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
Python3
# importing numpyimport 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 rowvector1 = np.array(list1) # creating a vector 2# vector as columnvector2 = np.array(list2) # showing horizontal vectorprint("Horizontal Vector")print(vector1) print("----------------") # showing vertical vectorprint("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
Python3
# importing numpyimport 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 vectorvector1 = np.array(list1) # printing vector1print("First Vector : " + str(vector1)) # creating second vectorvector2 = np.array(list2) # printing vector2print("Second Vector : " + str(vector2)) # adding both the vector# a + b = (a1 + b1, a2 + b2, a3 + b3)addition = vector1 + vector2 # printing addition vectorprint("Vector Addition : " + str(addition)) # subtracting both the vector# a - b = (a1 - b1, a2 - b2, a3 - b3)subtraction = vector1 - vector2 # printing addition vectorprint("Vector Subtraction : " + str(subtraction)) # multiplying both the vector# a * b = (a1 * b1, a2 * b2, a3 * b3)multiplication = vector1 * vector2 # printing multiplication vectorprint("Vector Multiplication : " + str(multiplication)) # dividing both the vector# a / b = (a1 / b1, a2 / b2, a3 / b3)division = vector1 / vector2 # printing division vectorprint("Vector Division : " + str(division)) |
Output :
First Vector: [5 6 9] Second Vector: [1 2 3] Vector Addition: [ 6 8 12] Vector Subtraction: [4 4 6] Vector Multiplication: [ 5 12 27] Vector Division: [5 3 3]
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.
Python3
# importing numpyimport 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 vector1print("First Vector : " + str(vector1)) # creating second vectorvector2 = np.array(list2) # printing vector2print("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 productprint("Dot Product : " + str(dot_product)) |
Output:
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.
Python3
# importing numpyimport numpy as np # creating a 1-D list (Horizontal)list1 = [1, 2, 3] # creating first vector vector = np.array(list1) # printing vector1print("Vector : " + str(vector)) # scalar value scalar = 2 # printing scalar valueprint("Scalar : " + str(scalar)) # getting scalar multiplication value# s * v = (s * v1, s * v2, s * v3)scalar_mul = vector * scalar # printing dot productprint("Scalar Multiplication : " + str(scalar_mul)) |
Output
Vector : [1 2 3] Scalar : 2 Scalar Multiplication : [2 4 6]
