



#
# Sort large text files in a minimum amount of memory
#
import argparse
import os
class lowerCAmelCase_       :







	'''simple docstring'''




	A_       :     Union[str, Any]									=		'block_{0}.dat'

	def __init__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  filename
				a__					=  []

	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  self.BLOCK_FILENAME_FORMAT.format(lowerCamelCase       )
				with open(lowerCamelCase   ,       """w"""       ) as file:
							file.write(lowerCamelCase       )
				self.block_filenames.append(lowerCamelCase       )

	def 				_A			(	self       ):



				'''simple docstring'''


				return self.block_filenames

	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase=None       ):



				'''simple docstring'''


				a__					=  0
				with open(self.filename       ) as file:
							while True:
										a__					=  file.readlines(lowerCamelCase       )

										if lines == []:
													break

										if sort_key is None:
													lines.sort()
										else:
													lines.sort(key=lowerCamelCase       )

										self.write_block("""""".join(lowerCamelCase       )   ,       lowerCamelCase       )
										i += 1







	def 				_A			(	self       ):



				'''simple docstring'''


				map(os.remove   ,       self.block_filenames       )


class lowerCAmelCase_       :







	'''simple docstring'''




	def 				_A			(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  -1
				a__					=  None

				for i in range(len(lowerCamelCase       )       ):
							if min_str is None or choices[i] < min_str:
										a__					=  i

				return min_index


class lowerCAmelCase_       :







	'''simple docstring'''




	def __init__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  files
				a__					=  set()
				a__					=  len(lowerCamelCase       )
				a__					=  {i: None for i in range(self.num_buffers       )}

	def 				_A			(	self       ):



				'''simple docstring'''


				return {
				    i: self.buffers[i] for i in range(self.num_buffers       ) if i not in self.empty
				}

	def 				_A			(	self       ):



				'''simple docstring'''


				for i in range(self.num_buffers       ):
							if self.buffers[i] is None and i not in self.empty:
										a__					=  self.files[i].readline()

										if self.buffers[i] == "":
													self.empty.add(lowerCamelCase       )
													self.files[i].close()

				if len(self.empty       ) == self.num_buffers:
							return False

				return True







	def 				_A			(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  self.buffers[index]
				a__					=  None

				return value


class lowerCAmelCase_       :







	'''simple docstring'''




	def __init__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  merge_strategy

	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  FilesArray(self.get_file_handles(lowerCamelCase   ,       lowerCamelCase       )       )
				with open(lowerCamelCase   ,       """w"""   ,       lowerCamelCase       ) as outfile:
							while buffers.refresh():
										a__					=  self.merge_strategy.select(buffers.get_dict()       )
										outfile.write(buffers.unshift(lowerCamelCase       )       )







	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  {}

				for i in range(len(lowerCamelCase       )       ):
							a__					=  open(filenames[i]   ,       """r"""   ,       lowerCamelCase       )  # noqa: UP015

				return files


class lowerCAmelCase_       :







	'''simple docstring'''




	def __init__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__					=  block_size

	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase=None       ):



				'''simple docstring'''


				a__					=  self.get_number_blocks(lowerCamelCase   ,       self.block_size       )
				a__					=  FileSplitter(lowerCamelCase       )
				splitter.split(self.block_size   ,       lowerCamelCase       )

				a__					=  FileMerger(NWayMerge()       )
				a__					=  self.block_size / (num_blocks + 1)
				merger.merge(splitter.get_block_filenames()   ,       filename + """.out"""   ,       lowerCamelCase       )

				splitter.cleanup()







	def 				_A			(	self   ,       lowerCamelCase   ,       lowerCamelCase       ):



				'''simple docstring'''


				return (os.stat(lowerCamelCase       ).st_size / block_size) + 1




def    UpperCAmelCase					(  lowercase__						:					Union[str, Any]	):



