def test_becke_transform(self):
"""Test becke transformation."""
btf = BeckeRTransform(0.1, 1.1)
tf_array = btf.transform(self.array)
single_v = btf.transform(self.num)
single_v2 = btf.transform(self.num_2)
new_array = btf.inverse(tf_array)
assert_allclose(new_array, self.array)
assert_allclose(tf_array[0], single_v)
assert_allclose(tf_array[-1], single_v2)
# test tf and inverse
self._transform_and_inverse(-1, 1, btf)
def test_becke_parameter_calc(self):
"""Test parameter function."""
R = BeckeRTransform.find_parameter(self.array, 0.1, 1.2)
# R = 1.1
assert np.isclose(R, 1.1)
btf = BeckeRTransform(0.1, R)
tf_array = btf.transform(self.array)
assert tf_array[9] == 1.2
# for even number of grid
R = BeckeRTransform.find_parameter(self.array_2, 0.2, 1.3)
btf_2 = BeckeRTransform(0.2, R)
tf_elemt = btf_2.transform(
np.array([(self.array_2[4] + self.array_2[5]) / 2]))
assert_allclose(tf_elemt, 1.3)
def test_becke_transform_f0_ode(self):
"""Test same result for 3rd order ode with becke tf and fx term."""
btf = BeckeRTransform(0.1, 10)
x = np.linspace(-0.9, 0.9, 20)
btf = BeckeRTransform(0.1, 5)
ibtf = InverseRTransform(btf)
r = btf.transform(x)
y = np.random.rand(2, x.size)
coeff = [-1, -1, 2]
def fx(x):
return -1 / x**2
def func(x, y):
dy_dx = ODE._rearrange_trans_ode(x, y, coeff, ibtf, fx)
return np.vstack((*y[1:], dy_dx))
def bc(ya, yb):
return np.array([ya[0], yb[0]])
res = solve_bvp(func, bc, x, y)
def func_ref(x, y):
dy_dx = ODE._rearrange_ode(x, y, coeff, fx(x))
return np.vstack((*y[1:], dy_dx))
res_ref = solve_bvp(func_ref, bc, r, y)
assert_allclose(res.sol(x)[0], res_ref.sol(r)[0], atol=1e-4)
def test_errors_assert(self):
"""Test errors raise."""
# parameter error
with self.assertRaises(ValueError):
BeckeRTransform.find_parameter(np.arange(5), 0.5, 0.1)
# transform non array type
with self.assertRaises(TypeError):
btf = BeckeRTransform(0.1, 1.1)
btf.transform("dafasdf")
# inverse init error
with self.assertRaises(TypeError):
InverseRTransform(0.5)
# type error for transform_1d_grid
with self.assertRaises(TypeError):
btf = BeckeRTransform(0.1, 1.1)
btf.transform_1d_grid(np.arange(3))
with self.assertRaises(ZeroDivisionError):
btf = BeckeRTransform(0.1, 0)
itf = InverseRTransform(btf)
itf._d1(0.5)
with self.assertRaises(ZeroDivisionError):
btf = BeckeRTransform(0.1, 0)
itf = InverseRTransform(btf)
itf._d1(np.array([0.1, 0.2, 0.3]))
def test_solver_ode_coeff_a_f_x_with_tf(self):
"""Test ode with a(x) and f(x) involved."""
x = np.linspace(-0.999, 0.999, 20)
btf = BeckeRTransform(0.1, 5)
r = btf.transform(x)
ibtf = InverseRTransform(btf)
def fx(x):
return 0 * x
coeffs = [lambda x: x**2, lambda x: 1 / x**2, 0.5]
bd_cond = [(0, 0, 0), (1, 0, 0)]
# calculate diff equation wt/w tf.
res = ODE.solve_ode(x, fx, coeffs, bd_cond, ibtf)
res_ref = ODE.solve_ode(r, fx, coeffs, bd_cond)
assert_allclose(res(x)[0], res_ref(r)[0], atol=1e-4)
def test_solver_ode_bvp_with_tf(self):
"""Test result for high level api solve_ode with fx term."""
x = np.linspace(-0.999, 0.999, 20)
btf = BeckeRTransform(0.1, 5)
r = btf.transform(x)
ibtf = InverseRTransform(btf)
def fx(x):
return 1 / x**2
coeffs = [-1, 1, 1]
bd_cond = [(0, 0, 0), (1, 0, 0)]
# calculate diff equation wt/w tf.
res = ODE.solve_ode(x, fx, coeffs, bd_cond, ibtf)
res_ref = ODE.solve_ode(r, fx, coeffs, bd_cond)
assert_allclose(res(x)[0], res_ref(r)[0], atol=1e-4)
def test_becke_infinite(self):
"""Test becke transformation when inf generated."""
