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test_knot_theory.py
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test_knot_theory.py
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__doc__ = """ Knot Theory class testing """
import pytest
import numpy as np
from numpy.testing import assert_allclose
from elastica.utils import MaxDimension
from mock_rod import MockTestRod
from elastica.rod.rod_base import RodBase
from elastica.rod.knot_theory import (
KnotTheoryCompatibleProtocol,
compute_twist,
compute_writhe,
compute_link,
_compute_additional_segment,
)
@pytest.fixture
def knot_theory():
from elastica.rod import knot_theory
return knot_theory
def test_knot_theory_protocol():
# To clear the protocol test coverage
with pytest.raises(TypeError) as e_info:
protocol = KnotTheoryCompatibleProtocol()
assert "cannot be instantiated" in e_info
def test_knot_theory_mixin_methods(knot_theory):
class TestRodWithKnotTheory(MockTestRod, knot_theory.KnotTheory):
def __init__(self):
super().__init__()
self.radius = np.random.randn(MaxDimension.value(), self.n_elems)
rod = TestRodWithKnotTheory()
assert hasattr(
rod, "MIXIN_PROTOCOL"
), "Expected to mix-in variables: MIXIN_PROTOCOL"
assert hasattr(
rod, "compute_writhe"
), "Expected to mix-in functionals into the rod class: compute_writhe"
assert hasattr(
rod, "compute_twist"
), "Expected to mix-in functionals into the rod class: compute_twist"
assert hasattr(
rod, "compute_link"
), "Expected to mix-in functionals into the rod class: compute_link"
def test_knot_theory_mixin_methods_with_no_radius(knot_theory):
class TestRodWithKnotTheoryWithoutRadius(MockTestRod, knot_theory.KnotTheory):
def __init__(self):
super().__init__()
rod = TestRodWithKnotTheoryWithoutRadius()
with pytest.raises(AttributeError) as e_info:
rod.compute_writhe()
with pytest.raises(AttributeError) as e_info:
rod.compute_link()
@pytest.mark.parametrize(
"position_collection, director_collection, radius, segment_length, sol_total_twist, sol_total_writhe, sol_total_link",
# fmt: off
[
(
np.array([[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0], [1, 1, 0]], # position_collection
dtype=np.float64).T,
np.array([[1, 0, 0], [0, 1, 1], [1, 1, 0], [0,1,0]], # director_collection
dtype=np.float64).T[None,...],
np.array([1, 2, 4, 2], dtype=np.float64), # radius
np.array([10.0]), # segment_length
0.75, # solution total twist
-0.477268070084, # solution total writhe
-0.703465518706
),
],
# solution total link
# fmt: on
)
def test_knot_theory_mixin_methods_arithmetic(
knot_theory,
position_collection,
director_collection,
radius,
segment_length,
sol_total_twist,
sol_total_writhe,
sol_total_link,
):
class TestRod(RodBase, knot_theory.KnotTheory):
def __init__(
self, position_collection, director_collection, radius, segment_length
):
self.position_collection = position_collection
self.director_collection = director_collection
self.radius = radius
self.rest_lengths = segment_length
test_rod = TestRod(position_collection, director_collection, radius, segment_length)
twist = test_rod.compute_twist()
writhe = test_rod.compute_writhe()
link = test_rod.compute_link()
assert np.isclose(twist, sol_total_twist)
assert np.isclose(writhe, sol_total_writhe)
assert np.isclose(link, sol_total_link)
def test_compute_twist_arithmetic():
# fmt: off
center_line = np.array(
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0], [1, 1, 0]],
dtype=np.float64).T[None, ...]
normal_collection = np.array(
[[1, 0, 0], [0, 1, 1], [1, 1, 0], [0,1,0]],
dtype=np.float64).T[None, ...]
# fmt: on
a, b = compute_twist(center_line, normal_collection)
assert np.isclose(a[0], 0.75)
assert_allclose(b[0], np.array([0.25, 0.125, 0.375]))
@pytest.mark.parametrize(
"type_str, sol",
[
("next_tangent", -0.477268070084),
("end_to_end", -0.37304522216388),
("net_tangent", -0.26423311709925),
],
)
def test_compute_writhe_arithmetic(type_str, sol):
# fmt: off
center_line = np.array(
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0], [1, 1, 0]],
dtype=np.float64).T[None, ...]
segment_length = 10.0
# fmt: on
a = compute_writhe(center_line, segment_length, type_str)
assert np.isclose(a[0], sol)
@pytest.mark.parametrize(
"type_str, sol",
[
("next_tangent", -0.703465518706),
("end_to_end", -0.4950786438825),
("net_tangent", -0.321184858244),
],
)
def test_compute_link_arithmetic(type_str, sol):
# fmt: off
center_line = np.array(
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0], [1, 1, 0]],
dtype=np.float64).T[None, ...]
