Index

A

a_0_sj_and_js_from_v_k_w() (in module biosspheres.helmholtz.crossinteractions) a_0_sj_and_js_from_v_sj() (in module biosspheres.helmholtz.crossinteractions) a_0_sj_and_js_v1d() (in module biosspheres.laplace.crossinteractions) a_0_sj_and_js_v2d() (in module biosspheres.laplace.crossinteractions) a_0j_linear_operator() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) a_0j_matrix() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions)

a_j_linear_operator() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) a_j_matrix() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) all_cross_interactions_n_spheres_v1d() (in module biosspheres.laplace.crossinteractions) all_cross_interactions_n_spheres_v2d() (in module biosspheres.laplace.crossinteractions) azimuthal_trace_to_general_with_zeros() (in module biosspheres.miscella.extensions)

B

b_vector_1_sphere_mtf() (in module biosspheres.formulations.mtf.righthands) b_vector_n_spheres_mtf_cte_function() (in module biosspheres.formulations.mtf.righthands) b_vector_n_spheres_mtf_linear_function_z() (in module biosspheres.formulations.mtf.righthands) b_vector_n_spheres_mtf_plane_wave() (in module biosspheres.formulations.mtf.righthands) b_vector_n_spheres_mtf_point_source() (in module biosspheres.formulations.mtf.righthands) big_l_validation() (in module biosspheres.utils.validation.inputs) bio_jj() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) biosspheres module biosspheres.formulations module biosspheres.formulations.massmatrices module biosspheres.formulations.mtf module biosspheres.formulations.mtf.mtf module biosspheres.formulations.mtf.propertieschecks module biosspheres.formulations.mtf.reconstructions module biosspheres.formulations.mtf.righthands module biosspheres.formulations.mtf.solvertemplates module biosspheres.formulations.mtf.timecouplings module biosspheres.formulations.mtf.timecouplings.linearoperators module biosspheres.formulations.mtf.timecouplings.righthands module biosspheres.formulations.mtf.timecouplings.solvertemplates module biosspheres.helmholtz module biosspheres.helmholtz.crossinteractions module biosspheres.helmholtz.selfinteractions module

biosspheres.laplace module biosspheres.laplace.crossinteractions module biosspheres.laplace.drawing module biosspheres.laplace.selfinteractions module biosspheres.miscella module biosspheres.miscella.extensions module biosspheres.miscella.forcouplings module biosspheres.miscella.forcouplings.currents module biosspheres.miscella.forcouplings.oderesolutions module biosspheres.miscella.harmonicex module biosspheres.miscella.mathfunctions module biosspheres.miscella.spherearrangements module biosspheres.quadratures module biosspheres.quadratures.sphere module biosspheres.timecouplings module biosspheres.utils module biosspheres.utils.auxindexes module biosspheres.utils.drawing module biosspheres.utils.validation module biosspheres.utils.validation.inputs module

C

complex_spherical_harmonic_transform_1d() (in module biosspheres.quadratures.sphere) complex_spherical_harmonics_at_points() (in module biosspheres.formulations.mtf.reconstructions)

cte() (in module biosspheres.miscella.mathfunctions) cube_vertex_positions() (in module biosspheres.miscella.spherearrangements)

D

dimensions_array_validation() (in module biosspheres.utils.validation.inputs) disjoint_spheres_validation() (in module biosspheres.utils.validation.inputs)

draw_cut_representation_formula_n_sphere() (in module biosspheres.laplace.drawing) draw_cut_representation_formula_one_sphere_azimuthal_symmetry() (in module biosspheres.laplace.drawing)

F

finite_values_in_array() (in module biosspheres.utils.validation.inputs) float_array_validation() (in module biosspheres.utils.validation.inputs) float_validation() (in module biosspheres.utils.validation.inputs) from_sphere_s_cartesian_to_j_spherical_1d() (in module biosspheres.quadratures.sphere)

from_sphere_s_cartesian_to_j_spherical_2d() (in module biosspheres.quadratures.sphere) from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_1d() (in module biosspheres.quadratures.sphere) from_sphere_s_cartesian_to_j_spherical_and_spherical_vectors_2d() (in module biosspheres.quadratures.sphere) full_float_array_validation() (in module biosspheres.utils.validation.inputs) function_cte() (in module biosspheres.miscella.harmonicex)