inf_array = np.linspace(-1, 1, 21)
R = BeckeRTransform.find_parameter(inf_array, 0.1, 1.2)
btf = BeckeRTransform(0.1, R, trim_inf=True)
tf_array = btf.transform(inf_array)
inv_array = btf.inverse(tf_array)
assert_allclose(inv_array, inf_array)
# extra test for neg inf
# test for number
result = btf._convert_inf(-np.inf)
assert_almost_equal(result, -1e16)
result = btf._convert_inf(np.inf)
assert_almost_equal(result, 1e16)
# test for array
test_array = np.random.rand(5)
test_array[3] = -np.inf
result = btf._convert_inf(test_array)
assert_almost_equal(result[3], -1e16)
test_array[3] = np.inf
result = btf._convert_inf(test_array)
assert_almost_equal(result[3], 1e16)
def test_poisson_solve(self):
"""Test the poisson solve function."""
oned = GaussChebyshev(30)
oned = GaussChebyshev(50)
btf = BeckeRTransform(1e-7, 1.5)
rad = btf.transform_1d_grid(oned)
l_max = 7
atgrid = AtomGrid(rad, degrees=[l_max])
value_array = self.helper_func_gauss(atgrid.points)
p_0 = atgrid.integrate(value_array)
# test density sum up to np.pi**(3 / 2)
assert_allclose(p_0, np.pi**1.5, atol=1e-4)
sph_coor = atgrid.convert_cart_to_sph()[:, 1:3]
spls_mt = Poisson._proj_sph_value(
atgrid.rgrid,
sph_coor,
l_max // 2,
value_array,
atgrid.weights,
atgrid.indices,
)
# test splines project fit gauss function well
def gauss(r):
return np.exp(-(r**2))
for _ in range(20):
coors = np.random.rand(10, 3)
r = np.linalg.norm(coors, axis=-1)
spl_0_0 = spls_mt[0, 0]
interp_v = spl_0_0(r)
ref_v = gauss(r) * np.sqrt(4 * np.pi)
# 0.28209479 is the value in spherical harmonic Z_0_0
assert_allclose(interp_v, ref_v, atol=1e-3)
ibtf = InverseRTransform(btf)
linsp = np.linspace(-1, 0.99, 50)
bound = p_0 * np.sqrt(4 * np.pi)
res_bv = Poisson.solve_poisson_bv(spls_mt[0, 0],
linsp,
bound,
tfm=ibtf)
near_rg_pts = np.array([1e-2, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 1.2])
near_tf_pts = ibtf.transform(near_rg_pts)
long_rg_pts = np.array([2, 3, 4, 5, 6, 7, 8, 9, 10])
long_tf_pts = ibtf.transform(long_rg_pts)
short_res = res_bv(near_tf_pts)[0] / near_rg_pts / (2 * np.sqrt(np.pi))
long_res = res_bv(long_tf_pts)[0] / long_rg_pts / (2 * np.sqrt(np.pi))
# ref are calculated with mathemetical
# integrate[exp[-x^2 - y^2 - z^2] / sqrt[(x - a)^2 + y^2 +z^2], range]
ref_short_res = [
6.28286, # 0.01
6.26219, # 0.1
6.20029, # 0.2
6.09956, # 0.3
5.79652, # 0.5
5.3916, # 0.7
4.69236, # 1.0
4.22403, # 1.2
]
ref_long_res = [
2.77108, # 2
1.85601, # 3
1.39203, # 4
1.11362, # 5
0.92802, # 6
0.79544, # 7
0.69601, # 8
0.61867, # 9
0.55680, # 10
]
assert_allclose(short_res, ref_short_res, atol=5e-4)
assert_allclose(long_res, ref_long_res, atol=5e-4)
# solve same poisson equation with gauss directly
gauss_pts = btf.transform(linsp)
res_gs = Poisson.solve_poisson_bv(gauss, gauss_pts, p_0)
gs_int_short = res_gs(near_rg_pts)[0] / near_rg_pts
gs_int_long = res_gs(long_rg_pts)[0] / long_rg_pts
assert_allclose(gs_int_short, ref_short_res, 5e-4)
assert_allclose(gs_int_long, ref_long_res, 5e-4)
def test_becke_inverse(self):
"""Test inverse transform basic function."""
btf = BeckeRTransform(0.1, 1.1)
inv = InverseRTransform(btf)
new_array = inv.transform(btf.transform(self.array))
assert_allclose(new_array, self.array)