OpenMC/tests/unit_tests/test_math.py

247 lines
7.5 KiB
Python

import numpy as np
import pytest
import scipy as sp
from scipy.stats import shapiro
import openmc
import openmc.lib
def test_t_percentile():
# Permutations include 1 DoF, 2 DoF, and > 2 DoF
# We will test 5 p-values at 3-DoF values
test_ps = [0.02, 0.4, 0.5, 0.6, 0.98]
test_dfs = [1, 2, 5]
# The reference solutions come from Scipy
ref_ts = [[sp.stats.t.ppf(p, df) for p in test_ps] for df in test_dfs]
test_ts = [[openmc.lib.math.t_percentile(p, df) for p in test_ps]
for df in test_dfs]
# The 5 DoF approximation in openmc.lib.math.t_percentile is off by up to
# 8e-3 from the scipy solution, so test that one separately with looser
# tolerance
assert np.allclose(ref_ts[:-1], test_ts[:-1])
assert np.allclose(ref_ts[-1], test_ts[-1], atol=1e-2)
def test_calc_pn():
max_order = 10
test_xs = np.linspace(-1., 1., num=5, endpoint=True)
# Reference solutions from scipy
ref_vals = np.array([sp.special.eval_legendre(n, test_xs)
for n in range(0, max_order + 1)])
test_vals = []
for x in test_xs:
test_vals.append(openmc.lib.math.calc_pn(max_order, x).tolist())
test_vals = np.swapaxes(np.array(test_vals), 0, 1)
assert np.allclose(ref_vals, test_vals)
def test_evaluate_legendre():
max_order = 10
# Coefficients are set to 1, but will incorporate the (2l+1)/2 norm factor
# for the reference solution
test_coeffs = [0.5 * (2. * l + 1.) for l in range(max_order + 1)]
test_xs = np.linspace(-1., 1., num=5, endpoint=True)
ref_vals = np.polynomial.legendre.legval(test_xs, test_coeffs)
# Set the coefficients back to 1s for the test values since
# evaluate legendre incorporates the (2l+1)/2 term on its own
test_coeffs = [1. for l in range(max_order + 1)]
test_vals = np.array([openmc.lib.math.evaluate_legendre(test_coeffs, x)
for x in test_xs])
assert np.allclose(ref_vals, test_vals)
def test_calc_rn():
max_order = 10
test_ns = np.array([i for i in range(0, max_order + 1)])
azi = 0.1 # Longitude
pol = 0.2 # Latitude
test_uvw = np.array([np.sin(pol) * np.cos(azi),
np.sin(pol) * np.sin(azi),
np.cos(pol)])
# Reference solutions from the equations
ref_vals = []
def coeff(n, m):
return np.sqrt((2. * n + 1) * sp.special.factorial(n - m) /
(sp.special.factorial(n + m)))
def pnm_bar(n, m, mu):
val = coeff(n, m)
if m != 0:
val *= np.sqrt(2.)
val *= sp.special.lpmv([m], [n], [mu])
return val[0]
ref_vals = []
for n in test_ns:
for m in range(-n, n + 1):
if m < 0:
ylm = pnm_bar(n, np.abs(m), np.cos(pol)) * \
np.sin(np.abs(m) * azi)
else:
ylm = pnm_bar(n, m, np.cos(pol)) * np.cos(m * azi)
# Un-normalize for comparison
ylm /= np.sqrt(2. * n + 1.)
