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#!/usr/bin/env python3
"""Contains routines to test the solvers module"""
import numpy as np
from numpy.typing import NDArray
import solvers
def test_elimination_3() -> None:
"""Tests elimination with 3 variables."""
aa = np.array([[2.0, 4.0, 4.0], [5.0, 4.0, 2.0], [1.0, 2.0, -1.0]], dtype=np.float_)
bb = np.array([1.0, 4.0, 2.0], dtype=np.float_)
xx_expected = np.array([0.666666666666667, 0.416666666666667, -0.5], dtype=np.float_)
xx_gauss = solvers.gaussian_eliminate(aa, bb)
assert np.allclose(xx_expected, xx_gauss)
def test_pivot_3() -> None:
"""Tests a solution with 3 variables, where pivot is necessary."""
aa = np.array([[2.0, 4.0, 4.0], [1.0, 2.0, -1.0], [5.0, 4.0, 2.0]])
bb = np.array([1.0, 2.0, 4.0])
xx_expected = np.array([0.666666666666667, 0.416666666666667, -0.5])
xx_gauss = solvers.gaussian_eliminate(aa, bb)
assert np.allclose(xx_expected, xx_gauss)
def test_lindep_3() -> None:
"""Tests a linearly dependent system wit three variables."""
aa = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]])
bb = np.array([1.0, 2.0, 3.0])
xx_expected = None
xx_gauss = solvers.gaussian_eliminate(aa, bb)
assert xx_expected == xx_gauss
def test_lu_factorization() -> None:
aa = np.array([[2.0, 4.0, 4.0], [1.0, 2.0, -1.0], [5.0, 4.0, 2.0]])
ll, uu, pp = solvers.lu_factorization(aa)
assert np.allclose(aa, pp.T @ ll @ uu)
def test_forward_substitution() -> None:
ll = np.array([[2.0, 0.0, 0.0], [-1.0, 2.0, 0.0], [4.0, 4.0, 2.0]])
bb = np.array([3.0, 2.0, 1.0])
xx_result = solvers.forward_substitution(ll, bb)
xx_expected = np.array([3 / 2, 7.0 / 4.0, -6])
print(xx_result)
assert np.allclose(xx_expected, xx_result)
def test_back_substitution() -> None:
uu = np.array([[2.0, 4.0, 4.0], [0.0, 2.0, -1.0], [0.0, 0.0, 2.0]])
bb = np.array([1.0, 2.0, 3.0])
xx_result = solvers.back_substitution(uu, bb)
xx_expected = np.array([-6, 7.0 / 4.0, 3.0 / 2.0])
print(xx_result)
assert np.allclose(xx_expected, xx_result)
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