Python Review
In the following sections, we will repeatedly use Python scripts. In case you are less familiar with Python, here is a short tutorial on what you need to know. Also, please take a look here: Google’s Python Class- https://developers.google.com/edu/python
Introduction
Python is a general-purpose programming language that, combining with a few popular libraries (numpy, scipy, matplotlib), becomes a powerful environment for scientific computing.
!python --version
Python 3.7.12
Basics of Python
Python is a high-level, dynamically typed multiparadigm programming language. Python code is often said to be almost like pseudocode, since it allows you to express very powerful ideas in very few lines of code while being very readable.
Basic data types
Numbers
Integers and floats work as you would expect from other languages:
x = 3
print(x, type(x))
3 <class 'int'>
print(x + 1) #addition
print(x - 1) #subtraction
print(x * 2) #multiplication
print(x ** 2) #exponentiation
4
2
6
9
x = 10; x += 1
print(x)
x = 10; x *= 2
print(x)
11
20
y = 2.5
print(y, y+1, y*2, y *2, type(y))
2.5 3.5 5.0 5.0 <class 'float'>
Booleans
Python implements all of the usual operators for Boolean logic, but uses English words rather than symbols:
t, f = True, False; print(type(t))
<class 'bool'>
Now we let’s look at the operations:
print(t and f) # Logical AND;
print(t or f) # Logical OR;
print(not t) # Logical NOT;
print(t != f) # Logical XOR;
False
True
False
True
Strings
hello = 'hello' # String literals can use single quotes
world = "world" # or double quotes; it does not matter
print(hello, len(hello))
hello 5
hw = hello + '-' + world+'!' # String concatenation
print(hw)
hello-world!
hw12 = '{} {} {}'.format(hello, world, 12) # string formatting
print(hw12)
hello world 12
String objects have a bunch of useful methods; for example:
s = "hello"
print(s.capitalize()) # Capitalize a string
print(s.upper()) # Convert a string to uppercase; prints "HELLO"
print(s.rjust(7)) # Right-justify a string, padding with spaces
print(s.center(7)) # Center a string, padding with spaces
print(s.replace('l', '(ell)')) # Replace all instances of one substring with another
print(' world '.strip()) # Strip leading and trailing whitespace
Hello
HELLO
hello
hello
he(ell)(ell)o
world
Lists
A list is the Python equivalent of an array, but is resizeable and can contain elements of different types:
xs = [3, 1, 2] # Create a list
print(xs, xs[2])
print(xs[-1]) # Negative indices count from the end of the list; prints "2"
[3, 1, 2] 2
2
xs[2] = 'foo' # Lists can contain elements of different types
print(xs)
[3, 1, 'foo']
xs.append('bar') # Add a new element to the end of the list
print(xs)
[3, 1, 'foo', 'bar']
x = xs.pop() # Remove and return the last element of the list
print(x, xs)
bar [3, 1, 'foo']
Slicing
In addition to accessing list elements one at a time, Python provides concise syntax to access sublists; this is known as slicing:
nums = list(range(5)) # range is a built-in function that creates a list of integers
print(nums) # Prints "[0, 1, 2, 3, 4]"
print(nums[2:4]) # Get a slice from index 2 to 4 (exclusive); prints "[2, 3]"
print(nums[2:]) # Get a slice from index 2 to the end; prints "[2, 3, 4]"
print(nums[:2]) # Get a slice from the start to index 2 (exclusive); prints "[0, 1]"
print(nums[:]) # Get a slice of the whole list; prints ["0, 1, 2, 3, 4]"
print(nums[:-1]) # Slice indices can be negative; prints ["0, 1, 2, 3]"
nums[2:4] = [8, 9] # Assign a new sublist to a slice
print(nums) # Prints "[0, 1, 8, 9, 4]"
[0, 1, 2, 3, 4]
[2, 3]
[2, 3, 4]
[0, 1]
[0, 1, 2, 3, 4]
[0, 1, 2, 3]
[0, 1, 8, 9, 4]
Loops
You can loop over the elements of a list like this:
animals = ['cat', 'dog', 'monkey']
for animal in animals:
print(animal)
cat
dog
monkey
If you want access to the index of each element within the body of a
loop, use the built-in enumerate function:
animals = ['cat', 'dog', 'monkey']
for idx, animal in enumerate(animals):
print('#{}: {}'.format(idx + 1, animal))
#1: cat
#2: dog
#3: monkey
List comprehensions:
When programming, frequently we want to transform one type of data into another. As a simple example, consider the following code that computes square numbers:
nums = [0, 1, 2, 3, 4]
squares = []
for x in nums:
squares.append(x ** 2)
print(squares)
[0, 1, 4, 9, 16]
You can make this code simpler using a list comprehension:
nums = [0, 1, 2, 3, 4]
squares = [x ** 2 for x in nums]
print(squares)
[0, 1, 4, 9, 16]
List comprehensions can also contain conditions:
nums = [0, 1, 2, 3, 4]
even_squares = [x ** 2 for x in nums if x % 2 == 0]
print(even_squares)
[0, 4, 16]
Dictionaries
A dictionary stores (key, value) pairs
d = {'cat': 'cute', 'dog': 'furry'} # Create a new dictionary with some data
print(d['cat']) # Get an entry from a dictionary; prints "cute"
print('cat' in d) # Check if a dictionary has a given key; prints "True"
cute
True
d['fish'] = 'wet' # Set an entry in a dictionary
print(d['fish']) # Prints "wet"
wet
print(d.get('monkey', 'N/A')) # Get an element with a default; prints "N/A"
print(d.get('fish', 'N/A')) # Get an element with a default; prints "wet"
N/A
wet
print(d)
{'cat': 'cute', 'dog': 'furry', 'fish': 'wet'}
del d['fish'] # Remove an element from a dictionary
print(d.get('fish', 'N/A')) # "fish" is no longer a key; prints "N/A"
N/A
print(d)
{'cat': 'cute', 'dog': 'furry'}
It is easy to iterate over the keys in a dictionary:
d = {'person': 2, 'cat': 4, 'spider': 8}
for animal, legs in d.items():
print('A {} has {} legs'.format(animal, legs))
A person has 2 legs
A cat has 4 legs
A spider has 8 legs
Dictionary comprehensions: These are similar to list comprehensions, but allow you to easily construct dictionaries. For example:
nums = [0, 1, 2, 3, 4]
even_num_to_square = {x: x ** 2 for x in nums if x % 2 == 0}
print(even_num_to_square)
{0: 0, 2: 4, 4: 16}
Sets
A set is an unordered collection of distinct elements. As a simple example, consider the following:
animals = {'cat', 'dog'}
print('cat' in animals) # Check if an element is in a set; prints "True"
print('fish' in animals) # prints "False"
print(animals)
True
False
{'dog', 'cat'}
animals.add('fish') # Add an element to a set
print('fish' in animals)
print(len(animals)) # Number of elements in a set;
print(animals)
True
3
{'dog', 'cat', 'fish'}
animals.add('cat') # Adding an element that is already in the set does nothing
print(len(animals))
animals.remove('cat') # Remove an element from a set
print(len(animals))
print(animals)
3
2
{'dog', 'fish'}
Loops: Iterating over a set has the same syntax as iterating over a list; however since sets are unordered, you cannot make assumptions about the order in which you visit the elements of the set:
animals = {'cat', 'dog', 'fish'}
for idx, animal in enumerate(animals):
print('#{}: {}'.format(idx + 1, animal))
#1: dog
#2: cat
#3: fish
Set comprehensions: Like lists and dictionaries, we can easily construct sets using set comprehensions:
from math import sqrt
print({int(sqrt(x)) for x in range(30)})
{0, 1, 2, 3, 4, 5}
Tuples
A tuple is an (immutable) ordered list of values. A tuple is in many ways similar to a list; one of the most important differences is that tuples can be used as keys in dictionaries and as elements of sets, while lists cannot. Here is a trivial example:
d = {(x, x + 1): x for x in range(7)} # Create a dictionary with tuple keys
t = (5, 6) # Create a tuple
print(type(t))
print(d)
print(d[t])
print(d[(1, 2)])
<class 'tuple'>
{(0, 1): 0, (1, 2): 1, (2, 3): 2, (3, 4): 3, (4, 5): 4, (5, 6): 5, (6, 7): 6}
5
1
Functions
Python functions are defined using the def keyword. For example:
def sign(x):
if x > 0:
return 'positive'
elif x < 0:
return 'negative'
else:
return 'zero'
for x in [-1, 0, 1]:
print(sign(x))
negative
zero
positive
We will often define functions to take optional keyword arguments, like this:
def hello(name, loud=False):
if loud:
print('HELLO, {}'.format(name.upper()))
else:
print('Hello, {}!'.format(name))
hello('Bob')
hello('Fred', loud=True)
Hello, Bob!
