

"""simple docstring"""




import os
from pickle import UnpicklingError
from typing import Dict, Tuple

import jax
import jax.numpy as jnp
import numpy as np
from flax.serialization import from_bytes
from flax.traverse_util import flatten_dict, unflatten_dict

import transformers

from .utils import logging


__UpperCAmelCase =				logging.get_logger(__name__)
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase=False      ):
 '''simple docstring'''





 try:
  import torch  # noqa: F401
 except ImportError:
  logger.error(
      """Loading a PyTorch model in Flax, requires both PyTorch and Flax to be installed. Please see"""
      """ https://pytorch.org/ and https://flax.readthedocs.io/en/latest/installation.html for installation"""
      """ instructions."""      )
  raise

 if not is_sharded:
  UpperCAmelCase__					:  List[Any]					   =					os.path.abspath(__UpperCamelCase      )
  logger.info(F"Loading PyTorch weights from {pt_path}"      )

  UpperCAmelCase__					:  Optional[Any]					   =					torch.load(__UpperCamelCase							,    map_location="""cpu"""      )
  logger.info(F"PyTorch checkpoint contains {sum(t.numel() for t in pt_state_dict.values()      ):,} parameters."      )

  UpperCAmelCase__					:  List[str]					   =					convert_pytorch_state_dict_to_flax(__UpperCamelCase							,    __UpperCamelCase      )
 else:
  # model is sharded and pytorch_checkpoint_path already contains the list of .pt shard files
  UpperCAmelCase__					:  List[Any]					   =					convert_pytorch_sharded_state_dict_to_flax(__UpperCamelCase							,    __UpperCamelCase      )
 return flax_state_dict
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase							,    ):
 '''simple docstring'''





 def is_key_or_prefix_key_in_dict(__UpperCamelCase      ) -> bool:
  return len(set(__UpperCamelCase      ) & {key, (model_prefix,) + key}      ) > 0

 # layer norm
 UpperCAmelCase__					:  Optional[int]					   =					pt_tuple_key[:-1] + ("""scale""",)
 if pt_tuple_key[-1] in ["weight", "gamma"] and is_key_or_prefix_key_in_dict(__UpperCamelCase      ):
  return renamed_pt_tuple_key, pt_tensor

 # batch norm layer mean
 UpperCAmelCase__					:  List[Any]					   =					pt_tuple_key[:-1] + ("""mean""",)
 if pt_tuple_key[-1] == "running_mean" and not is_key_or_prefix_key_in_dict(__UpperCamelCase      ):
  return renamed_pt_tuple_key, pt_tensor

 # batch norm layer var
 UpperCAmelCase__					:  List[Any]					   =					pt_tuple_key[:-1] + ("""var""",)
 if pt_tuple_key[-1] == "running_var" and not is_key_or_prefix_key_in_dict(__UpperCamelCase      ):
  return renamed_pt_tuple_key, pt_tensor

 # embedding
 UpperCAmelCase__					:  List[str]					   =					pt_tuple_key[:-1] + ("""embedding""",)
 if pt_tuple_key[-1] == "weight" and is_key_or_prefix_key_in_dict(__UpperCamelCase      ):
  return renamed_pt_tuple_key, pt_tensor

 # conv layer
 UpperCAmelCase__					:  int					   =					pt_tuple_key[:-1] + ("""kernel""",)
 if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4 and not is_key_or_prefix_key_in_dict(__UpperCamelCase      ):
  UpperCAmelCase__					:  Any					   =					pt_tensor.transpose(2							,    3							,    1							,    0      )
  return renamed_pt_tuple_key, pt_tensor

 # linear layer
 UpperCAmelCase__					:  str					   =					pt_tuple_key[:-1] + ("""kernel""",)
 if pt_tuple_key[-1] == "weight" and not is_key_or_prefix_key_in_dict(__UpperCamelCase      ):
  UpperCAmelCase__					:  Optional[int]					   =					pt_tensor.T
  return renamed_pt_tuple_key, pt_tensor

 # old PyTorch layer norm weight
 UpperCAmelCase__					:  Optional[Any]					   =					pt_tuple_key[:-1] + ("""weight""",)
 if pt_tuple_key[-1] == "gamma":
  return renamed_pt_tuple_key, pt_tensor

 # old PyTorch layer norm bias
 UpperCAmelCase__					:  str					   =					pt_tuple_key[:-1] + ("""bias""",)
 if pt_tuple_key[-1] == "beta":
  return renamed_pt_tuple_key, pt_tensor

