


"""simple docstring"""





def    _snake_case  (  _snake_case :	list[list[int | float]]	):
      lowerCAmelCase    :		Union[str, Any]				=      len(_snake_case	)
      lowerCAmelCase    :		List[Any]				=      len(matrix[0]	)
      lowerCAmelCase    :		str				=      min(_snake_case       ,      _snake_case	)

      for row in range(_snake_case	):
            # 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       ,      _snake_case	):
                        lowerCAmelCase    :		Dict				=      matrix[col][row] / matrix[row][row]
                        for i in range(_snake_case       ,      _snake_case	):
                              matrix[col][i] -= multiplier * matrix[row][i]
            else:
                  # Find a non-zero diagonal element to swap rows
                  lowerCAmelCase    :		Optional[Any]				=      True
                  for i in range(row + 1       ,      _snake_case	):
                        if matrix[i][row] != 0:
                              lowerCAmelCase,					lowerCAmelCase    :		List[Any]				=      matrix[i], matrix[row]
                              lowerCAmelCase    :		str				=      False
                              break
                  if reduce:
                        rank -= 1
                        for i in range(_snake_case	):
                              lowerCAmelCase    :		Optional[Any]				=      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 __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm


def    _snake_case  (  _snake_case :	np.ndarray       ,      _snake_case :	np.ndarray	):
      return math.sqrt(sum(pow(a - b       ,      2	) for a, b in zip(_snake_case       ,      _snake_case	)	)	)


def    _snake_case  (  _snake_case :	np.ndarray       ,      _snake_case :	np.ndarray	):

      if dataset.ndim != value_array.ndim:
            lowerCAmelCase    :		List[Any]				=      (
                '''Wrong input data\'s dimensions... '''
                f'''dataset : {dataset.ndim}, value_array : {value_array.ndim}'''
            )
            raise ValueError(_snake_case	)

      try:
            if dataset.shape[1] != value_array.shape[1]:
                  lowerCAmelCase    :		Dict				=      (
                      '''Wrong input data\'s shape... '''
                      f'''dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}'''
                  )
                  raise ValueError(_snake_case	)
      except IndexError:
            if dataset.ndim != value_array.ndim:
                  raise TypeError('''Wrong shape'''	)

      if dataset.dtype != value_array.dtype:
            lowerCAmelCase    :		Optional[Any]				=      (
                '''Input data have different datatype... '''
                f'''dataset : {dataset.dtype}, value_array : {value_array.dtype}'''
            )
            raise TypeError(_snake_case	)

      lowerCAmelCase    :		str				=      []

      for value in value_array:
            lowerCAmelCase    :		int				=      euclidean(_snake_case       ,      dataset[0]	)
            lowerCAmelCase    :		Union[str, Any]				=      dataset[0].tolist()

            for dataset_value in dataset[1:]:
                  lowerCAmelCase    :		Any				=      euclidean(_snake_case       ,      _snake_case	)

                  if dist > temp_dist:
                        lowerCAmelCase    :		List[Any]				=      temp_dist
                        lowerCAmelCase    :		Tuple				=      dataset_value.tolist()

            answer.append([vector, dist]	)

      return answer


def    _snake_case  (  _snake_case :	np.ndarray       ,      _snake_case :	np.ndarray	):
      return np.dot(_snake_case       ,      _snake_case	) / (norm(_snake_case	) * norm(_snake_case	))


if __name__ == "__main__":
 import doctest

 doctest.testmod()


