#!/usr/bin/env python
# coding: utf-8

# # Rössler attractor
# See https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor
# \begin{cases}  \frac{dx}{dt} = -y - z \\ \frac{dy}{dt} = x + ay \\ \frac{dz}{dt} = b + z(x-c) \end{cases}
# 
# 

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get_ipython().run_line_magic('matplotlib', 'ipympl')
import ipywidgets as widgets
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import solve_ivp

import mpl_interactions.ipyplot as iplt


# ## Define function to plot
# 
# ### Projecting on axes
# 
# The Rossler attractor is a 3 dimensional system, but as 3D plots are not yet supported by `mpl_interactions` we will only visualize the `x` and `y` components.
# 
# **Note:** Matplotlib supports 3D plots, but `mpl_interactions` does not yet support them. That makes this a great place to contribute to `mpl_interactions` if you're interested in doing so. If you want to have a crack at it feel free to comment on https://github.com/ianhi/mpl-interactions/issues/89 and `@ianhi` will be happy to help you through the process.
# 
# 
# ### Caching
# One thing to note here is that `mpl_interactions` will cache function calls for a given set of parameters so that the same function isn't called multiple times if you are plotting it on multiple axes. However, that cache will not persist as the parameters are modified. So here we can build in our own cache to speed up execution

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t_span = [0, 500]
t_eval = np.linspace(0, 500, 1550)
x0 = 0
y0 = 0
z0 = 0

cache = {}


def f(a, b, c):
    def deriv(t, cur_pos):
        x, y, z = cur_pos
        dxdt = -y - z
        dydt = x + a * y
        dzdt = b + z * (x - c)
        return [dxdt, dydt, dzdt]

    id_ = (float(a), float(b), float(c))
    if id_ not in cache:
        out = solve_ivp(deriv, t_span, y0=[x0, y0, z0], t_eval=t_eval).y[:2]
        cache[id_] = out
    else:
        out = cache[id_]
    return out.T  # requires shape (N, 2)


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fig, ax = plt.subplots()
controls = iplt.plot(
    f,
    ".-",
    a=(0.05, 0.3, 1000),
    b=0.2,
    c=(1, 20),
    parametric=True,
    alpha=0.5,
    play_buttons=True,
    play_button_pos="left",
    ylim="auto",
    xlim="auto",
)


# ## Coloring by time point
# 
# When we plot using `plot` we can't choose colors for individual points, so we can use the `scatter` function to color the points by the time point they have.
# 
# 
# The only difference to the function we used for plot is that we had to rename the `c` argument to `f` as `c` is reserved by `scatter` for setting the colors of the points.

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# use a different argument for c because `c` is an argument to plt.scatter
out = widgets.Output()
display(out)


def f(a, b, c_):
    def deriv(t, cur_pos):
        x, y, z = cur_pos
        dxdt = -y - z
        dydt = x + a * y
        dzdt = b + z * (x - c_)
        return [dxdt, dydt, dzdt]

    id_ = (float(a), float(b), float(c_))
    if id_ not in cache:
        out = solve_ivp(deriv, t_span, y0=[0, 1, 0], t_eval=t_eval).y[:2]
        cache[id_] = out
    else:
        out = cache[id_]
    return out.T  # requires shape (N, 2)


fig, ax = plt.subplots()
controls = iplt.scatter(
    f,
    a=(0.05, 0.3, 1000),
    b=0.2,
    c_=(1, 20),
    parametric=True,
    alpha=0.5,
    play_buttons=True,
    play_button_pos="left",
    s=8,
    c=t_eval,
)
controls = iplt.plot(
    f,
    "-",
    controls=controls,
    parametric=True,
    alpha=0.5,
    ylim="auto",
    xlim="auto",
)
plt.colorbar().set_label("Time Point")
plt.tight_layout()


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