




from __future__ import annotations

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





def 		__A		(	__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			)      ->       list[float]:
	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 		__A		(	__lowerCamelCase    )      ->       bool:
	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()







__UpperCamelCase					:       Optional[int]    					=      {
    "Pillow": "Pillow",
    "accelerate": "accelerate>=0.11.0",
    "compel": "compel==0.1.8",
    "black": "black~=23.1",
    "datasets": "datasets",
    "filelock": "filelock",
    "flax": "flax>=0.4.1",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.13.2",
    "requests-mock": "requests-mock==1.10.0",
    "importlib_metadata": "importlib_metadata",
    "invisible-watermark": "invisible-watermark",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2",
    "jaxlib": "jaxlib>=0.1.65",
    "Jinja2": "Jinja2",
    "k-diffusion": "k-diffusion>=0.0.12",
    "torchsde": "torchsde",
    "note_seq": "note_seq",
    "librosa": "librosa",
    "numpy": "numpy",
    "omegaconf": "omegaconf",
    "parameterized": "parameterized",
    "protobuf": "protobuf>=3.20.3,<4",
    "pytest": "pytest",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "ruff": "ruff>=0.0.241",
    "safetensors": "safetensors",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "scipy": "scipy",
    "onnx": "onnx",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "tensorboard": "tensorboard",
    "torch": "torch>=1.4",
    "torchvision": "torchvision",
    "transformers": "transformers>=4.25.1",
    "urllib3": "urllib3<=2.0.0",
}

