'''simple docstring'''
import pytest

from datasets.utils.sharding import _distribute_shards, _number_of_shards_in_gen_kwargs, _split_gen_kwargs







@pytest.mark.parametrize(
    'kwargs, expected'				,     [
        ({'num_shards': 0, 'max_num_jobs': 1}, []),
        ({'num_shards': 1_0, 'max_num_jobs': 1}, [range(1_0			)]),
        ({'num_shards': 1_0, 'max_num_jobs': 1_0}, [range(_a				,     i + 1			) for i in range(1_0			)]),
        ({'num_shards': 1, 'max_num_jobs': 1_0}, [range(1			)]),
        ({'num_shards': 1_0, 'max_num_jobs': 3}, [range(0				,     4			), range(4				,     7			), range(7				,     1_0			)]),
        ({'num_shards': 3, 'max_num_jobs': 1_0}, [range(0				,     1			), range(1				,     2			), range(2				,     3			)]),
    ]				,     )
def  _UpperCamelCase (     _a	:	Union[str, Any]				,     _a	:	Optional[Any]			):




    """simple docstring"""



    __UpperCamelCase	:	List[Any]		    =  _distribute_shards(**_a			)
    assert out == expected







@pytest.mark.parametrize(
    'gen_kwargs, max_num_jobs, expected'				,     [
        ({'foo': 0}, 1_0, [{'foo': 0}]),
        ({'shards': [0, 1, 2, 3]}, 1, [{'shards': [0, 1, 2, 3]}]),
        ({'shards': [0, 1, 2, 3]}, 4, [{'shards': [0]}, {'shards': [1]}, {'shards': [2]}, {'shards': [3]}]),
        ({'shards': [0, 1]}, 4, [{'shards': [0]}, {'shards': [1]}]),
        ({'shards': [0, 1, 2, 3]}, 2, [{'shards': [0, 1]}, {'shards': [2, 3]}]),
    ]				,     )
def  _UpperCamelCase (     _a	:	Optional[int]				,     _a	:	Optional[Any]				,     _a	:	Optional[Any]			):




    """simple docstring"""



    __UpperCamelCase	:	List[Any]		    =  _split_gen_kwargs(_a				,     _a			)
    assert out == expected







@pytest.mark.parametrize(
    'gen_kwargs, expected'				,     [
        ({'foo': 0}, 1),
        ({'shards': [0]}, 1),
        ({'shards': [0, 1, 2, 3]}, 4),
        ({'shards': [0, 1, 2, 3], 'foo': 0}, 4),
        ({'shards': [0, 1, 2, 3], 'other': (0, 1)}, 4),
        ({'shards': [0, 1, 2, 3], 'shards2': [0, 1]}, RuntimeError),
    ]				,     )
def  _UpperCamelCase (     _a	:	Optional[Any]				,     _a	:	Any			):




    """simple docstring"""



    if expected is RuntimeError:
        with pytest.raises(_a			):
            _number_of_shards_in_gen_kwargs(_a			)
    else:
        __UpperCamelCase	:	Optional[int]		    =  _number_of_shards_in_gen_kwargs(_a			)
        assert out == expected




'''simple docstring'''
from __future__ import annotations

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







def  _UpperCamelCase (     _a	:	NDArray[floataa]				,     _a	:	NDArray[floataa]				,     _a	:	list[int]				,     _a	:	int				,     ):




    """simple docstring"""



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

    if rowsa != colsa:
        __UpperCamelCase	:	Tuple		    =  f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
        raise ValueError(_a			)

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

    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(_a			)

    if len(_a			) != rowsa:
        __UpperCamelCase	:	Union[str, Any]		    =  (
            'Number of initial values must be equal to number of rows in coefficient '
            f"""matrix but received {len(_a			)} and {rowsa}"""
        )
        raise ValueError(_a			)

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

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

    __UpperCamelCase    ,					__UpperCamelCase	:	Union[str, Any]		    =  table.shape

    strictly_diagonally_dominant(_a			)

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

    return [float(_a			) for i in new_val]







def  _UpperCamelCase (     _a	:	NDArray[floataa]			):




    """simple docstring"""



    __UpperCamelCase    ,					__UpperCamelCase	:	str		    =  table.shape

    __UpperCamelCase	:	str		    =  True

    for i in range(0				,     _a			):
        __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()



