This article will help you get acquainted with the widely used array-processing library NumPy in Python.
What is NumPy?
NumPy is a general-purpose array-processing package. It provides a high-performance multidimensional array object and tools for working with these arrays. It is the fundamental package for scientific computing with Python. It is open-source software.
Features of NumPy
NumPy has various features including these important ones:
- A powerful N-dimensional array object
- Sophisticated (broadcasting) functions
- Tools for integrating C/C++ and Fortran code
- Useful linear algebra, Fourier transform, and random number capabilities
Besides its obvious scientific uses, NumPy in Python can also be used as an efficient multi-dimensional container of generic data. Arbitrary data types can be defined using Numpy which allows NumPy to seamlessly and speedily integrate with a wide variety of databases.
Install Python NumPy
Numpy can be installed for Mac and Linux users via the following pip command:
pip install numpy
Windows does not have any package manager analogous to that in Linux or Mac. Please download the pre-built Windows installer for NumPy from here (according to your system configuration and Python version). And then install the packages manually.
Note: All the examples discussed below will not run on an online IDE.
Arrays in NumPy
NumPy’s main object is the homogeneous multidimensional array.
- It is a table of elements (usually numbers), all of the same type, indexed by a tuple of positive integers.
- In NumPy, dimensions are called axes. The number of axes is rank.
- NumPy’s array class is called ndarray. It is also known by the alias array.
Example:
In this example, we are creating a two-dimensional array that has the rank of 2 as it has 2 axes. The first axis(dimension) is of length 2, i.e., the number of rows, and the second axis(dimension) is of length 3, i.e., the number of columns. The overall shape of the array can be represented as (2, 3)
Python3
import numpy as np # Creating array objectarr = np.array( [[ 1, 2, 3], [ 4, 2, 5]] ) # Printing type of arr objectprint("Array is of type: ", type(arr)) # Printing array dimensions (axes)print("No. of dimensions: ", arr.ndim) # Printing shape of arrayprint("Shape of array: ", arr.shape) # Printing size (total number of elements) of arrayprint("Size of array: ", arr.size) # Printing type of elements in arrayprint("Array stores elements of type: ", arr.dtype) |
Output:
Array is of type: <class 'numpy.ndarray'>
No. of dimensions: 2
Shape of array: (2, 3)
Size of array: 6
Array stores elements of type: int64
NumPy Array Creation
There are various ways of Numpy array creation in Python. They are as follows:
1. You can create an array from a regular Python list or tuple using the array() function. The type of the resulting array is deduced from the type of the elements in the sequences. Let’s see this implementation:
Python3
import numpy as np # Creating array from list with type floata = np.array([[1, 2, 4], [5, 8, 7]], dtype = 'float')print ("Array created using passed list:\n", a) # Creating array from tupleb = np.array((1 , 3, 2))print ("\nArray created using passed tuple:\n", b) |
Output:
Array created using passed list:
[[1. 2. 4.]
[5. 8. 7.]]
Array created using passed tuple:
[1 3 2]
2. Often, the element is of an array is originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. For example: np.zeros, np.ones, np.full, np.empty, etc.
To create sequences of numbers, NumPy provides a function analogous to the range that returns arrays instead of lists.
Python3
# Creating a 3X4 array with all zerosc = np.zeros((3, 4))print ("An array initialized with all zeros:\n", c) # Create a constant value array of complex typed = np.full((3, 3), 6, dtype = 'complex')print ("An array initialized with all 6s." "Array type is complex:\n", d) # Create an array with random valuese = np.random.random((2, 2))print ("A random array:\n", e) |
Output:
An array initialized with all zeros:
[[0. 0. 0. 0.]
[0. 0. 0. 0.]
[0. 0. 0. 0.]]
An array initialized with all 6s.Array type is complex:
[[6.+0.j 6.+0.j 6.+0.j]
[6.+0.j 6.+0.j 6.+0.j]
[6.+0.j 6.+0.j 6.+0.j]]
A random array:
[[0.15471821 0.47506745]
[0.03637972 0.15772238]]
3. arange: This function returns evenly spaced values within a given interval. Step size is specified.
Python3
# Create a sequence of integers # from 0 to 30 with steps of 5f = np.arange(0, 30, 5)print ("A sequential array with steps of 5:\n", f) |
Output:
A sequential array with steps of 5:
[ 0 5 10 15 20 25]
4. linspace: It returns evenly spaced values within a given interval.
Python3
# Create a sequence of 10 values in range 0 to 5g = np.linspace(0, 5, 10)print ("A sequential array with 10 values between" "0 and 5:\n", g) |
Output:
A sequential array with 10 values between0 and 5:
[0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778
3.33333333 3.88888889 4.44444444 5. ]
5. Reshaping array: We can use reshape method to reshape an array. Consider an array with shape (a1, a2, a3, …, aN). We can reshape and convert it into another array with shape (b1, b2, b3, …, bM). The only required condition is a1 x a2 x a3 … x aN = b1 x b2 x b3 … x bM. (i.e. the original size of the array remains unchanged.)
