
'''simple docstring'''







from typing import List, Optional, Union

import numpy as np
import tensorflow as tf

from .utils import logging


lowercase					:							Any   =      logging.get_logger(__name__)







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			List[int]:
	if isinstance(__A    ,       np.ndarray			):
		return list(tensor.shape			)

	_snake_case     		=	tf.shape(__A			)

	if tensor.shape == tf.TensorShape(__A			):
		return dynamic

	_snake_case     		=	tensor.shape.as_list()

	return [dynamic[i] if s is None else s for i, s in enumerate(__A			)]







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A = None    ,       __A = None			) ->			tf.Tensor:
	return tf.nn.softmax(logits=logits + 1e-9    ,       axis=__A    ,       name=__A			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A    ,       __A=1e-5    ,       __A=-1			) ->			List[str]:
	# This is a very simplified functional layernorm, designed to duplicate
	# the functionality of PyTorch nn.functional.layer_norm when this is needed to port
	# models in Transformers.

	if weight.shape.rank != 1 or bias.shape.rank != 1 or not isinstance(__A    ,       __A			):
		raise NotImplementedError('Only 1D weight and bias tensors are supported for now, with only a single axis.'			)

	# Get mean and variance on the axis to be normalized
	_snake_case		,				_snake_case     		=	tf.nn.moments(__A    ,       axes=[axis]    ,       keepdims=__A			)

	if axis != -1:
		# Reshape scale and weight to have the same rank as inputs, but with 1 dimensions
		# on every dimension except axis
		_snake_case     		=	[1] * inputs.shape.rank
		_snake_case     		=	shape_list(__A			)[axis]
		_snake_case     		=	tf.reshape(__A    ,       __A			)
		_snake_case     		=	tf.reshape(__A    ,       __A			)

	# Compute layer normalization using the batch_normalization
	# function.
	_snake_case     		=	tf.nn.batch_normalization(
	    __A    ,       __A    ,       __A    ,       offset=__A    ,       scale=__A    ,       variance_epsilon=__A    ,       )
	return outputs







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A=0    ,       __A=-1			) ->			Any:
	# Replicates the behavior of torch.flatten in TF

	# If end_dim or start_dim is negative, count them from the end
	if end_dim < 0:
		end_dim += input.shape.rank
	if start_dim < 0:
		start_dim += input.shape.rank

	if start_dim == end_dim:
		return input

	_snake_case     		=	tf.shape(__A			)
	_snake_case     		=	tf.math.reduce_prod(in_shape[start_dim : end_dim + 1]			)
	_snake_case     		=	tf.concat([in_shape[:start_dim], [flattened_dim], in_shape[end_dim + 1 :]]    ,       axis=0			)
	return tf.reshape(__A    ,       __A			)







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			tf.Tensor:
	if not isinstance(__A    ,       tf.Tensor			):
		_snake_case     		=	tf.convert_to_tensor(__A			)  # Catches stray NumPy inputs
	if encoder_attention_mask.shape.rank == 3:
		_snake_case     		=	encoder_attention_mask[:, None, :, :]
	if encoder_attention_mask.shape.rank == 2:
		_snake_case     		=	encoder_attention_mask[:, None, None, :]
	# T5 has a mask that can compare sequence ids, we can simulate this here with this transposition
	# Cf. https://github.com/tensorflow/mesh/blob/8d2465e9bc93129b913b5ccc6a59aa97abd96ec6/mesh_tensorflow
	# /transformer/transformer_layers.py#L270
	# encoder_extended_attention_mask = (encoder_extended_attention_mask ==
	# encoder_extended_attention_mask.transpose(-1, -2))
	_snake_case     		=	(
	    tf.cast(1    ,       encoder_attention_mask.dtype			) - encoder_extended_attention_mask
	) * encoder_extended_attention_mask.dtype.min

	return encoder_extended_attention_mask







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A = "input_ids"			) ->			None:
	tf.debugging.assert_less(
	    __A    ,       tf.cast(__A    ,       dtype=tensor.dtype			)    ,       message=(
	        F'The maximum value of {tensor_name} ({tf.math.reduce_max(__A			)}) must be smaller than the embedding '
	        F'layer\'s input dimension ({embed_dim}). The likely cause is some problem at tokenization time.'
	    )    ,       )







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A			) ->			Any:
	_snake_case     		=	64_512
	# Check that no item in `data` is larger than `HDF5_OBJECT_HEADER_LIMIT`
	# because in that case even chunking the array would not make the saving
	# possible.
	_snake_case     		=	[x for x in data if len(__A			) > HDF5_OBJECT_HEADER_LIMIT]

	# Expecting this to never be true.
	if bad_attributes:
		raise RuntimeError(
		    'The following attributes cannot be saved to HDF5 file because '
		    F'they are larger than {HDF5_OBJECT_HEADER_LIMIT} '
		    F'bytes: {bad_attributes}'			)

	_snake_case     		=	np.asarray(__A			)

	_snake_case     		=	1
	_snake_case     		=	np.array_split(__A    ,       __A			)

	# This will never loop forever thanks to the test above.
	while any(x.nbytes > HDF5_OBJECT_HEADER_LIMIT for x in chunked_data			):
		num_chunks += 1
		_snake_case     		=	np.array_split(__A    ,       __A			)

	if num_chunks > 1:
		for chunk_id, chunk_data in enumerate(__A			):
			_snake_case     		=	chunk_data
	else:
		_snake_case     		=	data







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			List[str]:
	if name in group.attrs:
		_snake_case     		=	[n.decode('utf8'			) if hasattr(__A    ,       'decode'			) else n for n in group.attrs[name]]
	else:
		_snake_case     		=	[]
		_snake_case     		=	0
		while "%s%d" % (name, chunk_id) in group.attrs:
			data.extend(
			    [n.decode('utf8'			) if hasattr(__A    ,       'decode'			) else n for n in group.attrs['%s%d' % (name, chunk_id)]]			)
			chunk_id += 1
	return data







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Any:

	def _expand_single_ad_tensor(__A			):
		if isinstance(__A    ,       tf.Tensor			) and t.shape.rank == 1:
			return tf.expand_dims(__A    ,       axis=-1			)
		return t

	return tf.nest.map_structure(_expand_single_ad_tensor    ,       __A			)



'''simple docstring'''







from typing import Any

import numpy as np







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			bool:
	return np.array_equal(__A    ,       matrix.conjugate().T			)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			Any:
	_snake_case     		=	v.conjugate().T
	_snake_case     		=	v_star.dot(__A			)
	assert isinstance(__A    ,       np.ndarray			)
	return (v_star_dot.dot(__A			)) / (v_star.dot(__A			))







def        SCREAMING_SNAKE_CASE__			(     ) ->			None:
	_snake_case     		=	np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]			)
	_snake_case     		=	np.array([[1], [2], [3]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	print(rayleigh_quotient(__A    ,       __A			)			)

	_snake_case     		=	np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]			)
	assert is_hermitian(__A			), F'{a} is not hermitian.'
	assert rayleigh_quotient(__A    ,       __A			) == float(3			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					tests()

