

'''simple docstring'''



from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff
def 						__lowerCamelCase	(       __snake_case					:		str,		__snake_case					:		float | Decimal,		__snake_case					:		float = 10**-10	)	->							float:






						"""simple docstring"""





						A__					:       List[Any]     =a
						while True:
												A__					:       Dict     =Decimal(__snake_case	) - (
												    Decimal(eval(__snake_case	)	) / Decimal(eval(str(diff(__snake_case	)	)	)	)  # noqa: S307
												)
												# This number dictates the accuracy of the answer
												if abs(eval(__snake_case	)	) < precision:  # noqa: S307
																		return float(__snake_case	)


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")
		# Find root of polynomial
		print(F"""The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}""")
		# Find Square Root of 5
		print(F"""The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}""")
		# Exponential Roots
		print(F"""The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}""")




'''simple docstring'''



from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np



class lowerCamelCase			(  lowercase_						):



			'''simple docstring'''






			def lowercase__						(				self	:						Any		,      lowerCAmelCase_	:						float			)      ->		float:





									'''simple docstring'''
									return 0.0


def 						__lowerCamelCase	(       __snake_case					:		np.ndarray,		__snake_case					:		int	)	->							tuple[int | float, int | float]:






						"""simple docstring"""





						A__					:       Tuple     =min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
						A__					:       str     =max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
						return lowest, highest
def 						__lowerCamelCase	(       __snake_case					:		FilterType,		__snake_case					:		int	)	->							None:






						"""simple docstring"""





						A__					:       Any     =512
						A__					:       int     =[1] + [0] * (size - 1)
						A__					:       int     =[filter_type.process(__snake_case	) for item in inputs]

						A__					:       Union[str, Any]     =[0] * (samplerate - size)  # zero-padding
						outputs += filler
						A__					:       List[Any]     =np.abs(np.fft.fft(__snake_case	)	)
						A__					:       int     =20 * np.logaa(__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
						A__					:       Union[str, Any]     =get_bounds(__snake_case,		__snake_case	)
						plt.ylim(max([-80, bounds[0]]	),		min([80, bounds[1]]	)	)
						plt.ylabel("""Gain (dB)"""	)

						plt.plot(__snake_case	)
						plt.show()
def 						__lowerCamelCase	(       __snake_case					:		FilterType,		__snake_case					:		int	)	->							None:






						"""simple docstring"""





						A__					:       List[Any]     =512
						A__					:       List[Any]     =[1] + [0] * (size - 1)
						A__					:       Dict     =[filter_type.process(__snake_case	) for item in inputs]

						A__					:       Union[str, Any]     =[0] * (samplerate - size)  # zero-padding
						outputs += filler
						A__					:       str     =np.angle(np.fft.fft(__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(__snake_case,		-2 * pi	)	)
						plt.show()