HELLO, FRED
Classes
The syntax for defining classes in Python is straightforward:
class Greeter:
# Constructor
def __init__(self, name):
self.name = name # Create an *instance* variable
# Instance method
def greet(self, loud=False):
if loud:
print('HELLO, {}'.format(self.name.upper()))
else:
print('Hello, {}!'.format(self.name))
g = Greeter('Fred') # Construct an instance of the Greeter class
print(g.name)
g.greet() # Call an instance method; prints "Hello, Fred"
g.greet(loud=True) # Call an instance method; prints "HELLO, FRED!"
Fred
Hello, Fred!
HELLO, FRED
Numpy
Numpy is the core library for scientific computing in Python. It provides a high-performance multidimensional array object, and tools for working with these arrays.
import numpy as np
Arrays
A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers. 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.
We can initialize numpy arrays from nested Python lists, and access elements using square brackets:
a = np.array([1, 2, 3]) # Create a rank 1 array
print(type(a), a.shape, a[0], a[1], a[2])
a[0] = 5 # Change an element of the array
print(a)
<class 'numpy.ndarray'> (3,) 1 2 3
[5 2 3]
b = np.array([[1,2,3],[4,5,6]]) # Create a rank 2 array
print(b)
[[1 2 3]
[4 5 6]]
print(b.shape)
print(b[0, 0], b[0, 1], b[1, 0])
(2, 3)
1 2 4
Numpy also provides many functions to create arrays:
a = np.zeros((2,2)) # Create an array of all zeros
print(a)
[[0. 0.]
[0. 0.]]
b = np.ones((1,2)) # Create an array of all ones
print(b)
[[1. 1.]]
c = np.full((2,2), 7) # Create a constant array
print(c)
[[7 7]
[7 7]]
d = np.eye(2) # Create a 2x2 identity matrix
print(d)
[[1. 0.]
[0. 1.]]
e = np.random.random((2,2)) # Create an array filled with random values between 0 and 1
print(e)
[[0.33426196 0.22871597]
[0.80676993 0.17307073]]
Array indexing
Numpy offers several ways to index into arrays.
Slicing: Similar to Python lists, numpy arrays can be sliced. Since arrays may be multidimensional, you must specify a slice for each dimension of the array:
import numpy as np
a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
print(a)
# Use slicing to pull out the subarray consisting of the first 2 rows
# and columns 1 and 2; b is the following array of shape (2, 2):
# [[2 3]
# [6 7]]
b = a[:2, 1:3]
print(b)
[[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]]
[[2 3]
[6 7]]
A slice of an array is a view into the same data, so modifying it will modify the original array.
print(a[0, 1])
b[0, 0] = 77 # b[0, 0] is the same piece of data as a[0, 1]
print(a[0, 1])
2
77
Two ways of accessing the data in the middle row of the array. Mixing integer indexing with slices yields an array of lower rank, while using only slices yields an array of the same rank as the original array:
row_r1 = a[1, :] # Rank 1 view of the second row of a
row_r2 = a[1:2, :] # Rank 2 view of the second row of a
row_r3 = a[[1], :] # Rank 2 view of the second row of a
print(row_r1, row_r1.shape)
print(row_r2, row_r2.shape)
print(row_r3, row_r3.shape)
[5 6 7 8] (4,)
[[5 6 7 8]] (1, 4)
[[5 6 7 8]] (1, 4)
# We can make the same distinction when accessing columns of an array:
col_r1 = a[:, 1]
col_r2 = a[:, 1:2]
print(col_r1, col_r1.shape)
print()
print(col_r2, col_r2.shape)
[77 6 10] (3,)
[[77]
[ 6]
[10]] (3, 1)
Integer array indexing: When you index into numpy arrays using slicing, the resulting array view will always be a subarray of the original array. In contrast, integer array indexing allows you to construct arbitrary arrays using the data from another array. Here is an example:
a = np.array([[1,2], [3, 4], [5, 6]])
# An example of integer array indexing.
# The returned array will have shape (3,) and
print(a[[0, 1, 2], [0, 1, 0]])
# The above example of integer array indexing is equivalent to this:
print(np.array([a[0, 0], a[1, 1], a[2, 0]]))
[1 4 5]
[1 4 5]
# When using integer array indexing, you can reuse the same
# element from the source array:
print(a[[0, 0], [1, 1]])
# Equivalent to the previous integer array indexing example
print(np.array([a[0, 1], a[0, 1]]))
[2 2]
[2 2]
One useful trick with integer array indexing is selecting or mutating one element from each row of a matrix:
# Create a new array from which we will select elements
a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
print(a)
[[ 1 2 3]
[ 4 5 6]
[ 7 8 9]
[10 11 12]]
# Create an array of indices
b = np.array([0, 2, 0, 1])
# Select one element from each row of a using the indices in b
print(a[np.arange(4), b]) # Prints "[ 1 6 7 11]"
[ 1 6 7 11]
# Mutate one element from each row of a using the indices in b
a[np.arange(4), b] += 10
print(a)
[[11 2 3]
[ 4 5 16]
[17 8 9]
[10 21 12]]
Boolean array indexing: Boolean array indexing lets you pick out arbitrary elements of an array. Frequently this type of indexing is used to select the elements of an array that satisfy some condition. Here is an example:
import numpy as np
a = np.array([[1,2], [3, 4], [5, 6]])
bool_idx = (a > 2) # Find the elements of a that are bigger than 2;
# this returns a numpy array of Booleans of the same
# shape as a, where each slot of bool_idx tells
# whether that element of a is > 2.
print(bool_idx)
[[False False]
[ True True]
[ True True]]
# We use boolean array indexing to construct a rank 1 array
# consisting of the elements of a corresponding to the True values
# of bool_idx
print(a[bool_idx])
# We can do all of the above in a single concise statement:
print(a[a > 2])
[3 4 5 6]
[3 4 5 6]
For brevity we have left out a lot of details about numpy array indexing; if you want to know more you should read the documentation.
