


from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class 			_a				(     UpperCamelCase__     ):

							def  lowerCamelCase_					(				self:      List[Any]       ,		UpperCamelCase_:      float				)     ->  float:





									"""simple docstring"""







									return 0.0
def      _a					( SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE	):


		"""simple docstring"""




		lowercase__				= min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
		lowercase__				= max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
		return lowest, highest
def      _a					( SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE	):


		"""simple docstring"""




		lowercase__				= 5_12
		lowercase__				= [1] + [0] * (size - 1)
		lowercase__				= [filter_type.process(SCREAMING_SNAKE_CASE	) for item in inputs]

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

		# 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
		lowercase__				= get_bounds(SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE	)
		plt.ylim(max([-80, bounds[0]]	)		,							min([80, bounds[1]]	)	)
		plt.ylabel('''Gain (dB)'''	)

		plt.plot(SCREAMING_SNAKE_CASE	)
		plt.show()
def      _a					( SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE	):


		"""simple docstring"""




		lowercase__				= 5_12
		lowercase__				= [1] + [0] * (size - 1)
		lowercase__				= [filter_type.process(SCREAMING_SNAKE_CASE	) for item in inputs]

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

		# 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(SCREAMING_SNAKE_CASE		,							-2 * pi	)	)
		plt.show()






"""simple docstring"""




from collections.abc import Callable





def       a_ (	lowercase__ :Callable[[float], float],			lowercase__ :float,			lowercase__ :float     ):
			__lowerCamelCase          =      a
			__lowerCamelCase          =      b
			if function(lowercase__     ) == 0:  # one of the a or b is a root for the function
						return a
			elif function(lowercase__     ) == 0:
						return b
			elif (
			    function(lowercase__     ) * function(lowercase__     ) > 0
			):  # if none of these are root and they are both positive or negative,
						# then this algorithm can't find the root
						raise ValueError("""could not find root in given interval."""     )
			else:
						__lowerCamelCase          =      start + (end - start) / 2.0
						while abs(start - mid     ) > 10**-7:  # until precisely equals to 10^-7
									if function(lowercase__     ) == 0:
												return mid
									elif function(lowercase__     ) * function(lowercase__     ) < 0:
												__lowerCamelCase          =      mid
									else:
												__lowerCamelCase          =      mid
									__lowerCamelCase          =      start + (end - start) / 2.0
						return mid





def       a_ (	lowercase__ :float     ):
			return x**3 - 2 * x - 5


if __name__ == "__main__":
					print(bisection(f, 1, 1_0_0_0))

					import doctest

					doctest.testmod()




