def test_transform_coeff_with_x_and_r(self):
"""Test coefficient transform between x and r."""
coeff = np.array([2, 3, 4])
ltf = LinearFiniteRTransform(1, 10) # (-1, 1) -> (r0, rmax)
inv_tf = InverseRTransform(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_transform_coeff_with_x_and_r():
"""Test coefficient transform between x and r."""
coeff = np.array([2, 3, 4])
ltf = LinearFiniteRTransform(1, 10) # (-1, 1) -> (r0, rmax)
inv_tf = InverseRTransform(ltf) # (r0, rmax) -> (-1, 1)
x = np.linspace(-1, 1, 20)
r = ltf.transform(x)
assert r[0] == 1
assert r[-1] == 10
# Transform ODE from [1, 10) to (-1, 1)
coeff_transform = _transform_ode_from_rtransform(coeff, inv_tf, x)
derivs_fun = [inv_tf.deriv, inv_tf.deriv2, inv_tf.deriv3]
coeff_transform_all_pts = _transform_ode_from_derivs(coeff, derivs_fun, r)
assert_allclose(coeff_transform, coeff_transform_all_pts)
def test_linear_inverse(self):
"""Test inverse transform and derivs function."""
ltf = LinearFiniteRTransform(0.1, 10)
iltf = InverseRTransform(ltf)
# transform & inverse
self._transform_and_inverse(0, 20, iltf)
# finite diff for derivs
self._deriv_finite_diff(0, 20, iltf)
def test_linear_transform_coeff(self):
"""Test coefficient with linear transformation."""
x = GaussLaguerre(10).points
ltf = LinearFiniteRTransform(1, 10)
inv_ltf = InverseRTransform(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_transformation_of_ode_with_linear_transform():
"""Test transformation of ODE with linear transformation."""
x = GaussLaguerre(10).points
# Obtain linear transformation with rmin = 1 and rmax = 10.
ltf = LinearFiniteRTransform(1, 10)
# The inverse is x_i = \frac{r_i - r_{min} - R} {r_i - r_{min} + R}
inv_ltf = InverseRTransform(ltf)
derivs_fun = [inv_ltf.deriv, inv_ltf.deriv2, inv_ltf.deriv3]
# Test with 2y + 3y` + 4y``
coeff = np.array([2, 3, 4])
coeff_b = _transform_ode_from_derivs(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_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_linear_finite_diff(self):
"""Test finite diff for linear derivs."""
ltf = LinearFiniteRTransform(0.1, 10)
self._deriv_finite_diff(-1, 1, ltf)
def test_linear_transform(self):
"""Test linear transformation."""
ltf = LinearFiniteRTransform(0.1, 10)
self._transform_and_inverse(-1, 1, ltf)