Datatypes
Every numpy array is a grid of elements of the same type. Numpy provides a large set of numeric datatypes that you can use to construct arrays. Numpy tries to guess a datatype when you create an array, but functions that construct arrays usually also include an optional argument to explicitly specify the datatype. Here is an example:
x = np.array([1, 2]) # Let numpy choose the datatype
y = np.array([1.0, 2.0]) # Let numpy choose the datatype
z = np.array([1, 2], dtype=np.int64) # Force a particular datatype
print(x.dtype, y.dtype, z.dtype)
int64 float64 int64
Array math
Basic mathematical functions operate elementwise on arrays, and are available both as operator overloads and as functions in the numpy module:
x = np.array([[1,2],[3,4]], dtype=np.float64)
y = np.array([[5,6],[7,8]], dtype=np.float64)
# Elementwise sum; both produce the array
print(x + y)
print(np.add(x, y))
[[ 6. 8.]
[10. 12.]]
[[ 6. 8.]
[10. 12.]]
# Elementwise difference; both produce the array
print(x - y)
print(np.subtract(x, y))
[[-4. -4.]
[-4. -4.]]
[[-4. -4.]
[-4. -4.]]
# Elementwise product; both produce the array
print(x * y)
print(np.multiply(x, y))
[[ 5. 12.]
[21. 32.]]
[[ 5. 12.]
[21. 32.]]
# Elementwise division; both produce the array
# [[ 0.2 0.33333333]
# [ 0.42857143 0.5 ]]
print(x / y)
print(np.divide(x, y))
[[0.2 0.33333333]
[0.42857143 0.5 ]]
[[0.2 0.33333333]
[0.42857143 0.5 ]]
# Elementwise square root; produces the array
# [[ 1. 1.41421356]
# [ 1.73205081 2. ]]
print(np.sqrt(x))
[[1. 1.41421356]
[1.73205081 2. ]]
The dot function is used 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:
x = np.array([[1,2],[3,4]])
y = np.array([[5,6],[7,8]])
v = np.array([9,10])
w = np.array([11, 12])
# Inner product of vectors; both produce 219
print(v.dot(w))
print(np.dot(v, w))
219
219
You can also use the @ operator which is equivalent to numpy’s
dot operator.
print(v @ w)
219
# Matrix / vector product; both produce the rank 1 array [29 67]
print(x.dot(v))
print(np.dot(x, v))
print(x @ v)
[29 67]
[29 67]
[29 67]
# Matrix / matrix product; both produce the rank 2 array
# [[19 22]
# [43 50]]
print(x.dot(y))
print(np.dot(x, y))
print(x @ y)
[[19 22]
[43 50]]
[[19 22]
[43 50]]
[[19 22]
[43 50]]
Numpy provides many useful functions for performing computations on
arrays; one of the most useful is sum:
x = np.array([[1,2],[3,4]])
print(np.sum(x)) # Compute sum of all elements; prints "10"
print(np.sum(x, axis=0)) # Compute sum of each column; prints "[4 6]"
print(np.sum(x, axis=1)) # Compute sum of each row; prints "[3 7]"
10
[4 6]
[3 7]
Apart from computing mathematical functions using arrays, we frequently need to reshape or otherwise manipulate data in arrays. The simplest example of this type of operation is transposing a matrix; to transpose a matrix, simply use the T attribute of an array object:
print(x)
print(x.T)
[[1 2]
[3 4]]
[[1 3]
[2 4]]
v = np.array([[1,2,3]])
print(v )
print(v.T)
[[1 2 3]]
[[1]
[2]
[3]]
Broadcasting
Broadcasting is a powerful mechanism that allows numpy to work with arrays of different shapes when performing arithmetic operations. Frequently we have a smaller array and a larger array, and we want to use the smaller array multiple times to perform some operation on the larger array.
For example, suppose that we want to add a constant vector to each row of a matrix. We could do it like this:
# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
y = np.zeros_like(x) # an array of zeros with the same shape and type as x
print(y)
print(x.shape,v.shape,y.shape)
# Add the vector v to each row of the matrix x with an explicit loop
for i in range(4):
y[i, :] = x[i, :] + v
print(y)
[[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]]
(4, 3) (3,) (4, 3)
[[ 2 2 4]
[ 5 5 7]
[ 8 8 10]
[11 11 13]]
This works; however when the matrix x is very large, computing an
explicit loop in Python could be slow. Note that adding the vector v to
each row of the matrix x is equivalent to forming a matrix vv by
stacking multiple copies of v vertically, then performing
elementwise summation of x and vv. We could implement this
approach like this:
print(v)
vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other
print(vv) # Prints "[[1 0 1]
# [1 0 1]
# [1 0 1]
# [1 0 1]]"
[1 0 1]
[[1 0 1]
[1 0 1]
[1 0 1]
[1 0 1]]
y = x + vv # Add x and vv elementwise
print(y)
[[ 2 2 4]
[ 5 5 7]
[ 8 8 10]
[11 11 13]]
Numpy broadcasting allows us to perform this computation without actually creating multiple copies of v. Consider this version, using broadcasting:
import numpy as np
# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
y = x + v # Add v to each row of x using broadcasting
print(y)
[[ 2 2 4]
[ 5 5 7]
[ 8 8 10]
[11 11 13]]
The line y = x + v works even though x has shape (4, 3) and
v has shape (3,) due to broadcasting; this line works as if v
actually had shape (4, 3), where each row was a copy of v, and
the sum was performed elementwise.
Broadcasting two arrays together follows these rules:
If the arrays do not have the same rank, prepend the shape of the lower rank array with 1s until both shapes have the same length.
The two arrays are said to be compatible in a dimension if they have the same size in the dimension, or if one of the arrays has size 1 in that dimension.
The arrays can be broadcast together if they are compatible in all dimensions.
After broadcasting, each array behaves as if it had shape equal to the elementwise maximum of shapes of the two input arrays.
In any dimension where one array had size 1 and the other array had size greater than 1, the first array behaves as if it were copied along that dimension
Here are some applications of broadcasting:
# Compute outer product of vectors
v = np.array([1,2,3]) # v has shape (3,)
w = np.array([4,5]) # w has shape (2,)
# To compute an outer product, we first reshape v to be a column
# vector of shape (3, 1); we can then broadcast it against w to yield
# an output of shape (3, 2), which is the outer product of v and w:
print(np.reshape(v, (3, 1)) * w)
print(v.shape, w.shape)
[[ 4 5]
[ 8 10]
[12 15]]
(3,) (2,)
# Add a vector to each row of a matrix
x = np.array([[1,2,3], [4,5,6]])
# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),
# giving the following matrix:
print(x + v)
[[2 4 6]
[5 7 9]]
# Add a vector to each column of a matrix
# x has shape (2, 3) and w has shape (2,).
# If we transpose x then it has shape (3, 2) and can be broadcast
# against w to yield a result of shape (3, 2); transposing this result
# yields the final result of shape (2, 3) which is the matrix x with
# the vector w added to each column. Gives the following matrix:
print((x.T + w).T)
[[ 5 6 7]
[ 9 10 11]]
# Another solution is to reshape w to be a row vector of shape (2, 1);
# we can then broadcast it directly against x to produce the same
# output.
print(x + np.reshape(w, (2, 1)))
[[ 5 6 7]
[ 9 10 11]]
# Multiply a matrix by a constant:
# x has shape (2, 3). Numpy treats scalars as arrays of shape ();
# these can be broadcast together to shape (2, 3), producing the
# following array:
print(x * 2)
[[ 2 4 6]
[ 8 10 12]]
Broadcasting typically makes your code more concise and faster, so you should strive to use it where possible.
