


'''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  UpperCamelCase__						(self       :       int  ,		UpperCamelCase       :       float					):

             '''simple docstring'''







             return 0.0






def _SCREAMING_SNAKE_CASE (A    ,					A			)			->			tuple[int | float, int | float]:






       """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 _SCREAMING_SNAKE_CASE (A    ,					A			)			->			None:






       """simple docstring"""







       lowercase__      =					512
       lowercase__      =					[1] + [0] * (size - 1)
       lowercase__      =					[filter_type.process(A			) for item in inputs]

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

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

       plt.plot(A			)
       plt.show()

def _SCREAMING_SNAKE_CASE (A    ,					A			)			->			None:






       """simple docstring"""







       lowercase__      =					512
       lowercase__      =					[1] + [0] * (size - 1)
       lowercase__      =					[filter_type.process(A			) for item in inputs]

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

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








'''simple docstring'''

import unittest

import numpy as np

def _SCREAMING_SNAKE_CASE (A    ,					A    ,					A    ,					A = None    ,					)			->			np.ndarray:






       """simple docstring"""







       lowercase__      =					np.shape(A			)
       lowercase__      =					np.shape(A			)
       lowercase__      =					np.shape(A			)

       if shape_a[0] != shape_b[0]:
              lowercase__      =					(
                  '''Expected the same number of rows for A and B. '''
                  f"Instead found A of size {shape_a} and B of size {shape_b}"
              )
              raise ValueError(A			)

       if shape_b[1] != shape_c[1]:
              lowercase__      =					(
                  '''Expected the same number of columns for B and C. '''
                  f"Instead found B of size {shape_b} and C of size {shape_c}"
              )
              raise ValueError(A			)

       lowercase__      =					pseudo_inv
       if a_inv is None:
              try:
                     lowercase__      =					np.linalg.inv(A			)
              except np.linalg.LinAlgError:
                     raise ValueError(
                         '''Input matrix A is not invertible. Cannot compute Schur complement.'''			)

       return mat_c - mat_b.T @ a_inv @ mat_b
class     __lowerCAmelCase		(unittest.TestCase	):





      '''simple docstring'''






      def  UpperCamelCase__						(self       :       Dict					):

             '''simple docstring'''







             lowercase__      =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
             lowercase__      =					np.array([[0, 3], [3, 0], [2, 3]]					)
             lowercase__      =					np.array([[2, 1], [6, 3]]					)

             lowercase__      =					schur_complement(UpperCamelCase  ,		UpperCamelCase  ,		UpperCamelCase					)

             lowercase__      =					np.block([[a, b], [b.T, c]]					)

             lowercase__      =					np.linalg.det(UpperCamelCase					)
             lowercase__      =					np.linalg.det(UpperCamelCase					)
             lowercase__      =					np.linalg.det(UpperCamelCase					)

             self.assertAlmostEqual(UpperCamelCase  ,		det_a * det_s					)



      def  UpperCamelCase__						(self       :       Optional[int]					):

             '''simple docstring'''







             lowercase__      =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
             lowercase__      =					np.array([[0, 3], [3, 0], [2, 3]]					)
             lowercase__      =					np.array([[2, 1], [6, 3]]					)

             with self.assertRaises(UpperCamelCase					):
                    schur_complement(UpperCamelCase  ,		UpperCamelCase  ,		UpperCamelCase					)






      def  UpperCamelCase__						(self       :       Union[str, Any]					):

             '''simple docstring'''







             lowercase__      =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
             lowercase__      =					np.array([[0, 3], [3, 0], [2, 3]]					)
             lowercase__      =					np.array([[2, 1, 3], [6, 3, 5]]					)

             with self.assertRaises(UpperCamelCase					):
                    schur_complement(UpperCamelCase  ,		UpperCamelCase  ,		UpperCamelCase					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()




