Numpy Matrix Multiplication

In this post, you will learn about the Numpy Matrix Multiplication.

NumPy is the fundamental package for scientific computing with Python. It is a highly optimised library for numerical operations. The support of NumPy makes the task easier. Several libraries, like OpenCV, SciPy, and Matplotlib, when combined with NumPy, increase the number of weapons in your arsenal.

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. Matrices are utilised substantially more in everyday life than individuals would have suspected. A square matrix can represent a linear transformation of a geometric object. A real-life example is Adobe Photoshop. It uses a matrix to process linear transformations to render images. In robotics and automation, matrices are the fundamental building blocks for robot development. The contributions for controlling robots are acquired based on the calculations from matrices.

NumPy matrix multiplication methods

These are the three different ways to perform NumPy matrix multiplication.

• Using numpy.dot() function
• Using numpy.matmul() function
• Using numpy.multiply() function

NumPy matrix multiplication using numpy.dot() function

Python provides a powerful numpy.dot() function for matrix computation. Here is the syntax of the numpy.dot() method.

numpy.dot(x, y, out=None)

Here, x and y are two input arrays. Both arrays should be 1-D or 2-D. The out is the output argument for 1-D array scalar to be returned. It returns a dot product of two arrays, x and y. If both the arrays 'x' and 'y' are 1-D arrays, the dot() function performs the inner product of vectors and returns a scalar. If both the arrays 'x' and 'y' are 2-D arrays, the dot() function performs the matrix multiplication. If 'x' is an N-dimensional array and 'y' is a 1-dimensional array, then the dot() function performs the sum-product over the last axis of x and y. For N-dimensional arrays, it is a sum product over the last axis of x and the second-last axis of y.

Here, we have the dot product of two matrices. It is equivalent to matrix multiplication.

import numpy as np

# take a 3x3 matrix 
X = [[4, 1, 6], 
    [7, 8, 2], 
    [5, 2, 8]] 
  
# take a 3x4 matrix 
Y = [[1, 4, 2, 7], 
    [7, 5, 9, 2], 
    [2, 8, 1, 1]] 
  
# result will be 3x4 
  
result= [[0,0,0,0], 
        [0,0,0,0], 
        [0,0,0,0]] 
  
result = np.dot(X,Y) 
  
for r in result: 
    print(r) 

[23 69 23 36]
[67 84 88 67]
[35 94 36 47]

NumPy matrix multiplication using numpy.matmul() function

The numpy.matmul() function returns the matrix product of two arrays.

numpy.matmul(x, y, out=None)

Here, x and y are two input arrays.

import numpy as np

# take two 3x3 matrix 
M1 = [[7, 3, 2],
      [5, 4, 3],
      [4, 8, 9]]
      
M2 = [[1, 2, 8],
      [4, 2, 7],
      [6, 5, 3]]
 
print(np.matmul(M1,M2))

[[ 31  30  83]
 [ 39  33  77]
 [ 90  69 115]]

NumPy matrix multiplication using np.multiply() function

The numpy multiply function np.multiply() calculates the product between the two numpy arrays.

numpy.multiply(m1, m2)

Here, m1 and m2 are two input arrays. This function returns the product between m1 and m2. The multiply() function can be a scalar of nd-array. It depends on m1 and m2. Suppose m1, and m2 are scalar, then numpy.multiply() will return a scalar value. Else it will return an nd-array.

import numpy as np

m1 = [[7, 3, 2],
      [5, 4, 3],
      [4, 8, 9]]
      
m2 = [[3, 2, 8],
      [4, 2, 7],
      [6, 5, 3]]
 
print(np.multiply(m1,m2))

[[21  6 16]
 [20  8 21]
 [24 40 27]]

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