Pandas
Pandas is a software library in Python for data manipulation and analysis. It offers data structures and operations for manipulating numerical tables and time series. The main data structure is the DataFrame, which is an in-memory 2D table similar to a spreadsheet, with column names and row labels.
import pandas as pd
Series objects
A Series object is 1D array, similar to a column in a spreadsheet, while a DataFrame objects is a 2D table with column names and row labels.
s = pd.Series([1,2,3,4]); s
0 1
1 2
2 3
3 4
dtype: int64
Series objects can be passed as parameters to NumPy functions
np.log(s)
0 0.000000
1 0.693147
2 1.098612
3 1.386294
dtype: float64
s = s + s + [1,2,3,4] # elementwise addition with a list
s
0 3
1 6
2 9
3 12
dtype: int64
s = s + 1 #Broadcasting
s
0 4
1 7
2 10
3 13
dtype: int64
s >=10
0 False
1 False
2 True
3 True
dtype: bool
Index labels
Each item in a Series object has a unique identifier called index label.
By default, it is simply the rank of the item in the Series (starting at
0) but you can also set the index labels manually
s2 = pd.Series([1, 2, 3, 4], index=["a", "b", "c", "d"])
s2
a 1
b 2
c 3
d 4
dtype: int64
You can then use the Series just like a dict object
s2['b']
2
access items by integer location
s2[1]
2
s2.loc['b'] #accessing by label
2
s2.iloc[1] #accessing by integer location
2
Slicing a Series
s2.iloc[1:3]
b 2
c 3
dtype: int64
s2.iloc[2:]
c 3
d 4
dtype: int64
Initializing from a dict
Create a Series object from a dict, keys are used as index labels
d = {"b": 1, "a": 2, "e": 3, "d": 4}
s3 = pd.Series(d)
s3
b 1
a 2
e 3
d 4
dtype: int64
s4 = pd.Series(d, index = ["c", "a"])
s4
c NaN
a 2.0
dtype: float64
s5 = pd.Series(10, ["a", "b", "c"], name="series")
s5
a 10
b 10
c 10
Name: series, dtype: int64
Automatic alignment
When an operation involves multiple Series objects, pandas
automatically aligns items by matching index labels.
print(s2.keys())
print(s3.keys())
s2 + s3
Index(['a', 'b', 'c', 'd'], dtype='object')
Index(['b', 'a', 'e', 'd'], dtype='object')
a 3.0
b 3.0
c NaN
d 8.0
e NaN
dtype: float64
The resulting Series contains the union of index labels from s2 and s3. But, missing index labels get the value of NaN
DataFrame objects
DataFrame object represents a spreadsheet, with cell values, column names and row index labels.
d = {
"feature1": pd.Series([1,2,3], index=["a", "b", "c"]),
"feature2": pd.Series([4,5,6], index=["b", "a", "c"]),
"feature3": pd.Series([7,8], index=["c", "b"]),
"feature4": pd.Series([9,10], index=["a", "b"]),
}
df = pd.DataFrame(d)
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| b | 2 | 4 | 8.0 | 10.0 |
| c | 3 | 6 | 7.0 | NaN |
You can access columns pretty much as you would expect. They are
returned as Series objects:
df["feature3"] #accessing a column
a NaN
b 8.0
c 7.0
Name: feature3, dtype: float64
df[["feature1", "feature3"]] #accessing ,multiple columns
| feature1 | feature3 | |
|---|---|---|
| a | 1 | NaN |
| b | 2 | 8.0 |
| c | 3 | 7.0 |
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| b | 2 | 4 | 8.0 | 10.0 |
| c | 3 | 6 | 7.0 | NaN |
Constructing a new DataFrame from an existing DataFrame
df2 = pd.DataFrame(
df,
columns=["feature1", "feature2", "feature3"],
index=["b", "a", "d"]
)
df2
| feature1 | feature2 | feature3 | |
|---|---|---|---|
| b | 2.0 | 4.0 | 8.0 |
| a | 1.0 | 5.0 | NaN |
| d | NaN | NaN | NaN |
Creating a DataFrame from a list of lists
lol = [
[11, 1, "a", np.nan],
[12, 3, "b", 14],
[13, np.nan, np.nan, 15]
]
df3 = pd.DataFrame(
lol,
columns=["feature1", "feature2", "feature3", "feature4"],
index=["a", "b", "c"]
)
df3
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 11 | 1.0 | a | NaN |
| b | 12 | 3.0 | b | 14.0 |
| c | 13 | NaN | NaN | 15.0 |
Creating a DataFrame with a dictionary of dictionaries
df5 = pd.DataFrame({
"feature1": {"a": 15, "b": 1984, "c": 4},
"feature2": {"a": "sentence", "b": "word"},
"feature3": {"a": 1, "b": 83, "c": 4},
"feature4": {"c": 2, "d": 0}
})
df5
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 15.0 | sentence | 1.0 | NaN |
| b | 1984.0 | word | 83.0 | NaN |
| c | 4.0 | NaN | 4.0 | 2.0 |
| d | NaN | NaN | NaN | 0.0 |
Multi-indexing
If all columns/rows are tuples of the same size, then they are understood as a multi-index
df5 = pd.DataFrame(
{
("features12", "feature1"):
{("rows_ab","a"): 444, ("rows_ab","b"): 444, ("rows_c","c"): 666},
("features12", "feature2"):
{("rows_ab","a"): 111, ("rows_ab","b"): 222},
("features34", "feature3"):
{("rows_ab","a"): 555, ("rows_ab","b"): 333, ("rows_c","c"): 777},
("features34", "feature4"):
{("rows_ab", "a"):333, ("rows_ab","b"): 999, ("rows_c","c"): 888}
}
)
df5
| features12 | features34 | ||||
|---|---|---|---|---|---|
| feature1 | feature2 | feature3 | feature4 | ||
| rows_ab | a | 444 | 111.0 | 555 | 333 |
| b | 444 | 222.0 | 333 | 999 | |
| rows_c | c | 666 | NaN | 777 | 888 |
df5['features12']
| feature1 | feature2 | ||
|---|---|---|---|
| rows_ab | a | 444 | 111.0 |
| b | 444 | 222.0 | |
| rows_c | c | 666 | NaN |
df5['features12','feature1']
rows_ab a 444
b 444
rows_c c 666
Name: (features12, feature1), dtype: int64
df5['features12','feature1']['rows_c']
c 666
Name: (features12, feature1), dtype: int64
df5.loc['rows_c']
| features12 | features34 | |||
|---|---|---|---|---|
| feature1 | feature2 | feature3 | feature4 | |
| c | 666 | NaN | 777 | 888 |
df5.loc['rows_ab','features12']
| feature1 | feature2 | |
|---|---|---|
| a | 444 | 111.0 |
| b | 444 | 222.0 |
Dropping a level
df5.columns = df5.columns.droplevel(level = 0);
df5
| feature1 | feature2 | feature3 | feature4 | ||
|---|---|---|---|---|---|
| rows_ab | a | 444 | 111.0 | 555 | 333 |
| b | 444 | 222.0 | 333 | 999 | |
| rows_c | c | 666 | NaN | 777 | 888 |
Transposing
swaping columns and indices
df6 = df5.T
df6
| rows_ab | rows_c | ||
|---|---|---|---|
