def test_main_integrate3d():
cube = [
[
(0, 0, 0),
(0, 0, 5),
(0, 5, 0),
(0, 5, 5),
(5, 0, 0),
(5, 0, 5),
(5, 5, 0),
(5, 5, 5),
],
[2, 6, 7, 3],
[3, 7, 5, 1],
[7, 6, 4, 5],
[1, 5, 4, 0],
[3, 1, 0, 2],
[0, 4, 6, 2],
]
vertices = cube[0]
faces = cube[1:]
hp_params = hyperplane_parameters(faces, vertices)
assert main_integrate3d(1, faces, vertices, hp_params) == -125
assert main_integrate3d(1, faces, vertices, hp_params, max_degree=1) == {
1: -125,
y: Rational(-625, 2),
z: Rational(-625, 2),
x: Rational(-625, 2),
}
def test_main_integrate():
triangle = Polygon((0, 3), (5, 3), (1, 1))
facets = triangle.sides
hp_params = hyperplane_parameters(triangle)
assert main_integrate(x**2 + y**2, facets, hp_params) == Rational(325, 6)
assert main_integrate(x**2 + y**2, facets, hp_params, max_degree=1) == \
{0: 0, 1: 5, y: Rational(35, 3), x: 10}
def test_main_integrate():
triangle = Polygon((0, 3), (5, 3), (1, 1))
facets = triangle.sides
hp_params = hyperplane_parameters(triangle)
assert main_integrate(x**2 + y**2, facets, hp_params) == S(325)/6
assert main_integrate(x**2 + y**2, facets, hp_params, max_degree=1) == \
{0: 0, 1: 5, y: S(35)/3, x: 10}
def test_main_integrate3d():
cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
(5, 0, 5), (5, 5, 0), (5, 5, 5)],\
[2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
[3, 1, 0, 2], [0, 4, 6, 2]]
vertices = cube[0]
faces = cube[1:]
hp_params = hyperplane_parameters(faces, vertices)
assert main_integrate3d(1, faces, vertices, hp_params) == -125
assert main_integrate3d(1, faces, vertices, hp_params, max_degree=1) == \
{1: -125, y: -S(625)/2, z: -S(625)/2, x: -S(625)/2}
def test_main_integrate3d():
cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
(5, 0, 5), (5, 5, 0), (5, 5, 5)],\
[2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
[3, 1, 0, 2], [0, 4, 6, 2]]
vertices = cube[0]
faces = cube[1:]
hp_params = hyperplane_parameters(faces, vertices)
assert main_integrate3d(1, faces, vertices, hp_params) == -125
assert main_integrate3d(1, faces, vertices, hp_params, max_degree=1) == \
{1: -125, y: -S(625)/2, z: -S(625)/2, x: -S(625)/2}
def test_integration_reduction_dynamic():
triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
facets = triangle.sides
a, b = hyperplane_parameters(triangle)[0]
x0 = facets[0].points[0]
monomial_values = [[0, 0, 0, 0], [1, 0, 0, 5],\
[y, 0, 1, 15], [x, 1, 0, None]]
assert integration_reduction_dynamic(facets, 0, a, b, x, 1, (x, y), 1,\
0, 1, x0, monomial_values, 3) == Rational(25, 2)
assert integration_reduction_dynamic(facets, 0, a, b, 0, 1, (x, y), 1,\
0, 1, x0, monomial_values, 3) == 0
def test_integration_reduction_dynamic():
triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
facets = triangle.sides
a, b = hyperplane_parameters(triangle)[0]
x0 = facets[0].points[0]
monomial_values = [[0, 0, 0, 0], [1, 0, 0, 5],\
[y, 0, 1, 15], [x, 1, 0, None]]
assert integration_reduction_dynamic(facets, 0, a, b, x, 1, (x, y), 1,\
0, 1, x0, monomial_values, 3) == S(25)/2
assert integration_reduction_dynamic(facets, 0, a, b, 0, 1, (x, y), 1,\
0, 1, x0, monomial_values, 3) == 0
def test_integration_reduction():
triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
facets = triangle.sides
a, b = hyperplane_parameters(triangle)[0]
assert integration_reduction(facets, 0, a, b, 1, (x, y), 0) == 5
assert integration_reduction(facets, 0, a, b, 0, (x, y), 0) == 0
def test_integration_reduction():
triangle = Polygon(Point(0, 3), Point(5, 3), Point(1, 1))
facets = triangle.sides
a, b = hyperplane_parameters(triangle)[0]
assert integration_reduction(facets, 0, a, b, 1, (x, y), 0) == 5
assert integration_reduction(facets, 0, a, b, 0, (x, y), 0) == 0
