# @Author: Thomas Firmin <ThomasFirmin>
# @Date: 2022-05-03T15:41:48+02:00
# @Email: thomas.firmin@univ-lille.fr
# @Project: Zellij
# @Last modified by: tfirmin
# @Last modified time: 2022-10-03T22:37:15+02:00
# @License: CeCILL-C (http://www.cecill.info/index.fr.html)
import numpy as np
import logging
logger = logging.getLogger("zellij.chaos_map")
[docs]class Chaos_map(object):
"""Chaos_map
:code:`Chaos_map` is in abstract class describing what a chaos map is.
Attributes
----------
vectors : int
Size of the map (rows).
params : int
Number of parameters (columns).
map : np.array
Chaos map of shape (vectors, params).
See Also
--------
Chaotic_optimization : Chaos map is used here.
"""
def __init__(self, vectors, params):
self.vectors = vectors
self.params = params
self.map = np.zeros([self.vectors, self.params])
def __add__(self, map):
assert (
self.params == map.params
), f"Error, maps must have equals `params`, got {self.params} and {map.params}"
new_map = Chaos_map(self.vectors + map.vectors, self.params)
new_map.map = np.append(self.map, map.map)
np.random.shuffle(new_map.map)
return new_map
[docs]class Henon(Chaos_map):
"""Henon chaotic map
.. math::
\\smash{
\\begin{cases}
\\begin{cases}
x_{n+1} = 1 - a x_n^2 + y_n\\\\
y_{n+1} = b x_n.
\\end{cases}\\\\
map = \\frac{y-min(y)}{max(y)-min(y)}
\\end{cases}}
Parameters
----------
vectors : int
Map size
params : int
Number of dimensions
a : float, default=1.4020560
Henon map parameter. Has an influence on the chaotic, intermittent or periodicity behaviors.
b : float, default=0.305620406
Henon map parameter. Has an influence on the chaotic, intermittent or periodicity behaviors.
Attributes
----------
map : numpy.ndarray
Chaos map of size (vectors,param)
"""
def __init__(self, vectors, params, a=1.4020560, b=0.305620406):
super().__init__(vectors, params)
self.a = a
self.b = b
# Initialization
y = np.zeros([self.vectors, self.params])
x = np.random.random(self.params)
for i in range(1, self.vectors):
# y_{k+1} = x_{k}
y[i, :] = b * x
# x_{k+1} = a.(1-x_{k}^2) + b.y_{k}
x = 1 - a * x**2 + y[i - 1, :]
# Min_{params}(y_{params,vectors})
alpha = np.amin(y, axis=0)
# Max_{params}(y_{params,vectors})
beta = np.amax(y, axis=0)
self.map = (y - alpha) / (beta - alpha)
[docs]class Kent(Chaos_map):
"""Kent chaotic map
.. math::
\\smash{
\\begin{cases}
x_{n+1} =
\\begin{cases}
\\frac{x_n}{\\beta} \\quad 0 < x_{n} \\leq \\beta \\\\
\\frac{1-x_n}{1-\\beta} \\quad \\beta < x_{n} \\leq 1
\\end{cases}\\\\
map=x
\\end{cases}}
Parameters
----------
vectors : int
Map size
params : int
Number of dimensions
beta : float, default=0.8
Kent map parameter. Has an influence on the chaotic, intermittent, convergence, or periodicity behaviors.
Attributes
----------
map : numpy.ndarray
Chaos map of size (vectors,param)
"""
def __init__(self, vectors, params, beta=0.8):
super().__init__(vectors, params)
self.beta = beta
self.map[0, :] = np.random.random(params)
for i in range(1, vectors):
self.map[i, :] = np.where(
self.map[i - 1, :] < beta,
self.map[i - 1, :] / beta,
(1 - self.map[i - 1, :]) / (1 - beta),
)
[docs]class Logistic(Chaos_map):
"""Logistic chaotic map
.. math::
\\smash{
\\begin{cases}
x_{n+1} = \\mu x_n(1-x_n)\\\\
map=x
\\end{cases}}
Parameters
----------
vectors : int
Map size
params : int
Number of dimensions
mu : float, default=3.57
Logistic map parameter. Has an influence on the chaotic, intermittent, convergence, or periodicity behaviors.
Attributes
----------
map : numpy.ndarray
Chaos map of size (vectors,param)
"""
def __init__(self, vectors, params, mu=3.57):
super().__init__(vectors, params)
self.mu = mu
self.map[0, :] = np.random.random(params)
for i in range(1, vectors):
self.map[i, :] = mu * self.map[i - 1, :] * (1 - self.map[i - 1, :])
[docs]class Tent(Chaos_map):
"""Tent chaotic map
.. math::
\\smash{
\\begin{cases}
x_{n+1} =
\\begin{cases}
\\mu x_n \\quad x_n < \\frac{1}{2} \\\\
\\mu (1-x_n) \\quad \\frac{1}{2} \\leq x_n
\\end{cases}\\\\
map = x
\\end{cases}}
Parameters
----------
vectors : int
Map size
params : int
Number of dimensions
Tent : float, default=1.9999999999
Logistic map parameter. Has an influence on the chaotic, intermittent, convergence, or periodicity behaviors.
Attributes
----------
map : numpy.ndarray
Chaos map of size (vectors,param)
"""
def __init__(self, vectors, params, mu=2 - 1e-10):
super().__init__(vectors, params)
self.mu = mu
self.map[0, :] = np.random.random(params)
for i in range(1, vectors):
self.map[i, :] = np.where(
self.map[i - 1, :] < 0.5,
self.mu * self.map[i - 1, :],
self.mu * (1 - self.map[i - 1, :]),
)
[docs]class Random(Chaos_map):
def __init__(self, vectors, params):
super().__init__(vectors, params)
self.map = np.random.random((vectors, params))