| a | b | c | |
| feature1 | 444.0 | 444.0 | 666.0 |
| feature2 | 111.0 | 222.0 | NaN |
| feature3 | 555.0 | 333.0 | 777.0 |
| feature4 | 333.0 | 999.0 | 888.0 |
Stacking and unstacking levels
expanding the lowest column level as the lowest index
df7 = df6.stack()
df7
| rows_ab | rows_c | ||
|---|---|---|---|
| feature1 | a | 444.0 | NaN |
| b | 444.0 | NaN | |
| c | NaN | 666.0 | |
| feature2 | a | 111.0 | NaN |
| b | 222.0 | NaN | |
| feature3 | a | 555.0 | NaN |
| b | 333.0 | NaN | |
| c | NaN | 777.0 | |
| feature4 | a | 333.0 | NaN |
| b | 999.0 | NaN | |
| c | NaN | 888.0 |
df8 = df7.unstack()
df8
| rows_ab | rows_c | |||||
|---|---|---|---|---|---|---|
| a | b | c | a | b | c | |
| feature1 | 444.0 | 444.0 | NaN | NaN | NaN | 666.0 |
| feature2 | 111.0 | 222.0 | NaN | NaN | NaN | NaN |
| feature3 | 555.0 | 333.0 | NaN | NaN | NaN | 777.0 |
| feature4 | 333.0 | 999.0 | NaN | NaN | NaN | 888.0 |
If we call unstack again, we end up with a Series object
df9 = df8.unstack()
df9
rows_ab a feature1 444.0
feature2 111.0
feature3 555.0
feature4 333.0
b feature1 444.0
feature2 222.0
feature3 333.0
feature4 999.0
c feature1 NaN
feature2 NaN
feature3 NaN
feature4 NaN
rows_c a feature1 NaN
feature2 NaN
feature3 NaN
feature4 NaN
b feature1 NaN
feature2 NaN
feature3 NaN
feature4 NaN
c feature1 666.0
feature2 NaN
feature3 777.0
feature4 888.0
dtype: float64
Accessing rows
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| b | 2 | 4 | 8.0 | 10.0 |
| c | 3 | 6 | 7.0 | NaN |
df.loc["c"] #access the c row
feature1 3.0
feature2 6.0
feature3 7.0
feature4 NaN
Name: c, dtype: float64
df.iloc[2] #access the 2nd column
feature1 3.0
feature2 6.0
feature3 7.0
feature4 NaN
Name: c, dtype: float64
slice of rows
df.iloc[1:3]
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| b | 2 | 4 | 8.0 | 10.0 |
| c | 3 | 6 | 7.0 | NaN |
slice rows using boolean array
df[np.array([True, False, True])]
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| c | 3 | 6 | 7.0 | NaN |
This is most useful when combined with boolean expressions:
df[df["feature2"] <=5]
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| b | 2 | 4 | 8.0 | 10.0 |
Adding and removing columns
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| b | 2 | 4 | 8.0 | 10.0 |
| c | 3 | 6 | 7.0 | NaN |
df['feature5'] = 5 - df['feature2'] #adding a column
df['feature6'] = df['feature3'] > 5
df
| feature1 | feature2 | feature3 | feature4 | feature5 | feature6 | |
|---|---|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 | 0 | False |
| b | 2 | 4 | 8.0 | 10.0 | 1 | True |
| c | 3 | 6 | 7.0 | NaN | -1 | True |
del df['feature6']
df
| feature1 | feature2 | feature3 | feature4 | feature5 | |
|---|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 | 0 |
| b | 2 | 4 | 8.0 | 10.0 | 1 |
| c | 3 | 6 | 7.0 | NaN | -1 |
df["feature6"] = pd.Series({"feature2": 1, "feature4": 51, "feature1":1})
df
| feature1 | feature2 | feature3 | feature4 | feature5 | feature6 | |
|---|---|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 | 0 | NaN |
| b | 2 | 4 | 8.0 | 10.0 | 1 | NaN |
| c | 3 | 6 | 7.0 | NaN | -1 | NaN |
df.insert(1, "feature1b", [0,1,2])
df
| feature1 | feature1b | feature2 | feature3 | feature4 | feature5 | feature6 | |
|---|---|---|---|---|---|---|---|
| a | 1 | 0 | 5 | NaN | 9.0 | 0 | NaN |
| b | 2 | 1 | 4 | 8.0 | 10.0 | 1 | NaN |
| c | 3 | 2 | 6 | 7.0 | NaN | -1 | NaN |
Assigning new columns
create a new DataFrame with new columns
df
| feature1 | feature1b | feature2 | feature3 | feature4 | feature5 | feature6 | |
|---|---|---|---|---|---|---|---|
| a | 1 | 0 | 5 | NaN | 9.0 | 0 | NaN |
| b | 2 | 1 | 4 | 8.0 | 10.0 | 1 | NaN |
| c | 3 | 2 | 6 | 7.0 | NaN | -1 | NaN |
df10 = df.assign(feature0 = df["feature1"] * df["feature2"] )
df10.assign(feature1 = df10["feature1"] +1)
df10
| feature1 | feature1b | feature2 | feature3 | feature4 | feature5 | feature6 | feature0 | |
|---|---|---|---|---|---|---|---|---|
| a | 1 | 0 | 5 | NaN | 9.0 | 0 | NaN | 5 |
| b | 2 | 1 | 4 | 8.0 | 10.0 | 1 | NaN | 8 |
| c | 3 | 2 | 6 | 7.0 | NaN | -1 | NaN | 18 |
Evaluating an expression
df = df[['feature1','feature2','feature3','feature4']]
df.eval("feature1 + feature2 ** 2")
a 26
b 18
c 39
dtype: int64
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | NaN | 9.0 |
| b | 2 | 4 | 8.0 | 10.0 |
| c | 3 | 6 | 7.0 | NaN |
use inplace=True to modify the original DataFrame
df.eval("feature3 = feature1 + feature2 ** 2", inplace=True)
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | 26 | 9.0 |
| b | 2 | 4 | 18 | 10.0 |
| c | 3 | 6 | 39 | NaN |
use a local or global variable in an expression by prefixing it with @
threshold = 30
df.eval("feature3 = feature1 + feature2 ** 2 > @threshold", inplace=True)
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | False | 9.0 |
| b | 2 | 4 | False | 10.0 |
| c | 3 | 6 | True | NaN |
Querying a DataFrame
The query method lets you filter a DataFrame
df.query("feature1 > 2 and feature2 == 6")
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| c | 3 | 6 | True | NaN |
Sorting a DataFrame
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | False | 9.0 |
| b | 2 | 4 | False | 10.0 |
| c | 3 | 6 | True | NaN |
df.sort_index(ascending=False)
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| c | 3 | 6 | True | NaN |
| b | 2 | 4 | False | 10.0 |
| a | 1 | 5 | False | 9.0 |
df.sort_index(axis=1, inplace=True)
df
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 1 | 5 | False | 9.0 |
| b | 2 | 4 | False | 10.0 |
| c | 3 | 6 | True | NaN |
df.sort_values(by="feature2", inplace=True)
df
/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: SettingWithCopyWarning:
A value is trying to be set on a copy of a slice from a DataFrame
See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
"""Entry point for launching an IPython kernel.