 # New `weight_norm` from https://github.com/huggingface/transformers/pull/24030
 UpperCAmelCase__					:  Union[str, Any]					   =					None
 if pt_tuple_key[-3::2] == ("parametrizations", "original0"):
  UpperCAmelCase__					:  List[str]					   =					pt_tuple_key[-2] + """_g"""
 elif pt_tuple_key[-3::2] == ("parametrizations", "original1"):
  UpperCAmelCase__					:  Optional[Any]					   =					pt_tuple_key[-2] + """_v"""
 if name is not None:
  UpperCAmelCase__					:  Optional[int]					   =					pt_tuple_key[:-3] + (name,)
  return renamed_pt_tuple_key, pt_tensor

 return pt_tuple_key, pt_tensor
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  int					   =					{k: v.numpy() for k, v in pt_state_dict.items()}

 UpperCAmelCase__					:  List[str]					   =					flax_model.base_model_prefix

 # use params dict if the model contains batch norm layers
 if "params" in flax_model.params:
  UpperCAmelCase__					:  Any					   =					flax_model.params["""params"""]
 else:
  UpperCAmelCase__					:  Optional[int]					   =					flax_model.params
 UpperCAmelCase__					:  Any					   =					flatten_dict(__UpperCamelCase      )

 # add batch_stats keys,values to dict
 if "batch_stats" in flax_model.params:
  UpperCAmelCase__					:  int					   =					flatten_dict(flax_model.params["""batch_stats"""]      )
  random_flax_state_dict.update(__UpperCamelCase      )

 UpperCAmelCase__					:  Any					   =					{}

 UpperCAmelCase__					:  List[str]					   =					(model_prefix not in flax_model_params) and (
     model_prefix in {k.split("""."""      )[0] for k in pt_state_dict.keys()}
 )
 UpperCAmelCase__					:  List[str]					   =					(model_prefix in flax_model_params) and (
     model_prefix not in {k.split("""."""      )[0] for k in pt_state_dict.keys()}
 )

 # Need to change some parameters name to match Flax names
 for pt_key, pt_tensor in pt_state_dict.items():
  UpperCAmelCase__					:  Tuple					   =					tuple(pt_key.split("""."""      )      )

  # remove base model prefix if necessary
  UpperCAmelCase__					:  Dict					   =					pt_tuple_key[0] == model_prefix
  if load_model_with_head_into_base_model and has_base_model_prefix:
   UpperCAmelCase__					:  Union[str, Any]					   =					pt_tuple_key[1:]

  # Correctly rename weight parameters
  UpperCAmelCase__   ,      UpperCAmelCase__					:  List[Any]					   =					rename_key_and_reshape_tensor(
      __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      )

  # add model prefix if necessary
  UpperCAmelCase__					:  Optional[Any]					   =					(model_prefix,) + flax_key in random_flax_state_dict
  if load_base_model_into_model_with_head and require_base_model_prefix:
   UpperCAmelCase__					:  Optional[int]					   =					(model_prefix,) + flax_key

  if flax_key in random_flax_state_dict:
   if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
    raise ValueError(
        F"PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape "
        F"{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}."      )

        # add batch stats if the model contains batchnorm layers
  if "batch_stats" in flax_model.params:
   if "mean" in flax_key[-1] or "var" in flax_key[-1]:
    UpperCAmelCase__					:  int					   =					jnp.asarray(__UpperCamelCase      )
    continue
   # remove num_batches_tracked key
   if "num_batches_tracked" in flax_key[-1]:
    flax_state_dict.pop(__UpperCamelCase							,    __UpperCamelCase      )
    continue

   # also add unexpected weight so that warning is thrown
   UpperCAmelCase__					:  Tuple					   =					jnp.asarray(__UpperCamelCase      )

  else:
   # also add unexpected weight so that warning is thrown
   UpperCAmelCase__					:  Union[str, Any]					   =					jnp.asarray(__UpperCamelCase      )

 return unflatten_dict(__UpperCamelCase      )
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 import torch

 # Load the index
 UpperCAmelCase__					:  Any					   =					{}
 for shard_file in shard_filenames:
  # load using msgpack utils
  UpperCAmelCase__					:  Optional[Any]					   =					torch.load(__UpperCamelCase      )
  UpperCAmelCase__					:  Union[str, Any]					   =					{k: v.numpy() for k, v in pt_state_dict.items()}

