
"""simple docstring"""

import unittest

import numpy as np
def 		UpperCAmelCase (		a_,						a_,						a_,						a_ = None,						):





		'''simple docstring'''


		lowerCamelCase					:      Dict          =   np.shape(a_      )
		lowerCamelCase					:      List[Any]          =   np.shape(a_      )
		lowerCamelCase					:      Union[str, Any]          =   np.shape(a_      )

		if shape_a[0] != shape_b[0]:
				lowerCamelCase					:      List[Any]          =   (
				    'Expected the same number of rows for A and B. '
				    F"""Instead found A of size {shape_a} and B of size {shape_b}"""
				)
				raise ValueError(a_      )

		if shape_b[1] != shape_c[1]:
				lowerCamelCase					:      Optional[int]          =   (
				    'Expected the same number of columns for B and C. '
				    F"""Instead found B of size {shape_b} and C of size {shape_c}"""
				)
				raise ValueError(a_      )

		lowerCamelCase					:      Tuple          =   pseudo_inv
		if a_inv is None:
				try:
						lowerCamelCase					:      List[Any]          =   np.linalg.inv(a_      )
				except np.linalg.LinAlgError:
						raise ValueError(
						    'Input matrix A is not invertible. Cannot compute Schur complement.'      )

		return mat_c - mat_b.T @ a_inv @ mat_b






class 	_lowercase       (    unittest.TestCase		):




	def       _UpperCamelCase   (			self )		->							None:
			lowerCamelCase					:      Optional[int]          =   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
			lowerCamelCase					:      str          =   np.array([[0, 3], [3, 0], [2, 3]] )
			lowerCamelCase					:      int          =   np.array([[2, 1], [6, 3]] )

			lowerCamelCase					:      Union[str, Any]          =   schur_complement(UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_ )

			lowerCamelCase					:      str          =   np.block([[a, b], [b.T, c]] )

			lowerCamelCase					:      Optional[Any]          =   np.linalg.det(UpperCAmelCase_ )
			lowerCamelCase					:      List[Any]          =   np.linalg.det(UpperCAmelCase_ )
			lowerCamelCase					:      Union[str, Any]          =   np.linalg.det(UpperCAmelCase_ )

			self.assertAlmostEqual(UpperCAmelCase_		,			det_a * det_s )




	def       _UpperCamelCase   (			self )		->							None:
			lowerCamelCase					:      List[Any]          =   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
			lowerCamelCase					:      Tuple          =   np.array([[0, 3], [3, 0], [2, 3]] )
			lowerCamelCase					:      List[Any]          =   np.array([[2, 1], [6, 3]] )

			with self.assertRaises(UpperCAmelCase_ ):
					schur_complement(UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_ )




	def       _UpperCamelCase   (			self )		->							None:
			lowerCamelCase					:      str          =   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]] )
			lowerCamelCase					:      Any          =   np.array([[0, 3], [3, 0], [2, 3]] )
			lowerCamelCase					:      Optional[Any]          =   np.array([[2, 1, 3], [6, 3, 5]] )

			with self.assertRaises(UpperCAmelCase_ ):
					schur_complement(UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_ )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					unittest.main()








"""simple docstring"""

from __future__ import annotations

_A						=			[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]
def 		UpperCAmelCase (		a_,						a_,						a_,						a_,						a_,						):





		'''simple docstring'''


		lowerCamelCase					:      Dict          =   [
		    [0 for col in range(len(grid[0]      )      )] for row in range(len(a_      )      )
		]  # the reference grid
		lowerCamelCase					:      Union[str, Any]          =   1
		lowerCamelCase					:      Any          =   [
		    [0 for col in range(len(grid[0]      )      )] for row in range(len(a_      )      )
		]  # the action grid

		lowerCamelCase					:      List[str]          =   init[0]
		lowerCamelCase					:      Optional[Any]          =   init[1]
		lowerCamelCase					:      List[Any]          =   0
		lowerCamelCase					:      List[str]          =   g + heuristic[x][y]  # cost from starting cell to destination cell
		lowerCamelCase					:      Union[str, Any]          =   [[f, g, x, y]]

		lowerCamelCase					:      Union[str, Any]          =   False  # flag that is set when search is complete
		lowerCamelCase					:      str          =   False  # flag set if we can't find expand

		while not found and not resign:
				if len(a_      ) == 0:
						raise ValueError('Algorithm is unable to find solution'      )
				else:  # to choose the least costliest action so as to move closer to the goal
						cell.sort()
						cell.reverse()
						lowerCamelCase					:      int          =   cell.pop()
						lowerCamelCase					:      str          =   next_cell[2]
						lowerCamelCase					:      Union[str, Any]          =   next_cell[3]
						lowerCamelCase					:      List[str]          =   next_cell[1]

						if x == goal[0] and y == goal[1]:
								lowerCamelCase					:      Any          =   True
						else:
								for i in range(len(a_      )      ):  # to try out different valid actions
										lowerCamelCase					:      Tuple          =   x + DIRECTIONS[i][0]
										lowerCamelCase					:      Union[str, Any]          =   y + DIRECTIONS[i][1]
										if xa >= 0 and xa < len(a_      ) and ya >= 0 and ya < len(grid[0]      ):
												if closed[xa][ya] == 0 and grid[xa][ya] == 0:
														lowerCamelCase					:      str          =   g + cost
														lowerCamelCase					:      Tuple          =   ga + heuristic[xa][ya]
														cell.append([fa, ga, xa, ya]      )
														lowerCamelCase					:      Union[str, Any]          =   1
														lowerCamelCase					:      Any          =   i
		lowerCamelCase					:      Any          =   []
		lowerCamelCase					:      Optional[int]          =   goal[0]
		lowerCamelCase					:      Dict          =   goal[1]
		invpath.append([x, y]      )  # we get the reverse path from here
		while x != init[0] or y != init[1]:
				lowerCamelCase					:      Dict          =   x - DIRECTIONS[action[x][y]][0]
				lowerCamelCase					:      Dict          =   y - DIRECTIONS[action[x][y]][1]
				lowerCamelCase					:      Optional[Any]          =   xa
				lowerCamelCase					:      Union[str, Any]          =   ya
				invpath.append([x, y]      )

		lowerCamelCase					:      Optional[int]          =   []
		for i in range(len(a_      )      ):
				path.append(invpath[len(a_      ) - 1 - i]      )
		return path, action


if __name__ == "__main__":
					_A						=			[
					    [0, 1, 0, 0, 0, 0],
					    [0, 1, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
					    [0, 1, 0, 0, 0, 0],
					    [0, 1, 0, 0, 1, 0],
					    [0, 0, 0, 0, 1, 0],
					]

					_A						=			[0, 0]
					# all coordinates are given in format [y,x]
					_A						=			[len(grid) - 1, len(grid[0]) - 1]
					_A						=			1

					# the cost map which pushes the path closer to the goal
					_A						=			[[0 for row in range(len(grid[0]))] for col in range(len(grid))]
					for i in range(len(grid)):
										for j in range(len(grid[0])):
															_A						=			abs(i - goal[0]) + abs(j - goal[1])
															if grid[i][j] == 1:
																				# added extra penalty in the heuristic map
																				_A						=			9_9

					_A					,  _A						=			search(grid, init, goal, cost, heuristic)

					print('ACTION MAP')
					for i in range(len(action)):
										print(action[i])

					for i in range(len(path)):
										print(path[i])






