Hello there!

Thanks for the General Workflow and tips in examples dir, and could you please provide an example for general workflow?

I ran the code but got this error.

Hi,
In the folder named lyapunov(pwd : nolitsa/examples/lyapunov/), you have shown some cases about how to calculate max Lyapunov exponent. Although it is obviously that the "accepted" value, well, I mean, the slope of the line is quite close to the estimate values we get here, how we calculate this "accepted" value?
I guess we should we calculate this "accepted" value by the least square method. However, it seems that many later estimate values we get are meaningless but will affect the "accepted" value.

Thanks for all the examples, it's really helpful in learning this.
There's an error in the d2 examples:

import numpy as np
import matplotlib.pyplot as plt
from nolitsa import d2, utils

t = np.linspace(0, 100 * np.pi, 5000)
x = np.sin(t) + np.sin(2 * t) + np.sin(3 * t) + np.sin(5 * t)
x = utils.corrupt(x, np.random.normal(size=5000), snr=1000)

# Time delay.
tau = 25

window = 100

# Embedding dimension.
dim = np.arange(1, 10)

plt.title('Local $D_2$ vs $r$ for a noisy closed curve')
plt.xlabel(r'Distance $r$')
plt.ylabel(r'Local $D_2$')

for r, c in d2.c2_embed(x, tau=tau, dim=dim, window=window):
    plt.semilogx(r[3:-3], d2.d2(r, c), color='#4682B4')

plt.plot(r[3:-3], np.ones(len(r) - 6), color='#000000')
plt.show()
Traceback (most recent call last):

  Cell In[206], line 28
    for r, c in d2.c2_embed(x, tau=tau, dim=dim, window=window):

  File ~\anaconda3\envs\pysindy\Lib\site-packages\nolitsa\d2.py:148 in c2_embed
    return utils.parallel_map(c2, yy, kwargs={

  File ~\anaconda3\envs\pysindy\Lib\site-packages\nolitsa\utils.py:254 in parallel_map
    return np.asarray([result.get() for result in results])

ValueError: setting an array element with a sequence. The requested array has an inhomogeneous shape after 2 dimensions. The detected shape was (9, 2) + inhomogeneous part.

The first 3 I tried all did this

I wrote a fnn test:

tau=3
x = np.linspace(0, 10, 1000)
dim = np.arange(1, max_dim)
f1, f2, f3 = dimension.fnn(x, tau=tau, dim=dim)
print(f1)

Program doesn't reach print(f1), instead gives the following error after getting stuck for several seconds:

File "C:\Users\Carlos\PycharmProjects\parkinson.venv\Lib\site-packages\nolitsa\dimension.py", line 187, in fnn
r = utils.parallel_map(_fnn, dim, (x,), {
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\PycharmProjects\parkinson.venv\Lib\site-packages\nolitsa\utils.py", line 247, in parallel_map
pool = Pool(processes=processes)
^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\context.py", line 119, in Pool
return Pool(processes, initializer, initargs, maxtasksperchild,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\pool.py", line 215, in init
self._repopulate_pool()
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\pool.py", line 306, in _repopulate_pool
return self._repopulate_pool_static(self._ctx, self.Process,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\pool.py", line 329, in _repopulate_pool_static
w.start()
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\process.py", line 121, in start
self._popen = self._Popen(self)
^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\context.py", line 337, in _Popen
return Popen(process_obj)
^^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\popen_spawn_win32.py", line 45, in init
prep_data = spawn.get_preparation_data(process_obj._name)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\spawn.py", line 164, in get_preparation_data
_check_not_importing_main()
File "C:\Users\Carlos\AppData\Local\Programs\Python\Python312\Lib\multiprocessing\spawn.py", line 140, in _check_not_importing_main
raise RuntimeError('''
RuntimeError:
An attempt has been made to start a new process before the
current process has finished its bootstrapping phase.

    This probably means that you are not using fork to start your
    child processes and you have forgotten to use the proper idiom
    in the main module:

        if __name__ == '__main__':
            freeze_support()
            ...

    The "freeze_support()" line can be omitted if the program
    is not going to be frozen to produce an executable.

    To fix this issue, refer to the "Safe importing of main module"
    section in https://docs.python.org/3/library/multiprocessing.html