mappy_ds.Diffeomorphism#

class mappy_ds.Diffeomorphism(fun, name='map')#

A discrete map \(y \mapsto f(y, p)\) on \(\mathbb{R}^n\).

Parameters:

funSystemFunction: The map, declared with mappy_ds.mapping(); its domain and codomain must have the same dimension.
namestr, optional: Name of the underlying mode, by default "map".

Examples

>>> import numpy as np
>>> from mappy_ds import Diffeomorphism, mapping
>>> @mapping(2)
... def henon(y, p):
...     x, u = y
...     return np.array([1 - p["a"] * x**2 + u, p["b"] * x])
>>> henon_map = Diffeomorphism(henon)
>>> henon_map.image([0.0, 0.0], {"a": 1.4, "b": 0.3}, n=2)
array([-0.4,  0.3])

Properties

`dim`	Dimension of the domain (and codomain) of the map.
`fun`	The underlying system function.
`param_keys`	Names of all parameters the map depends on.

Methods

`image`(y0[, params, n])	Compute the `n`-th image of `y0`.
`image_detail`(y0[, params, n, jacobian, ...])	Compute the `n`-th image of `y0`; see `Map.image_detail()`.
`trajectory`(y0[, params, n])	Compute the trajectory from `y0` over `n` iterations.