



from __future__ import annotations

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






def  lowerCamelCase_	(      lowerCAmelCase__	:	NDArray[floataa]			,	lowerCAmelCase__	:	NDArray[floataa]			,	lowerCAmelCase__	:	list[int]			,	lowerCAmelCase__	:	int			,	)       ->							list[float]:

							'''simple docstring'''






							A						,   A      						=    coefficient_matrix.shape
							A						,   A      						=    constant_matrix.shape

							if rowsa != colsa:
														A      						=    F'''Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'''
														raise ValueError(lowerCAmelCase__				)

							if colsa != 1:
														A      						=    F'''Constant matrix must be nx1 but received {rowsa}x{colsa}'''
														raise ValueError(lowerCAmelCase__				)

							if rowsa != rowsa:
														A      						=    (
														    '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:
														A      						=    (
														    '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'				)

							A      						=    np.concatenate(
							    (coefficient_matrix, constant_matrix)			,	axis=1				)

							A						,   A      						=    table.shape

							strictly_diagonally_dominant(lowerCAmelCase__				)

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

							return [float(lowerCAmelCase__				) for i in new_val]






def  lowerCamelCase_	(      lowerCAmelCase__	:	NDArray[floataa]				)       ->							bool:

							'''simple docstring'''






							A						,   A      						=    table.shape

							A      						=    True

							for i in range(0			,	lowerCAmelCase__				):
														A      						=    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()



import doctest
from collections import deque

import numpy as np
class 						lowerCamelCase_							:



					'''simple docstring'''







					def __init__(					self    ) ->      None:







								'''simple docstring'''

								__lowercase			       = [2, 1, 2, -1]
								__lowercase			       = [1, 2, 3, 4]






					def A   (					self    ) ->      list[float]:







								'''simple docstring'''

								__lowercase			       = len(self.first_signal    )
								__lowercase			       = len(self.second_signal    )

								__lowercase			       = max(snake_case_			,							snake_case_    )

								# create a zero matrix of max_length x max_length
								__lowercase			       = [[0] * max_length for i in range(snake_case_    )]

								# fills the smaller signal with zeros to make both signals of same length
								if length_first_signal < length_second_signal:
											self.first_signal += [0] * (max_length - length_first_signal)
								elif length_first_signal > length_second_signal:
											self.second_signal += [0] * (max_length - length_second_signal)
								for i in range(snake_case_    ):
											__lowercase			       = deque(self.second_signal    )
											rotated_signal.rotate(snake_case_    )
											for j, item in enumerate(snake_case_    ):
														matrix[i][j] += item

        # multiply the matrix with the first signal
								__lowercase			       = np.matmul(np.transpose(snake_case_    )			,							np.transpose(self.first_signal    )    )

								# rounding-off to two decimal places
								return [round(snake_case_			,							2    ) for i in final_signal]


if __name__ == "__main__":
	doctest.testmod()


