import copy
import fnmatch
import json
import os
import pickle as pkl
import shutil
import sys
import tarfile
import tempfile
from collections import OrderedDict
from contextlib import contextmanager
from functools import partial
from hashlib import shaaaa
from io import BytesIO
from pathlib import Path
from urllib.parse import urlparse
from zipfile import ZipFile, is_zipfile

import cva
import numpy as np
import requests
import wget
from filelock import FileLock
from PIL import Image
from tqdm.auto import tqdm
from yaml import Loader, dump, load


try:
					import torch

					UpperCamelCase			 =	True
except ImportError:
					UpperCamelCase			 =	False


try:
					from torch.hub import _get_torch_home

					UpperCamelCase			 =	_get_torch_home()
except ImportError:
					UpperCamelCase			 =	os.path.expanduser(
					    os.getenv('TORCH_HOME', os.path.join(os.getenv('XDG_CACHE_HOME', '~/.cache'), 'torch'))
					)

UpperCamelCase			 =	os.path.join(torch_cache_home, 'transformers')

UpperCamelCase			 =	"""https://cdn.huggingface.co"""
UpperCamelCase			 =	"""https://s3.amazonaws.com/models.huggingface.co/bert"""
UpperCamelCase			 =	"""/""".join(str(Path(__file__).resolve()).split('/')[:-1])
UpperCamelCase			 =	os.path.join(PATH, 'config.yaml')
UpperCamelCase			 =	os.path.join(PATH, 'attributes.txt')
UpperCamelCase			 =	os.path.join(PATH, 'objects.txt')
UpperCamelCase			 =	os.getenv('PYTORCH_PRETRAINED_BERT_CACHE', default_cache_path)
UpperCamelCase			 =	os.getenv('PYTORCH_TRANSFORMERS_CACHE', PYTORCH_PRETRAINED_BERT_CACHE)
UpperCamelCase			 =	os.getenv('TRANSFORMERS_CACHE', PYTORCH_TRANSFORMERS_CACHE)
UpperCamelCase			 =	"""pytorch_model.bin"""
UpperCamelCase			 =	"""config.yaml"""



def     lowerCamelCase_    (  _lowercase=OBJECTS					,	_lowercase=ATTRIBUTES				)							->       Optional[Any]:
		__A							:    Optional[int]         =      []
		with open(__lowerCamelCase				) as f:
				for object in f.readlines():
						vg_classes.append(object.split(","				)[0].lower().strip()				)

		__A							:    Dict         =      []
		with open(__lowerCamelCase				) as f:
				for object in f.readlines():
						vg_attrs.append(object.split(","				)[0].lower().strip()				)
		return vg_classes, vg_attrs



def     lowerCamelCase_    (  _lowercase				)							->       Dict:
		__A							:    Any         =      OrderedDict()
		with open(__lowerCamelCase					,	"rb"				) as f:
				__A							:    str         =      pkl.load(__lowerCamelCase				)["model"]
		for k in copy.deepcopy(list(ckp.keys()				)				):
				__A							:    Union[str, Any]         =      ckp.pop(__lowerCamelCase				)
				if isinstance(__lowerCamelCase					,	np.ndarray				):
						__A							:    str         =      torch.tensor(__lowerCamelCase				)
				else:
						assert isinstance(__lowerCamelCase					,	torch.tensor				), type(__lowerCamelCase				)
				__A							:    Any         =      v
		return r


class _a   :

	'''simple docstring'''



	lowerCamelCase_    :			List[Any]	  =       {}

	def __init__(   self							, __UpperCAmelCase							, __UpperCAmelCase = "root"							, __UpperCAmelCase=0    ):
			__A							:    int         =      name
			__A							:    Optional[int]         =      level
			__A							:    Optional[int]         =      {}
			for k, v in dictionary.items():
					if v is None:
							raise ValueError()
					__A							:    Any         =      copy.deepcopy(__UpperCAmelCase    )
					__A							:    List[Any]         =      copy.deepcopy(__UpperCAmelCase    )
					if isinstance(__UpperCAmelCase							, __UpperCAmelCase    ):
							__A							:    str         =      Config(__UpperCAmelCase							, name=__UpperCAmelCase							, level=level + 1    )
					__A							:    Optional[int]         =      v
					setattr(self							, __UpperCAmelCase							, __UpperCAmelCase    )

