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. Numpy is basically used for creating array of n dimensions.
Vector are built from components, which are ordinary numbers. We can think of a vector as a list of numbers, and vector algebra as operations performed on the numbers in the list. In other words vector is the numpy 1-D array.
In order to create a vector we use np.array method.
Syntax : np.array(list)
Argument : It take 1-D list it can be 1 row and n columns or n rows and 1 column
Return : It returns vector which is numpy.ndarray
Note : We can create vector with other method as well which return 1-D numpy array for example np.arange(10), np.zeros((4, 1)) gives 1-D array, but most appropriate way is using np.array with the 1-D list.
Creating a Vector
In this example we will create a horizontal vector and a vertical vector
# importing numpy import numpy as np # creating a 1-D list (Horizontal) list1 = [1, 2, 3] # creating a 1-D list (Vertical) list2 = [[10], [20], [30]] # creating a vector1 # vector as row vector1 = np.array(list1) # creating a vector 2 # vector as column vector2 = np.array(list2) # showing horizontal vector print("Horizontal Vector") print(vector1) print("----------------") # showing vertical vector print("Vertical Vector") print(vector2) |
Output :
Horizontal Vector [1 2 3] ---------------- Vertical Vector [[10] [20] [30]]
Basic Arithmetic operation:
In this example we will see do arithmetic operations which are element-wise between two vectors of equal length to result in a new vector with the same length
# importing numpy import numpy as np # creating a 1-D list (Horizontal) list1 = [5, 6, 9] # creating a 1-D list (Horizontal) list2 = [1, 2, 3] # creating first vector vector1 = np.array(list1) # printing vector1 print("First Vector : " + str(vector1)) # creating secodn vector vector2 = np.array(list2) # printing vector2 print("Second Vector : " + str(vector2)) # adding both the vector # a + b = (a1 + b1, a2 + b2, a3 + b3) addition = vector1 + vector2 # printing addition vector print("Vector Addition : " + str(addition)) # subtracting both the vector # a - b = (a1 - b1, a2 - b2, a3 - b3) subtraction = vector1 - vector2 # printing addition vector print("Vector Substraction : " + str(subtraction)) # multiplying both the vector # a * b = (a1 * b1, a2 * b2, a3 * b3) multiplication = vector1 * vector2 # printing multiplication vector print("Vector Multiplication : " + str(multiplication)) # dividing both the vector # a / b = (a1 / b1, a2 / b2, a3 / b3) division = vector1 / vector2 # printing multiplication vector print("Vector Division : " + str(multiplication)) |
Output :
First Vector : [5 6 9] Second Vector : [1 2 3] Vector Addition : [ 6 8 12] Vector Substraction : [4 4 6] Vector Multiplication : [ 5 12 27] Vector Division : [ 5 12 27]
Vector Dot Product
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number.
For this we will use dot method.
# importing numpy import numpy as np # creating a 1-D list (Horizontal) list1 = [5, 6, 9] # creating a 1-D list (Horizontal) list2 = [1, 2, 3] # creating first vector vector1 = np.array(list1) # printing vector1 print("First Vector : " + str(vector1)) # creating secodn vector vector2 = np.array(list2) # printing vector2 print("Second Vector : " + str(vector2)) # getting dot product of both the vectors # a . b = (a1 * b1 + a2 * b2 + a3 * b3) # a . b = (a1b1 + a2b2 + a3b3) dot_product = vector1.dot(vector2) # printing dot product print("Dot Product : " + str(dot_product)) |
First Vector : [5 6 9] Second Vector : [1 2 3] Dot Product : 44
Vector-Scalar Multiplication
Multiplying a vector by a scalar is called scalar multiplication. To perform scalar multiplication, we need to multiply the scalar by each component of the vector.
# importing numpy import numpy as np # creating a 1-D list (Horizontal) list1 = [1, 2, 3] # creating first vector vector = np.array(list1) # printing vector1 print("Vector : " + str(vector)) # scalar value scalar = 2 # printing scalar value print("Scalar : " + str(scalar)) # getting scalar multiplication value # s * v = (s * v1, s * v2, s * v3) scalar_mul = vector * scalar # printing dot product print("Scalar Multiplication : " + str(scalar_mul)) |
Output
Vector : [1 2 3] Scalar : 2 Scalar Multiplication : [2 4 6]
Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.
To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course.
