def test_analog_single_tet():
"""This test tests uniform sampling within a single tetrahedron. This is
done by dividing the tetrahedron in 4 smaller tetrahedrons and ensuring
that each sub-tet is sampled equally.
"""
seed(1953)
mesh = iMesh.Mesh()
v1 = [0, 0, 0]
v2 = [1, 0, 0]
v3 = [0, 1, 0]
v4 = [0, 0, 1]
verts = mesh.createVtx([v1, v2, v3, v4])
mesh.createEnt(iMesh.Topology.tetrahedron, verts)
m = Mesh(structured=False, mesh=mesh)
m.src = IMeshTag(1, float)
m.src[:] = np.array([1])
m.mesh.save("tet.h5m")
center = m.ve_center(list(m.iter_ve())[0])
subtets = [[center, v1, v2, v3], [center, v1, v2, v4], [center, v1, v3, v4], [center, v2, v3, v4]]
sampler = Sampler("tet.h5m", "src", np.array([0, 1]), False)
num_samples = 5000
score = 1.0 / num_samples
tally = np.zeros(shape=(4))
for i in range(num_samples):
s = sampler.particle_birth([uniform(0, 1) for x in range(6)])
assert_equal(s[4], 1.0)
for i, tet in enumerate(subtets):
if point_in_tet(tet, [s[0], s[1], s[2]]):
tally[i] += score
break
for t in tally:
assert abs(t - 0.25) / 0.25 < 0.2
def test_analog_single_hex():
"""This test tests that particles of sampled evenly within the phase-space
of a single mesh volume element with one energy group in an analog sampling
scheme. This done by dividing each dimension (x, y, z, E) in half, then
sampling particles and tallying on the basis of which of the 2^4 = 8 regions
of phase space the particle is born into.
"""
seed(1953)
m = Mesh(structured=True, structured_coords=[[0, 1], [0, 1], [0, 1]], mats=None)
m.src = IMeshTag(1, float)
m.src[0] = 1.0
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", np.array([0, 1]), False)
num_samples = 5000
score = 1.0 / num_samples
num_divs = 2
tally = np.zeros(shape=(num_divs, num_divs, num_divs, num_divs))
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
assert_equal(s[4], 1.0) # analog: all weights must be one
tally[int(s[0] * num_divs), int(s[1] * num_divs), int(s[2] * num_divs), int(s[3] * num_divs)] += score
# Test that each half-space of phase space (e.g. x > 0.5) is sampled about
# half the time.
for i in range(0, 4):
for j in range(0, 2):
assert abs(np.sum(np.rollaxis(tally, i)[j, :, :, :]) - 0.5) < 0.05
def test_analog_multiple_hex():
"""This test tests that particle are sampled uniformly from a uniform source
defined on eight mesh volume elements in two energy groups. This is done
using the exact same method ass test_analog_multiple_hex.
"""
seed(1953)
m = Mesh(structured=True, structured_coords=[[0, 0.5, 1], [0, 0.5, 1], [0, 0.5, 1]], mats=None)
m.src = IMeshTag(2, float)
m.src[:] = np.ones(shape=(8, 2))
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", np.array([0, 0.5, 1]), False)
num_samples = 5000
score = 1.0 / num_samples
num_divs = 2
tally = np.zeros(shape=(num_divs, num_divs, num_divs, num_divs))
for i in range(num_samples):
s = sampler.particle_birth([uniform(0, 1) for x in range(6)])
assert_equal(s[4], 1.0)
tally[int(s[0] * num_divs), int(s[1] * num_divs), int(s[2] * num_divs), int(s[3] * num_divs)] += score
for i in range(0, 4):
for j in range(0, 2):
halfspace_sum = np.sum(np.rollaxis(tally, i)[j, :, :, :])
assert abs(halfspace_sum - 0.5) / 0.5 < 0.1
def test_analog_multiple_hex():
"""This test tests that particle are sampled uniformly from a uniform source
defined on eight mesh volume elements in two energy groups. This is done
using the exact same method ass test_analog_multiple_hex.
"""
seed(1953)
m = Mesh(structured=True,
structured_coords=[[0, 0.5, 1], [0, 0.5, 1], [0, 0.5, 1]],
mats=None)
m.src = IMeshTag(2, float)
m.src[:] = np.ones(shape=(8, 2))
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", np.array([0, 0.5, 1]), False)
num_samples = 5000
score = 1.0 / num_samples
num_divs = 2
tally = np.zeros(shape=(num_divs, num_divs, num_divs, num_divs))
for i in range(num_samples):
s = sampler.particle_birth([uniform(0, 1) for x in range(6)])
assert_equal(s[4], 1.0)
tally[int(s[0] * num_divs),
int(s[1] * num_divs),
int(s[2] * num_divs),
int(s[3] * num_divs)] += score
for i in range(0, 4):
for j in range(0, 2):
halfspace_sum = np.sum(np.rollaxis(tally, i)[j, :, :, :])
assert (abs(halfspace_sum - 0.5) / 0.5 < 0.1)
def test_analog_single_hex():
"""This test tests that particles of sampled evenly within the phase-space
of a single mesh volume element with one energy group in an analog sampling
scheme. This done by dividing each dimension (x, y, z, E) in half, then
sampling particles and tallying on the basis of which of the 2^4 = 8 regions
of phase space the particle is born into.