  UpperCAmelCase__					:  List[str]					   =					flax_model.base_model_prefix

  # use params dict if the model contains batch norm layers and then add batch_stats keys,values to dict
  if "batch_stats" in flax_model.params:
   UpperCAmelCase__					:  int					   =					flax_model.params["""params"""]

   UpperCAmelCase__					:  Dict					   =					flatten_dict(__UpperCamelCase      )
   random_flax_state_dict.update(flatten_dict(flax_model.params["""batch_stats"""]      )      )
  else:
   UpperCAmelCase__					:  List[str]					   =					flax_model.params
   UpperCAmelCase__					:  Dict					   =					flatten_dict(__UpperCamelCase      )

  UpperCAmelCase__					:  Any					   =					(model_prefix not in flax_model_params) and (
      model_prefix in {k.split("""."""      )[0] for k in pt_state_dict.keys()}
  )
  UpperCAmelCase__					:  Dict					   =					(model_prefix in flax_model_params) and (
      model_prefix not in {k.split("""."""      )[0] for k in pt_state_dict.keys()}
  )
  # Need to change some parameters name to match Flax names
  for pt_key, pt_tensor in pt_state_dict.items():
   UpperCAmelCase__					:  Dict					   =					tuple(pt_key.split("""."""      )      )

   # remove base model prefix if necessary
   UpperCAmelCase__					:  Dict					   =					pt_tuple_key[0] == model_prefix
   if load_model_with_head_into_base_model and has_base_model_prefix:
    UpperCAmelCase__					:  Union[str, Any]					   =					pt_tuple_key[1:]

   # Correctly rename weight parameters
   UpperCAmelCase__   ,      UpperCAmelCase__					:  Union[str, Any]					   =					rename_key_and_reshape_tensor(
       __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      )
   # add model prefix if necessary
   UpperCAmelCase__					:  List[str]					   =					(model_prefix,) + flax_key in random_flax_state_dict
   if load_base_model_into_model_with_head and require_base_model_prefix:
    UpperCAmelCase__					:  Any					   =					(model_prefix,) + flax_key

   if flax_key in random_flax_state_dict:
    if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
     raise ValueError(
         F"PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape "
         F"{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}."      )

            # add batch stats if the model contains batchnorm layers
   if "batch_stats" in flax_model.params:
    if "mean" in flax_key[-1]:
     UpperCAmelCase__					:  Optional[Any]					   =					jnp.asarray(__UpperCamelCase      )
     continue
    if "var" in flax_key[-1]:
     UpperCAmelCase__					:  List[Any]					   =					jnp.asarray(__UpperCamelCase      )
     continue
    # remove num_batches_tracked key
    if "num_batches_tracked" in flax_key[-1]:
     flax_state_dict.pop(__UpperCamelCase							,    __UpperCamelCase      )
     continue

    # also add unexpected weight so that warning is thrown
    UpperCAmelCase__					:  Optional[int]					   =					jnp.asarray(__UpperCamelCase      )

   else:
    # also add unexpected weight so that warning is thrown
    UpperCAmelCase__					:  List[Any]					   =					jnp.asarray(__UpperCamelCase      )
 return unflatten_dict(__UpperCamelCase      )
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  List[str]					   =					os.path.abspath(__UpperCamelCase      )
 logger.info(F"Loading Flax weights from {flax_checkpoint_path}"      )

 # import correct flax class
 UpperCAmelCase__					:  Tuple					   =					getattr(__UpperCamelCase							,    """Flax""" + model.__class__.__name__      )

 # load flax weight dict
 with open(__UpperCamelCase							,    """rb"""      ) as state_f:
  try:
   UpperCAmelCase__					:  Dict					   =					from_bytes(__UpperCamelCase							,    state_f.read()      )
  except UnpicklingError:
   raise EnvironmentError(F"Unable to convert {flax_checkpoint_path} to Flax deserializable object. "      )

 return load_flax_weights_in_pytorch_model(__UpperCamelCase							,    __UpperCamelCase      )




def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 try:
  import torch  # noqa: F401
 except ImportError:
  logger.error(
      """Loading a Flax weights in PyTorch, requires both PyTorch and Flax to be installed. Please see"""
      """ https://pytorch.org/ and https://flax.readthedocs.io/en/latest/installation.html for installation"""
      """ instructions."""      )
  raise

