Python is an ever-growing programming language which entices the developers with its flourishing libraries. Numpy is one of the libraries in python, which supports the most important and most utilized functionalities of the Mathematical world making it absolutely indispensable. Numpy provides a great number of easy to understand formulae and functions to perform not only on basic mathematics but also with scientific and statistical problems.
In this blog, you shall learn numpy from the basic to advanced functions necessary for excelling in the mathematical library.
Table of Contents
Python NumPy Cheat Sheet
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This cheat sheet has been designed assuming, one has basic python knowledge and will provide you with all the basics that you need to get started with NumPy in Python.
Advanced NumPy Cheat Sheet
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What is NumPy?
It is a library consisting of multidimensional array objects and a collection of routines for processing those arrays. NumPy has put python lists out of the job as NumPy arrays are more efficient, convenient and make it faster to read or write an item.
1. Import Convention
Since NumPy is a Python library, it has to be imported first before you start using NumPy. To import NumPy, type in the following command:
| Absolute Import | Import numpy as np |
Creating and Initializing Arrays
1. N-dimensional Array
| Syntax | np.array() |
| 1D | np.array([1,2,3,4])
Output: array([1, 2, 3, 4]) |
| 2D | np.array([[1,2,3], [4,5,6]])
Output: array([[1, 2, 3], [4, 5, 6]]) |
| 3D | np.array([[[1,2,3], [4,5,6]]])
Output: array([[[1, 2, 3], [4, 5, 6]]]) |
| 4D | np.array([[[[1,2,3]]]])
Output: array([[[[1, 2, 3]]]]) |
2. Creating array
Just knowing what a NumPy array is not enough, we need to know how to create a Numpy array. You can create a NumPy array in the following ways:
| a = np.array([1,3,4,8])
Output: [1 3 4 8] |
| b = np.array([1.4, 3.2, 5], dtype = float)
Output: [1.4 3.2 5. ] |
| c = np.array([1,3,5,7,9,11], dtype = int64)
Output: [ 1 3 5 7 9 11] |
3. Initial Placeholders
When you have the data you need to import to python, you can use NumPy to convert that data into NumPy arrays but sometimes when you don’t initially have any data or when you are starting from scratch and need an empty array you can use later then you can use NumPy.zeros() function.
You can create empty arrays in following ways:
| Create an array with zeros. | np.zeros((3,8))
Output: 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.]]) |
| Create an array with ones. | np.ones((3,8))
Output: 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.]]) |
| Create an array with even-spaced step values. | np.arange(1, 30, 5)
Output: array([ 1, 6, 11, 16, 21, 26]) |
| Create an evenly-spaced array with a specified number of values. | np.linspace(0,4,8)
Output: array([0. , 0.57142857, 1.14285714, 1.71428571, 2.28571429, 2.85714286, 3.42857143, 4. ]) |
| Create an entire array with a constant value. | np.full((4,4),9)
Output: array([[9, 9, 9, 9], [9, 9, 9, 9], [9, 9, 9, 9], [9, 9, 9, 9]]) |
| Create an identity matrix. | np.identity(3)
Output: array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) |
| Create an identity matrix with m*n dimension. | np.eye(3,5)
Output: array([[1., 0., 0., 0., 0.], [0., 1., 0., 0., 0.], [0., 0., 1., 0., 0.]]) |
| Create an identity matrix with the m*n dimension with step shift. | np.eye(3, k=1)
Output: array([[0., 1., 0.], [0., 0., 1.], [0., 0., 0.]]) |
| Create a diagonal matrix. | np.diag([1,1,1])
Output: array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) |
| Create an array with random integers. | np.random.randint(2,8,3)
Output: array([2, 6, 3]) |
| Create an array between [0, 1). | np.random.rand(5,2)
Output: array([[0.52620975, 0.27200853], [0.04753095, 0.38419669], [0.29254718, 0.66309665], [0.09115936, 0.62305064], [0.7984203 , 0.39769068]]) |
| Create an array with a mean 0 and a standard deviation of 1. | np.random.randn(2,3)
Output: array([[-0.98863765, 0.33808866, 0.07083797], [-0.58465781, -1.53241981, -1.03018067]]) |
| Create a random array in the [0.0, 1.0) interval | np.random.random_sample(10)
Output: array([0.33360613, 0.54360933, 0.61117749, 0.52978991, 0.70083391, 0.61659811, 0.87412798, 0.62451739, 0.03659576, 0.12249504]) np.random.random(10) Output: array([0.79213708, 0.65407051, 0.70394522, 0.72384937, 0.80480269, 0.51195845, 0.00852462, 0.571088 , 0.59704964, 0.74560852]) |
Working with NumPy Arrays
1. Properties of Array
NumPy offers a few numbers of what we call ‘properties of NumPy array’ which can be used to check the nature of the array, that is, what kind of elements it contains or what is the size,etc.
