"""simple docstring"""







from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np







class        UpperCamelCase		(			lowercase_  ):
   def 			_UpperCAmelCase   (			self     ,__UpperCamelCase			)	->      float:


        '''simple docstring'''


        return 0.0






def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     np.ndarray     ,			__SCREAMING_SNAKE_CASE							:     int      ):
     lowercase_	:				Tuple													=	min([-20, np.min(fft_results[1 : samplerate // 2 - 1]      )]      )
     lowercase_	:				Any													=	max([20, np.max(fft_results[1 : samplerate // 2 - 1]      )]      )
     return lowest, highest



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     FilterType     ,			__SCREAMING_SNAKE_CASE							:     int      ):
     lowercase_	:				Tuple													=	5_12
     lowercase_	:				Any													=	[1] + [0] * (size - 1)
     lowercase_	:				Optional[int]													=	[filter_type.process(__SCREAMING_SNAKE_CASE      ) for item in inputs]

     lowercase_	:				Optional[int]													=	[0] * (samplerate - size)  # zero-padding
     outputs += filler
     lowercase_	:				Any													=	np.abs(np.fft.fft(__SCREAMING_SNAKE_CASE      )      )
     lowercase_	:				Tuple													=	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_	:				List[Any]													=	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 			lowercase__(       __SCREAMING_SNAKE_CASE							:     FilterType     ,			__SCREAMING_SNAKE_CASE							:     int      ):
     lowercase_	:				Optional[int]													=	5_12
     lowercase_	:				str													=	[1] + [0] * (size - 1)
     lowercase_	:				Any													=	[filter_type.process(__SCREAMING_SNAKE_CASE      ) for item in inputs]

     lowercase_	:				int													=	[0] * (samplerate - size)  # zero-padding
     outputs += filler
     lowercase_	:				str													=	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 __future__ import annotations

import math
from collections.abc import Callable



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Callable[[int | float], int | float]     ,			__SCREAMING_SNAKE_CASE							:     int | float     ,			__SCREAMING_SNAKE_CASE							:     int | float     ,			__SCREAMING_SNAKE_CASE							:     int = 1_00     ,			):
     lowercase_	:				Dict													=	x_start
     lowercase_	:				Optional[Any]													=	fnc(__SCREAMING_SNAKE_CASE      )
     lowercase_	:				Optional[Any]													=	0.0

     for _ in range(__SCREAMING_SNAKE_CASE      ):
          # Approximates curve as a sequence of linear lines and sums their length
          lowercase_	:				Union[str, Any]													=	(x_end - x_start) / steps + xa
          lowercase_	:				str													=	fnc(__SCREAMING_SNAKE_CASE      )
          length += math.hypot(xa - xa     ,			fxa - fxa      )

          # Increment step
          lowercase_	:				List[Any]													=	xa
          lowercase_	:				Optional[Any]													=	fxa

     return length


if __name__ == "__main__":



       def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Any      ):
            return math.sin(10 * x      )

       print("f(x) = sin(10 * x)")
       print("The length of the curve from x = -10 to x = 10 is:")
       __SCREAMING_SNAKE_CASE    	=10
       while i <= 10_0000:
              print(F"With {i} steps: {line_length(f, -10, 10, i)}")
              i *= 10

