biosspheres.miscella.harmonicex

This module has functions for returning the spherical harmonic expansions of selected functions.

Extended summary

This module has functions for returning the spherical harmonic expansions of selected functions: - The zero function. See function_zero. - The constant function. See function_cte. - Point source function, dirichlet and neumann expansions. See

point_source_coefficients_dirichlet_expansion_azimuthal_symmetry, point_source_coefficients_dirichlet_expansion, point_source_coefficients_neumann_expansion_0j_azimuthal_symmetry, point_source_coefficients_neumann_expansion_0j.

Routine listings

function_zero function_cte point_source_coefficients_dirichlet_expansion_azimuthal_symmetry point_source_coefficients_dirichlet_expansion point_source_coefficients_neumann_expansion_0j_azimuthal_symmetry point_source_coefficients_neumann_expansion_0j plane_wave_coefficients_dirichlet_expansion_0j plane_wave_coefficients_neumann_expansion_0j

Functions

function_cte(big_l, cte[, azimuthal])
function_zero(big_l[, azimuthal])
plane_wave_coefficients_dirichlet_expansion_0j(...)
plane_wave_coefficients_neumann_expansion_0j(...)
point_source_coefficients_dirichlet_expansion(...)	Returns a numpy array with the coefficients of the spherical harmonic expansion of the Dirichlet trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).
point_source_coefficients_dirichlet_expansion_azimuthal_symmetry(...)	Returns a numpy array with the coefficients of the spherical harmonic expansion of the dirichlet trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).
point_source_coefficients_neumann_expansion_0j(...)	Returns a numpy array with the coefficients of the spherical harmonic expansion of the Neumann trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).
point_source_coefficients_neumann_expansion_0j_azimuthal_symmetry(...)	Returns a numpy array with the coefficients of the spherical harmonic expansion of the Neumann trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).

biosspheres.miscella.harmonicex.function_cte(big_l: int, cte: float, azimuthal: bool = True) → ndarray

Parameters:

• big_l

• cte

• azimuthal

Returns:

function_coefficientes

Return type:

np.ndarray

biosspheres.miscella.harmonicex.point_source_coefficients_dirichlet_expansion(big_l: int, radius: float, p_0: ndarray, sigma_e: float, intensity: float) → ndarray

Returns a numpy array with the coefficients of the spherical harmonic expansion of the Dirichlet trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).

Parameters:

• big_l (int) – >= 0, max degree.

• radius (float) – > 0, sphere radius.

• p_0 (numpy array) – of three floats, position in cartesian coordinates relative to the center of the sphere.

• sigma_e (float) – > 0 , parameter.

• intensity (float) – > 0 , parameter.

Returns:

values – Length (big_l+1)**2.

Return type:

numpy array

biosspheres.miscella.harmonicex.point_source_coefficients_dirichlet_expansion_azimuthal_symmetry(big_l: int, radius: float, p_0_0: float, sigma_e: float, intensity: float) → ndarray

Returns a numpy array with the coefficients of the spherical harmonic expansion of the dirichlet trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).

Only works in one half of the z axis.

Parameters:

• big_l (int) – >= 0, max degree.

• radius (float) – > 0, sphere radius.

• p_0_0 (float) – > 0, norm of the position vector of the source.

• sigma_e (float) – > 0, parameter.

• intensity (float) – > 0, parameter.

Returns:

values – Length (big_l+1).

Return type:

numpy array

biosspheres.miscella.harmonicex.point_source_coefficients_neumann_expansion_0j(big_l: int, radius: float, p_0: ndarray, sigma_e: float, intensity: float) → ndarray

Returns a numpy array with the coefficients of the spherical harmonic expansion of the Neumann trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).

Parameters:

• big_l (int) – >= 0, max degree.

• radius (float) – > 0, sphere radius.

• p_0 (numpy array) – of three floats, position in cartesian coordinates relative to the center of the sphere.

• sigma_e (float) – > 0, parameter.

• intensity (float) – > 0, parameter.

Returns:

values – Length (big_l+1)**2.

Return type:

numpy array

biosspheres.miscella.harmonicex.point_source_coefficients_neumann_expansion_0j_azimuthal_symmetry(big_l: int, radius: float, p_0_0: float, sigma_e: float, intensity: float) → ndarray

Returns a numpy array with the coefficients of the spherical harmonic expansion of the Neumann trace, on the surface of the sphere of radius 1, of the function 1 / (4 pi sigma_e ||p_0 - r||_2).

Only works in one half of the z axis.

Parameters:

• big_l (int) – >= 0, max degree.

• radius (float) – > 0, sphere radius.

• p_0_0 (float) – > 0, norm of the position vector of the source.

• sigma_e (float) – > 0, parameter.

• intensity (float) – > 0, parameter.

Returns:

values – Length (big_l+1).

Return type:

numpy array