Taylor remainder test

This is a Python module that implements the Taylor remainder test. Based on Taylor's remainder theorem, it allows to check the accuracy of custom gradients and Jacobians.

Usage example

from math import cos, sin
import numpy as np
from taylor_remainder import taylor_remainder_test, taylor_remainder_test_jacobian


def fun1(x):
    return x[0] ** 2 - x[1] ** 3


def grad1(x):
    return np.array([2 * x[0], -3 * x[1] ** 2])

x = np.array([1., 2.])
taylor_remainder_test(fun1, grad1, x)
# True

def fun2(x):
    return x[0] ** 2 + x[1] ** 4


def grad2(x):
    return np.array([2 * x[0] ** 2, 4.001 * x[1] ** 3])

x = np.zeros(2)
taylor_remainder_test(fun2, grad2, x, sigma=0.1, eps=1e-10)
# False

def fun3(x):
    return np.array([x[0] ** 2 - x[1], cos(x[1])])


def jac(x):
    return np.array([[2 * x[0], -1.], [0., -sin(x[1])]])


x = np.zeros(2)
taylor_remainder_test_jacobian(fun=fun3, jac=jac, x=x, sigma=1.)
# True

FabianKP/taylor_remainder_test

Taylor remainder test

Usage example