
"""simple docstring"""


from typing import Any

import numpy as np






def        lowerCAmelCase_       (		snake_case_		:      Tuple      )       ->bool:
			assert np.shape(snake_case_      )[0] == np.shape(snake_case_      )[1]

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

			# Get eigenvalues and eignevectors for a symmetric matrix.
			lowerCamelCase__     :					int     	=np.linalg.eigh(snake_case_      )

			# Check sign of all eigenvalues.
			# np.all returns a value of type np.bool_
			return bool(np.all(eigen_values > 0      )      )






def        lowerCAmelCase_       (		snake_case_		:      Tuple      )       ->Any:
			lowerCamelCase__     :					Union[str, Any]     	=np.random.randn(snake_case_							,   snake_case_      )
			lowerCamelCase__     :					List[str]     	=np.dot(snake_case_							,   random_matrix.T      )
			assert _is_matrix_spd(snake_case_      )
			return spd_matrix






def        lowerCAmelCase_       (		snake_case_		:      int							,   snake_case_		:      List[Any]							,   snake_case_		:      Union[str, Any] = 1_0_0_0							,   snake_case_		:      Dict = 1E-8							,   )       ->Any:
			assert np.shape(snake_case_      )[0] == np.shape(snake_case_      )[1]
			assert np.shape(snake_case_      )[0] == np.shape(snake_case_      )[0]
			assert _is_matrix_spd(snake_case_      )

			# Initialize solution guess, residual, search direction.
			lowerCamelCase__     :					int     	=np.zeros((np.shape(snake_case_      )[0], 1)      )
			lowerCamelCase__     :					Optional[Any]     	=np.copy(snake_case_      )
			lowerCamelCase__     :					Optional[Any]     	=np.copy(snake_case_      )

			# Set initial errors in solution guess and residual.
			lowerCamelCase__     :					Dict     	=1E9
			lowerCamelCase__     :					List[Any]     	=1E9
			lowerCamelCase__     :					int     	=1E9

			# Set iteration counter to threshold number of iterations.
			lowerCamelCase__     :					Tuple     	=0

			while error > tol:
						# Save this value so we only calculate the matrix-vector product once.
						lowerCamelCase__     :					Optional[Any]     	=np.dot(snake_case_							,   snake_case_      )

						# The main algorithm.

						# Update search direction magnitude.
						lowerCamelCase__     :					Dict     	=np.dot(ra.T							,   snake_case_      ) / np.dot(pa.T							,   snake_case_      )
						# Update solution guess.
						lowerCamelCase__     :					Optional[Any]     	=xa + alpha * pa
						# Calculate new residual.
						lowerCamelCase__     :					List[str]     	=ra - alpha * w
						# Calculate new Krylov subspace scale.
						lowerCamelCase__     :					Optional[Any]     	=np.dot(r.T							,   snake_case_      ) / np.dot(ra.T							,   snake_case_      )
						# Calculate new A conjuage search direction.
						lowerCamelCase__     :					int     	=r + beta * pa

						# Calculate errors.
						lowerCamelCase__     :					List[str]     	=np.linalg.norm(r - ra      )
						lowerCamelCase__     :					Union[str, Any]     	=np.linalg.norm(x - xa      )
						lowerCamelCase__     :					Optional[int]     	=np.maximum(snake_case_							,   snake_case_      )

						# Update variables.
						lowerCamelCase__     :					str     	=np.copy(snake_case_      )
						lowerCamelCase__     :					Union[str, Any]     	=np.copy(snake_case_      )
						lowerCamelCase__     :					Tuple     	=np.copy(snake_case_      )

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

			return x






def        lowerCAmelCase_       (		)       ->None:
			lowerCamelCase__     :					int     	=3
			lowerCamelCase__     :					Dict     	=_create_spd_matrix(snake_case_      )
			lowerCamelCase__     :					str     	=np.random.randn(snake_case_							,   1      )
			lowerCamelCase__     :					Optional[Any]     	=np.dot(snake_case_							,   snake_case_      )

			# Numpy solution.
			lowerCamelCase__     :					Tuple     	=np.linalg.solve(snake_case_							,   snake_case_      )

			# Our implementation.
			lowerCamelCase__     :					Optional[Any]     	=conjugate_gradient(snake_case_							,   snake_case_      )

			# 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()

"""simple docstring"""


from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCAmelCase								=						logging.get_logger(__name__)

lowerCAmelCase								=						{
    """uw-madison/nystromformer-512""": """https://huggingface.co/uw-madison/nystromformer-512/resolve/main/config.json""",
    # See all Nystromformer models at https://huggingface.co/models?filter=nystromformer
}

class    A_     (					A__       ):



							"""simple docstring"""






							SCREAMING_SNAKE_CASE_     				=       """nystromformer"""





							def __init__(  self  :Optional[Any]					,							lowerCamelCase_  :Optional[Any]=30_000					,							lowerCamelCase_  :str=768					,							lowerCamelCase_  :str=12					,							lowerCamelCase_  :str=12					,							lowerCamelCase_  :Any=3_072					,							lowerCamelCase_  :Optional[int]="gelu_new"					,							lowerCamelCase_  :List[Any]=0.1					,							lowerCamelCase_  :List[str]=0.1					,							lowerCamelCase_  :Any=510					,							lowerCamelCase_  :Optional[int]=2					,							lowerCamelCase_  :List[Any]=64					,							lowerCamelCase_  :Union[str, Any]=64					,							lowerCamelCase_  :str=65					,							lowerCamelCase_  :Union[str, Any]=False					,							lowerCamelCase_  :str=0.02					,							lowerCamelCase_  :Any=1e-5					,							lowerCamelCase_  :int=1					,							lowerCamelCase_  :Optional[int]=0					,							lowerCamelCase_  :str=2					,							**lowerCamelCase_  :int					,							):





										"""simple docstring"""

										lowerCamelCase__     :					int		=vocab_size
										lowerCamelCase__     :					Optional[int]		=max_position_embeddings
										lowerCamelCase__     :					List[Any]		=hidden_size
										lowerCamelCase__     :					Tuple		=num_hidden_layers
										lowerCamelCase__     :					Optional[Any]		=num_attention_heads
										lowerCamelCase__     :					List[str]		=intermediate_size
										lowerCamelCase__     :					Union[str, Any]		=hidden_act
										lowerCamelCase__     :					int		=hidden_dropout_prob
										lowerCamelCase__     :					Tuple		=attention_probs_dropout_prob
										lowerCamelCase__     :					Dict		=initializer_range
										lowerCamelCase__     :					Tuple		=type_vocab_size
										lowerCamelCase__     :					Any		=segment_means_seq_len
										lowerCamelCase__     :					int		=num_landmarks
										lowerCamelCase__     :					Tuple		=conv_kernel_size
										lowerCamelCase__     :					Optional[int]		=inv_coeff_init_option
										lowerCamelCase__     :					List[str]		=layer_norm_eps
										super().__init__(pad_token_id=lowerCamelCase_					,							bos_token_id=lowerCamelCase_					,							eos_token_id=lowerCamelCase_					,							**lowerCamelCase_	)