: Key Difference: “Not” uses a different character.

  • & And
  • | Or
  • ~ Not

  Python

  np.array([True, True, False, False]) & np.array([True, False, True, False])

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

  np.array([True, True, False, False]) | np.array([True, False, True, False])

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

  ~np.array([True, True, False, False])

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

• You subset a vector using Booleans as you would in R

  Python

  vec[vec <= 3]

  array([2, 3, 1])

• When you are dealing with single logicals, instead of arrays of logicals, use and, or, and not instead

  Python

  True and False

  False

  True or False

  True

  not True

  False

• Exercise: Consider two vectors \[ y = (1, 7, 1, 2, 8, 2)\\ x = (4, 6, 2, 7, 8, 2) \] Calculate their inner product: \[ y_1x_1 + y_2x_2 + y_3x_3 + y_4x_4 + y_5x_5 + y_6x_6 \] Do this using vectorized operations.

• Exercise: Provide two ways of extracting the 2nd and 5th elements of this vector

  Python

  x = np.array([4, 7, 8, 1, 2])

• Exercise: Extract all elements from the previous vector between 5 and 8 (inclusive). Use predicates.