Module sleplet.functions

Set of classes to create functions on the sphere.

Sub-modules

sleplet.functions.africa

Contains the Africa class.

sleplet.functions.axisymmetric_wavelet_coefficients_africa

Contains the AxisymmetricWaveletCoefficientsAfrica class.

sleplet.functions.axisymmetric_wavelet_coefficients_earth

Contains the AxisymmetricWaveletCoefficientsEarth class.

sleplet.functions.axisymmetric_wavelet_coefficients_south_america

Contains the AxisymmetricWaveletCoefficientsSouthAmerica class.

sleplet.functions.axisymmetric_wavelets

Contains the AxisymmetricWavelets class.

sleplet.functions.coefficients

Contains the abstract Coefficients class.

sleplet.functions.dirac_delta

Contains the DiracDelta class.

sleplet.functions.earth

Contains the Earth class.

sleplet.functions.elongated_gaussian

Contains the ElongatedGaussian class.

sleplet.functions.flm

Contains the abstract Flm class.

sleplet.functions.fp

Contains the abstract Fp class.

sleplet.functions.gaussian

Contains the Gaussian class.

sleplet.functions.harmonic_gaussian

Contains the HarmonicGaussian class.

sleplet.functions.identity

Contains the Identity class.

sleplet.functions.noise_earth

Contains the NoiseEarth class.

sleplet.functions.ridgelets

Contains the Ridgelets class.

sleplet.functions.slepian

Contains the Slepian class.

sleplet.functions.slepian_africa

Contains the SlepianAfrica class.

sleplet.functions.slepian_dirac_delta

Contains the SlepianDiracDelta class.

sleplet.functions.slepian_identity

Contains the SlepianIdentity class.

sleplet.functions.slepian_noise_africa

Contains the SlepianNoiseAfrica class.

sleplet.functions.slepian_noise_south_america

Contains the SlepianNoiseSouthAmerica class.

sleplet.functions.slepian_south_america

Contains the SlepianSouthAmerica class.

sleplet.functions.slepian_wavelet_coefficients_africa

Contains the SlepianWaveletCoefficientsAfrica class.

sleplet.functions.slepian_wavelet_coefficients_south_america

Contains the SlepianWaveletCoefficientsSouthAmerica class.

sleplet.functions.slepian_wavelets

Contains the SlepianWavelets class.

sleplet.functions.south_america

Contains the SouthAmerica class.

sleplet.functions.spherical_harmonic

Contains the SphericalHarmonic class.

sleplet.functions.squashed_gaussian

Contains the SquashedGaussian class.

sleplet.functions.wmap

Contains the Wmap class.

Classes

class Africa (*args: Any, **kwargs: Any)

Create a topographic map of the Earth setting everything outide of the Africa region to zero.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class AxisymmetricWaveletCoefficientsAfrica (*args: Any, **kwargs: Any)

Create axisymmetric wavelet coefficients of the Africa region.

Ancestors

• Flm
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class AxisymmetricWaveletCoefficientsEarth (*args: Any, **kwargs: Any)

Create axisymmetric wavelet coefficients of the Earth.

Ancestors

• Flm
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class AxisymmetricWaveletCoefficientsSouthAmerica (*args: Any, **kwargs: Any)

Create axisymmetric wavelet coefficients of the South America region.

Ancestors

• Flm
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class AxisymmetricWavelets (*args: Any, **kwargs: Any)

Create scale-discretised axisymmetric wavelets. As seen in https://doi.org/10.1051/0004-6361/201220729.

Ancestors

• Flm
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class DiracDelta (*args: Any, **kwargs: Any)

Create a Dirac delta.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class Earth (*args: Any, **kwargs: Any)

Create the topographic map of the Earth.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class ElongatedGaussian (*args: Any, **kwargs: Any)

Create an elongated Gaussian $\exp(-(\frac{{(\theta-\overline{\theta})}^{2}}{2\sigma_{\theta}^{2}} + \frac{{(\phi-\overline{\phi})}^{2}}{2\sigma_{\phi}^{2}}))$.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var p_sigma : float

Sets the $\sigma_{\phi}$ value.

var t_sigma : float

Sets the $\sigma_{\theta}$ value.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class Gaussian (*args: Any, **kwargs: Any)

Create a Gaussian $\exp(-\frac{{\ell}^{2}}{2\sigma^{2}})$.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var sigma : float

