






from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class 						_a       (  UpperCAmelCase__    ):






  """simple docstring"""





  def    _UpperCAmelCase     (     self		,		_UpperCAmelCase )			-> float:
     return 0.0






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






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

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

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

   plt.plot(__lowercase)
   plt.show()






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

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

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













from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase = "x"    ,      __lowercase = 10**-10    ,      __lowercase = 1    ,      ):
   UpperCamelCase_									=     symbols(__lowercase)
   UpperCamelCase_									=     lambdify(__lowercase    ,      __lowercase)
   UpperCamelCase_									=     lambdify(__lowercase    ,      diff(__lowercase    ,      __lowercase))

   UpperCamelCase_									=     starting_point

   while True:
      if diff_function(__lowercase) != 0:
         UpperCamelCase_									=     prev_guess - multiplicity * func(__lowercase) / diff_function(
             __lowercase)
      else:
         raise ZeroDivisionError('Could not find root') from None

      # Precision is checked by comparing the difference of consecutive guesses
      if abs(next_guess - prev_guess) < precision:
         return next_guess

      UpperCamelCase_									=     next_guess


# 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
 # Find fourth Root of 5
 print(f'The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}')

 # Find value of e
 print(
     """The root of log(y) - 1 = 0 is """,
     f'{newton_raphson("log(y) - 1", 2, variable="y")}',
 )

 # Exponential Roots
 print(
     """The root of exp(x) - 1 = 0 is""",
     f'{newton_raphson("exp(x) - 1", 1_0, precision=0.005)}',
 )

 # Find root of cos(x)
 print(f'The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}')





