NumPy - dot() function

The NumPy dot() function is used to perform dot product of two arrays. Specifically,

• If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation).
• If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred.
• If either a or b is 0-D (scalar), it is equivalent to multiply and using numpy.multiply(a, b) or a * b is preferred.
• If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.
• If a is an N-D array and b is an M-D array (where M>=2), 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

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

Parameters

Return Value

Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.

Exception

Raises ValueError exception, if the last dimension of a is not the same size as the second-to-last dimension of b.

Example: dot() function with scalars

The example below shows the result when two scalars are used with dot() function.

import numpy as np
print(np.dot(5, 10))

The output of the above code will be:

50

Example: dot() function with 1-D arrays

When two 1-D arrays are used, the function returns inner product of the arrays.

import numpy as np
Arr1 = [5, 8]
Arr2 = [10, 20]

#returns 5*10 + 8*20 = 210
print(np.dot(Arr1, Arr2))

The output of the above code will be:

210

Example: dot() function with complex numbers

The dot() function can be used with complex numbers. Consider the following example.

import numpy as np
Arr1 = np.array([1+2j, 1+3j])
Arr2 = np.array([2+2j, 2+3j])

Arr3 = np.dot(Arr1, Arr2)

print(Arr3)

The output of the above code will be:

(-9+15j)

The dot product is calculated as:

= (1+2j)*(2+2j) + (1+3j)*(2+3j)
= (-2+6j) + (-7+9j)
= (-9+15j)

Example: dot() function with matrix

When two matrix are used, the function returns matrix multiplication.

import numpy as np
Arr1 = np.array([[1, 2], 
                 [3, 4]])
Arr2 = np.array([[10, 20], 
                 [30, 40]])
Arr3 = np.dot(Arr1, Arr2)

print(Arr3)

The output of the above code will be:

[[ 70 100]
 [150 220]]

The dot product is calculated as:

[[1*10+2*30 1*20+2*40]
 [3*10+4*30 3*20+4*40]]

= [[ 70 100]
   [150 220]]