			__A							:    Optional[Any]         =      d

	def __repr__(   self    ):
			return str(list((self._pointer.keys())    )    )

	def __setattr__(   self							, __UpperCAmelCase							, __UpperCAmelCase    ):
			__A							:    List[Any]         =      val
			__A							:    Optional[int]         =      val
			__A							:    Tuple         =      key.split("."    )
			__A							:    int         =      len(__UpperCAmelCase    ) - 1
			__A							:    Tuple         =      self._pointer
			if len(__UpperCAmelCase    ) > 1:
					for i, l in enumerate(__UpperCAmelCase    ):
							if hasattr(self							, __UpperCAmelCase    ) and isinstance(getattr(self							, __UpperCAmelCase    )							, __UpperCAmelCase    ):
									setattr(getattr(self							, __UpperCAmelCase    )							, ".".join(levels[i:]    )							, __UpperCAmelCase    )
							if l == last_level:
									__A							:    str         =      val
							else:
									__A							:    Any         =      pointer[l]

	def      __UpperCAmelCase(   self    ):
			return self._pointer

	def      __UpperCAmelCase(   self							, __UpperCAmelCase							, __UpperCAmelCase    ):
			with open(F"{file_name}"							, "w"    ) as stream:
					dump(__UpperCAmelCase							, __UpperCAmelCase    )

	def      __UpperCAmelCase(   self							, __UpperCAmelCase							, __UpperCAmelCase    ):
			with open(F"{file_name}"							, "w"    ) as stream:
					json.dump(__UpperCAmelCase							, __UpperCAmelCase    )

	@staticmethod
	def      __UpperCAmelCase(   __UpperCAmelCase    ):
			with open(__UpperCAmelCase    ) as stream:
					__A							:    Any         =      load(__UpperCAmelCase							, Loader=__UpperCAmelCase    )
			return data

	def __str__(   self    ):
			__A							:    List[Any]         =      "    "
			if self._name != "root":
					__A							:    Any         =      F"{t * (self._level-1)}{self._name}:\n"
			else:
					__A							:    Union[str, Any]         =      ""
			__A							:    Any         =      self._level
			for i, (k, v) in enumerate(self._pointer.items()    ):
					if isinstance(__UpperCAmelCase							, __UpperCAmelCase    ):
							r += F"{t * (self._level)}{v}\n"
							self._level += 1
					else:
							r += F"{t * (self._level)}{k}: {v} ({type(__UpperCAmelCase    ).__name__})\n"
					__A							:    Union[str, Any]         =      level
			return r[:-1]

	@classmethod
	def      __UpperCAmelCase(   cls							, __UpperCAmelCase							, **__UpperCAmelCase    ):
			__A  ,   __A							:    Dict         =      cls.get_config_dict(__UpperCAmelCase							, **__UpperCAmelCase    )
			return cls(__UpperCAmelCase    )







	@classmethod
	def      __UpperCAmelCase(   cls							, __UpperCAmelCase							, **__UpperCAmelCase    ):
			__A							:    Any         =      kwargs.pop("cache_dir"							, __UpperCAmelCase    )
			__A							:    List[Any]         =      kwargs.pop("force_download"							, __UpperCAmelCase    )
			__A							:    List[str]         =      kwargs.pop("resume_download"							, __UpperCAmelCase    )
			__A							:    Optional[int]         =      kwargs.pop("proxies"							, __UpperCAmelCase    )
			__A							:    int         =      kwargs.pop("local_files_only"							, __UpperCAmelCase    )

			if os.path.isdir(__UpperCAmelCase    ):
					__A							:    Tuple         =      os.path.join(__UpperCAmelCase							, __UpperCAmelCase    )
			elif os.path.isfile(__UpperCAmelCase    ) or is_remote_url(__UpperCAmelCase    ):
					__A							:    List[Any]         =      pretrained_model_name_or_path
			else:
					__A							:    Optional[Any]         =      hf_bucket_url(__UpperCAmelCase							, filename=__UpperCAmelCase							, use_cdn=__UpperCAmelCase    )

			try:
					# Load from URL or cache if already cached
					__A							:    List[str]         =      cached_path(
					    __UpperCAmelCase							, cache_dir=__UpperCAmelCase							, force_download=__UpperCAmelCase							, proxies=__UpperCAmelCase							, resume_download=__UpperCAmelCase							, local_files_only=__UpperCAmelCase							, )
					# Load config dict
					if resolved_config_file is None:
							raise EnvironmentError

