Finite Difference Laplacian Build

Problem

Build the 1D finite difference Laplacian matrix of size n:

diagonal entries are 2, the entries just above and below the diagonal are -1, and all others are 0.

Hint

This matrix discretizes the second derivative on a 1D grid.

case 1

in: [1]

expected: [[2]]

case 2

in: [2]

expected: [[2,-1],[-1,2]]

case 3

in: [3]

expected: [[2,-1,0],[-1,2,-1],[0,-1,2]]

case 4

in: [4]

expected: [[2,-1,0,0],[-1,2,-1,0],[0,-1,2,-1],[0,0,-1,2]]

Starter codePython

def laplacian_1d(n):
    # Your code here
    pass

4 test cases · run your code against them in the editor