Quadratic Taylor Linearization Error

Problem

For f(x) = x^T A x, the error of the first-order Taylor approximation at x0 evaluated at x is exactly d^T A d, where d = x - x0 and A must be symmetrized.

Given A as nested rows, x0, and x, return f(x) - f(x0) - grad f(x0) dot d.

Hint

For a quadratic the residual equals d^T A d regardless of the base point.

Test cases

case 1

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

expected: 5

case 2

in: [[[0,1],[0,0]],[1,1],[2,3]]

expected: 2

case 3

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

expected: 2

Starter codePython

def quadratic_taylor_linearization_error(a, x0, x):
    # Your code here
    pass

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