					__A							:    Union[str, Any]         =      Config.load_yaml(__UpperCAmelCase    )

			except EnvironmentError:
					__A							:    List[Any]         =      "Can\'t load config for"
					raise EnvironmentError(__UpperCAmelCase    )

			if resolved_config_file == config_file:
					print("loading configuration file from path"    )
			else:
					print("loading configuration file cache"    )

			return Config.load_yaml(__UpperCAmelCase    ), kwargs



def     lowerCamelCase_    (  _lowercase				)							->       List[str]:
		__A							:    Tuple         =      torch.load("dump.pt"					,	map_location=in_tensor.device				)
		__A							:    Union[str, Any]         =      in_tensor.numpy()
		__A							:    Dict         =      out_tensor.numpy()[0]
		print(na.shape					,	na[0, 0, :5]				)
		print(na.shape					,	na[0, 0, :5]				)
		assert np.allclose(__lowerCamelCase					,	__lowerCamelCase					,	rtol=0.01					,	atol=0.1				), (
		    F"{sum([1 for x in np.isclose(__lowerCamelCase					,	__lowerCamelCase					,	rtol=0.01					,	atol=0.1				).flatten() if x is False]				)/len(na.flatten()				)*100:.4f} %"
		    " element-wise mismatch"
		)
		raise Exception("tensors are all good"				)

		# Hugging face functions below



def     lowerCamelCase_    (  _lowercase				)							->       List[str]:
		__A							:    Dict         =      urlparse(__lowerCamelCase				)
		return parsed.scheme in ("http", "https")



def     lowerCamelCase_    (  _lowercase					,	_lowercase					,	_lowercase=True				)							->       int:
		__A							:    int         =      CLOUDFRONT_DISTRIB_PREFIX if use_cdn else S3_BUCKET_PREFIX
		__A							:    Optional[int]         =      "/" not in model_id
		if legacy_format:
				return F"{endpoint}/{model_id}-{filename}"
		else:
				return F"{endpoint}/{model_id}/{filename}"



def     lowerCamelCase_    (  _lowercase					,	_lowercase					,	_lowercase=None					,	_lowercase=0					,	_lowercase=None					,	)							->       Any:
		__A							:    List[str]         =      "python/{}".format(sys.version.split()[0]				)
		if _torch_available:
				ua += "; torch/{}".format(torch.__version__				)
		if isinstance(__lowerCamelCase					,	__lowerCamelCase				):
				ua += "; " + "; ".join("{}/{}".format(__lowerCamelCase					,	__lowerCamelCase				) for k, v in user_agent.items()				)
		elif isinstance(__lowerCamelCase					,	__lowerCamelCase				):
				ua += "; " + user_agent
		__A							:    Any         =      {"user-agent": ua}
		if resume_size > 0:
				__A							:    List[Any]         =      "bytes=%d-" % (resume_size,)
		__A							:    Optional[Any]         =      requests.get(__lowerCamelCase					,	stream=__lowerCamelCase					,	proxies=__lowerCamelCase					,	headers=__lowerCamelCase				)
		if response.status_code == 416:  # Range not satisfiable
				return
		__A							:    List[Any]         =      response.headers.get("Content-Length"				)
		__A							:    Dict         =      resume_size + int(__lowerCamelCase				) if content_length is not None else None
		__A							:    Any         =      tqdm(
		    unit="B"					,	unit_scale=__lowerCamelCase					,	total=__lowerCamelCase					,	initial=__lowerCamelCase					,	desc="Downloading"					,	)
		for chunk in response.iter_content(chunk_size=1_024				):
				if chunk:  # filter out keep-alive new chunks
						progress.update(len(__lowerCamelCase				)				)
						temp_file.write(__lowerCamelCase				)
		progress.close()



def     lowerCamelCase_    (  _lowercase					,	_lowercase=None					,	_lowercase=False					,	_lowercase=None					,	_lowercase=10					,	_lowercase=False					,	_lowercase=None					,	_lowercase=False					,	)							->       str:
		if cache_dir is None:
				__A							:    int         =      TRANSFORMERS_CACHE
		if isinstance(__lowerCamelCase					,	__lowerCamelCase				):
				__A							:    int         =      str(__lowerCamelCase				)

		os.makedirs(__lowerCamelCase					,	exist_ok=__lowerCamelCase				)

