 # Python Program for Markov Matrix

In the previous article, we have discussed Python Program for Sum of Middle Row and Column in Matrix

Markov Matrix:

The matrix where the sum of each row equals one.

Given a matrix, the task is to check if the given matrix is a Markov 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.

Examples:

Example1:

Input:

Given Matrix :
0.5 0.5 0
0 0 1
1 0 0



Output:

Yes, the given matrix is a Markov Matrix

Example2:

Input:

Given Matrix :
1 2 0
0 0.5 0.5
1 0 0

Output:

No, the given matrix is not a Markov Matrix

## Program for Markov Matrix in Python

Below are the ways to check if the given matrix is a Markov 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.
• Pass the given matrix as an argument to the chek_Markovmatrix function and check if the function returns true or false using the if conditional statement.
• If it is true then print  “Yes, the given matrix is a Markov Matrix”.
• Else print “No, the given matrix is not a Markov Matrix”.
• Create a function to say chek_Markovmatrix which takes the given matrix as an argument and returns True or false.
• Loop till the given number of rows using the For loop.
• Take a variable to say row_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 mtrx[p][q] to the above row_summ (where p is the iterator value of the parent for loop and q is the iterator value of the inner forloop).
• Store it in the same variable row_summ
• Check if the value of row_summ is not equal to 1 using the if conditional statement.
• If it is true then return false.
• Return True.
• The Exit of the Program.

Below is the implementation:

# Create a function to say chek_Markovmatrix which takes the given matrix as an argument
# and returns True or false.

def chek_Markovmatrix(mtrx):

# Loop till the given number of rows using the For loop.
for p in range(mtrxrows):
# Take a variable to say row_summ and initialize its value to 0.

row_summ = 0
# Inside the For loop, Iterate till the given number of rows using another Nested
# For loop (Inner For loop).
for q in range(mtrxrows):
# Add mtrx[p][q] to the above row_summ (where p is the iterator value of the
# parent for loop and q is the iterator value of the inner forloop).
# Store it in the same variable row_summ
row_summ = row_summ + mtrx[p][q]
# Check if the value of row_summ is not equal to 1 using the if conditional
# statement.
if (row_summ != 1):
# 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 = [[0.5, 0.5, 0], [0, 0, 1], [1, 0, 0]]
# 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)
# Pass the given matrix as an argument to the chek_Markovmatrix function and check if
# the function returns true or false using the if conditional statement.
if (chek_Markovmatrix(mtrx)):
# If it is true then print  "Yes, the given matrix is a Markov Matrix".
print("Yes, the given matrix is a Markov Matrix")
else:
# Else print "No, the given matrix is not a Markov Matrix".
print("No, the given matrix is not a Markov Matrix")


Output:

Yes, the given matrix is a Markov 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(), float(), split() functions and store it in a variable.
• Add the above row elements list to gvnmatrix using the append() function.
• Pass the given matrix as an argument to the chek_Markovmatrix function and check if the function returns true or false using the if conditional statement.
• If it is true then print  “Yes, the given matrix is a Markov Matrix”.
• Else print “No, the given matrix is not a Markov Matrix”.
• Create a function to say chek_Markovmatrix which takes the given matrix as an argument and returns True or false.
• Loop till the given number of rows using the For loop.
• Take a variable to say row_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 mtrx[p][q] to the above row_summ (where p is the iterator value of the parent for loop and q is the iterator value of the inner for loop).
• Store it in the same variable row_summ
• Check if the value of row_summ is not equal to 1 using the if conditional statement.
• If it is true then return false.
• Return True.
• The Exit of the Program.

Below is the implementation:

# Create a function to say chek_Markovmatrix which takes the given matrix as an argument
# and returns True or false.

def chek_Markovmatrix(mtrx):

# Loop till the given number of rows using the For loop.
for p in range(mtrxrows):
# Take a variable to say row_summ and initialize its value to 0.

row_summ = 0
# Inside the For loop, Iterate till the given number of rows using another Nested
# For loop (Inner For loop).
for q in range(mtrxrows):
# Add mtrx[p][q] to the above row_summ (where p is the iterator value of the
# parent for loop and q is the iterator value of the inner forloop).
# Store it in the same variable row_summ
row_summ = row_summ + mtrx[p][q]
# Check if the value of row_summ is not equal to 1 using the if conditional
# statement.
if (row_summ != 1):
# 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(),float(),split() functions and store it in a variable.
l = list(map(float, 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)

# Pass the given matrix as an argument to the chek_Markovmatrix function and check if
# the function returns true or false using the if conditional statement.
if (chek_Markovmatrix(mtrx)):
# If it is true then print  "Yes, the given matrix is a Markov Matrix".
print("Yes, the given matrix is a Markov Matrix")
else:
# Else print "No, the given matrix is not a Markov Matrix".
print("No, the given matrix is not a Markov 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 2 0
Enter {3} elements of row {2} separated by spaces = 0 0.5 0.5
Enter {3} elements of row {3} separated by spaces = 1 0 0
No, the given matrix is not a Markov Matrix

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