import numpy as np





def 				UpperCAmelCase						(    lowercase							,			lowercase							,			lowercase = 1E-12							,			lowercase = 100							,			):







				"""simple docstring"""



				assert np.shape(lowercase							)[0] == np.shape(lowercase							)[1]
				# Ensure proper dimensionality.
				assert np.shape(lowercase							)[0] == np.shape(lowercase							)[0]
				# Ensure inputs are either both complex or both real
				assert np.iscomplexobj(lowercase							) == np.iscomplexobj(lowercase							)
				__lowercase 			=							np.iscomplexobj(lowercase							)
				if is_complex:
								# Ensure complex input_matrix is Hermitian
								assert np.array_equal(lowercase							,			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 			=							False
				__lowercase 			=							0
				__lowercase 			=							0
				__lowercase 			=							1E12

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

								# Check convergence.
								__lowercase 			=							np.abs(lambda_ - lambda_previous							) / lambda_
								iterations += 1

								if error <= error_tol or iterations >= max_iterations:
												__lowercase 			=							True

								__lowercase 			=							lambda_

				if is_complex:
								__lowercase 			=							np.real(lambda_							)

				return lambda_, vector





def 				UpperCAmelCase						(    ):







				"""simple docstring"""



				__lowercase 			=							np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]							)
				__lowercase 			=							np.array([41, 4, 20]							)
				__lowercase 			=							real_input_matrix.astype(np.complexaaa							)
				__lowercase 			=							np.triu(1j * complex_input_matrix							,			1							)
				complex_input_matrix += imag_matrix
				complex_input_matrix += -1 * imag_matrix.T
				__lowercase 			=							np.array([41, 4, 20]							).astype(np.complexaaa							)

				for problem_type in ["real", "complex"]:
								if problem_type == "real":
												__lowercase 			=							real_input_matrix
												__lowercase 			=							real_vector
								elif problem_type == "complex":
												__lowercase 			=							complex_input_matrix
												__lowercase 			=							complex_vector

								# Our implementation.
								__lowercase			,     __lowercase 			=							power_iteration(lowercase							,			lowercase							)

								# Numpy implementation.

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		test_power_iteration()
# Copyright 2022 The HuggingFace Team and The OpenBMB Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


__a  :     Any       =  {
    """configuration_cpmant""": ["""CPMANT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """CpmAntConfig"""],
    """tokenization_cpmant""": ["""CpmAntTokenizer"""],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__a  :     List[Any]       =  [
		    """CPMANT_PRETRAINED_MODEL_ARCHIVE_LIST""",
		    """CpmAntForCausalLM""",
		    """CpmAntModel""",
		    """CpmAntPreTrainedModel""",
		]


if TYPE_CHECKING:
		from .configuration_cpmant import CPMANT_PRETRAINED_CONFIG_ARCHIVE_MAP, CpmAntConfig
		from .tokenization_cpmant import CpmAntTokenizer

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_cpmant import (
				    CPMANT_PRETRAINED_MODEL_ARCHIVE_LIST,
				    CpmAntForCausalLM,
				    CpmAntModel,
				    CpmAntPreTrainedModel,
				)


else:
		import sys

		__a  :     Any       =  _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)