





'''simple docstring'''


import numpy as np
def 							UpperCAmelCase_  (						__lowerCamelCase : np.ndarray     ,__lowerCamelCase : np.ndarray     ,__lowerCamelCase : float = 1e-12     ,__lowerCamelCase : int = 1_00     ,):
   assert np.shape(__lowerCamelCase			)[0] == np.shape(__lowerCamelCase			)[1]
   # Ensure proper dimensionality.
   assert np.shape(__lowerCamelCase			)[0] == np.shape(__lowerCamelCase			)[0]
   # Ensure inputs are either both complex or both real
   assert np.iscomplexobj(__lowerCamelCase			) == np.iscomplexobj(__lowerCamelCase			)
   lowercase_      :List[str]         =			np.iscomplexobj(__lowerCamelCase			)
   if is_complex:
      # Ensure complex input_matrix is Hermitian
      assert np.array_equal(__lowerCamelCase     ,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.

   lowercase_      :Dict         =			False
   lowercase_      :Any         =			0
   lowercase_      :str         =			0
   lowercase_      :str         =			1e12

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

      # Check convergence.
      lowercase_      :List[Any]         =			np.abs(lambda_ - lambda_previous			) / lambda_
      iterations += 1

      if error <= error_tol or iterations >= max_iterations:
         lowercase_      :List[Any]         =			True

      lowercase_      :str         =			lambda_

   if is_complex:
      lowercase_      :str         =			np.real(lambda_			)

   return lambda_, vector
def 							UpperCAmelCase_  (						):
   lowercase_      :Tuple         =			np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]			)
   lowercase_      :int         =			np.array([41, 4, 20]			)
   lowercase_      :List[str]         =			real_input_matrix.astype(np.complexaaa			)
   lowercase_      :Union[str, Any]         =			np.triu(1J * complex_input_matrix     ,1			)
   complex_input_matrix += imag_matrix
   complex_input_matrix += -1 * imag_matrix.T
   lowercase_      :int         =			np.array([41, 4, 20]			).astype(np.complexaaa			)

   for problem_type in ["real", "complex"]:
      if problem_type == "real":
         lowercase_      :Tuple         =			real_input_matrix
         lowercase_      :Tuple         =			real_vector
      elif problem_type == "complex":
         lowercase_      :List[str]         =			complex_input_matrix
         lowercase_      :Union[str, Any]         =			complex_vector

      # Our implementation.
      lowercase_      :Union[str, Any]         =			power_iteration(__lowerCamelCase     ,__lowerCamelCase			)

      # Numpy implementation.

      # Get eigenvalues and eigenvectors using built-in numpy
      # eigh (eigh used for symmetric or hermetian matrices).
      lowercase_      :Tuple         =			np.linalg.eigh(__lowerCamelCase			)
      # Last eigenvalue is the maximum one.
      lowercase_      :Optional[int]         =			eigen_values[-1]
      # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
      lowercase_      :List[Any]         =			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(__lowerCamelCase			) - np.abs(__lowerCamelCase			)			) <= 1e-6


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 test_power_iteration()







'''simple docstring'''


import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType
class 				a_       (    _lowerCAmelCase							):
     __A								=      ["image_processor", "tokenizer"]
     __A								=      "LayoutLMv3ImageProcessor"
     __A								=      ("LayoutLMv3Tokenizer", "LayoutLMv3TokenizerFast")





     def __init__(			self		: int     ,				lowercase		: Optional[Any]=None     ,				lowercase		: List[str]=None     ,				**lowercase		: Optional[int]						):





        """simple docstring"""




        lowercase_      :int         =			None
        if "feature_extractor" in kwargs:
           warnings.warn(
               "The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"
               " instead."     ,				lowercase     ,				)
           lowercase_      :Optional[int]         =			kwargs.pop("feature_extractor"						)

        lowercase_      :Union[str, Any]         =			image_processor if image_processor is not None else feature_extractor
        if image_processor is None:
           raise ValueError("You need to specify an `image_processor`."						)
        if tokenizer is None:
           raise ValueError("You need to specify a `tokenizer`."						)

        super().__init__(lowercase     ,				lowercase						)