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| b | 2 | 4 | False | 10.0 |
| a | 1 | 5 | False | 9.0 |
| c | 3 | 6 | True | NaN |
Operations on DataFrame
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
df = pd.DataFrame(a, columns=["q", "w", "e"], index=["a","b","c"])
df
| q | w | e | |
|---|---|---|---|
| a | 1 | 2 | 3 |
| b | 4 | 5 | 6 |
| c | 7 | 8 | 9 |
np.sqrt(df)
| q | w | e | |
|---|---|---|---|
| a | 1.000000 | 1.414214 | 1.732051 |
| b | 2.000000 | 2.236068 | 2.449490 |
| c | 2.645751 | 2.828427 | 3.000000 |
df + 1 #broadcasting
| q | w | e | |
|---|---|---|---|
| a | 2 | 3 | 4 |
| b | 5 | 6 | 7 |
| c | 8 | 9 | 10 |
df >= 5
| q | w | e | |
|---|---|---|---|
| a | False | False | False |
| b | False | True | True |
| c | True | True | True |
df.mean(), df.std(), df.max(), df.sum()
(q 4.0
w 5.0
e 6.0
dtype: float64, q 3.0
w 3.0
e 3.0
dtype: float64, q 7
w 8
e 9
dtype: int64, q 12
w 15
e 18
dtype: int64)
The All method checks whether all values are True or not
df
| q | w | e | |
|---|---|---|---|
| a | 1 | 2 | 3 |
| b | 4 | 5 | 6 |
| c | 7 | 8 | 9 |
(df > 2).all()
q False
w False
e True
dtype: bool
(df > 2).all(axis = 0) #executed vertically (on each column)
q False
w False
e True
dtype: bool
(df > 2).all(axis = 1) #execute the horizontally (on each row).
a False
b True
c True
dtype: bool
(df == 8).any(axis = 1)
a False
b False
c True
dtype: bool
df - df.mean()
| q | w | e | |
|---|---|---|---|
| a | -3.0 | -3.0 | -3.0 |
| b | 0.0 | 0.0 | 0.0 |
| c | 3.0 | 3.0 | 3.0 |
df - df.values.mean() # subtracts the global mean elementwise
| q | w | e | |
|---|---|---|---|
| a | -4.0 | -3.0 | -2.0 |
| b | -1.0 | 0.0 | 1.0 |
| c | 2.0 | 3.0 | 4.0 |
Handling missing data
Pandas offers a few tools to handle missing data (NaN).
df10
| feature1 | feature1b | feature2 | feature3 | feature4 | feature5 | feature6 | feature0 | |
|---|---|---|---|---|---|---|---|---|
| a | 1 | 0 | 5 | NaN | 9.0 | 0 | NaN | 5 |
| b | 2 | 1 | 4 | 8.0 | 10.0 | 1 | NaN | 8 |
| c | 3 | 2 | 6 | 7.0 | NaN | -1 | NaN | 18 |
df11 = df10.fillna(0)
df11
| feature1 | feature1b | feature2 | feature3 | feature4 | feature5 | feature6 | feature0 | |
|---|---|---|---|---|---|---|---|---|
| a | 1 | 0 | 5 | 0.0 | 9.0 | 0 | 0.0 | 5 |
| b | 2 | 1 | 4 | 8.0 | 10.0 | 1 | 0.0 | 8 |
| c | 3 | 2 | 6 | 7.0 | 0.0 | -1 | 0.0 | 18 |
df11.loc["d"] = np.nan
df11.fillna(0,inplace=True)
df11
#grades + fixed_bonus_points
| feature1 | feature1b | feature2 | feature3 | feature4 | feature5 | feature6 | feature0 | |
|---|---|---|---|---|---|---|---|---|
| a | 1.0 | 0.0 | 5.0 | 0.0 | 9.0 | 0.0 | 0.0 | 5.0 |
| b | 2.0 | 1.0 | 4.0 | 8.0 | 10.0 | 1.0 | 0.0 | 8.0 |
| c | 3.0 | 2.0 | 6.0 | 7.0 | 0.0 | -1.0 | 0.0 | 18.0 |
| d | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
Aggregating with groupby
Similar to the SQL language, pandas allows grouping your data into groups to run calculations over each group.
df5 = pd.DataFrame({
"feature1": {"a": 3, "b": 11, "c": 14, 'd':4},
"feature2": {"a": 2, "b": 2, "c": 4, 'd':4},
"feature3": {"a": 32, "b": 4, "c": 3, 'd':35},
"feature4": {"a": 5, "b": 11, "c": 2, 'd':13}
})
df5
| feature1 | feature2 | feature3 | feature4 | |
|---|---|---|---|---|
| a | 3 | 2 | 32 | 5 |
| b | 11 | 2 | 4 | 11 |
| c | 14 | 4 | 3 | 2 |
| d | 4 | 4 | 35 | 13 |
df5.groupby("feature2").mean()
| feature1 | feature3 | feature4 | |
|---|---|---|---|
| feature2 | |||
| 2 | 7.0 | 18.0 | 8.0 |
| 4 | 9.0 | 19.0 | 7.5 |
Pivot tables
pivot tables allows for quick data summarization
df9 = df8.stack().reset_index()
df9
| level_0 | level_1 | rows_ab | rows_c | |
|---|---|---|---|---|
| 0 | feature1 | a | 444.0 | NaN |
| 1 | feature1 | b | 444.0 | NaN |
| 2 | feature1 | c | NaN | 666.0 |
| 3 | feature2 | a | 111.0 | NaN |
| 4 | feature2 | b | 222.0 | NaN |
| 5 | feature3 | a | 555.0 | NaN |
| 6 | feature3 | b | 333.0 | NaN |
| 7 | feature3 | c | NaN | 777.0 |
| 8 | feature4 | a | 333.0 | NaN |
| 9 | feature4 | b | 999.0 | NaN |
| 10 | feature4 | c | NaN | 888.0 |
pd.pivot_table(df9, index="level_0")
| rows_ab | rows_c | |
|---|---|---|
| level_0 | ||
| feature1 | 444.0 | 666.0 |
| feature2 | 166.5 | NaN |
| feature3 | 444.0 | 777.0 |
| feature4 | 666.0 | 888.0 |
pd.pivot_table(df9, index="level_0", values=["rows_ab"], aggfunc=np.max)
| rows_ab | |
|---|---|
| level_0 | |
| feature1 | 444.0 |
| feature2 | 222.0 |
| feature3 | 555.0 |
| feature4 | 999.0 |
functions
When dealing with large DataFrames, it is useful to get a quick
overview of its content. Pandas offers a few functions for this. First,
let’s create a large DataFrame with a mix of numeric values, missing
values and text values. Notice how Jupyter displays only the corners of
the DataFrame:
df = np.fromfunction(lambda x,y: (x+y)%7*11, (10000, 26))
large_df = pd.DataFrame(df, columns=list("ABCDEFGHIJKLMNOPQRSTUVWXYZ"))
large_df.head(5)
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 |
| 1 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 |
| 2 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 |
| 3 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 |
| 4 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 | 22.0 | 33.0 | 44.0 | 55.0 | 66.0 | 0.0 | 11.0 |
large_df[large_df % 3 == 0] = np.nan
large_df.insert(3,"feature1", "xxx")
large_df.head(5)
| A | B | C | feature1 | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | NaN | 11.0 | 22.0 | xxx | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 |
| 1 | 11.0 | 22.0 | NaN | xxx | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 |
| 2 | 22.0 | NaN | 44.0 | xxx | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN |
| 3 | NaN | 44.0 | 55.0 | xxx | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN |
| 4 | 44.0 | 55.0 | NaN | xxx | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 |
large_df.tail(4)
| A | B | C | feature1 | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 9996 | NaN | 11.0 | 22.0 | xxx | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 |
| 9997 | 11.0 | 22.0 | NaN | xxx | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 |
| 9998 | 22.0 | NaN | 44.0 | xxx | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN |
| 9999 | NaN | 44.0 | 55.0 | xxx | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN |
large_df.describe()