Python3
# Reshaping 3X4 array to 2X2X3 arrayarr = np.array([[1, 2, 3, 4], [5, 2, 4, 2], [1, 2, 0, 1]]) newarr = arr.reshape(2, 2, 3) print ("Original array:\n", arr)print("---------------")print ("Reshaped array:\n", newarr) |
Output:
Original array:
[[1 2 3 4]
[5 2 4 2]
[1 2 0 1]]
---------------
Reshaped array:
[[[1 2 3]
[4 5 2]]
[[4 2 1]
[2 0 1]]]
6. Flatten array: We can use flatten method to get a copy of the array collapsed into one dimension. It accepts order argument. The default value is 𠆌’ (for row-major order). Use 𠆏’ for column-major order.
Python3
# Flatten arrayarr = np.array([[1, 2, 3], [4, 5, 6]])flat_arr = arr.flatten() print ("Original array:\n", arr)print ("Fattened array:\n", flat_arr) |
Output:
Original array:
[[1 2 3]
[4 5 6]]
Fattened array:
[1 2 3 4 5 6]
Note: The type of array can be explicitly defined while creating the array.
NumPy Array Indexing
Knowing the basics of NumPy array indexing is important for analyzing and manipulating the array object. NumPy in Python offers many ways to do array indexing.
- Slicing: Just like lists in Python, NumPy arrays can be sliced. As arrays can be multidimensional, you need to specify a slice for each dimension of the array.
- Integer array indexing: In this method, lists are passed for indexing for each dimension. One-to-one mapping of corresponding elements is done to construct a new arbitrary array.
- Boolean array indexing: This method is used when we want to pick elements from the array which satisfy some condition.
Python3
# Python program to demonstrate# indexing in numpyimport numpy as np # An exemplar arrayarr = np.array([[-1, 2, 0, 4], [4, -0.5, 6, 0], [2.6, 0, 7, 8], [3, -7, 4, 2.0]]) # Slicing arraytemp = arr[:2, ::2]print ("Array with first 2 rows and alternate" "columns(0 and 2):\n", temp) # Integer array indexing exampletemp = arr[[0, 1, 2, 3], [3, 2, 1, 0]]print ("\nElements at indices (0, 3), (1, 2), (2, 1)," "(3, 0):\n", temp) # boolean array indexing examplecond = arr > 0 # cond is a boolean arraytemp = arr[cond]print ("\nElements greater than 0:\n", temp) |
Output:
Array with first 2 rows and alternatecolumns(0 and 2):
[[-1. 0.]
[ 4. 6.]]
Elements at indices (0, 3), (1, 2), (2, 1),(3, 0):
[ 4. 6. 0. 3.]
Elements greater than 0:
[ 2. 4. 4. 6. 2.6 7. 8. 3. 4. 2. ]
NumPy Basic Operations
The Plethora of built-in arithmetic functions is provided in Python NumPy.
Operations on a single NumPy array
We can use overloaded arithmetic operators to do element-wise operations on the array to create a new array. In the case of +=, -=, *= operators, the existing array is modified.
Python3
# Python program to demonstrate# basic operations on single arrayimport numpy as np a = np.array([1, 2, 5, 3]) # add 1 to every elementprint ("Adding 1 to every element:", a+1) # subtract 3 from each elementprint ("Subtracting 3 from each element:", a-3) # multiply each element by 10print ("Multiplying each element by 10:", a*10) # square each elementprint ("Squaring each element:", a**2) # modify existing arraya *= 2print ("Doubled each element of original array:", a) # transpose of arraya = np.array([[1, 2, 3], [3, 4, 5], [9, 6, 0]]) print ("\nOriginal array:\n", a)print ("Transpose of array:\n", a.T) |
Output:
Adding 1 to every element: [2 3 6 4]
Subtracting 3 from each element: [-2 -1 2 0]
Multiplying each element by 10: [10 20 50 30]
Squaring each element: [ 1 4 25 9]
Doubled each element of original array: [ 2 4 10 6]
Original array:
[[1 2 3]
[3 4 5]
[9 6 0]]
Transpose of array:
[[1 3 9]
[2 4 6]
[3 5 0]]
NumPy – Unary Operators
Many unary operations are provided as a method of ndarray class. This includes sum, min, max, etc. These functions can also be applied row-wise or column-wise by setting an axis parameter.
Python3
# Python program to demonstrate# unary operators in numpyimport numpy as np arr = np.array([[1, 5, 6], [4, 7, 2], [3, 1, 9]]) # maximum element of arrayprint ("Largest element is:", arr.max())print ("Row-wise maximum elements:", arr.max(axis = 1)) # minimum element of arrayprint ("Column-wise minimum elements:", arr.min(axis = 0)) # sum of array elementsprint ("Sum of all array elements:", arr.sum()) # cumulative sum along each rowprint ("Cumulative sum along each row:\n", arr.cumsum(axis = 1)) |
Output:
Largest element is: 9
Row-wise maximum elements: [6 7 9]
Column-wise minimum elements: [1 1 2]
Sum of all array elements: 38
Cumulative sum along each row:
[[ 1 6 12]
[ 4 11 13]
[ 3 4 13]]
NumPy – Binary Operators
These operations apply to the array elementwise and a new array is created. You can use all basic arithmetic operators like +, -, /, etc. In the case of +=, -=, = operators, the existing array is modified.