Sets the $\sigma$ value.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class HarmonicGaussian (*args: Any, **kwargs: Any)

Create a harmonic Gaussian $\exp(-(\frac{{\ell}^{2}}{2\sigma_{\ell}^{2}} + \frac{{m}^{2}}{2\sigma_{m}^{2}}))$.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var l_sigma : float

Sets the $\sigma_{\ell}$ value.

var m_sigma : float

Sets the $\sigma_{m}$ value.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class Identity (*args: Any, **kwargs: Any)

Create an identity function.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class NoiseEarth (*args: Any, **kwargs: Any)

Create a noised signal of the topographic map of the Earth.

Ancestors

• Flm
• Coefficients

Class variables

var SNR : float

A parameter which controls the level of signal-to-noise in the noised data.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class Ridgelets (*args: Any, **kwargs: Any)

Crates scale-discretised wavelets. As seen in https://arxiv.org/abs/1510.01595.

Ancestors

• Flm
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var spin : int

Spin value.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class Slepian (*args: Any, **kwargs: Any)

Create Slepian functions of the selected region.

Ancestors

• Fp
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var rank : int

Slepian eigenvalues are ordered in decreasing value. The option rank selects a given Slepian function from the spectrum (p in the papers).

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianAfrica (*args: Any, **kwargs: Any)

Create a Slepian region on the topographic map of the Earth of the Africa region.

Ancestors

• Fp
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianDiracDelta (*args: Any, **kwargs: Any)

Create a Dirac delta of the Slepian coefficients.

Ancestors

• Fp
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianIdentity (*args: Any, **kwargs: Any)

Create an identify function in the Slepian region.

Ancestors

• Fp
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianNoiseAfrica (*args: Any, **kwargs: Any)

Create a noised Slepian region on the topographic map of the Earth of the Africa region.

Ancestors

• Fp
• Coefficients

Class variables

var SNR : float

A parameter which controls the level of signal-to-noise in the noised data.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianNoiseSouthAmerica (*args: Any, **kwargs: Any)

Create a noised Slepian region on the topographic map of the Earth of the South America region.

Ancestors

• Fp
• Coefficients

Class variables

var SNR : float

A parameter which controls the level of signal-to-noise in the noised data.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianSouthAmerica (*args: Any, **kwargs: Any)

Create a Slepian region on the topographic map of the Earth of the South America region.

Ancestors

• Fp
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianWaveletCoefficientsAfrica (*args: Any, **kwargs: Any)

Create Slepian wavelet coefficients of the Africa region.

Ancestors

• Fp
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianWaveletCoefficientsSouthAmerica (*args: Any, **kwargs: Any)

Create Slepian wavelet coefficients of the South America region.

Ancestors

• Fp
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SlepianWavelets (*args: Any, **kwargs: Any)

Create the Slepian wavelets.

Ancestors

• Fp
• Coefficients

Class variables

var B : int

The wavelet parameter. Represented as $\lambda$ in the papers.

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var j : int | None

Option to select a given wavelet. None indicates the scaling function, whereas 0 would correspond to the selected j_min.

var j_min : int

The minimum wavelet scale. Represented as $J_{0}$ in the papers.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Fp:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SouthAmerica (*args: Any, **kwargs: Any)

Create the South America region of the topographic map of the Earth.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SphericalHarmonic (*args: Any, **kwargs: Any)

Create spherical harmonic functions.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var ell : int

Degree $\ell \geq 0$.

var m : int

Order $\leq |\ell|$

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class SquashedGaussian (*args: Any, **kwargs: Any)

Create a squashed Gaussian $\exp(-\frac{1}{2}{(\frac{\theta-\overline{\theta}}{\sigma_{\theta}})}^{2}) \sin{(\nu_{\phi}\phi)}$.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var freq : float

Sets the $\nu_{\phi}$ value.

var t_sigma : float

Sets the $\sigma_{\theta}$ value.

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate

class Wmap (*args: Any, **kwargs: Any)

Create the WMAP data.

Ancestors

• Flm
• Coefficients

Class variables

var coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelet_coefficients : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

var wavelets : numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Inherited members

• Flm:
  • L
  • convolve
  • extra_args
  • noise
  • region
  • rotate
  • smoothing
  • translate