def test_invalid_values(self):
voxel_coords = np.array([[2, 0], [2, 1], [-2, 1]])
with self.assertRaises(ValueError, msg="Calling with negative R didn't error"):
AxisymmetricVoxel(voxel_coords)
voxel_coords = np.array([[2, 0], [3, 1]])
with self.assertRaises(TypeError, msg="Calling with 2 vertices didn't error"):
AxisymmetricVoxel(voxel_coords)
voxel_coords = np.asarray(RECTANGULAR_VOXEL_COORDS[0])
with self.assertRaises(ValueError, msg="Calling with bogus primitive type didn't error"):
AxisymmetricVoxel(voxel_coords, primitive_type="nonexistant")
def test_constant_emissivity(self):
def emiss_function(r, phi, z):
return 5
# Emissivity in the voxel should be the constant value of emiss_function
for polygon in TRIANGLE_VOXEL_COORDS + RECTANGULAR_VOXEL_COORDS + ARBITRARY_VOXEL_COORDS:
coords = np.asarray(polygon)
voxel = AxisymmetricVoxel(coords)
emiss = voxel.emissivity_from_function(emiss_function, 1000)
expected_emiss = emiss_function(0, 0, 0)
self.assertEqual(emiss, expected_emiss)
def test_invalid_types(self):
voxel_coords = {'v1': (2, 0), 'v2': (2, 1), 'v3': (3, 1)}
with self.assertRaises(TypeError, msg="Calling with dict with string keys didn't error"):
AxisymmetricVoxel(voxel_coords)
voxel_coords = {1: (2, 0), 2: (2, 1), 3: (3, 1)}
with self.assertRaises(TypeError, msg="Calling with dict with int keys didn't error"):
AxisymmetricVoxel(voxel_coords)
voxel_coords = [Point3D(2, 0, 0), Point3D(2, 0, 1), Point3D(3, 0, 1)]
with self.assertRaises(TypeError, msg="Calling with list of Point3D didn't error"):
AxisymmetricVoxel(voxel_coords)
voxel_coords = np.asarray([[2, 0, 0], [2, 0, 1], [3, 0, 1]])
with self.assertRaises(TypeError, msg="Calling with Nx3 array didn't error"):
AxisymmetricVoxel(voxel_coords)
def test_numpy_array(self):
voxel_coords = np.asarray(RECTANGULAR_VOXEL_COORDS[0])
voxel = AxisymmetricVoxel(voxel_coords)
for coord, vertex in zip(voxel_coords, voxel.vertices):
self.assertEqual([coord[0], coord[1]], [vertex.x, vertex.y],
"Nx2 array coordinate mismatch")
def test_rectangle_centroid(self):
for rectangle in RECTANGULAR_VOXEL_COORDS:
coords = np.asarray(rectangle)
voxel = AxisymmetricVoxel(coords)
x0, y0 = coords.mean(axis=0)
expected_centroid = Point2D(x0, y0)
self.assertEqual(voxel.cross_section_centroid, expected_centroid)
def voxel_matches_polygon(self, coordinate_list):
for voxel_coords in coordinate_list:
voxel_coords = np.asarray(voxel_coords)
rmax = voxel_coords[:, 0].max()
rmin = voxel_coords[:, 0].min()
zmax = voxel_coords[:, 1].max()
zmin = voxel_coords[:, 1].min()
router = 1.5 * rmax
rinner = 0.5 * rmin
zupper = 1.5 * zmax if zmax > 0 else 0.5 * zmax
zlower = 0.5 * zmin if zmin > 0 else 1.5 * zmin
test_rs = np.linspace(rinner, router, int(100 * (router - rinner)))
test_zs = np.linspace(zlower, zupper, int(100 * (zupper - zlower)))
voxel = AxisymmetricVoxel(voxel_coords, primitive_type='csg')
polygon = Polygon(voxel_coords, closed=True)
test_verts = list(itertools.product(test_rs, test_zs))
try:
inside_poly = polygon.contains_points(test_verts)
except AttributeError:
# Polygon.contains_points was only introduced in Matplotlib 2.2.
# Before that we need to convert to Path
inside_poly = Path(polygon.get_verts()).contains_points(test_verts)
inside_csg = [any(child.contains(Point3D(r, 0, z)) for child in voxel.children)
for (r, z) in test_verts]
self.assertSequenceEqual(inside_csg, inside_poly.tolist())
def test_rectangle_area(self):
for rectangle in RECTANGULAR_VOXEL_COORDS:
coords = np.asarray(rectangle)
voxel = AxisymmetricVoxel(coords)
dx = coords[:, 0].ptp()
dy = coords[:, 1].ptp()
expected_area = dx * dy
self.assertEqual(voxel.cross_sectional_area, expected_area)
def test_polygon_area(self):
for polygon in ARBITRARY_VOXEL_COORDS:
coords = np.asarray(polygon)
voxel = AxisymmetricVoxel(coords)
# Shoelace formula
x = coords[:, 0]
y = coords[:, 1]
expected_area = abs(np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1))) / 2
self.assertEqual(voxel.cross_sectional_area, expected_area)
def test_variable_emissivity_arbitrary(self):
# Use the same seed as Raysect's random tests
seed(1234567890)
quadpy_precalculated_emiss = {
((2, -1), (2, 2), (3, 4), (4, 3), (4, -1)): 3.5833333333333326,
((2, -1), (2, 2), (3, 4), (4, 3), (4, 0)): 4.349999999999999,
((2, -1), (2, 2), (3, 4), (4, 3), (5, 0)): 4.0482456140350855,
}
def emiss_function(r, phi, z):
return r * z
for polygon in ARBITRARY_VOXEL_COORDS:
coords = np.asarray(polygon)
voxel = AxisymmetricVoxel(coords)
nsamples = 10000
emiss = voxel.emissivity_from_function(emiss_function, nsamples)
if HAVE_QUADPY:
# Calculate the expected emissivity
triangle_indices = triangulate2d(coords)
triangles = coords[triangle_indices]
expected_emiss = 0
polygon_area = 0
for triangle in triangles:
# Calculate the area with the shoelace formula
x1, y1 = triangle[0]
x2, y2 = triangle[1]
x3, y3 = triangle[2]
triangle_area = 0.5 * abs(x1 * y2 + x2 * y3 + x3 * y1
- x2 * y1 - x3 * y2 - x1 * y3)
# Total emissivity is the area-weighted emissivity for each triangle
expected_emiss += quadpy.triangle.integrate(
lambda x: emiss_function(x[0], 0, x[1]), triangle, quadpy.triangle.Strang(6)
)
polygon_area += triangle_area
expected_emiss /= polygon_area
else:
# Use pre-calculated values from a machine which had quadpy
expected_emiss = quadpy_precalculated_emiss[tuple(polygon)]
max_relative_error = 0.0225 # Measured with seed(1234567890)
self.assertAlmostEqual(emiss, expected_emiss, delta=emiss * max_relative_error)
def test_triangle_centroid(self):
for triangle in TRIANGLE_VOXEL_COORDS:
coords = np.asarray(triangle)
voxel = AxisymmetricVoxel(coords)
# The centroid for a triangle is simply the mean position
# of the vertices
expected_centroid = Point2D(*coords.mean(axis=0))
if voxel.cross_sectional_area == 0:
self.assertRaises(ZeroDivisionError, getattr, voxel, "cross_section_centroid")
else:
self.assertEqual(voxel.cross_section_centroid, expected_centroid)
def test_variable_emissivity_rectangular(self):
# Use the same seed as Raysect's random tests
seed(1234567890)
def emiss_function(r, phi, z):
return r * z
# We can calculate the integrated emissivity analytically
for polygon in RECTANGULAR_VOXEL_COORDS:
coords = np.asarray(polygon)
voxel = AxisymmetricVoxel(coords)
nsamples = 10000
emiss = voxel.emissivity_from_function(emiss_function, nsamples)
rmax = coords[:, 0].max()
