Visualization

Visualize time series data.

• show_recurrence_plot
• calc_recurrence_plot
• simple_threshold

Recurrence Plot

show_recurrence_plot

Create Recurrence Plot (RP) [] from time series data. This function displays the RP.
Find the distance between two points on the orbit and draw according to the rule. The drawing rule uses the simplest one (simple_threshold).

This can be changed. The rule just takes a matrix and returns the matrix. *params and **kargs are the arguments to the rule.

from hundun.exploration import show_recurrence_plot

Parameters

• u_seq
• rule=simple_threshold
• cmap=False,
• path_save_plot=None
• *params
• **kargs

Returns

• recurrence_plot: numpy.ndarray

Example

sample 1

Here is the simplest example.

from hundun.equations import Lorenz
from hundun.exploration import show_recurrence_plot

u_seq = Lorenz.get_u_seq(5000)
show_recurrence_plot(u_seq)

sample 2

Shows the function and result when the Rule is changed.

from hundun.equations import Lorenz
from hundun.exploration import show_recurrence_plot
import numpy as np


def new_threshold(ds, func):
    if (d_max:=np.max(ds))!=0:
        pv = func(ds/d_max)*255
        return np.uint8(pv)
    return ds

u_seq = Lorenz.get_u_seq(5000)
show_recurrence_plot(u_seq, cmap=True, rule=new_threshold, func=np.log)

References

Recurrence Plots of Dynamical Systems

(1987) J.-P Eckmann and S. Oliffson Kamphorst and D Ruelle
DOI: 10.1209/0295-5075/4/9/004

calc_recurrence_plot

Unlike show_recurrence_plot, it returns only RP.

from hundun.exploration import calc_recurrence_plot

Parameters

• u_seq
• rule=simple_threshold
• *params
• **kargs

Returns

• recurrence_plot: numpy.ndarray

simple_threshold

When the distance is above the threshold value , it is 255, and when it is less than that, it is 0.
It is implemented as follows.

def simple_threshold(ds, theta=0.5):
    if (d_max:=_np.max(ds))!=0:
        pv = (ds/d_max>theta)*255
        return pv
    return ds

from hundun.exploration import simple_threshold