ref_vals.append(ylm)
test_vals = []
test_vals = openmc.lib.math.calc_rn(max_order, test_uvw)
assert np.allclose(ref_vals, test_vals)
def test_calc_zn():
n = 10
rho = 0.5
phi = 0.5
# Reference solution from running the C++ implementation
ref_vals = np.array([
1.00000000e+00, 2.39712769e-01, 4.38791281e-01,
2.10367746e-01, -5.00000000e-01, 1.35075576e-01,
1.24686873e-01, -2.99640962e-01, -5.48489101e-01,
8.84215021e-03, 5.68310892e-02, -4.20735492e-01,
-1.25000000e-01, -2.70151153e-01, -2.60091773e-02,
1.87022545e-02, -3.42888902e-01, 1.49820481e-01,
2.74244551e-01, -2.43159131e-02, -2.50357380e-02,
2.20500013e-03, -1.98908812e-01, 4.07587508e-01,
4.37500000e-01, 2.61708929e-01, 9.10321205e-02,
-1.54686328e-02, -2.74049397e-03, -7.94845816e-02,
4.75368705e-01, 7.11647284e-02, 1.30266162e-01,
3.37106977e-02, 1.06401886e-01, -7.31606787e-03,
-2.95625975e-03, -1.10250006e-02, 3.55194307e-01,
-1.44627826e-01, -2.89062500e-01, -9.28644588e-02,
-1.62557358e-01, 7.73431638e-02, -2.55329539e-03,
-1.90923851e-03, 1.57578403e-02, 1.72995854e-01,
-3.66267690e-01, -1.81657333e-01, -3.32521518e-01,
-2.59738162e-02, -2.31580576e-01, 4.20673902e-02,
-4.11710546e-04, -9.36449487e-04, 1.92156884e-02,
2.82515641e-02, -3.90713738e-01, -1.69280296e-01,
-8.98437500e-02, -1.08693628e-01, 1.78813094e-01,
-1.98191857e-01, 1.65964201e-02, 2.77013853e-04])
test_vals = openmc.lib.math.calc_zn(n, rho, phi)
assert np.allclose(ref_vals, test_vals)
def test_calc_zn_rad():
n = 10
rho = 0.5
# Reference solution from running the C++ implementation
ref_vals = np.array([
1.00000000e+00, -5.00000000e-01, -1.25000000e-01,
4.37500000e-01, -2.89062500e-01,-8.98437500e-02])
test_vals = openmc.lib.math.calc_zn_rad(n, rho)
assert np.allclose(ref_vals, test_vals)
def test_rotate_angle():
uvw0 = np.array([1., 0., 0.])
phi = 0.
mu = 0.
# reference: mu of 0 pulls the vector the bottom, so:
ref_uvw = np.array([0., 0., -1.])
test_uvw = openmc.lib.math.rotate_angle(uvw0, mu, phi)
assert np.array_equal(ref_uvw, test_uvw)
# Repeat for mu = 1 (no change)
mu = 1.
ref_uvw = np.array([1., 0., 0.])
test_uvw = openmc.lib.math.rotate_angle(uvw0, mu, phi)
assert np.array_equal(ref_uvw, test_uvw)
# Now to test phi is None
mu = 0.9
phi = None
prn_seed = 1
# When seed = 1, phi will be sampled as 1.9116495709698769
# The resultant reference is from hand-calculations given the above
ref_uvw = [0.9, -0.422746750548505, 0.10623175090659095]
test_uvw = openmc.lib.math.rotate_angle(uvw0, mu, phi, prn_seed)
assert np.allclose(ref_uvw, test_uvw)
def test_maxwell_spectrum():
prn_seed = 1
T = 0.5
ref_val = 0.27767406743161277
test_val = openmc.lib.math.maxwell_spectrum(T, prn_seed)
assert ref_val == test_val
def test_watt_spectrum():
prn_seed = 1
a = 0.5
b = 0.75
ref_val = 0.30957476387766697
test_val = openmc.lib.math.watt_spectrum(a, b, prn_seed)
assert ref_val == test_val
def test_normal_dist():
# When standard deviation is zero, sampled value should be mean
prn_seed = 1
mean = 14.08
stdev = 0.0
ref_val = 14.08
test_val = openmc.lib.math.normal_variate(mean, stdev, prn_seed)
assert ref_val == pytest.approx(test_val)
# Use Shapiro-Wilk test to ensure normality of sampled vairates
stdev = 1.0
samples = []
num_samples = 10000
for _ in range(num_samples):
# sample the normal distribution from openmc
samples.append(openmc.lib.math.normal_variate(mean, stdev, prn_seed))
prn_seed += 1
stat, p = shapiro(samples)
assert p > 0.05
def test_broaden_wmp_polynomials():
# Two branches of the code to worry about, beta > 6 and otherwise
# beta = sqrtE * dopp
# First lets do beta > 6
test_E = 0.5
test_dopp = 100. # approximately U235 at room temperature
n = 6
ref_val = [2., 1.41421356, 1.0001, 0.70731891, 0.50030001, 0.353907]
test_val = openmc.lib.math.broaden_wmp_polynomials(test_E, test_dopp, n)
assert np.allclose(ref_val, test_val)
# now beta < 6
test_dopp = 5.
ref_val = [1.99999885, 1.41421356, 1.04, 0.79195959, 0.6224, 0.50346003]
test_val = openmc.lib.math.broaden_wmp_polynomials(test_E, test_dopp, n)
assert np.allclose(ref_val, test_val)