"""
seed(1953)
m = Mesh(structured=True,
structured_coords=[[0, 1], [0, 1], [0, 1]],
mats=None)
m.src = IMeshTag(1, float)
m.src[0] = 1.0
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", np.array([0, 1]), False)
num_samples = 5000
score = 1.0 / num_samples
num_divs = 2
tally = np.zeros(shape=(num_divs, num_divs, num_divs, num_divs))
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
assert_equal(s[4], 1.0) # analog: all weights must be one
tally[int(s[0] * num_divs),
int(s[1] * num_divs),
int(s[2] * num_divs),
int(s[3] * num_divs)] += score
# Test that each half-space of phase space (e.g. x > 0.5) is sampled about
# half the time.
for i in range(0, 4):
for j in range(0, 2):
assert (abs(np.sum(np.rollaxis(tally, i)[j, :, :, :]) - 0.5) <
0.05)
def test_bias_spatial():
"""This test tests a user-specified biasing scheme for which the only 1
bias group is supplied for a source distribution containing two energy
groups. This bias group is applied to both energy groups. In this test,
the user-supplied bias distribution that was choosen, correspondes to
uniform sampling, so that results can be checked against Case 1 in the
theory manual.
"""
seed(1953)
m = Mesh(structured=True,
structured_coords=[[0, 3, 3.5], [0, 1], [0, 1]],
mats=None)
m.src = IMeshTag(2, float)
m.src[:] = [[2.0, 1.0], [9.0, 3.0]]
m.bias = IMeshTag(1, float)
m.bias[:] = [1, 1]
e_bounds = np.array([0, 0.5, 1.0])
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", e_bounds, "bias")
num_samples = 10000
score = 1.0 / num_samples
num_divs = 2
num_e = 2
spatial_tally = np.zeros(shape=(num_divs, num_divs, num_divs))
e_tally = np.zeros(shape=(4)) # number of phase space groups
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
if s[0] < 3.0:
assert_almost_equal(s[4], 0.7) # hand calcs
else:
assert_almost_equal(s[4], 2.8) # hand calcs
spatial_tally[int(s[0] * num_divs / 3.5),
int(s[1] * num_divs / 1.0),
int(s[2] * num_divs / 1.0)] += score
if s[0] < 3 and s[3] < 0.5:
e_tally[0] += score
elif s[0] < 3 and s[3] > 0.5:
e_tally[1] += score
if s[0] > 3 and s[3] < 0.5:
e_tally[2] += score
if s[0] > 3 and s[3] > 0.5:
e_tally[3] += score
for i in range(0, 3):
for j in range(0, 2):
halfspace_sum = np.sum(np.rollaxis(spatial_tally, i)[j, :, :])
assert (abs(halfspace_sum - 0.5) / 0.5 < 0.1)
expected_e_tally = [4. / 7, 2. / 7, 3. / 28, 1. / 28] # hand calcs
for i in range(4):
assert (abs(e_tally[i] - expected_e_tally[i]) / expected_e_tally[i] <
0.1)
def test_uniform():
"""This test tests that the uniform biasing scheme:
1. Samples space uniformly. This is checked using the same method
described in test_analog_single_hex().
2. Adjusts weights accordingly. Sample calculations are provided in Case 1
in the Theory Manual.
