Module sleplet.wavelet_methods
Methods to work with wavelet and wavelet coefficients.
Functions
def axisymmetric_wavelet_forward(L: int, flm: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]], wavelets: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]-
Compute the coefficients of the axisymmetric wavelets.
Args
L- The spherical harmonic bandlimit.
flm- The spherical harmonic coefficients.
wavelets- Axisymmetric wavelets.
Returns
Axisymmetric wavelets coefficients.
def axisymmetric_wavelet_inverse(L: int, wav_coeffs: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]], wavelets: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]-
Compute the inverse axisymmetric wavelet transform.
Args
L- The spherical harmonic bandlimit.
wav_coeffs- Axisymmetric wavelet coefficients.
wavelets- Axisymmetric wavelets.
Returns
Spherical harmonic coefficients of the signal.
def create_kappas(xlim: int, B: int, j_min: int) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]]-
Compute the Slepian wavelets.
Args
xlim- The x-axis value. L or L^2 in the harmonic or Slepian case.
B- The wavelet parameter. Represented as \lambda in the papers.
j_min- The minimum wavelet scale. Represented as J_{0} in the papers.
Returns
The Slepian wavelet generating functions.
def find_non_zero_wavelet_coefficients(wav_coeffs: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]], *, axis: int | tuple[int, ...]) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]-
Find the coefficients within the shannon number to speed up computations.
Args
wav_coeffs- The wavelet coefficients.
axis- The axis to search over.
Returns
The non-zero wavelet coefficients.
def slepian_wavelet_forward(f_p: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]], wavelets: numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]], shannon: int) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]-
Compute the coefficients of the given tiling function in Slepian space.
Args
f_p- The Slepian coefficients.
wavelets- The Slepian wavelets.
shannon- The Shannon number.
Returns
The Slepian wavelets coefficients of the signal.
def slepian_wavelet_inverse(wav_coeffs: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]], wavelets: numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]], shannon: int) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]-
Compute the inverse wavelet transform in Slepian space.
Args
wav_coeffs- The Slepian wavelet coefficients.
wavelets- The Slepian wavelets.
shannon- The Shannon number.
Returns
The coefficients of the signal in Slepian space.