




from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class 							__UpperCamelCase			( __lowerCamelCase  ):





    '''simple docstring'''



    def       __snake_case		( self       , UpperCAmelCase_						):
           return 0.0




def       UpperCAmelCase       (     _snake_case						, _snake_case							):
       lowerCAmelCase   =		min([-20, np.min(fft_results[1 : samplerate // 2 - 1]							)]							)
       lowerCAmelCase   =		max([20, np.max(fft_results[1 : samplerate // 2 - 1]							)]							)
       return lowest, highest



def       UpperCAmelCase       (     _snake_case						, _snake_case							):
       lowerCAmelCase   =		512
       lowerCAmelCase   =		[1] + [0] * (size - 1)
       lowerCAmelCase   =		[filter_type.process(A__							) for item in inputs]

       lowerCAmelCase   =		[0] * (samplerate - size)  # zero-padding
       outputs += filler
       lowerCAmelCase   =		np.abs(np.fft.fft(A__							)							)
       lowerCAmelCase   =		20 * np.logaa(A__							)

       # Frequencies on log scale from 24 to nyquist frequency
       plt.xlim(24						, samplerate / 2 - 1							)
       plt.xlabel('''Frequency (Hz)'''							)
       plt.xscale('''log'''							)

       # Display within reasonable bounds
       lowerCAmelCase   =		get_bounds(A__						, A__							)
       plt.ylim(max([-80, bounds[0]]							)						, min([80, bounds[1]]							)							)
       plt.ylabel('''Gain (dB)'''							)

       plt.plot(A__							)
       plt.show()



def       UpperCAmelCase       (     _snake_case						, _snake_case							):
       lowerCAmelCase   =		512
       lowerCAmelCase   =		[1] + [0] * (size - 1)
       lowerCAmelCase   =		[filter_type.process(A__							) for item in inputs]

       lowerCAmelCase   =		[0] * (samplerate - size)  # zero-padding
       outputs += filler
       lowerCAmelCase   =		np.angle(np.fft.fft(A__							)							)

       # Frequencies on log scale from 24 to nyquist frequency
       plt.xlim(24						, samplerate / 2 - 1							)
       plt.xlabel('''Frequency (Hz)'''							)
       plt.xscale('''log'''							)

       plt.ylim(-2 * pi						, 2 * pi							)
       plt.ylabel('''Phase shift (Radians)'''							)
       plt.plot(np.unwrap(A__						, -2 * pi							)							)
       plt.show()









from collections.abc import Sequence



def       UpperCAmelCase       (     _snake_case						, _snake_case = False							):
							if not arr:
														return 0

							lowerCAmelCase   =		0 if allow_empty_subarrays else float('''-inf'''							)
							lowerCAmelCase   =		0.0
							for num in arr:
														lowerCAmelCase   =		max(0 if allow_empty_subarrays else num						, curr_sum + num							)
														lowerCAmelCase   =		max(_snake_case						, _snake_case							)

							return max_sum


if __name__ == "__main__":
		from doctest import testmod

		testmod()

		UpperCAmelCase_						=[-2, 1, -3, 4, -1, 2, 1, -5, 4]
		print(F'''{max_subarray_sum(nums) = }''')