Python3
# Python program to demonstrate# binary operators in Numpyimport numpy as np a = np.array([[1, 2], [3, 4]])b = np.array([[4, 3], [2, 1]]) # add arraysprint ("Array sum:\n", a + b) # multiply arrays (elementwise multiplication)print ("Array multiplication:\n", a*b) # matrix multiplicationprint ("Matrix multiplication:\n", a.dot(b)) |
Output:
Array sum:
[[5 5]
[5 5]]
Array multiplication:
[[4 6]
[6 4]]
Matrix multiplication:
[[ 8 5]
[20 13]]
Introduction to NymPy’s ufuncs
NumPy provides familiar mathematical functions such as sin, cos, exp, etc. These functions also operate elementwise on an array, producing an array as output.
Note: All the operations we did above using overloaded operators can be done using ufuncs like np.add, np.subtract, np.multiply, np.divide, np.sum, etc.
Python3
# Python program to demonstrate# universal functions in numpyimport numpy as np # create an array of sine valuesa = np.array([0, np.pi/2, np.pi])print ("Sine values of array elements:", np.sin(a)) # exponential valuesa = np.array([0, 1, 2, 3])print ("Exponent of array elements:", np.exp(a)) # square root of array valuesprint ("Square root of array elements:", np.sqrt(a)) |
Output:
Sine values of array elements: [ 0.00000000e+00 1.00000000e+00 1.22464680e-16]
Exponent of array elements: [ 1. 2.71828183 7.3890561 20.08553692]
Square root of array elements: [ 0. 1. 1.41421356 1.73205081]
NumPy Sorting Arrays
There is a simple np.sort() method for sorting Python NumPy arrays. Let’s explore it a bit.
Python3
# Python program to demonstrate sorting in numpyimport numpy as np a = np.array([[1, 4, 2], [3, 4, 6], [0, -1, 5]]) # sorted arrayprint ("Array elements in sorted order:\n", np.sort(a, axis = None)) # sort array row-wiseprint ("Row-wise sorted array:\n", np.sort(a, axis = 1)) # specify sort algorithmprint ("Column wise sort by applying merge-sort:\n", np.sort(a, axis = 0, kind = 'mergesort')) # Example to show sorting of structured array# set alias names for dtypesdtypes = [('name', 'S10'), ('grad_year', int), ('cgpa', float)] # Values to be put in arrayvalues = [('Hrithik', 2009, 8.5), ('Ajay', 2008, 8.7), ('Pankaj', 2008, 7.9), ('Aakash', 2009, 9.0)] # Creating arrayarr = np.array(values, dtype = dtypes)print ("\nArray sorted by names:\n", np.sort(arr, order = 'name')) print ("Array sorted by graduation year and then cgpa:\n", np.sort(arr, order = ['grad_year', 'cgpa'])) |
Output:
Array elements in sorted order:
[-1 0 1 2 3 4 4 5 6]
Row-wise sorted array:
[[ 1 2 4]
[ 3 4 6]
[-1 0 5]]
Column wise sort by applying merge-sort:
[[ 0 -1 2]
[ 1 4 5]
[ 3 4 6]]
Array sorted by names:
[('Aakash', 2009, 9.0) ('Ajay', 2008, 8.7) ('Hrithik', 2009, 8.5)
('Pankaj', 2008, 7.9)]
Array sorted by graduation year and then cgpa:
[('Pankaj', 2008, 7.9) ('Ajay', 2008, 8.7) ('Hrithik', 2009, 8.5)
('Aakash', 2009, 9.0)]
FAQs
1. Why NumPy arrays are better than Python lists?
- NumPy is not only better in performance but it also provides us with several functionalities like broadcasting, indexing, slicing.
- NumPy arrays are memory efficient as it stores the homogenous data in contiguous blocks of memory, where lists can store heterogenous data.
- NumPy supports multidimensional arrays which allows easy representation.
2. What are ndarrays in NumPy?
ndarrays or n-dimensional arrays are capable of storing homogenous elements. They have a fixed size which is defined at the time of creation.
3. What is Broadcasting?
Broadcasting allows us to perform operations between arrays of different shapes. NumPy arrays can perform element-wise operations. Example:
arr1 = np.array([1, 2, 3])
arr2 = np.array([[5], [10], [15]])
result = arr1 + arr2 #[[6, 7, 8], [11, 12, 13], [16, 17, 18]]
So, this was a brief yet concise introduction-cum-tutorial of the NumPy library in Python. For a more detailed study, please refer NumPy Reference Guide .
