Program to Check Diagonally Dominant Matrix

Python Program to Check Diagonally Dominant Matrix

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In the previous article, we have discussed Python Program to Check if a Pair with Given Product Exists in a Matrix

Given a square matrix and the task is to check whether the given matrix is a diagonally dominant matrix or not.

What is a matrix:

A matrix is a rectangular sequence of numbers divided into columns and rows. A matrix element or entry is a number that appears in a matrix.

Example:

Above is the matrix which contains 5 rows and 4 columns and having elements from 1 to 20.

In this order, the dimensions of a matrix indicate the number of rows and columns.

Here as there are 5 rows and 4 columns it is called a 5*4 matrix.

Diagonally Dominant Matrix :

A square matrix is said to be diagonally dominating in mathematics if the magnitude of the diagonal entry in a row is greater than or equal to the sum of the magnitudes of all the other (non-diagonal) values in that row for each row of the matrix.

Examples:

Example1:

Input:

Given Matrix : 
5 1 3
2 7 1
4 0 9

Output:

Yes, the given matrix is a diagonally dominant matrix

Example2:

Input:

Given Matrix : 
 1 3 5
 2 4 6
 7 8 9

Output:

No, the given matrix is not a diagonally dominant matrix

Program to Check Diagonally Dominant Matrix in Python

Below are the ways to check whether the given matrix is a diagonally dominant matrix or not in python:

Method #1: Using For Loop (Static Input)

Approach:

  • Give the matrix as static input and store it in a variable.
  • Calculate the number of rows of the given matrix by calculating the length of the nested list using the len() function and store it in a variable mtrxrows.
  • Calculate the number of columns of the given matrix by calculating the length of the first list in the nested list using the len() function and store it in a variable mtrxcolums.
  • Create a function to say checkdiagnolydominant_matx() which takes the given matrix and the number of rows of the given matrix as the arguments and returns true or false.
  • Inside the function, Loop till the given number of rows using the For loop.
  • Take a variable to say rslt_summ and initialize its value to 0.
  • Inside the For loop, Iterate till the given number of rows using another Nested For loop(Inner For loop).
  • Add the absolute of mtrx[n][m] to the above-initialized rslt_summ and store it in the same variable.
  • Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the rslt_summ and store it in the same variable.
  • Check if the abs(mtrx[n][n]) (diagonal element) is less than the rslt_summ(Which is the sum of non diagonal elements) using the if conditional statement.
  • If it is true, then return False.
  • Return True.
  • Pass the given matrix and the number of rows of the given matrix as the arguments to the checkdiagnolydominant_matx() function and check if returns true or false using the if conditional statement.
  • If it is true, print “Yes, the given matrix is a diagonally dominant matrix”.
  • Else print “No, the given matrix is not a diagonally dominant matrix”.
  • The Exit of the Program.

Below is the implementation:

# Create a function to say checkdiagnolydominant_matx() which takes the given matrix
# and the number of rows of the given matrix as the arguments and returns true or false


def checkdiagnolydominant_matx(mtrx, mtrxrows):
    # Inside the function, Loop till the given number of rows using the For loop.
    for n in range(0, mtrxrows):
       # Take a variable to say rslt_summ and initialize its value to 0.
        rslt_summ = 0
        # Inside the For loop, Iterate till the given number of rows using another
        # Nested For loop(Inner For loop).

        for m in range(0, mtrxrows):
          # Add the absolute of mtrx[n][m] to the above-initialized rslt_summ and store
          # it in  the same variable.

            rslt_summ = rslt_summ + abs(mtrx[n][m])
       # Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the rslt_summ and
       # store it in the same variable.
        rslt_summ = rslt_summ - abs(mtrx[n][n])
        # Check if the abs(mtrx[n][n]) (diagonal element) is less than the rslt_summ
        # (Which is the #sum of non diagonal elements) using the if conditional statement.
        if (abs(mtrx[n][n]) < rslt_summ):
          # If it is true, then return False.
            return False
    # Return True.
    return True


# Give the matrix as static input and store it in a variable.
mtrx = [[5, 1, 3], [2, 7, 1], [4, 0, 9]]
# Calculate the number of rows of the given matrix by
# calculating the length of the nested list using the len() function
# and store it in a variable mtrxrows.
mtrxrows = len(mtrx)
# Calculate the number of columns of the given matrix by
# calculating the length of the first list in the nested list
# using the len() function and store it in a variable mtrxcols.
mtrxcols = len(mtrx[0])
# Pass the given matrix and the number of rows of the given matrix as the arguments
# to the checkdiagnolydominant_matx() function and check if returns true or false
# using the if conditional statement.
if((checkdiagnolydominant_matx(mtrx, mtrxrows))):
  # If it is true, print "Yes, the given matrix is a diagonally dominant matrix".
    print("Yes, the given matrix is a diagonally dominant matrix")
else:
  # Else print "No, the given matrix is not a diagonally dominant matrix".
    print("No, the given matrix is not a diagonally dominant matrix")

