'''simple docstring'''




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)						)					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				Any       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				Optional[Any]       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				int       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				List[str]       				=		_sin / (2 * q_factor)

       __UpperCAmelCase  :				str       				=		(1 - _cos) / 2
       __UpperCAmelCase  :				Dict       				=		1 - _cos

       __UpperCAmelCase  :				Optional[int]       				=		1 + alpha
       __UpperCAmelCase  :				Optional[Any]       				=		-2 * _cos
       __UpperCAmelCase  :				List[str]       				=		1 - alpha

       __UpperCAmelCase  :				Any       				=		IIRFilter(2						)
       filt.set_coefficients([aa, aa, aa]							,    [ba, ba, ba]						)
       return filt

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)						)					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				List[str]       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				List[str]       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				str       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				Any       				=		_sin / (2 * q_factor)

       __UpperCAmelCase  :				str       				=		(1 + _cos) / 2
       __UpperCAmelCase  :				Tuple       				=		-1 - _cos

       __UpperCAmelCase  :				int       				=		1 + alpha
       __UpperCAmelCase  :				Tuple       				=		-2 * _cos
       __UpperCAmelCase  :				int       				=		1 - alpha

       __UpperCAmelCase  :				str       				=		IIRFilter(2						)
       filt.set_coefficients([aa, aa, aa]							,    [ba, ba, ba]						)
       return filt

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)						)					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				Optional[Any]       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				List[Any]       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				str       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				Union[str, Any]       				=		_sin / (2 * q_factor)

       __UpperCAmelCase  :				Any       				=		_sin / 2
       __UpperCAmelCase  :				Dict       				=		0
       __UpperCAmelCase  :				Tuple       				=		-ba

       __UpperCAmelCase  :				List[str]       				=		1 + alpha
       __UpperCAmelCase  :				List[Any]       				=		-2 * _cos
       __UpperCAmelCase  :				Optional[int]       				=		1 - alpha

       __UpperCAmelCase  :				List[Any]       				=		IIRFilter(2						)
       filt.set_coefficients([aa, aa, aa]							,    [ba, ba, ba]						)
       return filt

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)						)					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				List[Any]       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				Any       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				List[Any]       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				Dict       				=		_sin / (2 * q_factor)

       __UpperCAmelCase  :				Optional[int]       				=		1 - alpha
       __UpperCAmelCase  :				Union[str, Any]       				=		-2 * _cos
       __UpperCAmelCase  :				Any       				=		1 + alpha

       __UpperCAmelCase  :				Optional[int]       				=		IIRFilter(2						)
       filt.set_coefficients([ba, ba, ba]							,    [ba, ba, ba]						)
       return filt

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)							,    )					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				Union[str, Any]       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				str       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				Tuple       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				Optional[int]       				=		_sin / (2 * q_factor)
       __UpperCAmelCase  :				Tuple       				=		10 ** (gain_db / 40)

       __UpperCAmelCase  :				Union[str, Any]       				=		1 + alpha * big_a
       __UpperCAmelCase  :				str       				=		-2 * _cos
       __UpperCAmelCase  :				Any       				=		1 - alpha * big_a
       __UpperCAmelCase  :				Optional[int]       				=		1 + alpha / big_a
       __UpperCAmelCase  :				Union[str, Any]       				=		-2 * _cos
       __UpperCAmelCase  :				List[str]       				=		1 - alpha / big_a

       __UpperCAmelCase  :				int       				=		IIRFilter(2						)
       filt.set_coefficients([aa, aa, aa]							,    [ba, ba, ba]						)
       return filt

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)							,    )					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				Dict       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				List[Any]       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				Optional[int]       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				Dict       				=		_sin / (2 * q_factor)
       __UpperCAmelCase  :				Optional[Any]       				=		10 ** (gain_db / 40)
       __UpperCAmelCase  :				str       				=		(big_a + 1) - (big_a - 1) * _cos
       __UpperCAmelCase  :				Tuple       				=		(big_a + 1) + (big_a - 1) * _cos
       __UpperCAmelCase  :				List[str]       				=		(big_a - 1) - (big_a + 1) * _cos
       __UpperCAmelCase  :				Optional[Any]       				=		(big_a - 1) + (big_a + 1) * _cos
       __UpperCAmelCase  :				Any       				=		2 * sqrt(lowerCamelCase__						) * alpha

       __UpperCAmelCase  :				Optional[int]       				=		big_a * (pmc + aaa)
       __UpperCAmelCase  :				Tuple       				=		2 * big_a * mpc
       __UpperCAmelCase  :				Union[str, Any]       				=		big_a * (pmc - aaa)
       __UpperCAmelCase  :				Optional[int]       				=		ppmc + aaa
       __UpperCAmelCase  :				Dict       				=		-2 * pmpc
       __UpperCAmelCase  :				Optional[Any]       				=		ppmc - aaa

