





'''simple docstring'''


def 		__a(SCREAMING_SNAKE_CASE_     :    Optional[int]			):



    '''simple docstring'''





    _lowerCAmelCase			=					len(A_			)
    _lowerCAmelCase			=					len(matrix[0]			)
    _lowerCAmelCase			=					min(A_						,				A_			)

    for row in range(A_			):
        # Check if diagonal element is not zero
        if matrix[row][row] != 0:
            # Eliminate all the elements below the diagonal
            for col in range(row + 1						,				A_			):
                _lowerCAmelCase			=					matrix[col][row] / matrix[row][row]
                for i in range(A_						,				A_			):
                    matrix[col][i] -= multiplier * matrix[row][i]
        else:
            # Find a non-zero diagonal element to swap rows
            _lowerCAmelCase			=					True
            for i in range(row + 1						,				A_			):
                if matrix[i][row] != 0:
                    _lowerCAmelCase			=					matrix[i], matrix[row]
                    _lowerCAmelCase			=					False
                    break
            if reduce:
                rank -= 1
                for i in range(A_			):
                    _lowerCAmelCase			=					matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
            row -= 1

    return rank


if __name__ == "__main__":
       import doctest

       doctest.testmod()





"""simple docstring"""





from ..utils import DummyObject, requires_backends







class 				SCREAMING_SNAKE_CASE					(		metaclass=a_       ):






					"""simple docstring"""



					lowercase__				 =       ["speech"]







					def __init__(       self			:				Tuple   ,*lowercase_			:				Tuple   ,**lowercase_			:				List[str]		):
						requires_backends(self   ,['''speech''']		)







class 				SCREAMING_SNAKE_CASE					(		metaclass=a_       ):






					"""simple docstring"""



					lowercase__				 =       ["speech"]







					def __init__(       self			:				Union[str, Any]   ,*lowercase_			:				List[str]   ,**lowercase_			:				Any		):
						requires_backends(self   ,['''speech''']		)