"""
seed(1953)
m = Mesh(structured=True,
structured_coords=[[0, 3, 3.5], [0, 1], [0, 1]],
mats=None)
m.src = IMeshTag(2, float)
m.src[:] = [[2.0, 1.0], [9.0, 3.0]]
e_bounds = np.array([0, 0.5, 1.0])
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", e_bounds, True)
num_samples = 10000
score = 1.0 / num_samples
num_divs = 2
num_e = 2
spatial_tally = np.zeros(shape=(num_divs, num_divs, num_divs))
e_tally = np.zeros(shape=(4)) # number of phase space groups
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
if s[0] < 3.0:
assert_almost_equal(s[4], 0.7) # hand calcs
else:
assert_almost_equal(s[4], 2.8) # hand calcs
spatial_tally[int(s[0] * num_divs / 3.5),
int(s[1] * num_divs / 1.0),
int(s[2] * num_divs / 1.0)] += score
if s[0] < 3 and s[3] < 0.5:
e_tally[0] += score
elif s[0] < 3 and s[3] > 0.5:
e_tally[1] += score
if s[0] > 3 and s[3] < 0.5:
e_tally[2] += score
if s[0] > 3 and s[3] > 0.5:
e_tally[3] += score
for i in range(0, 3):
for j in range(0, 2):
halfspace_sum = np.sum(np.rollaxis(spatial_tally, i)[j, :, :])
assert (abs(halfspace_sum - 0.5) / 0.5 < 0.1)
expected_e_tally = [4. / 7, 2. / 7, 3. / 28, 1. / 28] # hand calcs
for i in range(4):
assert(abs(e_tally[i] - expected_e_tally[i]) \
/expected_e_tally[i] < 0.1)
def test_bias_spatial():
"""This test tests a user-specified biasing scheme for which the only 1
bias group is supplied for a source distribution containing two energy
groups. This bias group is applied to both energy groups. In this test,
the user-supplied bias distribution that was choosen, correspondes to
uniform sampling, so that results can be checked against Case 1 in the
theory manual.
"""
seed(1953)
m = Mesh(structured=True, structured_coords=[[0, 3, 3.5], [0, 1], [0, 1]], mats=None)
m.src = IMeshTag(2, float)
m.src[:] = [[2.0, 1.0], [9.0, 3.0]]
m.bias = IMeshTag(1, float)
m.bias[:] = [1, 1]
e_bounds = np.array([0, 0.5, 1.0])
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", e_bounds, "bias")
num_samples = 10000
score = 1.0 / num_samples
num_divs = 2
num_e = 2
spatial_tally = np.zeros(shape=(num_divs, num_divs, num_divs))
e_tally = np.zeros(shape=(4)) # number of phase space groups
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
if s[0] < 3.0:
assert_almost_equal(s[4], 0.7) # hand calcs
else:
assert_almost_equal(s[4], 2.8) # hand calcs
spatial_tally[int(s[0] * num_divs / 3.5), int(s[1] * num_divs / 1.0), int(s[2] * num_divs / 1.0)] += score
if s[0] < 3 and s[3] < 0.5:
e_tally[0] += score
elif s[0] < 3 and s[3] > 0.5:
e_tally[1] += score
if s[0] > 3 and s[3] < 0.5:
e_tally[2] += score
if s[0] > 3 and s[3] > 0.5:
e_tally[3] += score
for i in range(0, 3):
for j in range(0, 2):
halfspace_sum = np.sum(np.rollaxis(spatial_tally, i)[j, :, :])
assert abs(halfspace_sum - 0.5) / 0.5 < 0.1
expected_e_tally = [4.0 / 7, 2.0 / 7, 3.0 / 28, 1.0 / 28] # hand calcs
for i in range(4):
assert abs(e_tally[i] - expected_e_tally[i]) / expected_e_tally[i] < 0.1
def test_uniform():
"""This test tests that the uniform biasing scheme:
1. Samples space uniformly. This is checked using the same method
described in test_analog_single_hex().
2. Adjusts weights accordingly. Sample calculations are provided in Case 1
in the Theory Manual.
"""
seed(1953)
m = Mesh(structured=True, structured_coords=[[0, 3, 3.5], [0, 1], [0, 1]], mats=None)
m.src = IMeshTag(2, float)
m.src[:] = [[2.0, 1.0], [9.0, 3.0]]
e_bounds = np.array([0, 0.5, 1.0])
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", e_bounds, True)
num_samples = 10000
score = 1.0 / num_samples
num_divs = 2
num_e = 2
spatial_tally = np.zeros(shape=(num_divs, num_divs, num_divs))
e_tally = np.zeros(shape=(4)) # number of phase space groups
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
if s[0] < 3.0:
assert_almost_equal(s[4], 0.7) # hand calcs
else:
assert_almost_equal(s[4], 2.8) # hand calcs
spatial_tally[int(s[0] * num_divs / 3.5), int(s[1] * num_divs / 1.0), int(s[2] * num_divs / 1.0)] += score
if s[0] < 3 and s[3] < 0.5:
e_tally[0] += score
elif s[0] < 3 and s[3] > 0.5:
e_tally[1] += score
if s[0] > 3 and s[3] < 0.5:
e_tally[2] += score
if s[0] > 3 and s[3] > 0.5:
e_tally[3] += score
for i in range(0, 3):
for j in range(0, 2):
halfspace_sum = np.sum(np.rollaxis(spatial_tally, i)[j, :, :])
assert abs(halfspace_sum - 0.5) / 0.5 < 0.1
expected_e_tally = [4.0 / 7, 2.0 / 7, 3.0 / 28, 1.0 / 28] # hand calcs
for i in range(4):
assert abs(e_tally[i] - expected_e_tally[i]) / expected_e_tally[i] < 0.1
def test_bias():
"""This test tests that a user-specified biasing scheme:
1. Samples space uniformly according to the scheme.
2. Adjusts weights accordingly. Sample calculations are provided in Case 2
in the Theory Manual.
