
"""simple docstring"""

import argparse
import os
import re


_A						=			'src/transformers'

# Pattern that looks at the indentation in a line.
_A						=			re.compile(r'^(\s*)\S')
# Pattern that matches `"key":" and puts `key` in group 0.
_A						=			re.compile(r'^\s*"([^"]+)":')
# Pattern that matches `_import_structure["key"]` and puts `key` in group 0.
_A						=			re.compile(r'^\s*_import_structure\["([^"]+)"\]')
# Pattern that matches `"key",` and puts `key` in group 0.
_A						=			re.compile(r'^\s*"([^"]+)",\s*$')
# Pattern that matches any `[stuff]` and puts `stuff` in group 0.
_A						=			re.compile(r'\[([^\]]+)\]')
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		lowerCamelCase					:      Union[str, Any]          =   _re_indent.search(a_      )
		return "" if search is None else search.groups()[0]
def 		UpperCAmelCase (		a_,						a_="",						a_=None,						a_=None      ):





		'''simple docstring'''


		lowerCamelCase					:      str          =   0
		lowerCamelCase					:      List[Any]          =   code.split('\n'      )
		if start_prompt is not None:
				while not lines[index].startswith(a_      ):
						index += 1
				lowerCamelCase					:      List[Any]          =   ['\n'.join(lines[:index]      )]
		else:
				lowerCamelCase					:      str          =   []

		# We split into blocks until we get to the `end_prompt` (or the end of the block).
		lowerCamelCase					:      int          =   [lines[index]]
		index += 1
		while index < len(a_      ) and (end_prompt is None or not lines[index].startswith(a_      )):
				if len(lines[index]      ) > 0 and get_indent(lines[index]      ) == indent_level:
						if len(a_      ) > 0 and get_indent(current_block[-1]      ).startswith(indent_level + ' '      ):
								current_block.append(lines[index]      )
								blocks.append('\n'.join(a_      )      )
								if index < len(a_      ) - 1:
										lowerCamelCase					:      Union[str, Any]          =   [lines[index + 1]]
										index += 1
								else:
										lowerCamelCase					:      Dict          =   []
						else:
								blocks.append('\n'.join(a_      )      )
								lowerCamelCase					:      Dict          =   [lines[index]]
				else:
						current_block.append(lines[index]      )
				index += 1

		# Adds current block if it's nonempty.
		if len(a_      ) > 0:
				blocks.append('\n'.join(a_      )      )

		# Add final block after end_prompt if provided.
		if end_prompt is not None and index < len(a_      ):
				blocks.append('\n'.join(lines[index:]      )      )

		return blocks
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		def _inner(a_      ):
				return key(a_      ).lower().replace('_',						''      )

		return _inner
def 		UpperCAmelCase (		a_,						a_=None      ):





		'''simple docstring'''


		def noop(a_      ):
				return x

		if key is None:
				lowerCamelCase					:      List[Any]          =   noop
		# Constants are all uppercase, they go first.
		lowerCamelCase					:      List[Any]          =   [obj for obj in objects if key(a_      ).isupper()]
		# Classes are not all uppercase but start with a capital, they go second.
		lowerCamelCase					:      List[str]          =   [obj for obj in objects if key(a_      )[0].isupper() and not key(a_      ).isupper()]
		# Functions begin with a lowercase, they go last.
		lowerCamelCase					:      str          =   [obj for obj in objects if not key(a_      )[0].isupper()]

		lowerCamelCase					:      Optional[Any]          =   ignore_underscore(a_      )
		return sorted(a_,						key=a_      ) + sorted(a_,						key=a_      ) + sorted(a_,						key=a_      )
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		def _replace(a_      ):
				lowerCamelCase					:      Dict          =   match.groups()[0]
				if "," not in imports:
						return F"""[{imports}]"""
				lowerCamelCase					:      Optional[int]          =   [part.strip().replace('"',						''      ) for part in imports.split(','      )]
				# We will have a final empty element if the line finished with a comma.
				if len(keys[-1]      ) == 0:
						lowerCamelCase					:      Any          =   keys[:-1]
				return "[" + ", ".join([F"""\"{k}\"""" for k in sort_objects(a_      )]      ) + "]"

		lowerCamelCase					:      int          =   import_statement.split('\n'      )
		if len(a_      ) > 3:
				# Here we have to sort internal imports that are on several lines (one per name):
				# key: [
				#     "object1",
				#     "object2",
				#     ...
				# ]