G

gauss_legendre_trapezoidal_1d() (in module biosspheres.quadratures.sphere) gauss_legendre_trapezoidal_2d() (in module biosspheres.quadratures.sphere)

gauss_legendre_trapezoidal_complex_sh_mapping_2d() (in module biosspheres.quadratures.sphere) gauss_legendre_trapezoidal_init() (in module biosspheres.quadratures.sphere) gauss_legendre_trapezoidal_real_sh_mapping_2d() (in module biosspheres.quadratures.sphere)

I

i_fitzhughnagumo_n_spheres_function_creation() (in module biosspheres.miscella.forcouplings.currents) i_fitzhughnagumo_one_sphere_function_creation() (in module biosspheres.miscella.forcouplings.currents) i_kavian_leguebe_ea_2014_1_sphere_2d() (in module biosspheres.miscella.forcouplings.currents) i_kavian_leguebe_ea_2014_n_sphere_2d() (in module biosspheres.miscella.forcouplings.currents)

i_linear_resistive_current_function_creation_n_spheres() (in module biosspheres.miscella.forcouplings.currents) i_linear_resistive_current_function_creation_one_sphere() (in module biosspheres.miscella.forcouplings.currents) integer_validation() (in module biosspheres.utils.validation.inputs) is_scipy_linear_op() (in module biosspheres.utils.validation.inputs) is_scipy_sparse_array() (in module biosspheres.utils.validation.inputs)

J

j_block() (in module biosspheres.formulations.massmatrices)

K

k_0_jj_azimuthal_symmetry() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) k_0_sj_from_v_0_sj() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions) k_0_sj_semi_analytic_v1d() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions) k_0_sj_semi_analytic_v2d() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions)

k_1_jj_azimuthal_symmetry() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) ka_0_sj_from_k_js() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions) ka_0_sj_from_v_sj() (in module biosspheres.laplace.crossinteractions) ka_0_sj_semi_analytic_recurrence_v1d() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions) ka_0_sj_semi_analytic_recurrence_v2d() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions)

L

laplace_almost_fundamental_function() (in module biosspheres.miscella.mathfunctions)

linear_function() (in module biosspheres.miscella.mathfunctions)

M

module biosspheres biosspheres.formulations biosspheres.formulations.massmatrices biosspheres.formulations.mtf biosspheres.formulations.mtf.mtf biosspheres.formulations.mtf.propertieschecks biosspheres.formulations.mtf.reconstructions biosspheres.formulations.mtf.righthands biosspheres.formulations.mtf.solvertemplates biosspheres.formulations.mtf.timecouplings biosspheres.formulations.mtf.timecouplings.linearoperators biosspheres.formulations.mtf.timecouplings.righthands biosspheres.formulations.mtf.timecouplings.solvertemplates biosspheres.helmholtz biosspheres.helmholtz.crossinteractions biosspheres.helmholtz.selfinteractions biosspheres.laplace biosspheres.laplace.crossinteractions biosspheres.laplace.drawing biosspheres.laplace.selfinteractions biosspheres.miscella biosspheres.miscella.extensions biosspheres.miscella.forcouplings biosspheres.miscella.forcouplings.currents biosspheres.miscella.forcouplings.oderesolutions biosspheres.miscella.harmonicex biosspheres.miscella.mathfunctions biosspheres.miscella.spherearrangements biosspheres.quadratures biosspheres.quadratures.sphere biosspheres.timecouplings biosspheres.utils biosspheres.utils.auxindexes biosspheres.utils.drawing biosspheres.utils.validation biosspheres.utils.validation.inputs

mtf_1_linear_operator() (in module biosspheres.formulations.mtf.mtf) mtf_1_matrix() (in module biosspheres.formulations.mtf.mtf) mtf_1_reduced_linear_operator() (in module biosspheres.formulations.mtf.mtf) mtf_1_reduced_linear_operator_helmholtz() (in module biosspheres.formulations.mtf.mtf) mtf_1_reduced_matrix_helmholtz() (in module biosspheres.formulations.mtf.mtf) mtf_1_reduced_matrix_laplace() (in module biosspheres.formulations.mtf.mtf) mtf_laplace_n_spheres_point_source_direct_solver() (in module biosspheres.formulations.mtf.solvertemplates) mtf_laplace_n_spheres_point_source_indirect_solver() (in module biosspheres.formulations.mtf.solvertemplates) mtf_laplace_one_sphere_point_source_azimuthal_direct_solver() (in module biosspheres.formulations.mtf.solvertemplates)

