Spherical Operations#
- s2scat.operators.spherical.make_flm_full(flm_real_only: Array, L: int) Array#
- Reflects real harmonic coefficients to a complete set of coefficients
using hermitian symmetry.
- Parameters:
flm_real_only (jnp.ndarray) – Positive half-plane of the spherical harmonic coefficients.
L (int) – Spherical harmonic bandlimit.
- Returns:
- Full set of spherical harmonic coefficients, reflected across \(m=0\)
by using hermitian symmetry.
- Return type:
jnp.ndarray
Notes
For real (spin-0) signals the harmonic coefficients obey \(f^*_{\ell, m} = (-1)^m f_{\ell, -m}\).
- s2scat.operators.spherical.make_flm_real(flm: Array, L: int) Array#
- Compresses harmonic coefficients of a real signal into positive coefficients only
which leverages hermitian symmetry.
- Parameters:
flm (jnp.ndarray) – Full set of spherical harmonic coefficients
L (int) – Spherical harmonic bandlimit.
- Returns:
Positive half-plane of the spherical harmonic coefficients
- Return type:
jnp.ndarray
Notes
For real (spin-0) signals the harmonic coefficients obey \(f^*_{\ell, m} = (-1)^m f_{\ell, -m}\).
- s2scat.operators.spherical.quadrature(L: int, J_min: int = 0) List[Array]#
Generates spherical quadrature weights associated Gauss-Legendre sampling points.
- Parameters:
L (int) – Spherical harmonic bandlimit.
J_min (int, optional) – Minimum dyadic wavelet scale to consider. Defaults to 0.
- Returns:
- Multiresolution quadrature weights for each \(\theta\)
corresponding to each wavelet scale \(j \in [J_{\text{min}}, J_{\text{max}}]\).
- Return type:
List[jnp.ndarray]