 # check if we have bf16 weights
 UpperCAmelCase__					:  List[Any]					   =					flatten_dict(jax.tree_util.tree_map(lambda __UpperCamelCase      : x.dtype == jnp.bfloataa							,    __UpperCamelCase      )      ).values()
 if any(__UpperCamelCase      ):
  # convert all weights to fp32 if the are bf16 since torch.from_numpy can-not handle bf16
  # and bf16 is not fully supported in PT yet.
  logger.warning(
      """Found ``bfloat16`` weights in Flax model. Casting all ``bfloat16`` weights to ``float32`` """
      """before loading those in PyTorch model."""      )
  UpperCAmelCase__					:  Tuple					   =					jax.tree_util.tree_map(
      lambda __UpperCamelCase      : params.astype(np.floataa      ) if params.dtype == jnp.bfloataa else params							,    __UpperCamelCase      )

 UpperCAmelCase__					:  int					   =					flatten_dict(__UpperCamelCase      )
 UpperCAmelCase__					:  List[str]					   =					pt_model.state_dict()

 UpperCAmelCase__					:  List[str]					   =					(pt_model.base_model_prefix in flax_state) and (
     pt_model.base_model_prefix not in {k.split("""."""      )[0] for k in pt_model_dict.keys()}
 )
 UpperCAmelCase__					:  Tuple					   =					(pt_model.base_model_prefix not in flax_state) and (
     pt_model.base_model_prefix in {k.split("""."""      )[0] for k in pt_model_dict.keys()}
 )

 # keep track of unexpected & missing keys
 UpperCAmelCase__					:  str					   =					[]
 UpperCAmelCase__					:  Any					   =					set(pt_model_dict.keys()      )

 for flax_key_tuple, flax_tensor in flax_state_dict.items():
  UpperCAmelCase__					:  Tuple					   =					flax_key_tuple[0] == pt_model.base_model_prefix
  UpperCAmelCase__					:  Any					   =					""".""".join((pt_model.base_model_prefix,) + flax_key_tuple      ) in pt_model_dict

  # adapt flax_key to prepare for loading from/to base model only
  if load_model_with_head_into_base_model and has_base_model_prefix:
   UpperCAmelCase__					:  List[str]					   =					flax_key_tuple[1:]
  elif load_base_model_into_model_with_head and require_base_model_prefix:
   UpperCAmelCase__					:  Tuple					   =					(pt_model.base_model_prefix,) + flax_key_tuple

  # rename flax weights to PyTorch format
  if flax_key_tuple[-1] == "kernel" and flax_tensor.ndim == 4 and ".".join(__UpperCamelCase      ) not in pt_model_dict:
   # conv layer
   UpperCAmelCase__					:  List[Any]					   =					flax_key_tuple[:-1] + ("""weight""",)
   UpperCAmelCase__					:  List[str]					   =					jnp.transpose(__UpperCamelCase							,    (3, 2, 0, 1)      )
  elif flax_key_tuple[-1] == "kernel" and ".".join(__UpperCamelCase      ) not in pt_model_dict:
   # linear layer
   UpperCAmelCase__					:  Any					   =					flax_key_tuple[:-1] + ("""weight""",)
   UpperCAmelCase__					:  Tuple					   =					flax_tensor.T
  elif flax_key_tuple[-1] in ["scale", "embedding"]:
   UpperCAmelCase__					:  Optional[int]					   =					flax_key_tuple[:-1] + ("""weight""",)

  # adding batch stats from flax batch norm to pt
  elif "mean" in flax_key_tuple[-1]:
   UpperCAmelCase__					:  Any					   =					flax_key_tuple[:-1] + ("""running_mean""",)
  elif "var" in flax_key_tuple[-1]:
   UpperCAmelCase__					:  List[str]					   =					flax_key_tuple[:-1] + ("""running_var""",)

  if "batch_stats" in flax_state:
   UpperCAmelCase__					:  Dict					   =					""".""".join(flax_key_tuple[1:]      )  # Remove the params/batch_stats header
  else:
   UpperCAmelCase__					:  Optional[Any]					   =					""".""".join(__UpperCamelCase      )

  # We also need to look at `pt_model_dict` and see if there are keys requiring further transformation.
  UpperCAmelCase__					:  Union[str, Any]					   =					{}
  # New `weight_norm` from https://github.com/huggingface/transformers/pull/24030
  for key in pt_model_dict:
   UpperCAmelCase__					:  Union[str, Any]					   =					key.split("""."""      )
   UpperCAmelCase__					:  List[Any]					   =					None
   if key_components[-3::2] == ["parametrizations", "original0"]:
    UpperCAmelCase__					:  int					   =					key_components[-2] + """_g"""
   elif key_components[-3::2] == ["parametrizations", "original1"]:
    UpperCAmelCase__					:  int					   =					key_components[-2] + """_v"""
   if name is not None:
    UpperCAmelCase__					:  Tuple					   =					key_components[:-3] + [name]
    UpperCAmelCase__					:  List[str]					   =					""".""".join(__UpperCamelCase      )
    UpperCAmelCase__					:  Any					   =					key

