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_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_3nd_order_ode(self):
"""Test same result for 3rd order ode with becke tf."""
btf = BeckeRTransform(0.1, 10)
ibtf = InverseRTransform(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_error_raises(self):
"""Test proper error raises."""
x = np.linspace(-0.999, 0.999, 20)
# r = btf.transform(x)
def fx(x):
return 1 / x**2
coeffs = [-1, -2, 1]
bd_cond = [(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)]
with self.assertRaises(NotImplementedError):
ODE.solve_ode(x, fx, coeffs, bd_cond[3:])
with self.assertRaises(NotImplementedError):
ODE.solve_ode(x, fx, coeffs, bd_cond)
with self.assertRaises(NotImplementedError):
test_coeff = [1, 2, 3, 4, 5]
ODE.solve_ode(x, fx, test_coeff, bd_cond)
with self.assertRaises(ValueError):
test_coeff = [1, 2, 3, 3]
tf = BeckeRTransform(0.1, 1)
def fx(x):
return x
ODE.solve_ode(x, fx, test_coeff, bd_cond[:3], tf)
def test_poisson_solve_mtr_cmpl(self):
"""Test solve poisson equation and interpolate the result."""
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,
)
ibtf = InverseRTransform(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(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_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_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_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_becke_integral(self):
"""Test transform integral."""
oned = GaussLegendre(20)
btf = BeckeRTransform(0.00001, 1.0)
rad = btf.transform_1d_grid(oned)
def gauss(x):
return np.exp(-(x**2))
result = rad.integrate(gauss(rad.points))
ref_result = np.sqrt(np.pi) / 2
assert_almost_equal(result, ref_result, decimal=5)
oned = GaussChebyshev(20)
rad = btf.transform_1d_grid(oned)
result = rad.integrate(gauss(rad.points))
assert_almost_equal(result, ref_result, decimal=3)
def test_domain(self):
"""Test domain errors."""
rad = UniformInteger(10)
with self.assertRaises(ValueError):
tf = BeckeRTransform(0.1, 1.2)
tf.transform_1d_grid(rad)
with self.assertRaises(ValueError):
tf = HandyModRTransform(0.1, 10.0, 2)
tf.transform_1d_grid(rad)
with self.assertRaises(ValueError):
tf = KnowlesRTransform(0.1, 1.2, 2)
tf.transform_1d_grid(rad)
with self.assertRaises(ValueError):
tf = LinearFiniteRTransform(0.1, 10)
tf.transform_1d_grid(rad)
with self.assertRaises(ValueError):
tf = MultiExpRTransform(0.1, 1.2)
tf.transform_1d_grid(rad)
def test_error_raises():
"""Test proper error raises."""
x = np.linspace(-0.999, 0.999, 20)
# r = btf.transform(x)
def fx(x):
return 1 / x**2
coeffs = [-1, -2, 1]
bd_cond = [(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)]
# Test the error that the number of boundary conditions should be equal to order.
assert_raises(ValueError, solve_ode, x, fx, coeffs, bd_cond[3:])
assert_raises(ValueError, solve_ode, x, fx, coeffs, bd_cond)
test_coeff = [1, 2, 3, 4, 5]
assert_raises(ValueError, solve_ode, x, fx, test_coeff, bd_cond)
test_coeff = [1, 2, 3, 3]
tf = BeckeRTransform(0.1, 1)
assert_raises(ValueError, solve_ode, x, fx, test_coeff, bd_cond[:3], tf)
def test_cubicspline_and_interp_gauss(self):
"""Test cubicspline interpolation values."""
oned = GaussLegendre(30)
btf = BeckeRTransform(0.0001, 1.5)
rad = btf.transform_1d_grid(oned)
atgrid = AtomGrid.from_pruned(rad, 1, sectors_r=[], sectors_degree=[7])
value_array = self.helper_func_gauss(atgrid.points)
# random test points on gauss function
for _ in range(20):
r = np.random.rand(1)[0] * 2
theta = np.random.rand(10)
phi = np.random.rand(10)
x = r * np.sin(phi) * np.cos(theta)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
input_points = np.array((x, y, z)).T
interfunc = atgrid.interpolate(value_array)
assert_allclose(self.helper_func_gauss(input_points),
interfunc(input_points),
atol=1e-4)
def test_cubicspline_and_interp_gauss(self):
"""Test cubicspline interpolation values."""
oned = GaussLegendre(30)
btf = BeckeRTransform(0.0001, 1.5)
rad = btf.transform_1d_grid(oned)
atgrid = AtomGrid.from_pruned(rad, 1, sectors_r=[], sectors_degree=[7])
value_array = self.helper_func_gauss(atgrid.points)
result = spline_with_atomic_grid(atgrid, value_array)
# random test points on gauss function
for _ in range(20):
r = np.random.rand(1)[0] * 2
theta = np.random.rand(10)
phi = np.random.rand(10)
inters = interpolate_given_splines(result, r, theta, phi)
x = r * np.sin(phi) * np.cos(theta)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
assert_allclose(self.helper_func_gauss(np.array([x, y, z]).T),
inters,
atol=1e-4)
def test_poisson_proj(self):
"""Test the project function."""
oned = GaussChebyshev(30)
btf = BeckeRTransform(0.0001, 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)
spl_res = spline_with_atomic_grid(atgrid, value_array)
# test for random, r, theta, phi
for _ in range(20):
r = np.random.rand(1)[0] * 2
theta = np.random.rand(10) * 3.14
phi = np.random.rand(10) * 3.14
result = interpolate(spl_res, r, theta, phi)
x = r * np.sin(phi) * np.cos(theta)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
result_ref = self.helper_func_gauss(np.array([x, y, z]).T)
# assert similar value less than 1e-4 discrepancy
assert_allclose(result, result_ref, 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 each point is the same
for _ in range(20):
r = np.random.rand(1)[0] * 2
# random spherical point
int_res = np.zeros((l_max, l_max // 2 + 1), dtype=float)
for j in range(l_max // 2 + 1):
for i in range(-j, j + 1):
int_res[i, j] += spls_mt[i, j](r)
assert_allclose(spl_res(r), int_res)
def test_raises_errors(self):
"""Test proper error raises."""
