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 = BeckeTF(0.1, 1)
def fx(x):
return x
ODE.solve_ode(x, fx, test_coeff, bd_cond[:3], tf)
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_solve_ode_bvp(self):
"""Test result for high level api solve_ode."""
x = np.linspace(0, 2, 10)
def fx(x):
return 1 if isinstance(x, Number) else np.ones(x.size)
coeffs = [0, 0, 1]
bd_cond = [[0, 0, 0], [1, 0, 0]]
res = ODE.solve_ode(x, fx, coeffs, bd_cond)
assert_almost_equal(res(0)[0], 0)
assert_almost_equal(res(1)[0], -0.5)
assert_almost_equal(res(2)[0], 0)
assert_almost_equal(res(0)[1], -1)
assert_almost_equal(res(1)[1], 0)
assert_almost_equal(res(2)[1], 1)
def solve_poisson_bv(fx, x_range, boundary, m_l=(0, 0), tfm=None):
"""Solve poisson equation for given function.
.. math::
Parameters
----------
fx : Callable
Callable function on the right hand side of equation
x_range : np.narray(K,)
An array with points for numerically solve the ODE
The boundary point should be within radial points range
boundary : float
Boundary value when x to go infinite
m_l : tuple, optional
m and l value of given spherical harmonics
tfm : None, optional
Transformation for given x variable
Returns
-------
scipy.PPline
A callable spline for result.
"""
m_value, l_value = m_l
def f_x(r):
return fx(r) * -4 * np.pi * r
def coeff_0(r):
return -l_value * (l_value + 1) / r**2
coeffs = [coeff_0, 0, 1]
if l_value == 0 and m_value == 0:
bd_cond = [(0, 0, 0), (1, 0, boundary)]
else:
bd_cond = [(0, 0, 0), (1, 0, 0)]
return ODE.solve_ode(x_range, f_x, coeffs, bd_cond, transform=tfm)