awesome-cheatsheets/tools/NumPy.md

NumPy Cheat Sheet

NumPy is the fundamental package for scientific computing with Python.

Installation

If you don't already have it installed, you can do so using Pip or Anaconda:

$ pip install numpy

or

$ conda install numpy

This cheat sheet acts as a intro to Python for data science.

Index

1. Basics
   • Placeholders
   • Examples
2. Arrays
   • Properties
   • Copying/Sorting
     • Examples
   • Array Manipulation
     • Adding/Removing Elements
       • Examples
     • Combining Arrays
       • Examples
     • Splitting Arrays
       • Examples
     • Shaping
     • Misc
3. Mathematics
   • Arithmetic Operations
     • Examples
   • Comparison
     • Examples
   • Basic Statistics
     • Examples
   • More
4. Slicing and Subsetting
   • Examples
5. Tricks
6. Credits

Basics

One of the most commonly used functions of NumPy are NumPy arrays: The essential difference between lists and NumPy arrays is functionality and speed. lists give you basic operation, but NumPy adds FFTs, convolutions, fast searching, basic statistics, linear algebra, histograms, etc.
The most important difference for data science is the ability to do element-wise calculations with NumPy arrays.

axis 0 always refers to row
axis 1 always refers to column

Operator	Description	Documentation
np.array([1,2,3])	1d array	link
np.array([(1,2,3),(4,5,6)])	2d array	see above
np.arange(start,stop,step)	range array	link

Placeholders

Operators	Description	Documentation
np.linspace(0,2,9)	Add evenly spaced values btw interval to array of length	link
np.zeros((1,2))	Create and array filled with zeros	link
np.ones((1,2))	Creates an array filled with ones	link
np.random.random((5,5))	Creates random array	link
np.empty((2,2))	Creates an empty array	link

Examples

import numpy as np

# 1 dimensional
x = np.array([1,2,3])
# 2 dimensional
y = np.array([(1,2,3),(4,5,6)])

x = np.arange(3)
>>> array([0, 1, 2])

y = np.arange(3.0)
>>> array([ 0.,  1.,  2.])

x = np.arange(3,7)
>>> array([3, 4, 5, 6])

y = np.arange(3,7,2)
>>> array([3, 5])

Array

Array Properties

Syntax	Description	Documentation
array.shape	Dimensions (Rows,Columns)	link
len(array)	Length of Array	link
array.ndim	Number of Array Dimensions	link
array.size	Number of Array Elements	link
array.dtype	Data Type	link
array.astype(type)	Converts to Data Type	link
type(array)	Type of Array	link

Copying/Sorting

Operators	Descriptions	Documentation
np.copy(array)	Creates copy of array	link
other = array.copy()	Creates deep copy of array	see above
array.sort()	Sorts an array	link
array.sort(axis=0)	Sorts axis of array	see above

Examples

import numpy as np
# Sort sorts in ascending order
y = np.array([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
y.sort()
print(y)
>>> [ 1  2  3  4  5  6  7  8  9  10]

Array Manipulation Routines

Adding or Removing Elements

Operator	Description	Documentation
np.append(a,b)	Append items to array	link
np.insert(array, 1, 2, axis)	Insert items into array at axis 0 or 1	link
np.resize((2,4))	Resize array to shape(2,4)	link
np.delete(array,1,axis)	Deletes items from array	link

Example

import numpy as np
# Append items to array
a = np.array([(1, 2, 3),(4, 5, 6)])
b = np.append(a, [(7, 8, 9)])
print(b)
>>> [1 2 3 4 5 6 7 8 9]

# Remove index 2 from previous array
print(np.delete(b, 2))
>>> [1 2 4 5 6 7 8 9]

Combining Arrays

Operator	Description	Documentation
np.concatenate((a,b),axis=0)	Concatenates 2 arrays, adds to end	link
np.vstack((a,b))	Stack array row-wise	link
np.hstack((a,b))	Stack array column wise	link

Example

import numpy as np
a = np.array([1, 3, 5])
b = np.array([2, 4, 6])

# Stack two arrays row-wise
print(np.vstack((a,b)))
>>> [[1 3 5]
     [2 4 6]]

# Stack two arrays column-wise
print(np.hstack((a,b)))
>>> [1 3 5 2 4 6]

Splitting Arrays

Operator	Description	Documentation
numpy.split()		link
np.array_split(array, 3)	Split an array in sub-arrays of (nearly) identical size	link
numpy.hsplit(array, 3)	Split the array horizontally at 3rd index	link

Example

# Split array into groups of ~3
a = np.array([1, 2, 3, 4, 5, 6, 7, 8])
print(np.array_split(a, 3))
>>> [array([1, 2, 3]), array([4, 5, 6]), array([7, 8])]

