## Subclasses

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

SHWindowCap | Class for windows concentrated within a spherical cap. |

SHWindowMask | Class for windows concentrated in an arbitrary domain. |

## Initialization

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

`x = SHWindow.from_cap()` |
Construct windows concentrated within a spherical cap. |

`x = SHWindow.from_mask()` |
Construct windows concentrated within an arbitrary region. |

## Attributes

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

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

`coeffs` |
Array of spherical harmonic coefficients of the rotated spherical-cap localization windows. |

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

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

`eigenvalues` |
Concentration factors of the localization windows. |

`orders` |
The angular orders for each of the spherical-cap localization windows. |

`weights` |
Taper weights used with the multitaper spectral analyses. Default is `None` . |

`lmax` |
Spherical harmonic bandwidth of the localization windows. |

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

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

`nwin` |
Number of localization windows. Default is `(lmax+1)**2` . |

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

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

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

`taper_degrees` |
Boolean or int array defining which spherical harmonic degrees were used to construct the windows. |

## Methods

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

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

`to_shcoeffs()` |
Return the spherical harmonic coefficients of taper `i` , where `i` =`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 taper `i` , where `i` =`0` is the best concentrated window. |

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

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

`spectra()` |
Return the spectra of one or more localization windows. |

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

`coupling_matrix()` |
Return the coupling matrix of the first `nwin` . |

`biased_spectrum()` |
Calculate the multitaper (cross-) spectrum expectation of a localized function. |

`multitaper_spectrum()` |
Return the multitaper spectrum estimate and uncertainty for the input SHCoeffs class instance. |

`multitaper_cross_spectrum()` |
Return the multitaper cross-spectrum estimate and uncertainty for two input SHCoeffs class instances. |

`variance()` |
Compute the theoretical variance of a windowed function for a given input power spectrum. |

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

`plot_windows()` |
Plot the best concentrated localization windows using a simple cylindrical projection. |

`plot_spectra()` |
Plot the spectra of the best concentrated localization windows. |

`plot_coupling_matrix()` |
Plot the multitaper coupling matrix. |

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