  if flax_key in special_pt_names:
   UpperCAmelCase__					:  Dict					   =					special_pt_names[flax_key]

  if flax_key in pt_model_dict:
   if flax_tensor.shape != pt_model_dict[flax_key].shape:
    raise ValueError(
        F"Flax checkpoint seems to be incorrect. Weight {flax_key_tuple} was expected "
        F"to be of shape {pt_model_dict[flax_key].shape}, but is {flax_tensor.shape}."      )
   else:
    # add weight to pytorch dict
    UpperCAmelCase__					:  Optional[Any]					   =					np.asarray(__UpperCamelCase      ) if not isinstance(__UpperCamelCase							,    np.ndarray      ) else flax_tensor
    UpperCAmelCase__					:  Optional[int]					   =					torch.from_numpy(__UpperCamelCase      )
    # remove from missing keys
    missing_keys.remove(__UpperCamelCase      )
  else:
   # weight is not expected by PyTorch model
   unexpected_keys.append(__UpperCamelCase      )

 pt_model.load_state_dict(__UpperCamelCase      )

 # re-transform missing_keys to list
 UpperCAmelCase__					:  Optional[Any]					   =					list(__UpperCamelCase      )

 if len(__UpperCamelCase      ) > 0:
  logger.warning(
      """Some weights of the Flax model were not used when initializing the PyTorch model"""
      F" {pt_model.__class__.__name__}: {unexpected_keys}\n- This IS expected if you are initializing"
      F" {pt_model.__class__.__name__} from a Flax model trained on another task or with another architecture"
      """ (e.g. initializing a BertForSequenceClassification model from a FlaxBertForPreTraining model).\n- This"""
      F" IS NOT expected if you are initializing {pt_model.__class__.__name__} from a Flax model that you expect"
      """ to be exactly identical (e.g. initializing a BertForSequenceClassification model from a"""
      """ FlaxBertForSequenceClassification model)."""      )
 else:
  logger.warning(F"All Flax model weights were used when initializing {pt_model.__class__.__name__}.\n"      )
 if len(__UpperCamelCase      ) > 0:
  logger.warning(
      F"Some weights of {pt_model.__class__.__name__} were not initialized from the Flax model and are newly"
      F" initialized: {missing_keys}\nYou should probably TRAIN this model on a down-stream task to be able to"
      """ use it for predictions and inference."""      )
 else:
  logger.warning(
      F"All the weights of {pt_model.__class__.__name__} were initialized from the Flax model.\n"
      """If your task is similar to the task the model of the checkpoint was trained on, """
      F"you can already use {pt_model.__class__.__name__} for predictions without further training."      )

 return pt_model








"""simple docstring"""




from __future__ import annotations

from typing import Any







class      __lowercase			:

  def __init__(  self		:			Optional[int]					,A		:			int					,A		:			int					,A		:			float = 0    ):






   '''simple docstring'''
   UpperCAmelCase__   ,      UpperCAmelCase__					:  str					   =					row, column
   UpperCAmelCase__					:  int					   =					[[default_value for c in range(A    )] for r in range(A    )]

  def __str__(  self		:			Union[str, Any]    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Union[str, Any]					   =					f"Matrix consist of {self.row} rows and {self.column} columns\n"

   # Make string identifier
   UpperCAmelCase__					:  Optional[Any]					   =					0
   for row_vector in self.array:
    for obj in row_vector:
     UpperCAmelCase__					:  Optional[int]					   =					max(A					,len(str(A    )    )    )
   UpperCAmelCase__					:  int					   =					f"%{max_element_length}s"

   # Make string and return
   def single_line(A		:			list[float]    ) -> str:
    nonlocal string_format_identifier
    UpperCAmelCase__					:  List[str]					   =					"""["""
    line += ", ".join(string_format_identifier % (obj,) for obj in row_vector    )
    line += "]"
    return line

   s += "\n".join(single_line(A    ) for row_vector in self.array    )
   return s

  def __repr__(  self		:			Dict    ):






   '''simple docstring'''
   return str(self    )

  def    __lowercase       (  self		:			int					,A		:			tuple[int, int]    ):