N

n_j_blocks() (in module biosspheres.formulations.massmatrices) n_two_j_blocks() (in module biosspheres.formulations.massmatrices)

n_validation() (in module biosspheres.utils.validation.inputs) numpy_array_validation() (in module biosspheres.utils.validation.inputs)

P

pes_y_kus() (in module biosspheres.utils.auxindexes) phi_part_for_real_sh_mapping_2d() (in module biosspheres.quadratures.sphere) pi_validation() (in module biosspheres.utils.validation.inputs) pii_validation() (in module biosspheres.utils.validation.inputs) plane_wave() (in module biosspheres.miscella.mathfunctions) point_source() (in module biosspheres.miscella.mathfunctions)

point_source_coefficients_dirichlet_expansion() (in module biosspheres.miscella.harmonicex) point_source_coefficients_dirichlet_expansion_azimuthal_symmetry() (in module biosspheres.miscella.harmonicex) point_source_coefficients_neumann_expansion_0j() (in module biosspheres.miscella.harmonicex) point_source_coefficients_neumann_expansion_0j_azimuthal_symmetry() (in module biosspheres.miscella.harmonicex) pre_vector_1d_init() (in module biosspheres.quadratures.sphere) pre_vector_2d_init() (in module biosspheres.quadratures.sphere)

R

radii_validation() (in module biosspheres.utils.validation.inputs) radius_validation() (in module biosspheres.utils.validation.inputs) real_sh_mapping_2d() (in module biosspheres.quadratures.sphere)

real_spherical_harmonic_transform_1d() (in module biosspheres.quadratures.sphere) rf_helmholtz_n_spheres() (in module biosspheres.formulations.mtf.reconstructions) rf_laplace_one_sphere_azimuthal_symmetry() (in module biosspheres.formulations.mtf.reconstructions) rows_columns_big_a_sparse_1_sphere() (in module biosspheres.utils.auxindexes)

S

same_shape_check() (in module biosspheres.utils.validation.inputs) same_type_check() (in module biosspheres.utils.validation.inputs)

semi_implicit_fitzhughnagumo_n_spheres_next_creation() (in module biosspheres.miscella.forcouplings.oderesolutions) semi_implicit_fitzhughnagumo_one_sphere_next_step() (in module biosspheres.miscella.forcouplings.oderesolutions) square_array_check() (in module biosspheres.utils.validation.inputs)

T

template_3d_surface_plot() (in module biosspheres.utils.drawing) theta_part_for_real_sh_mapping_2d() (in module biosspheres.quadratures.sphere)

trigonometric_arrays_validation() (in module biosspheres.utils.validation.inputs) two_dimensional_array_check() (in module biosspheres.utils.validation.inputs) two_j_blocks() (in module biosspheres.formulations.massmatrices)

V

v_0_js_from_v_0_sj() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions) v_0_sj_semi_analytic_v1d() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions)

v_0_sj_semi_analytic_v2d() (in module biosspheres.helmholtz.crossinteractions) (in module biosspheres.laplace.crossinteractions) v_jj_azimuthal_symmetry() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions) v_k_w_0_sj_from_quadratures_1d() (in module biosspheres.helmholtz.crossinteractions)

W

w_0_sj_from_ka_sj() (in module biosspheres.helmholtz.crossinteractions) w_0_sj_from_v_sj() (in module biosspheres.laplace.crossinteractions) w_0_sj_semi_analytic_recurrence_v1d() (in module biosspheres.helmholtz.crossinteractions)

w_0_sj_semi_analytic_recurrence_v2d() (in module biosspheres.helmholtz.crossinteractions) w_jj_azimuthal_symmetry() (in module biosspheres.helmholtz.selfinteractions) (in module biosspheres.laplace.selfinteractions)

X

x_diagonal_with_its_inv() (in module biosspheres.formulations.mtf.mtf)

x_j_diagonal() (in module biosspheres.formulations.mtf.mtf) x_j_diagonal_inv() (in module biosspheres.formulations.mtf.mtf)