NumPyis 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.
Vectorare 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 numpyimportnumpyasnp# 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 numpyimportnumpyasnp# 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 numpyimportnumpyasnp# 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))# 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 numpyimportnumpyasnp# creating a 1-D list (Horizontal)list1=[1,2,3]# creating first vectorvector=np.array(list1)# printing vector1print("Vector : "+str(vector))# scalar valuescalar=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 : 2Scalar Multiplication : [2 4 6]