taylor_approximation.py

taylor_approximation.py

import numpy as np
import argparse


def f(x, func_id):
    if func_id == 0:
        return x[0] * x[1] + np.log(x[0])
    elif func_id == 1:
        return np.sin(x[0]) + np.cos(x[1])
    else:
        raise NotImplementedError("err")


def grad(x, func_id):
    if func_id == 0:
        return np.array([x[1] + 1 / x[0], x[1]])
    elif func_id == 1:
        return np.array([np.cos(x[0]), -np.sin(x[1])])
    else:
        raise NotImplementedError("err")


def hessian(x, func_id):
    if func_id == 0:
        return np.array([[-1 / (x[0] ** 2), 1], [1, 0]])
    elif func_id == 1:
        return np.array([[-np.sin(x[0]), 0], [0, -np.cos(x[1])]])
    else:
        raise NotImplementedError("err")


if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument("--func_id", "-f", type=int, default=0)
    args = parser.parse_args()
    func_id = int(args.func_id)

    x1 = np.array([1, 1])
    x2 = np.array([1.2, 1.2])
    print("GT f(x1): ", f(x1, func_id=func_id))
    print("GT f(x2): ", f(x2, func_id=func_id))

    app_0 = f(x1, func_id=func_id)
    app_1 = app_0 + grad(x1, func_id=func_id) @ (x2 - x1)
    app_2 = app_1 + 1 / 2 * (x2 - x1).transpose() @ hessian(x1, func_id=func_id) @ (x2 - x1)
    print("0-approx: ", app_0, ", loss: ", (app_0 - f(x2, func_id=func_id)) ** 2)
    print("1-approx: ", app_1, ", loss: ", (app_1 - f(x2, func_id=func_id)) ** 2)
    print("2-approx: ", app_2, ", loss: ", (app_2 - f(x2, func_id=func_id)) ** 2)