       __UpperCAmelCase  :				Union[str, Any]       				=		IIRFilter(2						)
       filt.set_coefficients([aa, aa, aa]							,    [ba, ba, ba]						)
       return filt


def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__ = 1 / sqrt(2						)							,    )					->       IIRFilter:





       """simple docstring"""


       __UpperCAmelCase  :				Union[str, Any]       				=		tau * frequency / samplerate
       __UpperCAmelCase  :				Any       				=		sin(lowerCamelCase__						)
       __UpperCAmelCase  :				Optional[int]       				=		cos(lowerCamelCase__						)
       __UpperCAmelCase  :				Any       				=		_sin / (2 * q_factor)
       __UpperCAmelCase  :				List[Any]       				=		10 ** (gain_db / 40)
       __UpperCAmelCase  :				str       				=		(big_a + 1) - (big_a - 1) * _cos
       __UpperCAmelCase  :				Tuple       				=		(big_a + 1) + (big_a - 1) * _cos
       __UpperCAmelCase  :				int       				=		(big_a - 1) - (big_a + 1) * _cos
       __UpperCAmelCase  :				Tuple       				=		(big_a - 1) + (big_a + 1) * _cos
       __UpperCAmelCase  :				Optional[int]       				=		2 * sqrt(lowerCamelCase__						) * alpha

       __UpperCAmelCase  :				int       				=		big_a * (ppmc + aaa)
       __UpperCAmelCase  :				Any       				=		-2 * big_a * pmpc
       __UpperCAmelCase  :				Optional[Any]       				=		big_a * (ppmc - aaa)
       __UpperCAmelCase  :				Tuple       				=		pmc + aaa
       __UpperCAmelCase  :				Union[str, Any]       				=		2 * mpc
       __UpperCAmelCase  :				Optional[int]       				=		pmc - aaa

       __UpperCAmelCase  :				Optional[int]       				=		IIRFilter(2						)
       filt.set_coefficients([aa, aa, aa]							,    [ba, ba, ba]						)
       return filt







'''simple docstring'''




from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    )					->       list[float]:





       """simple docstring"""


       __UpperCAmelCase				, __UpperCAmelCase  :				Union[str, Any]       				=		coefficient_matrix.shape
       __UpperCAmelCase				, __UpperCAmelCase  :				Any       				=		constant_matrix.shape

       if rowsa != colsa:
              __UpperCAmelCase  :				str       				=		f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
              raise ValueError(lowerCamelCase__						)

       if colsa != 1:
              __UpperCAmelCase  :				Optional[Any]       				=		f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
              raise ValueError(lowerCamelCase__						)

       if rowsa != rowsa:
              __UpperCAmelCase  :				Optional[int]       				=		(
                  "Coefficient and constant matrices dimensions must be nxn and nx1 but "
                  f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
              )
              raise ValueError(lowerCamelCase__						)

       if len(lowerCamelCase__						) != rowsa:
              __UpperCAmelCase  :				List[str]       				=		(
                  "Number of initial values must be equal to number of rows in coefficient "
                  f"""matrix but received {len(lowerCamelCase__						)} and {rowsa}"""
              )
              raise ValueError(lowerCamelCase__						)

       if iterations <= 0:
              raise ValueError("Iterations must be at least 1"						)

       __UpperCAmelCase  :				NDArray[floataa]       				=		np.concatenate(
           (coefficient_matrix, constant_matrix)							,    axis=1						)

       __UpperCAmelCase				, __UpperCAmelCase  :				Tuple       				=		table.shape

       strictly_diagonally_dominant(lowerCamelCase__						)

       # Iterates the whole matrix for given number of times
       for _ in range(lowerCamelCase__						):
              __UpperCAmelCase  :				int       				=		[]
              for row in range(lowerCamelCase__						):
                     __UpperCAmelCase  :				List[str]       				=		0
                     for col in range(lowerCamelCase__						):
                            if col == row:
                                   __UpperCAmelCase  :				int       				=		table[row][col]
                            elif col == cols - 1:
                                   __UpperCAmelCase  :				Any       				=		table[row][col]
                            else:
                                   temp += (-1) * table[row][col] * init_val[col]
                     __UpperCAmelCase  :				List[Any]       				=		(temp + val) / denom
                     new_val.append(lowerCamelCase__						)
              __UpperCAmelCase  :				str       				=		new_val

       return [float(lowerCamelCase__						) for i in new_val]

def _lowercase	(      lowerCamelCase__						)					->       bool:





       """simple docstring"""


       __UpperCAmelCase				, __UpperCAmelCase  :				Optional[int]       				=		table.shape

       __UpperCAmelCase  :				str       				=		True

       for i in range(0							,    lowerCamelCase__						):
              __UpperCAmelCase  :				Union[str, Any]       				=		0
              for j in range(0							,    cols - 1						):
                     if i == j:
                            continue
                     else:
                            total += table[i][j]

              if table[i][i] <= total:
                     raise ValueError("Coefficient matrix is not strictly diagonally dominant"						)

       return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
   import doctest

   doctest.testmod()






