

'''simple docstring'''






from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np
class       SCREAMING_SNAKE_CASE__     (							a__ ):




    def     __lowerCamelCase (   self							,	lowercase__     ):






          """simple docstring"""






          return 0.0






def    __lowerCamelCase     ( SCREAMING_SNAKE_CASE_	:      np.ndarray    ,    SCREAMING_SNAKE_CASE_	:      int       )				->  tuple[int | float, int | float]:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_ :     List[str]	=			min([-2_0, np.min(fft_results[1 : samplerate // 2 - 1]       )]       )
      SCREAMING_SNAKE_CASE_ :     Union[str, Any]	=			max([2_0, np.max(fft_results[1 : samplerate // 2 - 1]       )]       )
      return lowest, highest


def    __lowerCamelCase     ( SCREAMING_SNAKE_CASE_	:      FilterType    ,    SCREAMING_SNAKE_CASE_	:      int       )				->  None:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_ :     int	=			5_1_2
      SCREAMING_SNAKE_CASE_ :     int	=			[1] + [0] * (size - 1)
      SCREAMING_SNAKE_CASE_ :     int	=			[filter_type.process(A__       ) for item in inputs]

      SCREAMING_SNAKE_CASE_ :     Any	=			[0] * (samplerate - size)  # zero-padding
      outputs += filler
      SCREAMING_SNAKE_CASE_ :     str	=			np.abs(np.fft.fft(A__       )       )
      SCREAMING_SNAKE_CASE_ :     Dict	=			2_0 * np.logaa(A__       )

      # Frequencies on log scale from 24 to nyquist frequency
      plt.xlim(2_4    ,    samplerate / 2 - 1       )
      plt.xlabel("Frequency (Hz)"       )
      plt.xscale("log"       )

      # Display within reasonable bounds
      SCREAMING_SNAKE_CASE_ :     Union[str, Any]	=			get_bounds(A__    ,    A__       )
      plt.ylim(max([-8_0, bounds[0]]       )    ,    min([8_0, bounds[1]]       )       )
      plt.ylabel("Gain (dB)"       )

      plt.plot(A__       )
      plt.show()





def    __lowerCamelCase     ( SCREAMING_SNAKE_CASE_	:      FilterType    ,    SCREAMING_SNAKE_CASE_	:      int       )				->  None:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_ :     Tuple	=			5_1_2
      SCREAMING_SNAKE_CASE_ :     Any	=			[1] + [0] * (size - 1)
      SCREAMING_SNAKE_CASE_ :     Optional[Any]	=			[filter_type.process(A__       ) for item in inputs]

      SCREAMING_SNAKE_CASE_ :     List[Any]	=			[0] * (samplerate - size)  # zero-padding
      outputs += filler
      SCREAMING_SNAKE_CASE_ :     str	=			np.angle(np.fft.fft(A__       )       )

      # Frequencies on log scale from 24 to nyquist frequency
      plt.xlim(2_4    ,    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()





def    __lowerCamelCase   (      A__						: float						,						A__						: float						,						A__						: float						,						A__						: float						,						A__						: float						,						)     ->    float:
   lowerCamelCase_						:   List[str]		= [redshift, radiation_density, matter_density, dark_energy]
   if any(p < 0 for p in parameters					):
      raise ValueError("""All input parameters must be positive"""					)

   if any(p > 1 for p in parameters[1:4]					):
      raise ValueError("""Relative densities cannot be greater than one"""					)
   else:
      lowerCamelCase_						:   Union[str, Any]		= 1 - (matter_density + radiation_density + dark_energy)

      lowerCamelCase_						:   int		= (
          radiation_density * (redshift + 1) ** 4
          + matter_density * (redshift + 1) ** 3
          + curvature * (redshift + 1) ** 2
          + dark_energy
      )

      lowerCamelCase_						:   Dict		= hubble_constant * e_a ** (1 / 2)
      return hubble


if __name__ == "__main__":
      import doctest

      # run doctest
      doctest.testmod()

      # demo LCDM approximation
      snake_case__				:	str					       =					0.3

      print(
          hubble_parameter(
              hubble_constant=6_8.3,
              radiation_density=1e-4,
              matter_density=matter_density,
              dark_energy=1 - matter_density,
              redshift=0,
          )
      )