Output:

Yes, the given matrix is a diagonally dominant matrix

Method #2: Using For loop (User Input)

Approach:

  • Give the number of rows of the matrix as user input using the int(input()) function and store it in a variable.
  • Give the number of columns of the matrix as user input using the int(input()) function and store it in another variable.
  • Take a list and initialize it with an empty value using [] or list() to say gvnmatrix.
  • Loop till the given number of rows using the For loop
  • Inside the For loop, Give all the row elements of the given Matrix as a list using the list(),map(),int(),split() functions and store it in a variable.
  • Add the above row elements list to gvnmatrix using the append() function.
  • Create a function to say checkdiagnolydominant_matx() which takes the given matrix and the number of rows of the given matrix as the arguments and returns true or false.
  • Inside the function, Loop till the given number of rows using the For loop.
  • Take a variable to say rslt_summ and initialize its value to 0.
  • Inside the For loop, Iterate till the given number of rows using another Nested For loop(Inner For loop).
  • Add the absolute of mtrx[n][m] to the above-initialized rslt_summ and store it in the same variable.
  • Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the rslt_summ and store it in the same variable.
  • Check if the abs(mtrx[n][n]) (diagonal element) is less than the rslt_summ(Which is the sum of non diagonal elements) using the if conditional statement.
  • If it is true, then return False.
  • Return True.
  • Pass the given matrix and the number of rows of the given matrix as the arguments to the checkdiagnolydominant_matx() function and check if returns true or false using the if conditional statement.
  • If it is true, print “Yes, the given matrix is a diagonally dominant matrix”.
  • Else print “No, the given matrix is not a diagonally dominant matrix”.
  • The Exit of the Program.

Below is the implementation:

# Create a function to say checkdiagnolydominant_matx() which takes the given matrix
# and the number of rows of the given matrix as the arguments and returns true or false


def checkdiagnolydominant_matx(mtrx, mtrxrows):
    # Inside the function, Loop till the given number of rows using the For loop.
    for n in range(0, mtrxrows):
       # Take a variable to say rslt_summ and initialize its value to 0.
        rslt_summ = 0
        # Inside the For loop, Iterate till the given number of rows using another
        # Nested For loop(Inner For loop).

        for m in range(0, mtrxrows):
          # Add the absolute of mtrx[n][m] to the above-initialized rslt_summ and store
          # it in  the same variable.

            rslt_summ = rslt_summ + abs(mtrx[n][m])
       # Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the rslt_summ and
       # store it in the same variable.
        rslt_summ = rslt_summ - abs(mtrx[n][n])
        # Check if the abs(mtrx[n][n]) (diagonal element) is less than the rslt_summ
        # (Which is the #sum of non diagonal elements) using the if conditional statement.
        if (abs(mtrx[n][n]) < rslt_summ):
          # If it is true, then return False.
            return False
    # Return True.
    return True


# Give the number of rows of the matrix as user input using the int(input()) function
# and store it in a variable.
mtrxrows = int(input('Enter some random number of rows of the matrix = '))
# Give the number of columns of the matrix as user input using the int(input()) function
# and store it in another variable.
mtrxcols = int(input('Enter some random number of columns of the matrix = '))
# Take a list and initialize it with an empty value using [] or list() to say gvnmatrix.
mtrx = []
# Loop till the given number of rows using the For loop
for n in range(mtrxrows):
    # Inside the For loop, Give all the row elements of the given Matrix as a list using
    # the list(),map(),int(),split() functions and store it in a variable.
    l = list(map(int, input(
        'Enter {'+str(mtrxcols)+'} elements of row {'+str(n+1)+'} separated by spaces = ').split()))
    # Add the above row elements list to gvnmatrix using the append() function.
    mtrx.append(l)
if((checkdiagnolydominant_matx(mtrx, mtrxrows))):
  # If it is true, print "Yes, the given matrix is a diagonally dominant matrix".
    print("Yes, the given matrix is a diagonally dominant matrix")
else:
  # Else print "No, the given matrix is not a diagonally dominant matrix".
    print("No, the given matrix is not a diagonally dominant matrix")

Output:

Enter some random number of rows of the matrix = 3
Enter some random number of columns of the matrix = 3
Enter {3} elements of row {1} separated by spaces = 1 3 5
Enter {3} elements of row {2} separated by spaces = 2 4 6
Enter {3} elements of row {3} separated by spaces = 7 8 9
No, the given matrix is not a diagonally dominant matrix

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