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()
with self.assertRaises(ValueError):
Poisson._proj_sph_value(
atgrid.rgrid,
sph_coor,
l_max // 2,
value_array,
atgrid.weights,
atgrid.indices,
)
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)
"""Compute 3rd order deriv of TF."""
return (self._exp - 2) * (self._exp -
1) * (self._exp) * x**(self._exp - 3)
@pytest.mark.parametrize(
"transform, fx, coeffs",
[
[IdentityRTransform(), fx_ones, [-1, 1, 1]],
[SqTF(), fx_ones, np.random.uniform(-100, 100, (3, ))],
[
KnowlesRTransform(0.01, 1, 5), fx_ones,
np.random.uniform(-10, 10, (3, ))
],
[
BeckeRTransform(0.1, 100.0), fx_ones,
np.random.uniform(0, 100, (3, ))
],
[SqTF(1, 3), fx_complicated_example,
np.random.uniform(0, 100, (3, ))],
[SqTF(3, 1), fx_complicated_example, [2, 3, 2]],
[SqTF(), fx_quadratic,
np.random.uniform(-100, 100, (3, ))],
[
SqTF(1, 4), fx_complicated_example,
np.random.uniform(-10, 10, (3, ))
],
[SqTF(1, 4), fx_complicated_example2, [1, -1, 1]],
],
)
def test_transform_and_rearrange_to_explicit_ode_with_simple_boundary(
def test_error_raises(self):
"""Tests for error raises."""
with self.assertRaises(TypeError):
AtomGrid.from_pruned(np.arange(3),
1.0,
sectors_r=np.arange(2),
sectors_degree=np.arange(3))
with self.assertRaises(ValueError):
AtomGrid.from_pruned(
OneDGrid(np.arange(3), np.arange(3)),
radius=1.0,
sectors_r=np.arange(2),
sectors_degree=np.arange(0),
)
with self.assertRaises(ValueError):
AtomGrid.from_pruned(
OneDGrid(np.arange(3), np.arange(3)),
radius=1.0,
sectors_r=np.arange(2),
sectors_degree=np.arange(4),
)
with self.assertRaises(ValueError):
AtomGrid._generate_atomic_grid(
OneDGrid(np.arange(3), np.arange(3)), np.arange(2))
with self.assertRaises(ValueError):
AtomGrid.from_pruned(
OneDGrid(np.arange(3), np.arange(3)),
radius=1.0,
sectors_r=np.array([0.3, 0.5, 0.7]),
sectors_degree=np.array([3, 5, 7, 5]),
center=np.array([0, 0, 0, 0]),
)
# test preset
with self.assertRaises(ValueError):
AtomGrid.from_preset(atnum=1, preset="fine")
with self.assertRaises(TypeError):
AtomGrid(OneDGrid(np.arange(3), np.arange(3)), sizes=110)
with self.assertRaises(TypeError):
AtomGrid(OneDGrid(np.arange(3), np.arange(3)), degrees=17)
with self.assertRaises(ValueError):
AtomGrid(OneDGrid(np.arange(3), np.arange(3)),
degrees=[17],
rotate=-1)
with self.assertRaises(TypeError):
AtomGrid(OneDGrid(np.arange(3), np.arange(3)),
degrees=[17],
rotate="asdfaf")
# error of radial grid
with self.assertRaises(TypeError):
AtomGrid(Grid(np.arange(1, 5, 1), np.ones(4)),
degrees=[2, 3, 4, 5])
with self.assertRaises(TypeError):
AtomGrid(OneDGrid(np.arange(-2, 2, 1), np.ones(4)),
degrees=[2, 3, 4, 5])
with self.assertRaises(TypeError):
rgrid = OneDGrid(np.arange(1, 3, 1), np.ones(2), domain=(-1, 5))
AtomGrid(rgrid, degrees=[2])
with self.assertRaises(TypeError):
rgrid = OneDGrid(np.arange(-1, 1, 1), np.ones(2))
AtomGrid(rgrid, degrees=[2])
with self.assertRaises(ValueError):
oned = GaussLegendre(30)
btf = BeckeRTransform(0.0001, 1.5)
rad = btf.transform_1d_grid(oned)
atgrid = AtomGrid.from_preset(rad, atnum=1, preset="fine")
atgrid.radial_component_splines(np.random.rand(100))
def test_becke_deriv(self):
"""Test becke transform derivatives with finite diff."""
btf = BeckeRTransform(0.1, 1.1)
# call finite diff test function with given arrays
self._deriv_finite_diff(-1, 0.90, btf)
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)
def test_becke_inverse_deriv(self):
"""Test inverse transformation derivatives with finite diff."""
btf = BeckeRTransform(0.1, 1.1)
inv = InverseRTransform(btf)
self._deriv_finite_diff(0, 20, inv)
def test_becke_inverse_inverse(self):
"""Test inverse of inverse of Becke transformation."""
btf = BeckeRTransform(0.1, 1.1)
inv = InverseRTransform(btf)
inv_inv = inv.inverse(inv.transform(self.array))
assert_allclose(inv_inv, self.array, atol=1e-7)
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_tf(self):
"""Test Becke initializaiton."""
btf = BeckeRTransform(0.1, 1.2)
assert btf.R == 1.2
assert btf.rmin == 0.1