arr1 = np.array([[1,2,3], [4,5,6]])
| Array dimensions | arr1.ndim
Output: 2 |
| Length of array | len(arr1)
Output: 2 |
| Shape of the array | arr1.shape
Output: (2,3) |
| Name of datatype | arr1.dtype.name
Output: ’int’ |
| Type-cast array | arr1.astype(int)
Output: array([[1, 2, 3], [4, 5, 6]]) |
| Data type of an array | arr1.dtype
Output: dtype(‘int64’) |
2. Indexing and Slicing, Subsetting
-
- Boolean Indexing
- Fancy Indexing
- Subsetting
- Slicing
| Indexing | #forward Index
arr= [‘a’, ‘b’, ‘c’, ‘d’, ‘e’] index-> 0 , 1 , 2, 3, 4 #backward indexing arr= [‘a’, ‘b’, ‘c’, ‘d’, ‘e’] index-> -5 , -4 , -3, -2, -1 |
| Boolean Indexing | arr1 = np.array([[1,2,3], [4,5,6]])
arr1[arr1 > 3] #Selects elements from an array based on boolean condition Output: array([4, 5, 6]) |
| Fancy Indexing | arr = np.array([0, 10, 20, 30, 40, 50])
indices = np.array([0, 1, 5]) #indexing using fancy indexing fancy_ind = arr[indices] print(fancy_ind) # Output: [ 0 10 50] Output: [ 0 10 50] |
| Subset | a = arr1[1] #selects the second element
Output: [4 5 6] |
| Slicing | arr1[0:3] #selecting elements from 0-3
Output: array([[1, 2, 3], [4, 5, 6]]) |
3. Data Types
| signed 64-bit int type | np.int64 |
| Double standard float point | np.float32 |
| Complex numbers | np.complex |
| Boolean data type | np.bool |
| Object type | np.object |
| Fixed-length string | np.string_ |
| Unicode | np.unicode_ |
Array Operations
1. Array Mathematics
Following are some mathematical operations you can perform using NumPy arrays:Note: While performing arithmetic operations in NumPy arrays, you should make sure that the items are of same shape.
1.1. Creating an Numpy Array
| #Create arrays | arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6]) Output: [1 2 3] Output: [4 5 6] |
1.2. Arithmetic Functions
| Arithmetic Function | |
| Addition | np.add(arr1, arr2)
Output: array([5, 7, 9]) |
| Subtraction | np.subtract(arr1, arr2)
Output: array([-3, -3, -3]) |
| Multiplication | np.multiply(arr1, arr2)
Output: array([ 4, 10, 18]) |
| Division | np.divide(arr1,arr2)
Output: array([0.25, 0.4 , 0.5 ]) |
| Exponentiation | np.power(arr1, arr2)
Output: array([ 1, 32, 729]) |
| Floor/Integer Division | np.floor_divide(arr1, arr2)
Output: array([0, 0, 0]) |
| Modulus | np.mod(arr1, arr2)
Output: array([1, 2, 3]) |
| Square Root | np.sqrt(arr1)
Output: array([1. , 1.41421356, 1.73205081]) |
| Unary Negation | np.negative(arr1, arr2)
Output: array([-1, -2, -3]) |
1.3. Mathematical Functions
| Mathematical Functions | |
| Trigonometric Functions | np.sin(arr1)
Output: array([0.84147098, 0.90929743, 0.14112001]) np.cos(arr1) Output: array([ 0.54030231, -0.41614684, -0.9899925 ]) np.tan(arr1) Output: array([ 1.55740772, -2.18503986, -0.14254654]) |
| Exponential and Logarithmic Functions | np.exp(arr1)
Output: array([ 2.71828183, 7.3890561 , 20.08553692]) |
| np.log(arr1)
Output: array([0. , 0.69314718, 1.09861229]) |
| Statistical Functions | np.mean(arr1) #Finding mean
Output: 2.0 |
| np.std(arr1)#Finding standard deviation
Output: 0.816496580927726 |
|
| np.median(arr1) #finding median
Output: 2.0 |
1.4. Comparison and Logical Operator
| Comparison and Logical Operator |
| np.equal(arr1, arr2)
Output: [False False False] np.not_equal(arr1, arr2) Output: [ True True True] np.greater(arr1, arr2) Output: [False False False] |
| np.logical_and(arr1, arr2)
Output: [ True True True] np.logical_or(arr1,arr2) Output: [ True True True] np.logical_not(arr1) Output: [False False False] |