				# We may have to ignore one or two lines on each side.
				lowerCamelCase					:      int          =   2 if lines[1].strip() == '[' else 1
				lowerCamelCase					:      Union[str, Any]          =   [(i, _re_strip_line.search(a_      ).groups()[0]) for i, line in enumerate(lines[idx:-idx]      )]
				lowerCamelCase					:      Tuple          =   sort_objects(a_,						key=lambda a_      : x[1]      )
				lowerCamelCase					:      List[Any]          =   [lines[x[0] + idx] for x in sorted_indices]
				return "\n".join(lines[:idx] + sorted_lines + lines[-idx:]      )
		elif len(a_      ) == 3:
				# Here we have to sort internal imports that are on one separate line:
				# key: [
				#     "object1", "object2", ...
				# ]
				if _re_bracket_content.search(lines[1]      ) is not None:
						lowerCamelCase					:      List[Any]          =   _re_bracket_content.sub(_replace,						lines[1]      )
				else:
						lowerCamelCase					:      Any          =   [part.strip().replace('"',						''      ) for part in lines[1].split(','      )]
						# We will have a final empty element if the line finished with a comma.
						if len(keys[-1]      ) == 0:
								lowerCamelCase					:      Dict          =   keys[:-1]
						lowerCamelCase					:      Dict          =   get_indent(lines[1]      ) + ', '.join([F"""\"{k}\"""" for k in sort_objects(a_      )]      )
				return "\n".join(a_      )
		else:
				# Finally we have to deal with imports fitting on one line
				lowerCamelCase					:      Tuple          =   _re_bracket_content.sub(_replace,						a_      )
				return import_statement
def 		UpperCAmelCase (		a_,						a_=True      ):





		'''simple docstring'''


		with open(a_,						encoding='utf-8'      ) as f:
				lowerCamelCase					:      Union[str, Any]          =   f.read()

		if "_import_structure" not in code:
				return

		# Blocks of indent level 0
		lowerCamelCase					:      Any          =   split_code_in_indented_blocks(
		    a_,						start_prompt='_import_structure = {',						end_prompt='if TYPE_CHECKING:'      )

		# We ignore block 0 (everything untils start_prompt) and the last block (everything after end_prompt).
		for block_idx in range(1,						len(a_      ) - 1      ):
				# Check if the block contains some `_import_structure`s thingy to sort.
				lowerCamelCase					:      List[Any]          =   main_blocks[block_idx]
				lowerCamelCase					:      str          =   block.split('\n'      )

				# Get to the start of the imports.
				lowerCamelCase					:      int          =   0
				while line_idx < len(a_      ) and "_import_structure" not in block_lines[line_idx]:
						# Skip dummy import blocks
						if "import dummy" in block_lines[line_idx]:
								lowerCamelCase					:      Optional[int]          =   len(a_      )
						else:
								line_idx += 1
				if line_idx >= len(a_      ):
						continue

				# Ignore beginning and last line: they don't contain anything.
				lowerCamelCase					:      Union[str, Any]          =   '\n'.join(block_lines[line_idx:-1]      )
				lowerCamelCase					:      Dict          =   get_indent(block_lines[1]      )
				# Slit the internal block into blocks of indent level 1.
				lowerCamelCase					:      int          =   split_code_in_indented_blocks(a_,						indent_level=a_      )
				# We have two categories of import key: list or _import_structure[key].append/extend
				lowerCamelCase					:      Union[str, Any]          =   _re_direct_key if '_import_structure = {' in block_lines[0] else _re_indirect_key
				# Grab the keys, but there is a trap: some lines are empty or just comments.
				lowerCamelCase					:      Optional[int]          =   [(pattern.search(a_      ).groups()[0] if pattern.search(a_      ) is not None else None) for b in internal_blocks]
				# We only sort the lines with a key.
				lowerCamelCase					:      List[Any]          =   [(i, key) for i, key in enumerate(a_      ) if key is not None]
				lowerCamelCase					:      Union[str, Any]          =   [x[0] for x in sorted(a_,						key=lambda a_      : x[1]      )]

				# We reorder the blocks by leaving empty lines/comments as they were and reorder the rest.
				lowerCamelCase					:      Dict          =   0
				lowerCamelCase					:      str          =   []
				for i in range(len(a_      )      ):
						if keys[i] is None:
								reorderded_blocks.append(internal_blocks[i]      )
						else:
								lowerCamelCase					:      Tuple          =   sort_objects_in_import(internal_blocks[sorted_indices[count]]      )
								reorderded_blocks.append(a_      )
								count += 1

        # And we put our main block back together with its first and last line.
				lowerCamelCase					:      Union[str, Any]          =   '\n'.join(block_lines[:line_idx] + reorderded_blocks + [block_lines[-1]]      )

		if code != "\n".join(a_      ):
				if check_only:
						return True
				else:
						print(F"""Overwriting {file}."""      )
						with open(a_,						'w',						encoding='utf-8'      ) as f:
								f.write('\n'.join(a_      )      )
def 		UpperCAmelCase (		a_=True      ):





