





from __future__ import annotations

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


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase						,	)			->     list[float]:
    lowerCamelCase__ ,							lowerCamelCase__    :      List[str]					 =		coefficient_matrix.shape
    lowerCamelCase__ ,							lowerCamelCase__    :      Tuple					 =		constant_matrix.shape

    if rowsa != colsa:
        lowerCamelCase__    :      List[Any]					 =		F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
        raise ValueError(_UpperCAmelCase )

    if colsa != 1:
        lowerCamelCase__    :      Tuple					 =		F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
        raise ValueError(_UpperCAmelCase )

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

    if len(_UpperCAmelCase ) != rowsa:
        lowerCamelCase__    :      Tuple					 =		(
            'Number of initial values must be equal to number of rows in coefficient '
            F"""matrix but received {len(_UpperCAmelCase )} and {rowsa}"""
        )
        raise ValueError(_UpperCAmelCase )

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

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

    lowerCamelCase__ ,							lowerCamelCase__    :      List[str]					 =		table.shape

    strictly_diagonally_dominant(_UpperCAmelCase )

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

    return [float(_UpperCAmelCase ) for i in new_val]


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase )			->     bool:
    lowerCamelCase__ ,							lowerCamelCase__    :      List[Any]					 =		table.shape

    lowerCamelCase__    :      Optional[int]					 =		True

    for i in range(0						,	_UpperCAmelCase ):
        lowerCamelCase__    :      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()







'''simple docstring'''




import pytest

import datasets.config
from datasets.utils.info_utils import is_small_dataset







@pytest.mark.parametrize('''dataset_size'''		,				[None, 400 * 2**20, 600 * 2**20]						)
@pytest.mark.parametrize('''input_in_memory_max_size'''		,				['''default''', 0, 100 * 2**20, 900 * 2**20]						)
def 		lowerCAmelCase_				(   snake_case__		,				snake_case__		,				snake_case__						):




    '''simple docstring'''



    if input_in_memory_max_size != "default":
        monkeypatch.setattr(datasets.config		,				'''IN_MEMORY_MAX_SIZE'''		,				snake_case__						)
    A       :   Dict					=						datasets.config.IN_MEMORY_MAX_SIZE
    if input_in_memory_max_size == "default":
        assert in_memory_max_size == 0
    else:
        assert in_memory_max_size == input_in_memory_max_size
    if dataset_size and in_memory_max_size:
        A       :   Dict					=						dataset_size < in_memory_max_size
    else:
        A       :   Tuple					=						False
    A       :   int					=						is_small_dataset(snake_case__						)
    assert result == expected




