def test_tan_x():
"""
Example also taken from literature/NewtonRaphson.pdf
"""
assert tan_func(0.5) == approx(-0.04630248)
value = newton_raphson(4.6, 1e-6, root=tan_func)
assert value == approx(4.49341)
def test_basic_sanity():
"""
Pedagogical example from S. Gourley's notes at
University of Surrey.
In this repo see `literature/NewtonRaphson.pdf`
Online:
http://personal.maths.surrey.ac.uk/st/S.Gourley/NewtonRaphson.pdf
Solves x^3 - x - 1, starting at x0=1.0 to 5d.p.
"""
no_kwargs = newton_raphson(1, 1e-6)
assert no_kwargs == 0.0
assert func(0.5) == approx(-1.375)
value = nr_func(1, 1e-6)
assert value == approx(1.324717)
assert newton_raphson(1, 1e-6) == 0.0
assert func(0.5) == approx(-1.375)
def test_with_local_function():
"""
Example also taken from literature/NewtonRaphson.pdf
"""
def cos_func(x):
return cos(x) - 2 * x
assert cos_func(0.5) == approx(-0.12241743)
value = newton_raphson(0.5, 1e-6, root=cos_func)
assert value == approx(0.4501836)
assert cos_func(0.5) == approx(-0.12241743)
from numpy import cos
from pytest import approx
from fastats.optimise.newton_raphson import newton_raphson
def func(x):
return x**3 - x - 1
def less_or_equal(x, compared_to, rel=1e-6):
return ((x < compared_to) or ((x - compared_to) == approx(0.0, rel=rel))
or (x == approx(x, rel=rel)))
nr_func = newton_raphson(1, 1e-6, root=func, return_callable=True)
@given(floats(min_value=0.01, max_value=3.5))
def test_minimal(x):
"""
Tests that the value output from the solver
is less than or equal to the value of the
objective.
"""
eps = 1e-12
value = nr_func(x, eps)
assume(func(x) > 0.0)
assert less_or_equal(value, compared_to=func(x))
def test_non_converging():
"""
Example also taken from literature/NewtonRaphson.pdf
"""
with raises(ZeroDivisionError): # Runtime Warning in Python
_ = newton_raphson(5.0, 1e-6, root=tan_func)
from hypothesis import given
from hypothesis.strategies import floats
from numpy import cos, tan
from pytest import approx, raises
from fastats.optimise.newton_raphson import (newton_raphson, root)
def func(x):
return x**3 - x - 1
nr_func = newton_raphson(1, 1e-6, root=func, return_callable=True)
def test_basic_sanity():
"""
Pedagogical example from S. Gourley's notes at
University of Surrey.
In this repo see `literature/NewtonRaphson.pdf`
Online:
http://personal.maths.surrey.ac.uk/st/S.Gourley/NewtonRaphson.pdf
Solves x^3 - x - 1, starting at x0=1.0 to 5d.p.
"""
no_kwargs = newton_raphson(1, 1e-6)
assert no_kwargs == 0.0
assert func(0.5) == approx(-1.375)
value = nr_func(1, 1e-6)
assert value == approx(1.324717)