			'''simple docstring'''





			if string[-1].lower() == "k":
						return int(string[:-1]	) * 1024
			elif string[-1].lower() == "m":
						return int(string[:-1]	) * 1024 * 1024
			elif string[-1].lower() == "g":
						return int(string[:-1]	) * 1024 * 1024 * 1024
			else:
						return int(lowercase__	)




def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  argparse.ArgumentParser()
			parser.add_argument(
			    """-m"""				,					"""--mem"""				,					help="""amount of memory to use for sorting"""				,					default="""100M"""	)
			parser.add_argument(
			    """filename"""				,					metavar="""<filename>"""				,					nargs=1				,					help="""name of file to sort"""	)
			a__					=  parser.parse_args()

			a__					=  ExternalSort(parse_memory(args.mem	)	)
			sorter.sort(args.filename[0]	)


if __name__ == "__main__":
	main()






from typing import Any

import numpy as np




def    UpperCAmelCase					(  lowercase__						:					np.ndarray	):



			'''simple docstring'''





			assert np.shape(lowercase__	)[0] == np.shape(lowercase__	)[1]

			# If matrix not symmetric, exit right away.
			if np.allclose(lowercase__				,					matrix.T	) is False:
						return False

			# Get eigenvalues and eignevectors for a symmetric matrix.
			a__				,       a__					=  np.linalg.eigh(lowercase__	)

			# Check sign of all eigenvalues.
			# np.all returns a value of type np.bool_
			return bool(np.all(eigen_values > 0	)	)




def    UpperCAmelCase					(  lowercase__						:					int	):



			'''simple docstring'''





			a__					=  np.random.randn(lowercase__				,					lowercase__	)
			a__					=  np.dot(lowercase__				,					random_matrix.T	)
			assert _is_matrix_spd(lowercase__	)
			return spd_matrix




def    UpperCAmelCase					(  lowercase__						:					np.ndarray				,					lowercase__						:					np.ndarray				,					lowercase__						:					int = 1000				,					lowercase__						:					float = 1e-8				,					):



			'''simple docstring'''





			assert np.shape(lowercase__	)[0] == np.shape(lowercase__	)[1]
			assert np.shape(lowercase__	)[0] == np.shape(lowercase__	)[0]
			assert _is_matrix_spd(lowercase__	)

			# Initialize solution guess, residual, search direction.
			a__					=  np.zeros((np.shape(lowercase__	)[0], 1)	)
			a__					=  np.copy(lowercase__	)
			a__					=  np.copy(lowercase__	)

			# Set initial errors in solution guess and residual.
			a__					=  1e9
			a__					=  1e9
			a__					=  1e9

			# Set iteration counter to threshold number of iterations.
			a__					=  0

			while error > tol:
						# Save this value so we only calculate the matrix-vector product once.
						a__					=  np.dot(lowercase__				,					lowercase__	)

						# The main algorithm.

						# Update search direction magnitude.
						a__					=  np.dot(ra.T				,					lowercase__	) / np.dot(pa.T				,					lowercase__	)
						# Update solution guess.
						a__					=  xa + alpha * pa
						# Calculate new residual.
						a__					=  ra - alpha * w
						# Calculate new Krylov subspace scale.
						a__					=  np.dot(r.T				,					lowercase__	) / np.dot(ra.T				,					lowercase__	)
						# Calculate new A conjuage search direction.
						a__					=  r + beta * pa

						# Calculate errors.
						a__					=  np.linalg.norm(r - ra	)
						a__					=  np.linalg.norm(x - xa	)
						a__					=  np.maximum(lowercase__				,					lowercase__	)

						# Update variables.
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)
						a__					=  np.copy(lowercase__	)

						# Update number of iterations.
						iterations += 1
						if iterations > max_iterations:
									break

			return x




def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  3
			a__					=  _create_spd_matrix(lowercase__	)
			a__					=  np.random.randn(lowercase__				,					1	)
			a__					=  np.dot(lowercase__				,					lowercase__	)

			# Numpy solution.
			a__					=  np.linalg.solve(lowercase__				,					lowercase__	)

			# Our implementation.
			a__					=  conjugate_gradient(lowercase__				,					lowercase__	)

			# Ensure both solutions are close to x_true (and therefore one another).
			assert np.linalg.norm(x_numpy - x_true	) <= 1e-6
			assert np.linalg.norm(x_conjugate_gradient - x_true	) <= 1e-6


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	test_conjugate_gradient()

