NumPy dot() function

In this tutorial, we will cover the dot() function of the Numpy library.

The dot() function is mainly used to calculate the dot product of two vectors.

• This function can handle 2D arrays but it will consider them as matrix and will then perform matrix multiplication.

• In the case, if an array a is an N-D array and array b is an M-D array (where, M >= 2) then it is a sum product over the last axis of a and the second-to-last axis of b:

dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

Syntax of numpy.dot():

The syntax required to use this function is as follows:

numpy.dot(a, b, out=None)

Parameters:

Let us discuss the parameters of this function:

• a
  This is the first parameter. If "a" is complex number then its complex conjugate is used for the calculation of the dot product.

• b
  This is the second parameter. If "b" is complex then its complex conjugate is used for the calculation of the dot product.

• out
  This indicates the output argument. This out must have the exact kind that would be returned if it was not used. Otherwise it must be C-contiguous and its dtype must be the dtype that would be returned for dot(a, b).

Returned Values:

The dot() function will return the dot product of a and b. If both a and b are scalars or if both are 1-D arrays then a scalar value is returned, otherwise an array is returned. If out is given, then it is returned.

Note: The ValueError is raised in the case if the last dimension of a is not the same size as the second-to-last dimension of b.

Example 1:

The code snippet is as follows where we will use dot() function:

import numpy as np

#Let us take scalars first 
a = np.dot(8, 4) 
print("The dot Product of above given scalar values : ")
print(a) 

# Now we will take 1-D arrays 
vect_a = 4 + 3j
vect_b = 8 + 5j

dot_product = np.dot(vect_a, vect_b) 
print("The Dot Product of two 1-D arrays is : ")
print(dot_product) 

The dot Product of above given scalar values :
32
The Dot Product of two 1-D arrays is :
(17+44j)

Explanation of the calculation of dot product of two 1D Arrays:

vect_a = 4+ 3j
vect_b = 8 + 5j

Now calculating the dot product:
= 4(8 + 5j) + 3j(8 – 5j)
= 32+ 20j + 24j – 15
= 17 + 44j

Example 2:

Now let's create two numpy arrays and then find the dot product for them using the dot() function:

import numpy as np

a = np.array([[50,100],[12,13]])  
print("The Matrix a is:")
print (a)

b = np.array([[10,20],[12,21]])  
print("The Matrix b is :")
print(b)

dot = np.dot(a,b)  
print("The dot product of a and b is :")
print(dot)

Summary

In this tutorial, we covered the dot() function of the Numpy library. We covered how it is used with its syntax and values returned by this function along with few code examples.