rmin = coords[:, 0].min()
zmax = coords[:, 1].max()
zmin = coords[:, 1].min()
area = (rmax - rmin) * (zmax - zmin)
expected_emiss = (rmax**2 - rmin**2) * (zmax**2 - zmin**2) / 4 / area
max_relative_error = 0.0221 # Measured with seed(1234567890)
self.assertAlmostEqual(emiss, expected_emiss, delta=emiss * max_relative_error)
def test_triangle_area(self):
for triangle in TRIANGLE_VOXEL_COORDS:
coords = np.asarray(triangle)
voxel = AxisymmetricVoxel(coords)
# Calculate the area with the shoelace formula
x1, y1 = coords[0]
x2, y2 = coords[1]
x3, y3 = coords[2]
expected_area = 0.5 * abs(x1 * y2 + x2 * y3 + x3 * y1
- x2 * y1 - x3 * y2 - x1 * y3)
# Different algorithms have some floating point rounding error
self.assertAlmostEqual(voxel.cross_sectional_area, expected_area)
def test_polygon_centroid(self):
for polygon in ARBITRARY_VOXEL_COORDS:
coords = np.asarray(polygon)
voxel = AxisymmetricVoxel(coords)
x = coords[:, 0]
y = coords[:, 1]
signed_area = (np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1))) / 2
xroll = np.roll(x, 1)
yroll = np.roll(y, 1)
cx = np.sum((x + xroll) * (x * yroll - xroll * y)) / (6 * signed_area)
cy = np.sum((y + yroll) * (x * yroll - xroll * y)) / (6 * signed_area)
expected_centroid = Point2D(cx, cy)
self.assertEqual(voxel.cross_section_centroid, expected_centroid)
def voxel_matches_polygon(self, coordinate_list):
for voxel_coords in coordinate_list:
voxel_coords = np.asarray(voxel_coords)
rmax = voxel_coords[:, 0].max()
rmin = voxel_coords[:, 0].min()
zmax = voxel_coords[:, 1].max()
zmin = voxel_coords[:, 1].min()
router = 1.5 * rmax
rinner = 0.5 * rmin
zupper = 1.5 * zmax if zmax > 0 else 0.5 * zmax
zlower = 0.5 * zmin if zmin > 0 else 1.5 * zmin
test_rs = np.linspace(rinner, router, int(50 * (router - rinner)))
test_zs = np.linspace(zlower, zupper, int(50 * (zupper - zlower)))
# Test for 0 area: not supported by mesh representation
x, y = voxel_coords.T
area = 0.5 * np.abs(np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1)))
if area == 0:
continue
voxel = AxisymmetricVoxel(voxel_coords, primitive_type='mesh')
polygon = Polygon(voxel_coords, closed=True).get_path()
test_verts = list(itertools.product(test_rs, test_zs))
inside_poly = polygon.contains_points(test_verts)
inside_voxel = [any(child.contains(Point3D(r, 0, z)) for child in voxel.children)
for (r, z) in test_verts]
# Due to numerical precision, some points may be inside the
# Matplotlib polygon but not the Mesh. Check in this case that the
# "failing" points are just very close to the edge of the polygon
fails = np.nonzero(np.not_equal(inside_voxel, inside_poly))[0]
for fail in fails:
if inside_voxel[fail] and not inside_poly[fail]:
# Polygon should be made slightly bigger
inside_poly[fail] = polygon.contains_point(test_verts[fail], radius=-0.01)
elif inside_poly[fail] and not inside_voxel[fail]:
# Polygon should be made slightly smaller
inside_poly[fail] = polygon.contains_point(test_verts[fail], radius=0.01)
self.assertSequenceEqual(inside_voxel, inside_poly.tolist(),
"Failed for vertices {}".format(voxel_coords))
def test_list_of_point2d(self):
voxel_coords = [Point2D(*v) for v in RECTANGULAR_VOXEL_COORDS[0]]
voxel = AxisymmetricVoxel(voxel_coords)
for coord, vertex in zip(voxel_coords, voxel.vertices):
