Tridiagonal matrix in python

Tridiagonal matrix in python

A tridiagonal matrix is a matrix in which non-zero entries are located on the main diagonal, one diagonal below the main diagonal, and one diagonal above the main diagonal. All other entries are zero.

Here's a visual representation of a tridiagonal matrix:

| a b 0 0 0 | | c a b 0 0 | | 0 c a b 0 | | 0 0 c a b | | 0 0 0 c a |

To create a tridiagonal matrix in Python, you can use the numpy library and its diag function:

import numpy as np # Define the size of the matrix n = 5 # Define the diagonals a = [1]*n # main diagonal b = [2]*(n-1) # diagonal above main diagonal c = [3]*(n-1) # diagonal below main diagonal # Create the tridiagonal matrix matrix = np.diag(a) + np.diag(b, 1) + np.diag(c, -1) print(matrix)

Output:

[[1 2 0 0 0] [3 1 2 0 0] [0 3 1 2 0] [0 0 3 1 2] [0 0 0 3 1]]

You can adjust the values of a, b, and c arrays to customize the values on the diagonals.

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