		__A							:    Dict         =      None
		if not local_files_only:
				try:
						__A							:    str         =      requests.head(__lowerCamelCase					,	allow_redirects=__lowerCamelCase					,	proxies=__lowerCamelCase					,	timeout=__lowerCamelCase				)
						if response.status_code == 200:
								__A							:    str         =      response.headers.get("ETag"				)
				except (EnvironmentError, requests.exceptions.Timeout):
						# etag is already None
						pass

		__A							:    Union[str, Any]         =      url_to_filename(__lowerCamelCase					,	__lowerCamelCase				)

		# get cache path to put the file
		__A							:    Optional[Any]         =      os.path.join(__lowerCamelCase					,	__lowerCamelCase				)

		# etag is None = we don't have a connection, or url doesn't exist, or is otherwise inaccessible.
		# try to get the last downloaded one
		if etag is None:
				if os.path.exists(__lowerCamelCase				):
						return cache_path
				else:
						__A							:    List[Any]         =      [
						    file
						    for file in fnmatch.filter(os.listdir(__lowerCamelCase				)					,	filename + ".*"				)
						    if not file.endswith(".json"				) and not file.endswith(".lock"				)
						]
						if len(__lowerCamelCase				) > 0:
								return os.path.join(__lowerCamelCase					,	matching_files[-1]				)
						else:
								# If files cannot be found and local_files_only=True,
								# the models might've been found if local_files_only=False
								# Notify the user about that
								if local_files_only:
										raise ValueError(
										    "Cannot find the requested files in the cached path and outgoing traffic has been"
										    " disabled. To enable model look-ups and downloads online, set \'local_files_only\'"
										    " to False."				)
								return None

    # From now on, etag is not None.
		if os.path.exists(__lowerCamelCase				) and not force_download:
				return cache_path

		# Prevent parallel downloads of the same file with a lock.
		__A							:    Optional[int]         =      cache_path + ".lock"
		with FileLock(__lowerCamelCase				):
				# If the download just completed while the lock was activated.
				if os.path.exists(__lowerCamelCase				) and not force_download:
						# Even if returning early like here, the lock will be released.
						return cache_path

				if resume_download:
						__A							:    List[Any]         =      cache_path + ".incomplete"

						@contextmanager
						def _resumable_file_manager():
								with open(__lowerCamelCase					,	"a+b"				) as f:
										yield f

						__A							:    List[Any]         =      _resumable_file_manager
						if os.path.exists(__lowerCamelCase				):
								__A							:    List[str]         =      os.stat(__lowerCamelCase				).st_size
						else:
								__A							:    str         =      0
				else:
						__A							:    Tuple         =      partial(tempfile.NamedTemporaryFile					,	dir=__lowerCamelCase					,	delete=__lowerCamelCase				)
						__A							:    Optional[Any]         =      0

				# Download to temporary file, then copy to cache dir once finished.
				# Otherwise you get corrupt cache entries if the download gets interrupted.
				with temp_file_manager() as temp_file:
						print(
						    "%s not found in cache or force_download set to True, downloading to %s"					,	__lowerCamelCase					,	temp_file.name					,	)

						http_get(
						    __lowerCamelCase					,	__lowerCamelCase					,	proxies=__lowerCamelCase					,	resume_size=__lowerCamelCase					,	user_agent=__lowerCamelCase					,	)

				os.replace(temp_file.name					,	__lowerCamelCase				)