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 5714.000000 | 5715.000000 | 5715.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5715.000000 | 5715.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5715.000000 | 5715.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5714.000000 | 5715.000000 | 5715.000000 | 5714.000000 | 5714.000000 |
| mean | 32.994225 | 32.996150 | 33.003850 | 33.005775 | 33.005775 | 33.000000 | 32.994225 | 32.994225 | 32.996150 | 33.003850 | 33.005775 | 33.005775 | 33.000000 | 32.994225 | 32.994225 | 32.996150 | 33.003850 | 33.005775 | 33.005775 | 33.000000 | 32.994225 | 32.994225 | 32.996150 | 33.003850 | 33.005775 | 33.005775 |
| std | 17.394048 | 17.393135 | 17.393135 | 17.394048 | 17.394048 | 17.395876 | 17.394048 | 17.394048 | 17.393135 | 17.393135 | 17.394048 | 17.394048 | 17.395876 | 17.394048 | 17.394048 | 17.393135 | 17.393135 | 17.394048 | 17.394048 | 17.395876 | 17.394048 | 17.394048 | 17.393135 | 17.393135 | 17.394048 | 17.394048 |
| min | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 | 11.000000 |
| 25% | 13.750000 | 16.500000 | 22.000000 | 22.000000 | 22.000000 | 13.750000 | 13.750000 | 13.750000 | 16.500000 | 22.000000 | 22.000000 | 22.000000 | 13.750000 | 13.750000 | 13.750000 | 16.500000 | 22.000000 | 22.000000 | 22.000000 | 13.750000 | 13.750000 | 13.750000 | 16.500000 | 22.000000 | 22.000000 | 22.000000 |
| 50% | 22.000000 | 22.000000 | 44.000000 | 44.000000 | 44.000000 | 33.000000 | 22.000000 | 22.000000 | 22.000000 | 44.000000 | 44.000000 | 44.000000 | 33.000000 | 22.000000 | 22.000000 | 22.000000 | 44.000000 | 44.000000 | 44.000000 | 33.000000 | 22.000000 | 22.000000 | 22.000000 | 44.000000 | 44.000000 | 44.000000 |
| 75% | 44.000000 | 44.000000 | 49.500000 | 52.250000 | 52.250000 | 52.250000 | 44.000000 | 44.000000 | 44.000000 | 49.500000 | 52.250000 | 52.250000 | 52.250000 | 44.000000 | 44.000000 | 44.000000 | 49.500000 | 52.250000 | 52.250000 | 52.250000 | 44.000000 | 44.000000 | 44.000000 | 49.500000 | 52.250000 | 52.250000 |
| max | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 | 55.000000 |
saving and loading
large_df
| A | B | C | feature1 | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | NaN | 11.0 | 22.0 | xxx | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 |
| 1 | 11.0 | 22.0 | NaN | xxx | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 |
| 2 | 22.0 | NaN | 44.0 | xxx | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN |
| 3 | NaN | 44.0 | 55.0 | xxx | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN |
| 4 | 44.0 | 55.0 | NaN | xxx | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 9995 | NaN | NaN | 11.0 | xxx | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN |
| 9996 | NaN | 11.0 | 22.0 | xxx | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 |
| 9997 | 11.0 | 22.0 | NaN | xxx | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 |
| 9998 | 22.0 | NaN | 44.0 | xxx | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN |
| 9999 | NaN | 44.0 | 55.0 | xxx | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN | 11.0 | 22.0 | NaN | 44.0 | 55.0 | NaN | NaN |
10000 rows × 27 columns
save and load
large_df.to_csv("my_df.csv")
large_df.to_csv("my_df.xlsx")
df0 = pd.read_csv("my_df.csv", index_col=0)
combining DataFrames
pandas has the ability to perform SQL-like joins: inner joins, left/right outer joins and full joins
city_loc = pd.DataFrame(
[
["CA", "San Francisco", 37.781334, -122.416728],
["NY", "New York", 40.705649, -74.008344],
["FL", "Miami", 25.791100, -80.320733],
["OH", "Cleveland", 41.473508, -81.739791],
["UT", "Salt Lake City", 40.755851, -111.896657]
], columns=["state", "city", "lat", "lon"])
city_loc
| state | city | lat | lon | |
|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 |
| 1 | NY | New York | 40.705649 | -74.008344 |
| 2 | FL | Miami | 25.791100 | -80.320733 |
| 3 | OH | Cleveland | 41.473508 | -81.739791 |
| 4 | UT | Salt Lake City | 40.755851 | -111.896657 |
city_pop = pd.DataFrame(
[
[808976, "San Francisco", "California"],
[8363710, "New York", "New York"],
[413201, "Miami", "Florida"],
[2242193, "Houston", "Texas"]
], index=[3,4,5,6], columns=["population", "city", "state"])
city_pop
| population | city | state | |
|---|---|---|---|
| 3 | 808976 | San Francisco | California |
| 4 | 8363710 | New York | New York |
| 5 | 413201 | Miami | Florida |
| 6 | 2242193 | Houston | Texas |
pd.merge(left=city_loc, right=city_pop, on="city")
| state_x | city | lat | lon | population | state_y | |
|---|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | 808976 | California |
| 1 | NY | New York | 40.705649 | -74.008344 | 8363710 | New York |
| 2 | FL | Miami | 25.791100 | -80.320733 | 413201 | Florida |
Note that both DataFrames have a column named state, so in the
result they got renamed to state_x and state_y.
Also, note that Cleveland, Salt Lake City and Houston were dropped
because they don’t exist in both DataFrames. This is the
equivalent of a SQL INNER JOIN. If you want a FULL OUTER JOIN,
where no city gets dropped and NaN values are added, you must
specify how="outer":
all_cities = pd.merge(left=city_loc, right=city_pop, on="city", how="outer")
all_cities
| state_x | city | lat | lon | population | state_y | |
|---|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | 808976.0 | California |
| 1 | NY | New York | 40.705649 | -74.008344 | 8363710.0 | New York |
| 2 | FL | Miami | 25.791100 | -80.320733 | 413201.0 | Florida |
| 3 | OH | Cleveland | 41.473508 | -81.739791 | NaN | NaN |
| 4 | UT | Salt Lake City | 40.755851 | -111.896657 | NaN | NaN |
| 5 | NaN | Houston | NaN | NaN | 2242193.0 | Texas |
Of course LEFT OUTER JOIN is also available by setting
how="left": only the cities present in the left DataFrame end up
in the result. Similarly, with how="right" only cities in the right
DataFrame appear in the result. For example:
pd.merge(left=city_loc, right=city_pop, on="city", how="right")
| state_x | city | lat | lon | population | state_y | |
|---|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | 808976 | California |
| 1 | NY | New York | 40.705649 | -74.008344 | 8363710 | New York |
| 2 | FL | Miami | 25.791100 | -80.320733 | 413201 | Florida |
| 3 | NaN | Houston | NaN | NaN | 2242193 | Texas |
If the key to join on is actually in one (or both) DataFrame’s
index, you must use left_index=True and/or right_index=True. If
the key column names differ, you must use left_on and right_on.
