QR Solve Small System

Problem

Solve the least squares problem A*x = b for a matrix A (n x 2) with linearly independent columns using the QR factorization A = Q*R.

Build Q from the columns of A with Gram-Schmidt, then solve R*x = Q^T*b by back substitution. Return [x0, x1].

Hint

For full column rank A, Q spans the same column space, so the normal equations become R*x = Q^T*b.

case 1

in: [[[1,1],[1,2],[1,3]],[1,2,3]]

expected: [0,1]

case 2

in: [[[1,0],[0,1]],[3,4]]

expected: [3,4]

case 3

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

expected: [1,1]

case 4

in: [[[1,0],[1,1],[1,2]],[1,2,2]]

expected: [1.1666666666666667,0.5]

Starter codePython

def qr_solve(A, b):
    # Your code here
    pass

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