"""
seed(1953)
m = Mesh(structured=True,
structured_coords=[[0, 3, 3.5], [0, 1], [0, 1]],
mats=None)
m.src = IMeshTag(2, float)
m.src[:] = [[2.0, 1.0], [9.0, 3.0]]
e_bounds = np.array([0, 0.5, 1.0])
m.bias = IMeshTag(2, float)
m.bias[:] = [[1.0, 2.0], [3.0, 3.0]]
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", e_bounds, "bias")
num_samples = 10000
score = 1.0 / num_samples
num_divs = 2
tally = np.zeros(shape=(4))
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
if s[0] < 3:
if s[3] < 0.5:
assert_almost_equal(s[4], 1.6) # hand calcs
tally[0] += score
else:
assert_almost_equal(s[4], 0.4) # hand calcs
tally[1] += score
else:
if s[3] < 0.5:
assert_almost_equal(s[4], 2.4) # hand calcs
tally[2] += score
else:
assert_almost_equal(s[4], 0.8) # hand calcs
tally[3] += score
expected_tally = [0.25, 0.5, 0.125, 0.125] # hand calcs
for a, b in zip(tally, expected_tally):
assert (abs(a - b) / b < 0.25)
def test_bias():
"""This test tests that a user-specified biasing scheme:
1. Samples space uniformly according to the scheme.
2. Adjusts weights accordingly. Sample calculations are provided in Case 2
in the Theory Manual.
"""
seed(1953)
m = Mesh(structured=True, structured_coords=[[0, 3, 3.5], [0, 1], [0, 1]], mats=None)
m.src = IMeshTag(2, float)
m.src[:] = [[2.0, 1.0], [9.0, 3.0]]
e_bounds = np.array([0, 0.5, 1.0])
m.bias = IMeshTag(2, float)
m.bias[:] = [[1.0, 2.0], [3.0, 3.0]]
m.mesh.save("sampling_mesh.h5m")
sampler = Sampler("sampling_mesh.h5m", "src", e_bounds, "bias")
num_samples = 10000
score = 1.0 / num_samples
num_divs = 2
tally = np.zeros(shape=(4))
for i in range(num_samples):
s = sampler.particle_birth(np.array([uniform(0, 1) for x in range(6)]))
if s[0] < 3:
if s[3] < 0.5:
assert_almost_equal(s[4], 1.6) # hand calcs
tally[0] += score
else:
assert_almost_equal(s[4], 0.4) # hand calcs
tally[1] += score
else:
if s[3] < 0.5:
assert_almost_equal(s[4], 2.4) # hand calcs
tally[2] += score
else:
assert_almost_equal(s[4], 0.8) # hand calcs
tally[3] += score
expected_tally = [0.25, 0.5, 0.125, 0.125] # hand calcs
for a, b in zip(tally, expected_tally):
assert abs(a - b) / b < 0.25
def test_analog_single_tet():
"""This test tests uniform sampling within a single tetrahedron. This is
done by dividing the tetrahedron in 4 smaller tetrahedrons and ensuring
that each sub-tet is sampled equally.
"""
seed(1953)
mesh = iMesh.Mesh()
v1 = [0, 0, 0]
v2 = [1, 0, 0]
v3 = [0, 1, 0]
v4 = [0, 0, 1]
verts = mesh.createVtx([v1, v2, v3, v4])
mesh.createEnt(iMesh.Topology.tetrahedron, verts)
m = Mesh(structured=False, mesh=mesh)
m.src = IMeshTag(1, float)
m.src[:] = np.array([1])
m.mesh.save("tet.h5m")
center = m.ve_center(list(m.iter_ve())[0])
subtets = [[center, v1, v2, v3], [center, v1, v2, v4],
[center, v1, v3, v4], [center, v2, v3, v4]]
sampler = Sampler("tet.h5m", "src", np.array([0, 1]), False)
num_samples = 5000
score = 1.0 / num_samples
tally = np.zeros(shape=(4))
for i in range(num_samples):
s = sampler.particle_birth([uniform(0, 1) for x in range(6)])
assert_equal(s[4], 1.0)
for i, tet in enumerate(subtets):
if point_in_tet(tet, [s[0], s[1], s[2]]):
tally[i] += score
break
for t in tally:
assert (abs(t - 0.25) / 0.25 < 0.2)