self.assertEqual([coord[0], coord[1]], [vertex.x, vertex.y],
"Nx2 array coordinate mismatch")
def test_variable_emissivity_triangular(self):
# Use the same seed as Raysect's random tests
seed(1234567890)
quadpy_precalculated_emiss = {
((4, 3), (3, 2), (2, -1)): 4.333333333333331,
((4, 3), (3, -1), (2, -1)): 1.333333333333333,
((4, 3), (3, 3), (2, -1)): 5.333333333333333,
((4, 3), (3, -1), (2, 2)): 4.083333333333334,
((4, 3), (3, 2), (2, 2)): 7.083333333333333,
((4, 3), (3, -1), (2, 3)): 5.000000000000001,
((4, 2), (3, -1), (2, 3)): 3.916666666666668,
((4, -1), (3, -1), (2, 3)): 0.6666666666666656,
((4, 3), (3, -1), (2, 3)): 5.000000000000001,
((4, 2), (3, 3), (2, -1)): 4.250000000000001,
((4, -1), (3, 3), (2, -1)): 0.9999999999999998,
((4, 3), (3, 3), (2, -1)): 5.333333333333333,
((4, -1), (3, 3), (2, 2)): 3.75,
((4, -1), (3, 3), (2, -1)): 0.9999999999999998,
((4, -1), (3, 3), (2, 3)): 4.666666666666663,
((4, -1), (3, 2), (2, 3)): 3.6666666666666674,
((4, -1), (3, -1), (2, 3)): 0.6666666666666656,
((4, -1), (3, 3), (2, 3)): 4.666666666666663,
((4, 3), (4, 2), (2, -1)): 4.833333333333337,
((4, 3), (4, -1), (2, -1)): 1.3333333333333337,
((4, 3), (4, -1), (2, 2)): 4.333333333333332,
((4, 3), (4, -1), (2, -1)): 1.3333333333333337,
((4, 3), (4, -1), (2, 3)): 5.333333333333333,
((4, 2), (4, -1), (2, 3)): 4.166666666666666,
((4, 3), (4, -1), (2, 3)): 5.333333333333333,
((4, 2), (4, 3), (2, -1)): 4.833333333333332,
((4, -1), (4, 3), (2, -1)): 1.3333333333333337,
((4, -1), (4, 3), (2, 2)): 4.333333333333331,
((4, -1), (4, 3), (2, -1)): 1.3333333333333337,
((4, -1), (4, 3), (2, 3)): 5.333333333333331,
((4, -1), (4, 2), (2, 3)): 4.166666666666665,
((4, -1), (4, 3), (2, 3)): 5.333333333333331,
((4, 3), (2, 2), (2, -1)): 3.833333333333334,
((4, 3), (2, 3), (2, -1)): 4.666666666666666,
((4, 3), (2, -1), (2, 2)): 3.833333333333334,
((4, 3), (2, -1), (2, 3)): 4.666666666666666,
((4, 2), (2, -1), (2, 3)): 3.666666666666666,
((4, -1), (2, -1), (2, 3)): 0.6666666666666659,
((4, 3), (2, -1), (2, 3)): 4.666666666666666,
((4, 2), (2, 3), (2, -1)): 3.666666666666666,
((4, -1), (2, 3), (2, -1)): 0.666666666666666,
((4, 3), (2, 3), (2, -1)): 4.666666666666666,
((4, -1), (2, 3), (2, 2)): 3.16666666666666,
((4, -1), (2, 3), (2, -1)): 0.666666666666666,
((4, -1), (2, 2), (2, 3)): 3.16666666666666,
((4, -1), (2, -1), (2, 3)): 0.6666666666666659,
}
def emiss_function(r, phi, z):
return r * z
for polygon in TRIANGLE_VOXEL_COORDS:
coords = np.asarray(polygon)
voxel = AxisymmetricVoxel(coords)
nsamples = 10000
emiss = voxel.emissivity_from_function(emiss_function, nsamples)
if HAVE_QUADPY:
# Calculate the expected emissivity
x1, y1 = coords[0]
x2, y2 = coords[1]
x3, y3 = coords[2]
triangle_area = 0.5 * abs(x1 * y2 + x2 * y3 + x3 * y1
- x2 * y1 - x3 * y2 - x1 * y3)
# Doesn't make any sense to sample from a <2D cross section area
if triangle_area == 0:
continue
expected_emiss = quadpy.triangle.integrate(
lambda x: emiss_function(x[0], 0, x[1]), coords, quadpy.triangle.Strang(6)
) / triangle_area
else:
try:
expected_emiss = quadpy_precalculated_emiss[tuple(polygon)]
except KeyError: # For triangles with zero area
continue
max_relative_error = 0.0723 # Measured with seed(1234567890)
self.assertAlmostEqual(emiss, expected_emiss, delta=emiss * max_relative_error)