Bandlimits & Indexing#
- s2ball.wavelets.helper_functions.angular_bandlimit(jl: int, lam_l: float) int#
Computes the angular band-limit for scale \(j_{\ell}\). :param jl: Wavelet angular scale. :type jl: int :param lam_l: Angular wavelet parameter which determines the scale factor
between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Returns:
Angular band-limit for scale \(j_l\).
- Return type:
int
- s2ball.wavelets.helper_functions.j_max(L: int, lam: float = 2) int#
Computes the highest wavelet scale \(J_{ ext{max}}\). :param L: Harmonic band-limit. :type L: int :param lam: Wavelet parameter which determines the scale factor
between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Returns:
Maximum wavelet scale \(J_{ ext{max}}\).
- Return type:
int
- s2ball.wavelets.helper_functions.radial_bandlimit(jp: int, lam_p: float = 2) int#
Computes the radial band-limit for scale \(j_p\). :param jp: Wavelet radial scale. :type jp: int :param lam_p: Radial wavelet parameter which determines the scale factor
between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Returns:
Radial band-limit for scale \(j_p\).
- Return type:
int
- s2ball.wavelets.helper_functions.wavelet_scale_limits(L: int, P: int, jl: int, jp: int, lam_l: float = 2, lam_p: float = 2) Tuple[int, int]#
Computes the angular and radial band-limits for scale \(j_{\ell}/j_p\). :param L: Harmonic band-limit. :type L: int :param P: Radial band-limit. :type P: int :param jl: Wavelet angular scale. :type jl: int :param jp: Wavelet radial scale. :type jp: int :param lam_l: Angular wavelet parameter which determines the scale factor
between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Parameters:
lam_p (float, optional) – Radial wavelet parameter which determines the scale factor between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Returns:
Angular and Radial band-limit for scale \(j_{\ell}/j_p\).
- Return type:
Tuple[int,int]
- s2ball.wavelets.helper_functions.wavelet_scale_limits_N(L: int, P: int, N: int, jl: int, jp: int, lam_l: float = 2, lam_p: float = 2) Tuple[int, int, int]#
Computes the angular and radial band-limits and multiresolution directionality \(N_j\) for scale \(j_{\ell}/j_p\). :param L: Harmonic band-limit. :type L: int :param P: Radial band-limit. :type P: int :param N: Azimuthal (directional) band-limit. :type N: int :param jl: Wavelet angular scale. :type jl: int :param jp: Wavelet radial scale. :type jp: int :param lam_l: Angular wavelet parameter which determines the scale factor
between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Parameters:
lam_p (float, optional) – Radial wavelet parameter which determines the scale factor between consecutive wavelet scales. Note that \(\lambda = 2\) indicates dyadic wavelets. Defaults to 2.
- Returns:
Angular and Radial band-limit for scale \(j_{\ell}/j_p\).
- Return type:
Tuple[int,int]