## Subclasses

Subclass name | Description |
---|---|

SlepianCap | Class for Slepian functions concentrated within a spherical cap. |

SlepianMask | Class for Slepian functions concentrated in an arbitrary domain. |

## Initialization

Initialization method | Description |
---|---|

`x = Slepian.from_cap()` |
Construct Slepian functions concentrated within a spherical cap. |

`x = Slepian.from_mask()` |
Construct Slepian functions concentrated within an arbitrary region. |

## Attributes

Attribute | Description |
---|---|

`kind` |
Either `'cap'` or `'mask'` . |

`coeffs` |
Array of spherical harmonic coefficients of the rotated spherical-cap Slepian functions. |

`shannon` |
The Shannon number, which approximates the number of well localized functions. |

`area` |
Area of the concentration domain, in radians. |

`eigenvalues` |
Concentration factors of the Slepian functions. |

`orders` |
The angular orders for each of the spherical-cap Slepian functions. |

`lmax` |
Spherical harmonic bandwidth of the Slepian functions. |

`theta` |
Angular radius of the spherical-cap localization domain (default in degrees). |

`theta_degrees` |
`True` (default) if theta is in degrees. |

`nmax` |
Number of Slepian functions. Default is `(lmax+1)**2` . |

`nrot` |
The number of best-concentrated spherical cap Slepian functions that were rotated and whose coefficients are stored in `coeffs` . |

`clat` , `clon` |
Latitude and longitude of the center of the rotated spherical-cap Slepian functions (default in degrees). |

`coord_degrees` |
`True` (default) if `clat` and `clon` are in degrees. |

`slepian_degrees` |
Boolean or int array defining which spherical harmonic degrees were used to construct the Slepian functions. |

## Methods

Method | Description |
---|---|

`expand()` |
Expand the input function in Slepian functions. |

`to_array()` |
Return an array of the spherical harmonic coefficients for function `alpha` , where `alpha` =`0` is the best concentrated, optionally using a different normalization convention. |

`to_shcoeffs()` |
Return the spherical harmonic coefficients of function `alpha` , where `alpha` =`0` is the best concentrated, as a new SHCoeffs class instance, optionally using a different normalization convention. |

`to_shgrid()` |
Return as a new SHGrid instance a grid of function `alpha` , where `alpha` =`0` is the best concentrated. |

`number_concentrated()` |
Return the number of Slepian functions that have concentration factors greater or equal to a specified value. |

`degrees()` |
Return an array containing the spherical harmonic degrees of the Slepian functions, from `0` to `lmax` . |

`spectra()` |
Return the spectra of one or more Slepian functions. |

`rotate()` |
Rotate the spherical cap Slepian functions, originally located at the North pole, to `clat` and `clon` and save the spherical harmonic coefficients in `coeffs` . |

`variance()` |
Calculate the theoretical variance of the power of a function expanded in spherical-cap Slepian functions. |

`copy()` |
Return a copy of the class instance. |

`plot()` |
Plot the best concentrated Slepian functions using a simple cylindrical projection. |

`plot_spectra()` |
Plot the spectra of the best concentrated Slepian functions. |

`info()` |
Print a summary of the data stored in the Slepian instance. |