
'''simple docstring'''







from __future__ import annotations

_snake_case					: List[Any]     			=					[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]


class       lowerCAmelCase			:




		def __init__(					self       ,    UpperCamelCase   ):
								_SCREAMING_SNAKE_CASE					=			-1
								_SCREAMING_SNAKE_CASE					=			-1
								_SCREAMING_SNAKE_CASE					=			[-1] * length
								_SCREAMING_SNAKE_CASE					=			None
								_SCREAMING_SNAKE_CASE					=			None




		def __repr__(					self   ):
								return F'Node(min_value={self.minn} max_value={self.maxx})'



def       _a		(						_SCREAMING_SNAKE_CASE		: list[int]	):
						_SCREAMING_SNAKE_CASE					=			Node(len(_SCREAMING_SNAKE_CASE	)	)
						_SCREAMING_SNAKE_CASE,				_SCREAMING_SNAKE_CASE					=			min(_SCREAMING_SNAKE_CASE	), max(_SCREAMING_SNAKE_CASE	)
						# Leaf node case where the node contains only one unique value
						if root.minn == root.maxx:
												return root
						_SCREAMING_SNAKE_CASE					=			(root.minn + root.maxx) // 2

						_SCREAMING_SNAKE_CASE					=			[]
						_SCREAMING_SNAKE_CASE					=			[]

						for index, num in enumerate(_SCREAMING_SNAKE_CASE	):
												if num <= pivot:
																		left_arr.append(_SCREAMING_SNAKE_CASE	)
												else:
																		right_arr.append(_SCREAMING_SNAKE_CASE	)
												_SCREAMING_SNAKE_CASE					=			len(_SCREAMING_SNAKE_CASE	)
						_SCREAMING_SNAKE_CASE					=			build_tree(_SCREAMING_SNAKE_CASE	)
						_SCREAMING_SNAKE_CASE					=			build_tree(_SCREAMING_SNAKE_CASE	)
						return root



def       _a		(						_SCREAMING_SNAKE_CASE		: Node | None						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int	):
						if index < 0 or node is None:
												return 0
						# Leaf node cases
						if node.minn == node.maxx:
												return index + 1 if node.minn == num else 0
						_SCREAMING_SNAKE_CASE					=			(node.minn + node.maxx) // 2
						if num <= pivot:
												# go the left subtree and map index to the left subtree
												return rank_till_index(node.left						,      _SCREAMING_SNAKE_CASE						,      node.map_left[index] - 1	)
						else:
												# go to the right subtree and map index to the right subtree
												return rank_till_index(node.right						,      _SCREAMING_SNAKE_CASE						,      index - node.map_left[index]	)



def       _a		(						_SCREAMING_SNAKE_CASE		: Node | None						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int	):
						if start > end:
												return 0
						_SCREAMING_SNAKE_CASE					=			rank_till_index(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						_SCREAMING_SNAKE_CASE					=			rank_till_index(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      start - 1	)
						return rank_till_end - rank_before_start



def       _a		(						_SCREAMING_SNAKE_CASE		: Node | None						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int	):
						if index > (end - start) or start > end or node is None:
												return -1
						# Leaf node case
						if node.minn == node.maxx:
												return node.minn
						# Number of elements in the left subtree in interval [start, end]
						_SCREAMING_SNAKE_CASE					=			node.map_left[end] - (
						    node.map_left[start - 1] if start else 0
						)
						if num_elements_in_left_tree > index:
												return quantile(
												    node.left						,      _SCREAMING_SNAKE_CASE						,      (node.map_left[start - 1] if start else 0)						,      node.map_left[end] - 1						,      )
						else:
												return quantile(
												    node.right						,      index - num_elements_in_left_tree						,      start - (node.map_left[start - 1] if start else 0)						,      end - node.map_left[end]						,      )



