pymiediff.special

Special functions used by pymiediff.

This module provides autograd-friendly spherical Bessel/Hankel functions and their derivatives, together with Riccati-Bessel forms and vector spherical harmonic (VSH) helpers used by Mie coefficient and near-field solvers.

Both SciPy-backed and torch-native recurrence implementations are available. The Peña/Yang log-derivative recurrences are also implemented for stable multilayer computations.

Functions

D1n_torch(n, z[, n_add, n_add_min, ...])	Vectorized D(1)n logrithmic derivative via downward recurrence
D3n_torch(n, z, D1ns[, eps, precision])
Ql_torch(n, l, m, x[, eps])
bessel2ndDer(n, z, bessel, **kwargs)	Evaluate second derivative of a spherical Bessel function.
chi(n, z, **kwargs)	Riccati-Bessel function chi_n(z) and derivative.
chi_torch(n, z, **kwargs)	Torch-native Riccati-Bessel chi_n and derivative.
f_der(n, z, f_n, **kwargs)	Differentiate order-indexed spherical Bessel-like sequences.
pena_D1_n(n, z[, n_add, eps, precision])	Compute D_n^(1)(z) = psi'_n(z) / psi_n(z) by downward recurrence.
pena_D3_n(n, z[, D1, eps, precision])	Compute D_n^(3)(z) = zeta'_n(z) / zeta_n(z) recurrence.
pena_Q_n(n, z1, z2, x1, x2, D1_z1, D1_z2, ...)	Evaluate Peña/Pal interface ratio recurrence Q_n.
pena_psi_zeta_n(n, z, D1, D3[, eps, precision])	Build psi_n and zeta_n sequences from Peña derivatives.
pi_tau(n, mu, **kwargs)	Compute angular functions pi_n and tau_n up to order n.
psi(n, z, **kwargs)	Riccati-Bessel function psi_n(z) and derivative.
psi_torch(n, z, **kwargs)	Torch-native Riccati-Bessel psi_n and derivative.
psi_torch_logdir(n, l, m, x[, eps])
sph_h1n(n, z, **kwargs)	Spherical Hankel function of the first kind.
sph_h1n_der(n, z, **kwargs)	Derivative of spherical Hankel function of the first kind.
sph_h1n_torch(n, z, **kwargs)	Torch-native spherical Hankel function h_n^(1).
sph_jn(n, z, **kwargs)	Spherical Bessel function of the first kind.
sph_jn_der(n, z, **kwargs)	Derivative of spherical Bessel function of the first kind.
sph_jn_torch(n, z[, n_add, max_n_add, ...])	Torch-native j_n via continued-fraction ratios.
sph_jn_torch_via_rec(n, z[, n_add, ...])	Torch-native j_n via downward recurrence.
sph_yn(n, z, **kwargs)	Spherical Bessel function of the second kind.
sph_yn_der(n, z, **kwargs)	Derivative of spherical Bessel function of the second kind.
sph_yn_torch(n, z[, eps])	Torch-native y_n via upward recurrence.
vsh(n_max, k0, n_medium, r, theta, phi, kind)	Compute vector spherical harmonics with standard radial kernels.
vsh_pena(n_max, k0, n_medium, r, theta, phi, ...)	Compute VSH terms using Peña log-derivative recurrences.
xi(n, z, **kwargs)	Riccati-Bessel function xi_n(z) and derivative.
xi_torch(n, z, **kwargs)	Torch-native Riccati-Bessel xi_n and derivative.
xi_torch_logdir(n, l, m, x[, eps])