For example:
city_pop2 = city_pop.copy()
city_pop2.columns = ["population", "name", "state"]
pd.merge(left=city_loc, right=city_pop2, left_on="city", right_on="name")
| state_x | city | lat | lon | population | name | state_y | |
|---|---|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | 808976 | San Francisco | California |
| 1 | NY | New York | 40.705649 | -74.008344 | 8363710 | New York | New York |
| 2 | FL | Miami | 25.791100 | -80.320733 | 413201 | Miami | Florida |
Concatenation
Rather than joining DataFrames, we may just want to concatenate
them. That’s what concat() is for:
result_concat = pd.concat([city_loc, city_pop])
result_concat
| state | city | lat | lon | population | |
|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | NaN |
| 1 | NY | New York | 40.705649 | -74.008344 | NaN |
| 2 | FL | Miami | 25.791100 | -80.320733 | NaN |
| 3 | OH | Cleveland | 41.473508 | -81.739791 | NaN |
| 4 | UT | Salt Lake City | 40.755851 | -111.896657 | NaN |
| 3 | California | San Francisco | NaN | NaN | 808976.0 |
| 4 | New York | New York | NaN | NaN | 8363710.0 |
| 5 | Florida | Miami | NaN | NaN | 413201.0 |
| 6 | Texas | Houston | NaN | NaN | 2242193.0 |
Note that this operation aligned the data horizontally (by columns) but not vertically (by rows). In this example, we end up with multiple rows having the same index (eg. 3). Pandas handles this rather gracefully:
result_concat.loc[3]
| state | city | lat | lon | population | |
|---|---|---|---|---|---|
| 3 | OH | Cleveland | 41.473508 | -81.739791 | NaN |
| 3 | California | San Francisco | NaN | NaN | 808976.0 |
Or you can tell pandas to just ignore the index:
pd.concat([city_loc, city_pop], ignore_index=True)
| state | city | lat | lon | population | |
|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | NaN |
| 1 | NY | New York | 40.705649 | -74.008344 | NaN |
| 2 | FL | Miami | 25.791100 | -80.320733 | NaN |
| 3 | OH | Cleveland | 41.473508 | -81.739791 | NaN |
| 4 | UT | Salt Lake City | 40.755851 | -111.896657 | NaN |
| 5 | California | San Francisco | NaN | NaN | 808976.0 |
| 6 | New York | New York | NaN | NaN | 8363710.0 |
| 7 | Florida | Miami | NaN | NaN | 413201.0 |
| 8 | Texas | Houston | NaN | NaN | 2242193.0 |
Notice that when a column does not exist in a DataFrame, it acts as
if it was filled with NaN values. If we set join="inner", then
only columns that exist in both DataFrames are returned:
pd.concat([city_loc, city_pop], join="inner")
| state | city | |
|---|---|---|
| 0 | CA | San Francisco |
| 1 | NY | New York |
| 2 | FL | Miami |
| 3 | OH | Cleveland |
| 4 | UT | Salt Lake City |
| 3 | California | San Francisco |
| 4 | New York | New York |
| 5 | Florida | Miami |
| 6 | Texas | Houston |
You can concatenate DataFrames horizontally instead of vertically
by setting axis=1:
pd.concat([city_loc, city_pop], axis=1)
| state | city | lat | lon | population | city | state | |
|---|---|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | NaN | NaN | NaN |
| 1 | NY | New York | 40.705649 | -74.008344 | NaN | NaN | NaN |
| 2 | FL | Miami | 25.791100 | -80.320733 | NaN | NaN | NaN |
| 3 | OH | Cleveland | 41.473508 | -81.739791 | 808976.0 | San Francisco | California |
| 4 | UT | Salt Lake City | 40.755851 | -111.896657 | 8363710.0 | New York | New York |
| 5 | NaN | NaN | NaN | NaN | 413201.0 | Miami | Florida |
| 6 | NaN | NaN | NaN | NaN | 2242193.0 | Houston | Texas |
In this case it really does not make much sense because the indices do
not align well (eg. Cleveland and San Francisco end up on the same row,
because they shared the index label 3). So let’s reindex the
DataFrames by city name before concatenating:
pd.concat([city_loc.set_index("city"), city_pop.set_index("city")], axis=1)
| state | lat | lon | population | state | |
|---|---|---|---|---|---|
| San Francisco | CA | 37.781334 | -122.416728 | 808976.0 | California |
| New York | NY | 40.705649 | -74.008344 | 8363710.0 | New York |
| Miami | FL | 25.791100 | -80.320733 | 413201.0 | Florida |
| Cleveland | OH | 41.473508 | -81.739791 | NaN | NaN |
| Salt Lake City | UT | 40.755851 | -111.896657 | NaN | NaN |
| Houston | NaN | NaN | NaN | 2242193.0 | Texas |
This looks a lot like a FULL OUTER JOIN, except that the state
columns were not renamed to state_x and state_y, and the
city column is now the index.
The append() method is a useful shorthand for concatenating
DataFrames vertically:
city_loc.append(city_pop)
| state | city | lat | lon | population | |
|---|---|---|---|---|---|
| 0 | CA | San Francisco | 37.781334 | -122.416728 | NaN |
| 1 | NY | New York | 40.705649 | -74.008344 | NaN |
| 2 | FL | Miami | 25.791100 | -80.320733 | NaN |
| 3 | OH | Cleveland | 41.473508 | -81.739791 | NaN |
| 4 | UT | Salt Lake City | 40.755851 | -111.896657 | NaN |
| 3 | California | San Francisco | NaN | NaN | 808976.0 |
| 4 | New York | New York | NaN | NaN | 8363710.0 |
| 5 | Florida | Miami | NaN | NaN | 413201.0 |
| 6 | Texas | Houston | NaN | NaN | 2242193.0 |
As always in pandas, the append() method does not actually modify
city_loc: it works on a copy and returns the modified copy.
Categories
It is quite frequent to have values that represent categories, for
example 1 for female and 2 for male, or "A" for Good,
"B" for Average, "C" for Bad. These categorical values can be
hard to read and cumbersome to handle, but fortunately pandas makes it
easy. To illustrate this, let’s take the city_pop DataFrame we
created earlier, and add a column that represents a category:
city_eco = city_pop.copy()
city_eco["eco_code"] = [17, 17, 34, 20]
city_eco
| population | city | state | eco_code | |
|---|---|---|---|---|
| 3 | 808976 | San Francisco | California | 17 |
| 4 | 8363710 | New York | New York | 17 |
| 5 | 413201 | Miami | Florida | 34 |
| 6 | 2242193 | Houston | Texas | 20 |
Right now the eco_code column is full of apparently meaningless
codes. Let’s fix that. First, we will create a new categorical column
based on the eco_codes:
city_eco["economy"] = city_eco["eco_code"].astype('category')
city_eco["economy"].cat.categories
Int64Index([17, 20, 34], dtype='int64')
Now we can give each category a meaningful name:
city_eco["economy"].cat.categories = ["Finance", "Energy", "Tourism"]
city_eco
| population | city | state | eco_code | economy | |
|---|---|---|---|---|---|
| 3 | 808976 | San Francisco | California | 17 | Finance |
| 4 | 8363710 | New York | New York | 17 | Finance |
| 5 | 413201 | Miami | Florida | 34 | Tourism |
| 6 | 2242193 | Houston | Texas | 20 | Energy |
Note that categorical values are sorted according to their categorical order, not their alphabetical order:
city_eco.sort_values(by="economy", ascending=False)
| population | city | state | eco_code | economy | |
|---|---|---|---|---|---|
| 5 | 413201 | Miami | Florida | 34 | Tourism |
| 6 | 2242193 | Houston | Texas | 20 | Energy |
| 3 | 808976 | San Francisco | California | 17 | Finance |
| 4 | 8363710 | New York | New York | 17 | Finance |