Portability | portable |
---|---|

Stability | unstable |

Maintainer | claudiusmaximus@goto10.org |

Safe Haskell | None |

Mu-atom period, nucleus and bond point finding.

- findPeriod :: (Floating r, Ord r) => Integer -> r -> Complex r -> Maybe Integer
- findNucleus :: (Floating r, Fractional r) => Integer -> Complex r -> [Complex r]
- findBond :: (Floating r, Fractional r) => Integer -> Complex r -> r -> [Complex r]
- findInternal :: (Floating r, Fractional r) => Integer -> Complex r -> r -> r -> [Complex r]

# Documentation

Find the period of the lowest period nucleus inside a square.

The algorithm is based on Robert Munafo's page,
*Finding the Period of a mu-Atom*
http://mrob.com/pub/muency/period.html.

:: (Floating r, Fractional r) | |

=> Integer | period |

-> Complex r | estimate |

-> [Complex r] |

Given the period and approximate location, successively refine this estimate to a nucleus.

The algorithm is based on Robert Munafo's page
*Newton-Raphson method*
http://mrob.com/pub/muency/newtonraphsonmethod.html.

:: (Floating r, Fractional r) | |

=> Integer | period |

-> Complex r | nucleus |

-> r | angle |

-> [Complex r] |

Given the period and nucleus, find succesive refinements to the bond point at a given internal angle.

The algorithm is based on ideas from http://mrob.com/pub/muency/derivative.html.

:: (Floating r, Fractional r) | |

=> Integer | period |

-> Complex r | nucleus |

-> r | radius |

-> r | angle |

-> [Complex r] |

Given the period and nucleus, find an interior point at a given internal angle and radius in (0,1].