Shaping Arrays

TODO

Operator	Description	Documentation
other = ndarray.flatten()	Flattens a 2d array to 1d	link
numpy.flip()	Flips order of elements in 1D array
np.ndarray[::-1]	Same as above
reshape
squeeze
expand_dims

Misc

Operator	Description	Documentation
other = ndarray.flatten()	Flattens a 2d array to 1d	link
array = np.transpose(other) array.T	Transpose array	link
inverse = np.linalg.inv(matrix)	Inverse of a given matrix	link

Example

# Find inverse of a given matrix
>>> np.linalg.inv([[3,1],[2,4]])
array([[ 0.4, -0.1],
       [-0.2,  0.3]])

Mathematics

Operations

Operator	Description	Documentation
np.add(x,y) x + y	Addition	link
np.substract(x,y) x - y	Subtraction	link
np.divide(x,y) x / y	Division	link
np.multiply(x,y) x @ y	Multiplication	link
np.sqrt(x)	Square Root	link
np.sin(x)	Element-wise sine	link
np.cos(x)	Element-wise cosine	link
np.log(x)	Element-wise natural log	link
np.dot(x,y)	Dot product	link
np.roots([1,0,-4])	Roots of a given polynomial coefficients	link

Remember: NumPy array operations work element-wise.

Example

# If a 1d array is added to a 2d array (or the other way), NumPy
# chooses the array with smaller dimension and adds it to the one
# with bigger dimension
a = np.array([1, 2, 3])
b = np.array([(1, 2, 3), (4, 5, 6)])
print(np.add(a, b))
>>> [[2 4 6]
     [5 7 9]]
     
# Example of np.roots
# Consider a polynomial function (x-1)^2 = x^2 - 2*x + 1
# Whose roots are 1,1
>>> np.roots([1,-2,1])
array([1., 1.])
# Similarly x^2 - 4 = 0 has roots as x=±2
>>> np.roots([1,0,-4])
array([-2.,  2.])

Comparison

Operator	Description	Documentation
==	Equal	link
!=	Not equal	link
<	Smaller than	link
>	Greater than	link
<=	Smaller than or equal	link
>=	Greater than or equal	link
np.array_equal(x,y)	Array-wise comparison	link

Example

# Using comparison operators will create boolean NumPy arrays
z = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
c = z < 6
print(c)
>>> [ True  True  True  True  True False False False False False]

Basic Statistics

Operator	Description	Documentation
np.mean(array)	Mean	link
np.median(array)	Median	link
array.corrcoef()	Correlation Coefficient	link
np.std(array)	Standard Deviation	link

Example

# Statistics of an array
a = np.array([1, 1, 2, 5, 8, 10, 11, 12])

# Standard deviation
print(np.std(a))
>>> 4.2938910093294167

# Median
print(np.median(a))
>>> 6.5

More

Operator	Description	Documentation
array.sum()	Array-wise sum	link
array.min()	Array-wise minimum value	link
array.max(axis=0)	Maximum value of specified axis
array.cumsum(axis=0)	Cumulative sum of specified axis	link

Slicing and Subsetting

Operator	Description	Documentation
array[i]	1d array at index i	link
array[i,j]	2d array at index[i][j]	see above
array[i<4]	Boolean Indexing, see Tricks	see above
array[0:3]	Select items of index 0, 1 and 2	see above
array[0:2,1]	Select items of rows 0 and 1 at column 1	see above
array[:1]	Select items of row 0 (equals array[0:1, :])	see above
array[1:2, :]	Select items of row 1	see above
[comment]: <> (	array[1,...]	equals array[1,:,:]
array[ : :-1]	Reverses array	see above

Examples

b = np.array([(1, 2, 3), (4, 5, 6)])

# The index *before* the comma refers to *rows*,
# the index *after* the comma refers to *columns*
print(b[0:1, 2])
>>> [3]

print(b[:len(b), 2])
>>> [3 6]

print(b[0, :])
>>> [1 2 3]

print(b[0, 2:])
>>> [3]

print(b[:, 0])
>>> [1 4]

c = np.array([(1, 2, 3), (4, 5, 6)])
d = c[1:2, 0:2]
print(d)
>>> [[4 5]]

Tricks

This is a growing list of examples. Know a good trick? Let me know in a issue or fork it and create a pull request.

boolean indexing

# Index trick when working with two np-arrays
a = np.array([1,2,3,6,1,4,1])
b = np.array([5,6,7,8,3,1,2])

# Only saves a at index where b == 1
other_a = a[b == 1]
#Saves every spot in a except at index where b != 1
other_other_a = a[b != 1]

import numpy as np
x = np.array([4,6,8,1,2,6,9])
y = x > 5
print(x[y])
>>> [6 8 6 9]

# Even shorter
x = np.array([1, 2, 3, 4, 4, 35, 212, 5, 5, 6])
print(x[x < 5])
>>> [1 2 3 4 4]