def calc_eigen_coeffs(
self,
F_z_t0: DataArray = None,
):
"""Calculates the coefficients from the eigenvalues and eigenvectors for the
time evolution equation.
Parameters
----------
F_z_t0
Initial fractional abundance for given impurity element. (Optional)
Returns
-------
eig_coeffs
Coefficients calculated from the eigenvalues and eigenvectors needed
for the time evolution equation.
F_z_t0
Initial fractional abundance, either user-provided or fully neutral
eg. [1.0, 0.0, 0.0, 0.0, 0.0] for Beryllium.
"""
x1_coord = self.x1_coord
if F_z_t0 is None:
# mypy doesn't understand contionals or reassignments either.
F_z_t0 = np.zeros(self.F_z_tinf.shape, dtype=np.complex128) # type: ignore
F_z_t0[0, :] = np.array( # type: ignore
[1.0 + 0.0j for i in range(x1_coord.size)]
)
F_z_t0 = DataArray(
data=F_z_t0,
coords=[
(
"ion_charges",
np.linspace(
0, self.num_of_ion_charges - 1, self.num_of_ion_charges
),
),
x1_coord, # type: ignore
],
dims=["ion_charges", x1_coord.dims[0]],
)
else:
input_check("F_z_t0", F_z_t0, DataArray, greater_than_or_equal_zero=True)
try:
assert F_z_t0.ndim < 3
except AssertionError:
raise ValueError("F_z_t0 must be at most 2-dimensional.")
F_z_t0 = F_z_t0 / np.sum(F_z_t0, axis=0)
F_z_t0 = F_z_t0.as_type(dtype=np.complex128) # type: ignore
F_z_t0 = DataArray(
data=F_z_t0.values, # type: ignore
coords=[
(
"ion_charges",
np.linspace(
0, self.num_of_ion_charges - 1, self.num_of_ion_charges
),
),
x1_coord, # type: ignore
],
dims=["ion_charges", x1_coord.dims[0]],
)
eig_vals = self.eig_vals
eig_vecs_inv = np.zeros(self.eig_vecs.shape, dtype=np.complex128)
for ix1 in range(x1_coord.size):
eig_vecs_inv[:, :, ix1] = np.linalg.pinv(
np.transpose(self.eig_vecs[:, :, ix1])
)
boundary_conds = F_z_t0 - self.F_z_tinf
eig_coeffs = np.zeros(eig_vals.shape, dtype=np.complex128)
for ix1 in range(x1_coord.size):
eig_coeffs[:, ix1] = np.dot(boundary_conds[:, ix1], eig_vecs_inv[:, :, ix1])
self.eig_coeffs = eig_coeffs
# If argument to numpy functions is of type DataArray then output is of
# type DataArray
F_z_t0 = np.abs(np.real(F_z_t0)) # type: ignore
self.F_z_t0 = F_z_t0 # type: ignore
return eig_coeffs, F_z_t0