   '''simple docstring'''
   if not (isinstance(A					,(list, tuple)    ) and len(A    ) == 2):
    return False
   elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
    return False
   else:
    return True

  def __getitem__(  self		:			Optional[int]					,A		:			tuple[int, int]    ):






   '''simple docstring'''
   assert self.validate_indicies(A    )
   return self.array[loc[0]][loc[1]]

  def __setitem__(  self		:			List[Any]					,A		:			tuple[int, int]					,A		:			float    ):






   '''simple docstring'''
   assert self.validate_indicies(A    )
   UpperCAmelCase__					:  str					   =					value

  def __add__(  self		:			Any					,A		:			Matrix    ):






   '''simple docstring'''
   assert isinstance(A					,A    )
   assert self.row == another.row and self.column == another.column

   # Add
   UpperCAmelCase__					:  Optional[int]					   =					Matrix(self.row					,self.column    )
   for r in range(self.row    ):
    for c in range(self.column    ):
     UpperCAmelCase__					:  Union[str, Any]					   =					self[r, c] + another[r, c]
   return result

  def __neg__(  self		:			Union[str, Any]    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Tuple					   =					Matrix(self.row					,self.column    )
   for r in range(self.row    ):
    for c in range(self.column    ):
     UpperCAmelCase__					:  int					   =					-self[r, c]
   return result

  def __sub__(  self		:			str					,A		:			Matrix    ):






   '''simple docstring'''
   return self + (-another)

  def __mul__(  self		:			Union[str, Any]					,A		:			int | float | Matrix    ):






   '''simple docstring'''

   if isinstance(A					,(int, float)    ):  # Scalar multiplication
    UpperCAmelCase__					:  Dict					   =					Matrix(self.row					,self.column    )
    for r in range(self.row    ):
     for c in range(self.column    ):
      UpperCAmelCase__					:  Any					   =					self[r, c] * another
    return result
   elif isinstance(A					,A    ):  # Matrix multiplication
    assert self.column == another.row
    UpperCAmelCase__					:  Optional[int]					   =					Matrix(self.row					,another.column    )
    for r in range(self.row    ):
     for c in range(another.column    ):
      for i in range(self.column    ):
       result[r, c] += self[r, i] * another[i, c]
    return result
   else:
    UpperCAmelCase__					:  Union[str, Any]					   =					f"Unsupported type given for another ({type(A    )})"
    raise TypeError(A    )

  def    __lowercase       (  self		:			str    ):






   '''simple docstring'''
   UpperCAmelCase__					:  List[Any]					   =					Matrix(self.column					,self.row    )
   for r in range(self.row    ):
    for c in range(self.column    ):
     UpperCAmelCase__					:  Optional[int]					   =					self[r, c]
   return result




  def    __lowercase       (  self		:			Any					,A		:			Matrix					,A		:			Matrix    ):






   '''simple docstring'''
   assert isinstance(A					,A    ) and isinstance(A					,A    )
   assert self.row == self.column == u.row == v.row  # u, v should be column vector
   assert u.column == v.column == 1  # u, v should be column vector

   # Calculate
   UpperCAmelCase__					:  Optional[Any]					   =					v.transpose()
   UpperCAmelCase__					:  Union[str, Any]					   =					(v_t * self * u)[0, 0] + 1
   if numerator_factor == 0:
    return None  # It's not invertable
   return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":
      def   lowerCAmelCase						(					):
       '''simple docstring'''





       UpperCAmelCase__					:  List[str]					   =					Matrix(3							,    3							,    0      )
       for i in range(3      ):
        UpperCAmelCase__					:  List[str]					   =					1
       print(F"a^(-1) is {ainv}"      )
       # u, v
       UpperCAmelCase__					:  List[Any]					   =					Matrix(3							,    1							,    0      )
       UpperCAmelCase__   ,      UpperCAmelCase__   ,      UpperCAmelCase__					:  Optional[int]					   =					1, 2, -3
       UpperCAmelCase__					:  List[str]					   =					Matrix(3							,    1							,    0      )
       UpperCAmelCase__   ,      UpperCAmelCase__   ,      UpperCAmelCase__					:  Tuple					   =					4, -2, 5
       print(F"u is {u}"      )
       print(F"v is {v}"      )
       print(F"uv^T is {u * v.transpose()}"      )
       # Sherman Morrison
       print(F"(a + uv^T)^(-1) is {ainv.sherman_morrison(__UpperCamelCase							,    __UpperCamelCase      )}"      )
      def   lowerCAmelCase						(					):
       '''simple docstring'''





       import doctest

       doctest.testmod()




      testa()