				__A							:    str         =      {"url": url, "etag": etag}
				__A							:    Dict         =      cache_path + ".json"
				with open(__lowerCamelCase					,	"w"				) as meta_file:
						json.dump(__lowerCamelCase					,	__lowerCamelCase				)

		return cache_path



def     lowerCamelCase_    (  _lowercase					,	_lowercase=None				)							->       Tuple:
		__A							:    Optional[Any]         =      url.encode("utf-8"				)
		__A							:    Dict         =      shaaaa(__lowerCamelCase				)
		__A							:    Tuple         =      url_hash.hexdigest()

		if etag:
				__A							:    Dict         =      etag.encode("utf-8"				)
				__A							:    Optional[Any]         =      shaaaa(__lowerCamelCase				)
				filename += "." + etag_hash.hexdigest()

		if url.endswith(".h5"				):
				filename += ".h5"

		return filename



def     lowerCamelCase_    (  _lowercase					,	_lowercase=None					,	_lowercase=False					,	_lowercase=None					,	_lowercase=False					,	_lowercase=None					,	_lowercase=False					,	_lowercase=False					,	_lowercase=False					,	)							->       List[str]:
		if cache_dir is None:
				__A							:    Union[str, Any]         =      TRANSFORMERS_CACHE
		if isinstance(__lowerCamelCase					,	__lowerCamelCase				):
				__A							:    Any         =      str(__lowerCamelCase				)
		if isinstance(__lowerCamelCase					,	__lowerCamelCase				):
				__A							:    Tuple         =      str(__lowerCamelCase				)

		if is_remote_url(__lowerCamelCase				):
				# URL, so get it from the cache (downloading if necessary)
				__A							:    str         =      get_from_cache(
				    __lowerCamelCase					,	cache_dir=__lowerCamelCase					,	force_download=__lowerCamelCase					,	proxies=__lowerCamelCase					,	resume_download=__lowerCamelCase					,	user_agent=__lowerCamelCase					,	local_files_only=__lowerCamelCase					,	)
		elif os.path.exists(__lowerCamelCase				):
				# File, and it exists.
				__A							:    Union[str, Any]         =      url_or_filename
		elif urlparse(__lowerCamelCase				).scheme == "":
				# File, but it doesn't exist.
				raise EnvironmentError("file {} not found".format(__lowerCamelCase				)				)
		else:
				# Something unknown
				raise ValueError("unable to parse {} as a URL or as a local path".format(__lowerCamelCase				)				)

		if extract_compressed_file:
				if not is_zipfile(__lowerCamelCase				) and not tarfile.is_tarfile(__lowerCamelCase				):
						return output_path

				# Path where we extract compressed archives
				# We avoid '.' in dir name and add "-extracted" at the end: "./model.zip" => "./model-zip-extracted/"
				__A  ,   __A							:    Union[str, Any]         =      os.path.split(__lowerCamelCase				)
				__A							:    Tuple         =      output_file.replace("."					,	"-"				) + "-extracted"
				__A							:    Any         =      os.path.join(__lowerCamelCase					,	__lowerCamelCase				)

				if os.path.isdir(__lowerCamelCase				) and os.listdir(__lowerCamelCase				) and not force_extract:
						return output_path_extracted

				# Prevent parallel extractions
				__A							:    List[str]         =      output_path + ".lock"
				with FileLock(__lowerCamelCase				):
						shutil.rmtree(__lowerCamelCase					,	ignore_errors=__lowerCamelCase				)
						os.makedirs(__lowerCamelCase				)
						if is_zipfile(__lowerCamelCase				):
								with ZipFile(__lowerCamelCase					,	"r"				) as zip_file:
										zip_file.extractall(__lowerCamelCase				)
										zip_file.close()
						elif tarfile.is_tarfile(__lowerCamelCase				):
								__A							:    Dict         =      tarfile.open(__lowerCamelCase				)
								tar_file.extractall(__lowerCamelCase				)
								tar_file.close()
						else:
								raise EnvironmentError("Archive format of {} could not be identified".format(__lowerCamelCase				)				)

				return output_path_extracted

		return output_path



def     lowerCamelCase_    (  _lowercase					,	_lowercase=","				)							->       Optional[int]:
		assert isinstance(__lowerCamelCase					,	__lowerCamelCase				)
		if os.path.isfile(__lowerCamelCase				):
				with open(__lowerCamelCase				) as f:
						__A							:    Optional[Any]         =      eval(f.read()				)
		else:
				__A							:    Optional[int]         =      requests.get(__lowerCamelCase				)
				try:
						__A							:    Tuple         =      requests.json()
				except Exception:
						__A							:    List[Any]         =      req.content.decode()
						assert data is not None, "could not connect"
						try:
								__A							:    int         =      eval(__lowerCamelCase				)
						except Exception:
								__A							:    List[str]         =      data.split("\n"				)
				req.close()
		return data