2. Functions
-
- Updating array elements
- Removing array elements
- Copy array
- Return condition specific element
- Find unique element
- Sorting
| Updating array elements | arr = [11,12,15,17,19] #update 12 with 13
arr[1]= 13 arr Output: [11,13,15,17,19] |
| Removing array elements | np.delete(arr, 2) #removes element at index 2
Output: [11,13,17,19] |
| Copying arrays | arr.view() #create view of the array with the same data
np.copy(arr1) #creates a copy of array arr1.copy() #creates deep copy of array |
| Return a condition-specific element. | ele = arr[arr > 3] # return elements greater than 3
Output: [11 12 15 17 19] |
| Find a unique element | np.unique(arr) #returns unique elements
Output: array([11, 12, 15, 17, 19]) |
| Sorting | #ascending order
np.sort(arr) Output: array([11, 12, 15, 17, 19]) #descending order np.sort(arr)[ ::-1] Output: array([19, 17, 15, 12, 11]) |
3. Array Manipulation
-
- Reshaping array
- Flattening array
- Transposing array
- Concatenating arrays vertically and horizontally
- Splitting array
- Flip array
| Reshaping Array | arr.reshape(3,4) #changes to 3*4 matrix
Output: array([[1, 4, 7, 9], [2, 4, 7, 9], [2, 3, 4, 5]]) |
| Flattening Array | arr.flatten()
Output: array([1, 4, 7, 9, 2, 4, 7, 9, 2, 3, 4, 5]) arr.ravel() Output: array([1, 4, 7, 9, 2, 4, 7, 9, 2, 3, 4, 5]) |
| Transposing Array | arr.T
Output: array([[1, 2, 2], [4, 4, 3], [7, 7, 4], [9, 9, 5]]) |
| Concatenating Arrays | #vertical
np.vstack((arr1, arr2)) Output: array([[1, 2, 3], [4, 5, 6]]) #horizontal np.hstack((arr1, arr2)) Output: array([1, 2, 3, 4, 5, 6]) |
| Splitting Array | #splitting array into n sub-arrays
np.split(arr, 3) Output: [array([[1, 4, 7, 9]]), array([[2, 4, 7, 9]]), array([[2, 3, 4, 5]])] |
| Flip Array | np.flip(arr, axis=0) #vertical flip
np.flip(arr, axis=1) #horizontal flip |
Advanced Numpy Operations
1. Linear Algebra
-
- Matrix Operations
- Matrix Properties
- Solving Equations
- Eigenvalues and Eigenvectors
1.1. Matrix Operations
| Matrix Operations |
| c = np.add(a, b) # Matrix addition
d = np.subtract(a, b) # Matrix subtraction e = np.dot(a, b) # Matrix multiplication f = np.divide(a, b) # Matrix division |
1.2. Matrix Properties
| Matrix Properties |
| det_a = np.linalg.det(a) # Determinant
a_transpose = np.transpose(a) # Transpose a_inv = np.linalg.inv(a)# Inverse |
1.3. Solving Equations
| Solving Equations |
| # Solving linear equations
x = np.linalg.solve(a, b) |
1.4. Eigenvalues and EigenVectors
| Eigenvalues and Eigenvectors |
| # Eigenvalues and eigenvectorseigenvalues, eigenvectors = np.linalg.eig(a) |
Saving, Loading and Help
1. Saving and Loading
Next comes, how to save or load an array or a file in NumPy
| Saving and Loading on Disk |
| a = np.array([[1,2,3], [4,5,6]])
np.save(‘arr’ ,a) |
| b = np.savez(‘arr’, a) #saving array |
| c =np.load(‘arr’) #loading array
print(c) |
| Saving and Loading text/csv Files |
| np.loadtxt(‘New_file.txt’) #From a text file |
| np.savetxt(‘New_file.txt’,arr,delimiter=’ ‘) #Writes to a text file |
| np.genfromtxt(‘New_file.csv’,delimiter=’,’) #From a CSV file |
| np.savetxt(‘New_file.csv’,arr,delimiter=’,’) #Writes to a CSV file |
2. Help in Numpy
| Help in NumPy |
| np.info(np.ndarray.dtype)
help(np.ndarray.dtype) |
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Learn Python easily with our related cheat sheets, designed to simplify basic and advanced concepts.
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