normal_collection = np.array(
[[1, 0, 0], [0, 1, 1], [1, 1, 0], [0,1,0]], dtype=np.float64
).T[None, ...]
radius = np.array([1, 2, 4, 2], dtype=np.float64)[None,...]
segment_length = 10.0
# fmt: on
a = compute_link(center_line, normal_collection, radius, segment_length, type_str)
assert np.isclose(a[0], sol)
@pytest.mark.parametrize("type_str", ["randomstr1", "nextnext_tangent", " "])
def test_knot_theory_compute_additional_segment_integrity(type_str):
center_line = np.zeros([1, 3, 10])
center_line[:, 2, :] = np.arange(10)
with pytest.raises(NotImplementedError) as e_info:
_compute_additional_segment(center_line, 10.0, type_str)
@pytest.mark.parametrize("n_elem", [2, 3, 8])
@pytest.mark.parametrize("segment_length", [1.0, 10.0, 100.0])
@pytest.mark.parametrize("type_str", ["next_tangent", "end_to_end", "net_tangent"])
def test_knot_theory_compute_additional_segment_straight_case(
n_elem, segment_length, type_str
):
# If straight rod give, result should be same regardless of type
center_line = np.zeros([1, 3, n_elem])
center_line[0, 2, :] = np.linspace(0, 5, n_elem)
ncl, bd, ed = _compute_additional_segment(center_line, segment_length, type_str)
assert_allclose(ncl[0, :, 0], np.array([0, 0, -segment_length]))
assert_allclose(
ncl[0, :, -1], np.array([0, 0, center_line[0, 2, -1] + segment_length])
)
assert_allclose(bd[0], np.array([0, 0, -1]))
assert_allclose(ed[0], np.array([0, 0, 1]))
def test_knot_theory_compute_additional_segment_next_tangent_case():
center_line = np.array(
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0]], dtype=np.float64
).T[None, ...]
segment_length = 10
ncl, bd, ed = _compute_additional_segment(
center_line, segment_length, "next_tangent"
)
# fmt: off
assert_allclose(ncl[0],
np.array([[ 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 1., 1., 1.],
[-10., 0., 1., 1., 0., -10.]]))
assert_allclose(bd[0], np.array([ 0., 0., -1.]))
assert_allclose(ed[0], np.array([ 0., 0., -1.]))
# fmt: on
def test_knot_theory_compute_additional_segment_end_to_end_case():
center_line = np.array(
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0]], dtype=np.float64
).T[None, ...]
segment_length = 10
ncl, bd, ed = _compute_additional_segment(center_line, segment_length, "end_to_end")
# fmt: off
assert_allclose(ncl[0],
np.array([[ 0., 0., 0., 0., 0., 0.],
[-10., 0., 0., 1., 1., 11.],
[ 0., 0., 1., 1., 0., 0.]]))
assert_allclose(bd[0], np.array([ 0., -1., 0.]))
assert_allclose(ed[0], np.array([-0., 1., -0.]))
# fmt: on
def test_knot_theory_compute_additional_segment_net_tangent_case():
center_line = np.array(
[[0, 0, 0], [0, 0, 1], [0, 1, 1], [0, 1, 0]], dtype=np.float64
).T[None, ...]
segment_length = 10
ncl, bd, ed = _compute_additional_segment(
center_line, segment_length, "net_tangent"
)
# fmt: off
assert_allclose(ncl[0],
np.array([[ 0. , 0. , 0. , 0. , 0. , 0. ],
[-9.701425 , 0. , 0. , 1. , 1. , 10.701425 ],
[ 2.42535625, 0. , 1. , 1. , 0. , -2.42535625]]))
assert_allclose(bd[0], np.array([ 0. , -0.9701425 , 0.24253563]))
assert_allclose(ed[0], np.array([-0. , 0.9701425 , -0.24253563]))
# fmt: on
@pytest.mark.parametrize("timesteps", [1, 5, 10])
@pytest.mark.parametrize("n_elem", [1, 3, 8])
@pytest.mark.parametrize("segment_length", [1.0, 10.0, 100.0])
def test_knot_theory_compute_additional_segment_none_case(
timesteps, n_elem, segment_length
):
center_line = np.random.random([timesteps, 3, n_elem])
new_center_line, beginning_direction, end_direction = _compute_additional_segment(
center_line, segment_length, None
)
assert_allclose(new_center_line, center_line)
assert_allclose(beginning_direction, 0.0)
assert_allclose(end_direction, 0.0)
assert_allclose(new_center_line.shape, [timesteps, 3, n_elem])
assert_allclose(beginning_direction.shape[0], timesteps)
assert_allclose(end_direction.shape[0], timesteps)