     def __call__(			self		: Optional[Any]     ,				lowercase		: List[str]     ,				lowercase		: Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None     ,				lowercase		: Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None     ,				lowercase		: Union[List[List[int]], List[List[List[int]]]] = None     ,				lowercase		: Optional[Union[List[int], List[List[int]]]] = None     ,				lowercase		: bool = True     ,				lowercase		: Union[bool, str, PaddingStrategy] = False     ,				lowercase		: Union[bool, str, TruncationStrategy] = None     ,				lowercase		: Optional[int] = None     ,				lowercase		: int = 0     ,				lowercase		: Optional[int] = None     ,				lowercase		: Optional[bool] = None     ,				lowercase		: Optional[bool] = None     ,				lowercase		: bool = False     ,				lowercase		: bool = False     ,				lowercase		: bool = False     ,				lowercase		: bool = False     ,				lowercase		: bool = True     ,				lowercase		: Optional[Union[str, TensorType]] = None     ,				**lowercase		: List[Any]     ,				):





        """simple docstring"""




        if self.image_processor.apply_ocr and (boxes is not None):
           raise ValueError(
               "You cannot provide bounding boxes if you initialized the image processor with apply_ocr set to True."						)

        if self.image_processor.apply_ocr and (word_labels is not None):
           raise ValueError(
               "You cannot provide word labels if you initialized the image processor with apply_ocr set to True."						)

        # first, apply the image processor
        lowercase_      :Dict         =			self.image_processor(images=lowercase     ,				return_tensors=lowercase						)

        # second, apply the tokenizer
        if text is not None and self.image_processor.apply_ocr and text_pair is None:
           if isinstance(lowercase     ,				lowercase						):
              lowercase_      :str         =			[text]  # add batch dimension (as the image processor always adds a batch dimension)
           lowercase_      :Union[str, Any]         =			features["words"]

        lowercase_      :Optional[Any]         =			self.tokenizer(
            text=text if text is not None else features["words"]     ,				text_pair=text_pair if text_pair is not None else None     ,				boxes=boxes if boxes is not None else features["boxes"]     ,				word_labels=lowercase     ,				add_special_tokens=lowercase     ,				padding=lowercase     ,				truncation=lowercase     ,				max_length=lowercase     ,				stride=lowercase     ,				pad_to_multiple_of=lowercase     ,				return_token_type_ids=lowercase     ,				return_attention_mask=lowercase     ,				return_overflowing_tokens=lowercase     ,				return_special_tokens_mask=lowercase     ,				return_offsets_mapping=lowercase     ,				return_length=lowercase     ,				verbose=lowercase     ,				return_tensors=lowercase     ,				**lowercase     ,				)

        # add pixel values
        lowercase_      :Any         =			features.pop("pixel_values"						)
        if return_overflowing_tokens is True:
           lowercase_      :Any         =			self.get_overflowing_images(lowercase     ,				encoded_inputs["overflow_to_sample_mapping"]						)
        lowercase_      :Any         =			images

        return encoded_inputs





     def 							lowercase__				(			self		: List[Any]     ,				lowercase		: Any     ,				lowercase		: Optional[Any]						):





        """simple docstring"""




        lowercase_      :Union[str, Any]         =			[]
        for sample_idx in overflow_to_sample_mapping:
           images_with_overflow.append(images[sample_idx]						)

        if len(lowercase						) != len(lowercase						):
           raise ValueError(
               "Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got"
               F' {len(lowercase						)} and {len(lowercase						)}'						)

        return images_with_overflow





     def 							lowercase__				(			self		: Union[str, Any]     ,				*lowercase		: List[Any]     ,				**lowercase		: Optional[Any]						):





        """simple docstring"""




        return self.tokenizer.batch_decode(*lowercase     ,				**lowercase						)





     def 							lowercase__				(			self		: List[Any]     ,				*lowercase		: Any     ,				**lowercase		: str						):





        """simple docstring"""




        return self.tokenizer.decode(*lowercase     ,				**lowercase						)





     @property
     def 							lowercase__				(			self		: Optional[Any]						):





        """simple docstring"""




        return ["input_ids", "bbox", "attention_mask", "pixel_values"]





     @property
     def 							lowercase__				(			self		: str						):





        """simple docstring"""




        warnings.warn(
            "`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."     ,				lowercase     ,				)
        return self.image_processor_class







     @property
     def 							lowercase__				(			self		: Tuple						):





        """simple docstring"""




        warnings.warn(
            "`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."     ,				lowercase     ,				)
        return self.image_processor


