Pycsou-sphere is an extension module of the Python 3 package Pycsou for solving linear inverse problems on the sphere. The extension offers implementations of spherical zonal convolution operators as well as the spherical harmonic and Fourier-Legendre transforms (all compatible with Pycsou’s interface for linear operators). It also provides numerical routines for computing the Green kernels of common spherical pseudo-differential operators and generating spherical meshes/point sets.
This module heavily relies and follows similar conventions as the healpy package for spherical signal processing with Python.
Content¶
The package is organised as follows:
The module
pycsphere.linopimplements the following common spherical linear operators:
Zonal spherical convolution. |
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Spherical pooling operator. |
Discrete spherical Laplacian. |
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Discrete spherical gradient. |
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Spherical Harmonic Transform (SHT). |
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Fourier Legendre Transform (FLT). |
The module
pycsphere.meshprovides routines for generating spherical meshes:
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Fibonacci point set. |
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HEALPix point set. |
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Random uniform point set. |
The module
pycsphere.greenprovides numerical routines for computing the Green kernels of common spherical pseudo-differential operators:
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Zonal Green kernel of the Sobolev operator \((\alpha^2\mbox{Id} -\Delta_{\mathbb{S}^2})^{\beta/2}\). |
Zonal Green kernel of the Fractional Laplace-Beltrami operator \((-\Delta_{\mathbb{S}^2})^{\beta/2}\). |
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Zonal Green kernel of the iterated Laplace-Beltrami operator \(\Delta_{\mathbb{S}^2}^{k}\). |
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Zonal Green kernel of the Beltrami operator \(\partial_k=k(k+1)\mbox{Id}+\Delta_{\mathbb{S}^2}\). |
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Zonal Green kernel of the Beltrami operator \(\partial_{0\cdots k}=\partial_0\cdots\partial_k\). |
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Matern zonal Green kernel. |
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Wendland zonal Green kernel. |