def test_becke_transform_3nd_order_ode(self):
"""Test same result for 3rd order ode with becke tf."""
btf = BeckeTF(0.1, 10)
ibtf = InverseTF(btf)
coeff = np.array([0, 2, 3, 3])
# transform
# r = np.linspace(1, 2, 10) # r
# x = ibtf.transform(r) # transformed x
x = np.linspace(-0.9, 0.9, 20)
r = ibtf.inverse(x)
y = np.random.rand(3, r.size)
def fx(x):
return 1 / x ** 4
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], ya[1]])
res = solve_bvp(func, bc, x, y)
# print(res.sol(x)[0])
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)
# print(res_ref.sol(r)[0])
assert_allclose(res.sol(x)[0], res_ref.sol(r)[0], atol=1e-4)
def test_poisson_solve_mtr_cmpl(self):
"""Test solve poisson equation and interpolate the result."""
oned = GaussChebyshev(50)
btf = BeckeTF(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,
)
ibtf = InverseTF(btf)
linsp = np.linspace(-1, 0.99, 50)
bound = p_0 * np.sqrt(4 * np.pi)
pois_mtr = Poisson.solve_poisson(spls_mt, linsp, bound, tfm=ibtf)
assert pois_mtr.shape == (7, 4)
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)
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
]
for i, j in enumerate(near_tf_pts):
assert_almost_equal(
Poisson.interpolate_radial(pois_mtr, j, 0, True) /
near_rg_pts[i],
ref_short_res[i] * np.sqrt(4 * np.pi),
decimal=3,
)
matrix_result = Poisson.interpolate_radial(pois_mtr, j)
assert_almost_equal(
matrix_result[0, 0] / near_rg_pts[i],
ref_short_res[i] * np.sqrt(4 * np.pi),
decimal=3,
)
# test interpolate with sph
result = Poisson.interpolate(pois_mtr, j, np.random.rand(5),
np.random.rand(5))
assert_allclose(result / near_rg_pts[i] - ref_short_res[i],
np.zeros(5),
atol=1e-3)
def test_becke_transform_f0_ode(self):
"""Test same result for 3rd order ode with becke tf and fx term."""
btf = BeckeTF(0.1, 10)
x = np.linspace(-0.9, 0.9, 20)
btf = BeckeTF(0.1, 5)
ibtf = InverseTF(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_linear_inverse(self):
"""Test inverse transform and derivs function."""
ltf = LinearTF(0.1, 10)
iltf = InverseTF(ltf)
# transform & inverse
self._transform_and_inverse(0, 20, iltf)
# finite diff for derivs
self._deriv_finite_diff(0, 20, iltf)
def test_transform_coeff(self):
"""Test coefficient transform with r."""
# d^2y / dx^2 = 1
itf = IdentityRTransform()
inv_tf = InverseTF(itf)
derivs_fun = [inv_tf.deriv, inv_tf.deriv2, inv_tf.deriv3]
coeff = np.array([0, 0, 1])
x = np.linspace(0, 1, 10)
coeff_b = ODE._transformed_coeff_ode_with_r(coeff, derivs_fun, x)
# compute transformed coeffs
assert_allclose(coeff_b, np.zeros((3, 10), dtype=float) + coeff[:, None])
def test_linear_transform_coeff(self):
"""Test coefficient with linear transformation."""
x = GaussLaguerre(10).points
ltf = LinearTF(1, 10)
inv_ltf = InverseTF(ltf)
derivs_fun = [inv_ltf.deriv, inv_ltf.deriv2, inv_ltf.deriv3]
coeff = np.array([2, 3, 4])
coeff_b = ODE._transformed_coeff_ode_with_r(coeff, derivs_fun, x)
# assert values
assert_allclose(coeff_b[0], np.ones(len(x)) * coeff[0])
assert_allclose(coeff_b[1], 1 / 4.5 * coeff[1])
assert_allclose(coeff_b[2], (1 / 4.5) ** 2 * coeff[2])
def test_transform_coeff_with_x_and_r(self):
"""Test coefficient transform between x and r."""
