




"""simple docstring"""


import re

import jax.numpy as jnp
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.random import PRNGKey

from ..utils import logging


A_						=				logging.get_logger(__name__)


def 					UpperCAmelCase__       (snake_case__							:					List[Any]    ):
  """simple docstring"""

  _snake_case							:		Optional[Any]								=  R"""\w+[.]\d+"""
  _snake_case							:		Union[str, Any]								=  re.findall(snake_case__		,   snake_case__    )
  for pat in pats:
    _snake_case							:		str								=  key.replace(snake_case__		,   """_""".join(pat.split("""."""    )    )    )
  return key


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					Dict		,   snake_case__							:					List[Any]    ):
  """simple docstring"""

  _snake_case							:		Optional[int]								=  pt_tuple_key[:-1] + ("""scale""",)
  if (
      any("""norm""" in str_ for str_ in pt_tuple_key    )
      and (pt_tuple_key[-1] == "bias")
      and (pt_tuple_key[:-1] + ("bias",) not in random_flax_state_dict)
      and (pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict)
  ):
    _snake_case							:		List[str]								=  pt_tuple_key[:-1] + ("""scale""",)
    return renamed_pt_tuple_key, pt_tensor
  elif pt_tuple_key[-1] in ["weight", "gamma"] and pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict:
    _snake_case							:		Tuple								=  pt_tuple_key[:-1] + ("""scale""",)
    return renamed_pt_tuple_key, pt_tensor

  # embedding
  if pt_tuple_key[-1] == "weight" and pt_tuple_key[:-1] + ("embedding",) in random_flax_state_dict:
    _snake_case							:		Tuple								=  pt_tuple_key[:-1] + ("""embedding""",)
    return renamed_pt_tuple_key, pt_tensor

  # conv layer
  _snake_case							:		Tuple								=  pt_tuple_key[:-1] + ("""kernel""",)
  if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4:
    _snake_case							:		Dict								=  pt_tensor.transpose(2		,   3		,   1		,   0    )
    return renamed_pt_tuple_key, pt_tensor

  # linear layer
  _snake_case							:		Any								=  pt_tuple_key[:-1] + ("""kernel""",)
  if pt_tuple_key[-1] == "weight":
    _snake_case							:		Optional[Any]								=  pt_tensor.T
    return renamed_pt_tuple_key, pt_tensor

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

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

  return pt_tuple_key, pt_tensor






def 					UpperCAmelCase__       (snake_case__							:					Union[str, Any]		,   snake_case__							:					Tuple		,   snake_case__							:					Union[str, Any]=42    ):
  """simple docstring"""

  _snake_case							:		Dict								=  {k: v.numpy() for k, v in pt_state_dict.items()}

  # Step 2: Since the model is stateless, get random Flax params
  _snake_case							:		List[str]								=  flax_model.init_weights(PRNGKey(snake_case__    )    )

  _snake_case							:		int								=  flatten_dict(snake_case__    )
  _snake_case							:		List[str]								=  {}

  # Need to change some parameters name to match Flax names
  for pt_key, pt_tensor in pt_state_dict.items():
    _snake_case							:		List[str]								=  rename_key(snake_case__    )
    _snake_case							:		List[Any]								=  tuple(renamed_pt_key.split("""."""    )    )

    # Correctly rename weight parameters
    _snake_case		,					_snake_case							:		int								=  rename_key_and_reshape_tensor(snake_case__		,   snake_case__		,   snake_case__    )

    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}."    )

        # also add unexpected weight so that warning is thrown
    _snake_case							:		Optional[Any]								=  jnp.asarray(snake_case__    )

  return unflatten_dict(snake_case__    )



import numpy as np



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE = 1e-12  ,			SCREAMING_SNAKE_CASE = 100  ,			):
    '''simple docstring'''







    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[1]
    # Ensure proper dimensionality.
    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[0]
    # Ensure inputs are either both complex or both real
    assert np.iscomplexobj(SCREAMING_SNAKE_CASE	) == np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    __UpperCamelCase     :List[Any]			  =		np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    if is_complex:
        # Ensure complex input_matrix is Hermitian
        assert np.array_equal(SCREAMING_SNAKE_CASE  ,			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.

    __UpperCamelCase     :str			  =		False
    __UpperCamelCase     :int			  =		0
    __UpperCamelCase     :Optional[Any]			  =		0
    __UpperCamelCase     :Union[str, Any]			  =		1e12

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

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

        if error <= error_tol or iterations >= max_iterations:
            __UpperCamelCase     :Dict			  =		True

        __UpperCamelCase     :List[Any]			  =		lambda_

    if is_complex:
        __UpperCamelCase     :Tuple			  =		np.real(lambda_	)

    return lambda_, vector



def lowerCamelCase  (   ):
    '''simple docstring'''







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

    for problem_type in ["real", "complex"]:
        if problem_type == "real":
            __UpperCamelCase     :Any			  =		real_input_matrix
            __UpperCamelCase     :int			  =		real_vector
        elif problem_type == "complex":
            __UpperCamelCase     :Tuple			  =		complex_input_matrix
            __UpperCamelCase     :Optional[Any]			  =		complex_vector

        # Our implementation.
        __UpperCamelCase  ,       __UpperCamelCase     :Dict			  =		power_iteration(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)

        # Numpy implementation.

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    test_power_iteration()