def     lowerCamelCase_    (  _lowercase				)							->       int:
		__A							:    Dict         =      requests.get(__lowerCamelCase				)
		__A							:    Tuple         =      np.array(Image.open(BytesIO(response.content				)				)				)
		return img



def     lowerCamelCase_    (  _lowercase				)							->       int:
		__A							:    Any         =      url.split("/"				)[-1]
		if fn not in os.listdir(os.getcwd()				):
				wget.download(__lowerCamelCase				)
		with open(__lowerCamelCase					,	"rb"				) as stream:
				__A							:    int         =      pkl.load(__lowerCamelCase				)
		__A							:    Optional[int]         =      weights.pop("model"				)
		__A							:    Dict         =      {}
		for k, v in model.items():
				__A							:    Optional[Any]         =      torch.from_numpy(__lowerCamelCase				)
				if "running_var" in k:
						__A							:    List[str]         =      torch.tensor([0]				)
						__A							:    Optional[int]         =      k.replace("running_var"					,	"num_batches_tracked"				)
						__A							:    Optional[Any]         =      zero
		return new



def     lowerCamelCase_    (  )							->       Tuple:
		print(F"{os.path.abspath(os.path.join(__lowerCamelCase					,	os.pardir				)				)}/demo.ipynb"				)



def     lowerCamelCase_    (  _lowercase					,	_lowercase="RGB"				)							->       Union[str, Any]:
		assert isinstance(__lowerCamelCase					,	__lowerCamelCase				)
		if os.path.isfile(__lowerCamelCase				):
				__A							:    Union[str, Any]         =      cva.imread(__lowerCamelCase				)
		else:
				__A							:    Union[str, Any]         =      get_image_from_url(__lowerCamelCase				)
				assert img is not None, F"could not connect to: {im}"
		__A							:    str         =      cva.cvtColor(__lowerCamelCase					,	cva.COLOR_BGR2RGB				)
		if input_format == "RGB":
				__A							:    List[Any]         =      img[:, :, ::-1]
		return img





def     lowerCamelCase_    (  _lowercase					,	_lowercase=1				)							->       Optional[Any]:
		return (images[i : i + batch] for i in range(0					,	len(__lowerCamelCase				)					,	__lowerCamelCase				))






from typing import Any

import numpy as np
def 							lowerCAmelCase(	__lowerCamelCase						):
					assert np.shape(__lowerCamelCase						)[0] == np.shape(__lowerCamelCase						)[1]

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

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

					# Check sign of all eigenvalues.
					# np.all returns a value of type np.bool_
					return bool(np.all(eigen_values > 0						)						)
def 							lowerCAmelCase(	__lowerCamelCase						):
					__a							=   np.random.randn(__lowerCamelCase      ,				__lowerCamelCase						)
					__a							=   np.dot(__lowerCamelCase      ,				random_matrix.T						)
					assert _is_matrix_spd(__lowerCamelCase						)
					return spd_matrix
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase = 1000      ,				__lowerCamelCase = 1e-8      ,				):
					assert np.shape(__lowerCamelCase						)[0] == np.shape(__lowerCamelCase						)[1]
					assert np.shape(__lowerCamelCase						)[0] == np.shape(__lowerCamelCase						)[0]
					assert _is_matrix_spd(__lowerCamelCase						)

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

					# 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(__lowerCamelCase      ,				__lowerCamelCase						)

										# The main algorithm.

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

										# Update variables.
										__a							=   np.copy(__lowerCamelCase						)
										__a							=   np.copy(__lowerCamelCase						)
										__a							=   np.copy(__lowerCamelCase						)

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

					return x
def 							lowerCAmelCase(	):
					__a							=   3
					__a							=   _create_spd_matrix(__lowerCamelCase						)
					__a							=   np.random.randn(__lowerCamelCase      ,				1						)
					__a							=   np.dot(__lowerCamelCase      ,				__lowerCamelCase						)

					# Numpy solution.
					__a							=   np.linalg.solve(__lowerCamelCase      ,				__lowerCamelCase						)

					# Our implementation.
					__a							=   conjugate_gradient(__lowerCamelCase      ,				__lowerCamelCase						)

					# 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()