def       _a		(						_SCREAMING_SNAKE_CASE		: Node | None						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int						,      _SCREAMING_SNAKE_CASE		: int	):
						if (
						    start > end
						    or node is None
						    or start_num > end_num
						    or node.minn > end_num
						    or node.maxx < start_num
						):
												return 0
						if start_num <= node.minn and node.maxx <= end_num:
												return end - start + 1
						_SCREAMING_SNAKE_CASE					=			range_counting(
						    node.left						,      (node.map_left[start - 1] if start else 0)						,      node.map_left[end] - 1						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      )
						_SCREAMING_SNAKE_CASE					=			range_counting(
						    node.right						,      start - (node.map_left[start - 1] if start else 0)						,      end - node.map_left[end]						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      )
						return left + right


if __name__ == "__main__":
						import doctest

						doctest.testmod()

'''simple docstring'''







import logging

# standard libraries
import sys

import numpy as np
import pytest  # type: ignore

# Custom/local libraries
from matrix import matrix_operation as matop

_snake_case					: List[str]     			=					[[12, 10], [3, 9]]
_snake_case					: Any     			=					[[3, 4], [7, 4]]
_snake_case					: List[str]     			=					[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
_snake_case					: Any     			=					[[3, 0, -2], [2, 0, 2], [0, 1, 1]]
_snake_case					: Any     			=					[[3, 0, 2], [2, 0, -2], [0, 1, 1], [2, 0, -2]]
_snake_case					: Optional[Any]     			=					[1]
_snake_case					: str     			=					[2]

_snake_case					: Optional[int]     			=					logging.getLogger()
_snake_case					: Optional[Any]     			=					logging.DEBUG
_snake_case					: Tuple     			=					logging.StreamHandler(sys.stdout)
logger.addHandler(stream_handler)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: List[Any]						,      _SCREAMING_SNAKE_CASE		: Tuple	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_addition.__name__} returned integer'	)
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_addition.__name__} with same matrix dims'	)
												_SCREAMING_SNAKE_CASE					=			(np.array(_SCREAMING_SNAKE_CASE	) + np.array(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_addition.__name__} with different matrix dims'	)
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Optional[Any]						,      _SCREAMING_SNAKE_CASE		: List[str]	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_subtraction.__name__} returned integer'	)
																		matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_subtraction.__name__} with same matrix dims'	)
												_SCREAMING_SNAKE_CASE					=			(np.array(_SCREAMING_SNAKE_CASE	) - np.array(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_subtraction.__name__} with different matrix dims'	)
																		assert matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Any						,      _SCREAMING_SNAKE_CASE		: List[str]	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												logger.info(F'\n\t{test_multiplication.__name__} returned integer'	)
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_multiplication.__name__} meets dim requirements'	)
												_SCREAMING_SNAKE_CASE					=			(np.matmul(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.multiply(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(
																		    F'\n\t{test_multiplication.__name__} does not meet dim requirements'	)
																		assert matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
def       _a		(						):
						_SCREAMING_SNAKE_CASE					=			(3.5 * np.array(_SCREAMING_SNAKE_CASE	)).tolist()
						_SCREAMING_SNAKE_CASE					=			matop.scalar_multiply(_SCREAMING_SNAKE_CASE						,      3.5	)
						assert theo == act



@pytest.mark.mat_ops
def       _a		(						):
						_SCREAMING_SNAKE_CASE					=			(np.identity(5	)).tolist()
						_SCREAMING_SNAKE_CASE					=			matop.identity(5	)
						assert theo == act




@pytest.mark.mat_ops
@pytest.mark.parametrize("mat"						,      [mat_a, mat_b, mat_c, mat_d, mat_e, mat_f]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Tuple	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_transpose.__name__} returned integer'	)
																		matop.transpose(_SCREAMING_SNAKE_CASE	)
						else:
												_SCREAMING_SNAKE_CASE					=			(np.transpose(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.transpose(_SCREAMING_SNAKE_CASE						,      return_map=_SCREAMING_SNAKE_CASE	)
												assert theo == act