Question

Matrix multiplication with arrays

In this question you will verify that the numpy.ndarray matrix multiplication operator, @, does a proper matrix multiplcation. To do this, first write a function, mat_mult(a1, a2) that creates a new 2d array of zeros, and using nested for loops, fill in the elements of the matrix multiplication, and return this new array.

Then, write a second function, matrix_diff(b, c) that takes two arrays as arguments then generates and returns the following ratio:

sqrt((∑(??,?−??,?)^2)/(∑(??,?+??,?)^2))

This function gives a measure of how different two arrays are, giving 0 if the arrays are identical.

Your functions can assume that both matrix arguments are two-dimensional, but they should check that the shapes are compatible and return None if they are not.

Answer 1

Dear Learner,

Here is the solution to your code,

CODE:

import numpy as np

def mat_mult(matrix1,matrix2):
   result = [[0 for x in range(len(matrix1))] for y in range(len(matrix2[0]))] #initializing the result array
   for i in range(0,len(matrix1)):
       for j in range(0,len(matrix2[0])):
           for k in range(0,len(matrix2)):
               result[i][j] += matrix1[i][k] * matrix2[k][j]
   for r in result:
       print(r)

def matrix_diff(matrix1,matrix2):
   result=0
   numrows1 = len(matrix1) # number of rows in matrix 1
   numcols1 = len(matrix1[0]) # number of columns in matrix 1
   numrows2 = len(matrix2) # number of rows in matrix 2
   numcols2 = len(matrix2[0]) # number of columns in matrix 2
   if(numrows1 == numrows2) and (numcols1 == numcols2) :
       for i in range (0,numrows1):
           for j in range(0,numcols1):
               result += ((matrix1[i][j] - matrix2[i][j])**2)/((matrix1[i][j] + matrix2[i][j])**2)
   else:
       print("Error")
   print(result)
  

matrix1 = [[1,2],[3,4]]
matrix2 = [[1,2],[3,4]]
mat_mult(matrix1,matrix2) #call to multiply the 2 matrices
a = np.matrix(matrix1)
b = np.matrix(matrix2)
print(a@b) #numpy operator
matrix_diff(matrix1,matrix2) #call to the function to calculate difference

SCREENSHOT:

OUTPUT:

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