coeff = np.array([2, 3, 4])
ltf = LinearTF(1, 10) # (-1, 1) -> (r0, rmax)
inv_tf = InverseTF(ltf) # (r0, rmax) -> (-1, 1)
x = np.linspace(-1, 1, 20)
r = ltf.transform(x)
assert r[0] == 1
assert r[-1] == 10
coeff_b = ODE._transformed_coeff_ode(coeff, inv_tf, x)
derivs_fun = [inv_tf.deriv, inv_tf.deriv2, inv_tf.deriv3]
coeff_b_ref = ODE._transformed_coeff_ode_with_r(coeff, derivs_fun, r)
assert_allclose(coeff_b, coeff_b_ref)
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 = BeckeTF(0.1, 5)
r = btf.transform(x)
ibtf = InverseTF(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 = BeckeTF(0.1, 5)
r = btf.transform(x)
ibtf = InverseTF(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_errors_assert(self):
"""Test errors raise."""
# parameter error
with self.assertRaises(ValueError):
BeckeTF.find_parameter(np.arange(5), 0.5, 0.1)
# transform non array type
with self.assertRaises(TypeError):
btf = BeckeTF(0.1, 1.1)
btf.transform(0.5)
# inverse init error
with self.assertRaises(TypeError):
InverseTF(0.5)
# type error for transform_grid
with self.assertRaises(TypeError):
btf = BeckeTF(0.1, 1.1)
btf.transform_grid(np.arange(3))
def test_errors_assert(self):
"""Test errors raise."""
# parameter error
with self.assertRaises(ValueError):
BeckeTF.find_parameter(np.arange(5), 0.5, 0.1)
# transform non array type
with self.assertRaises(TypeError):
btf = BeckeTF(0.1, 1.1)
btf.transform("dafasdf")
# inverse init error
with self.assertRaises(TypeError):
InverseTF(0.5)
# type error for transform_1d_grid
with self.assertRaises(TypeError):
btf = BeckeTF(0.1, 1.1)
btf.transform_1d_grid(np.arange(3))
with self.assertRaises(ZeroDivisionError):
btf = BeckeTF(0.1, 0)
itf = InverseTF(btf)
itf._d1(0.5)
with self.assertRaises(ZeroDivisionError):
btf = BeckeTF(0.1, 0)
itf = InverseTF(btf)
itf._d1(np.array([0.1, 0.2, 0.3]))
def test_handymod_inverse(self):
"""Test inverse transform basic function."""
btf = HandyModTF(0.1, 10.0, 2)
inv = InverseTF(btf)
new_array = inv.transform(btf.transform(self.array))
assert_allclose(new_array, self.array)
def test_multiexp_inverse(self):
"""Test inverse transform basic function."""
btf = MultiExpTF(0.1, 1.1)
inv = InverseTF(btf)
new_array = inv.transform(btf.transform(self.array))
assert_allclose(new_array, self.array)
def test_becke_inverse_inverse(self):
"""Test inverse of inverse of Becke transformation."""
btf = BeckeTF(0.1, 1.1)
inv = InverseTF(btf)
inv_inv = inv.inverse(inv.transform(self.array))
assert_allclose(inv_inv, self.array, atol=1e-7)
def test_becke_inverse_deriv(self):
"""Test inverse transformation derivatives with finite diff."""
btf = BeckeTF(0.1, 1.1)
inv = InverseTF(btf)
self._deriv_finite_diff(0, 20, inv)
def test_poisson_solve(self):
"""Test the poisson solve function."""
oned = GaussChebyshev(30)
oned = GaussChebyshev(50)
btf = BeckeTF(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 = InverseTF(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_knowles_inverse(self):
"""Test inverse transform basic function."""
btf = KnowlesTF(0.1, 1.1, 2)
inv = InverseTF(btf)
new_array = inv.transform(btf.transform(self.array))
assert_allclose(new_array, self.array)
def test_becke_inverse_deriv(self):
"""Test inverse transformation derivatives with finite diff."""
btf = BeckeTF(0.1, 1.1)
inv = InverseTF(btf)
r_array = 2**(np.arange(-1, 8, dtype=float))
self._deriv_finite_diff(inv, r_array)