from __future__ import annotations

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



def lowerCamelCase  (       SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE  ,      ):
				'''simple docstring'''







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

				if rowsa != colsa:
								__UpperCamelCase					:Optional[int]        =		f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
								raise ValueError(SCREAMING_SNAKE_CASE     )

				if colsa != 1:
								__UpperCamelCase					:Any        =		f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
								raise ValueError(SCREAMING_SNAKE_CASE     )

				if rowsa != rowsa:
								__UpperCamelCase					:int        =		(
								    'Coefficient and constant matrices dimensions must be nxn and nx1 but '
								    f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
								)
								raise ValueError(SCREAMING_SNAKE_CASE     )

				if len(SCREAMING_SNAKE_CASE     ) != rowsa:
								__UpperCamelCase					:Dict        =		(
								    'Number of initial values must be equal to number of rows in coefficient '
								    f"""matrix but received {len(SCREAMING_SNAKE_CASE     )} and {rowsa}"""
								)
								raise ValueError(SCREAMING_SNAKE_CASE     )

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

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

				__UpperCamelCase					:Optional[Any]        =		table.shape

				strictly_diagonally_dominant(SCREAMING_SNAKE_CASE     )

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

				return [float(SCREAMING_SNAKE_CASE     ) for i in new_val]



def lowerCamelCase  (       SCREAMING_SNAKE_CASE     ):
				'''simple docstring'''







				__UpperCamelCase					:List[str]        =		table.shape

				__UpperCamelCase					:Tuple        =		True

				for i in range(0  ,      SCREAMING_SNAKE_CASE     ):
								__UpperCamelCase					:Optional[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()






from ...utils import is_note_seq_available, is_transformers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


try:
    if not (is_transformers_available() and is_torch_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
    from .notes_encoder import SpectrogramNotesEncoder
    from .continous_encoder import SpectrogramContEncoder
    from .pipeline_spectrogram_diffusion import (
        SpectrogramContEncoder,
        SpectrogramDiffusionPipeline,
        TaFilmDecoder,
    )

try:
    if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ...utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
    from .midi_utils import MidiProcessor





