A tridiagonal matrix is a matrix that has non-zero elements only at the main diagonal, diagonal below and above it. All other elements are zero. For this reason tridiagonal matrices of dimension smaller than or equal to 3 seem meaningless.
Example 1:
[a11, a22, 0 , 0 , 0 , 0 ]
[a21, a22, a23, 0 , 0 , 0 ]
[0 , a32, a33, a34, 0 , 0 ]
[0 , 0 , a43, a44, a55, 0 ]
[0 , 0 , 0 , a54, a55, a56]
[0 , 0 , 0 , 0 , a65, a66]
Example 2:
[1, 1, 0, 0, 0, 0]
[1, 1, 1, 0, 0, 0]
[0, 1, 1, 1, 0, 0]
[0, 0, 1, 1, 1, 0]
[0, 0, 0, 1, 1, 1]
[0, 0, 0, 0, 1, 1]
Approach
- Take the size of the matrix as input
- Check if greater than 3
- if not, exit
- if yes, proceed further
- Take elements of the matrix as input
- Now put zero everywhere except at main diagonal and diagonals below and above the main diagonal.
Program:
Python3
# if you enter number n it will automatically # be considered as a square matrix of size n by n size_of_a_matrix = int(input("Enter size the matrix that you want : ")) if size_of_a_matrix <= 3: # since size should be greater than 3 print("Please enter the size that is greater than 3") exit() diagonal = [] numbers1 = [[0 for j in range(0, size_of_a_matrix)] for i in range(0, size_of_a_matrix)] # created a loop to enter numbers for a in range(size_of_a_matrix): numbers1 = int(input(f"Enter the numbers for the main diagonal for position[{a}][{a}] : ")) # appending the values to the list diagonal.append(numbers1) diagonalAbove = [] print("*********") # created a loop to enter numbers for k in range(size_of_a_matrix-1): numbers2 = int(input(f"Enter the numbers for diagonal above the main diagonal for position[{k}][{k+1}]: ")) # appending the values to the list diagonalAbove.append(numbers2) diagonalBelow = [] print("*********") # created a loop to enter numbers for z in range(size_of_a_matrix-1): numbers3 = int(input(f"Enter the numbers for diagonal below the main diagonal for position[{z+1}][{z}]: ")) # appending the values to the list diagonalBelow.append(numbers3) print("*********") def tridiagonal(size_of_a_matrix, diagonal, diagonalAbove, diagonalBelow): matrix = [[0 for j in range(size_of_a_matrix)] for i in range(size_of_a_matrix)] for k in range(size_of_a_matrix-1): matrix[k][k] = diagonal[k] matrix[k][k+1] = diagonalAbove[k] matrix[k+1][k] = diagonalBelow[k] matrix[size_of_a_matrix-1][size_of_a_matrix - 1] = diagonal[size_of_a_matrix-1] # so that the values will print row by row for row in matrix: print(row) return "this is the tridiagonal matrix" # printing final values print(tridiagonal(size_of_a_matrix, diagonal, diagonalAbove, diagonalBelow)) |
Output:
output of our program