		'''simple docstring'''


		lowerCamelCase					:      Tuple          =   []
		for root, _, files in os.walk(a_      ):
				if "__init__.py" in files:
						lowerCamelCase					:      int          =   sort_imports(os.path.join(a_,						'__init__.py'      ),						check_only=a_      )
						if result:
								lowerCamelCase					:      Optional[Any]          =   [os.path.join(a_,						'__init__.py'      )]
		if len(a_      ) > 0:
				raise ValueError(F"""Would overwrite {len(a_      )} files, run `make style`."""      )


if __name__ == "__main__":
					_A						=			argparse.ArgumentParser()
					parser.add_argument('--check_only', action='store_true', help='Whether to only check or fix style.')
					_A						=			parser.parse_args()

					sort_imports_in_all_inits(check_only=args.check_only)








"""simple docstring"""

import numpy as np
def 		UpperCAmelCase (		a_,						a_,						a_ = 1E-12,						a_ = 100,						):





		'''simple docstring'''


		assert np.shape(a_      )[0] == np.shape(a_      )[1]
		# Ensure proper dimensionality.
		assert np.shape(a_      )[0] == np.shape(a_      )[0]
		# Ensure inputs are either both complex or both real
		assert np.iscomplexobj(a_      ) == np.iscomplexobj(a_      )
		lowerCamelCase					:      Optional[int]          =   np.iscomplexobj(a_      )
		if is_complex:
				# Ensure complex input_matrix is Hermitian
				assert np.array_equal(a_,						input_matrix.conj().T      )

		# Set convergence to False. Will define convergence when we exceed max_iterations
		# or when we have small changes from one iteration to next.

		lowerCamelCase					:      Union[str, Any]          =   False
		lowerCamelCase					:      List[str]          =   0
		lowerCamelCase					:      Any          =   0
		lowerCamelCase					:      Dict          =   1E12

		while not convergence:
				# Multiple matrix by the vector.
				lowerCamelCase					:      Optional[int]          =   np.dot(a_,						a_      )
				# Normalize the resulting output vector.
				lowerCamelCase					:      Optional[int]          =   w / np.linalg.norm(a_      )
				# Find rayleigh quotient
				# (faster than usual b/c we know vector is normalized already)
				lowerCamelCase					:      Optional[Any]          =   vector.conj().T if is_complex else vector.T
				lowerCamelCase					:      str          =   np.dot(a_,						np.dot(a_,						a_      )      )

				# Check convergence.
				lowerCamelCase					:      Optional[int]          =   np.abs(lambda_ - lambda_previous      ) / lambda_
				iterations += 1

				if error <= error_tol or iterations >= max_iterations:
						lowerCamelCase					:      int          =   True

				lowerCamelCase					:      Optional[Any]          =   lambda_

		if is_complex:
				lowerCamelCase					:      Any          =   np.real(lambda_      )

		return lambda_, vector
def 		UpperCAmelCase (		):





		'''simple docstring'''


		lowerCamelCase					:      str          =   np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]      )
		lowerCamelCase					:      str          =   np.array([41, 4, 20]      )
		lowerCamelCase					:      Optional[Any]          =   real_input_matrix.astype(np.complexaaa      )
		lowerCamelCase					:      Dict          =   np.triu(1j * complex_input_matrix,						1      )
		complex_input_matrix += imag_matrix
		complex_input_matrix += -1 * imag_matrix.T
		lowerCamelCase					:      List[Any]          =   np.array([41, 4, 20]      ).astype(np.complexaaa      )

		for problem_type in ["real", "complex"]:
				if problem_type == "real":
						lowerCamelCase					:      str          =   real_input_matrix
						lowerCamelCase					:      Any          =   real_vector
				elif problem_type == "complex":
						lowerCamelCase					:      str          =   complex_input_matrix
						lowerCamelCase					:      Dict          =   complex_vector

				# Our implementation.
				lowerCamelCase     ,   lowerCamelCase					:      List[str]          =   power_iteration(a_,						a_      )

				# Numpy implementation.

				# Get eigenvalues and eigenvectors using built-in numpy
				# eigh (eigh used for symmetric or hermetian matrices).
				lowerCamelCase     ,   lowerCamelCase					:      Optional[Any]          =   np.linalg.eigh(a_      )
				# Last eigenvalue is the maximum one.
				lowerCamelCase					:      Dict          =   eigen_values[-1]
				# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
				lowerCamelCase					:      List[str]          =   eigen_vectors[:, -1]

				# Check our implementation and numpy gives close answers.
				assert np.abs(eigen_value - eigen_value_max      ) <= 1E-6
				# Take absolute values element wise of each eigenvector.
				# as they are only unique to a minus sign.
				assert np.linalg.norm(np.abs(a_      ) - np.abs(a_      )      ) <= 1E-6


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					test_power_iteration()






