
'''simple docstring'''

from typing import Any

import numpy as np







def 					A       ( UpperCamelCase_   :       np.ndarray )   ->    bool:







					'''simple docstring'''



					assert np.shape(UpperCamelCase_ )[0] == np.shape(UpperCamelCase_ )[1]

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

					# Get eigenvalues and eignevectors for a symmetric matrix.
					lowerCAmelCase__		,lowerCAmelCase__									=							np.linalg.eigh(UpperCamelCase_ )

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







def 					A       ( UpperCamelCase_   :       int )   ->    Any:







					'''simple docstring'''



					lowerCAmelCase__									=							np.random.randn(UpperCamelCase_  ,		UpperCamelCase_ )
					lowerCAmelCase__									=							np.dot(UpperCamelCase_  ,		random_matrix.T )
					assert _is_matrix_spd(UpperCamelCase_ )
					return spd_matrix







def 					A       ( UpperCamelCase_   :       np.ndarray  ,		UpperCamelCase_   :       np.ndarray  ,		UpperCamelCase_   :       int = 10_00  ,		UpperCamelCase_   :       float = 1E-8  ,		)   ->    Any:







					'''simple docstring'''



					assert np.shape(UpperCamelCase_ )[0] == np.shape(UpperCamelCase_ )[1]
					assert np.shape(UpperCamelCase_ )[0] == np.shape(UpperCamelCase_ )[0]
					assert _is_matrix_spd(UpperCamelCase_ )

					# Initialize solution guess, residual, search direction.
					lowerCAmelCase__									=							np.zeros((np.shape(UpperCamelCase_ )[0], 1) )
					lowerCAmelCase__									=							np.copy(UpperCamelCase_ )
					lowerCAmelCase__									=							np.copy(UpperCamelCase_ )

					# Set initial errors in solution guess and residual.
					lowerCAmelCase__									=							1E9
					lowerCAmelCase__									=							1E9
					lowerCAmelCase__									=							1E9

					# Set iteration counter to threshold number of iterations.
					lowerCAmelCase__									=							0

					while error > tol:
										# Save this value so we only calculate the matrix-vector product once.
										lowerCAmelCase__									=							np.dot(UpperCamelCase_  ,		UpperCamelCase_ )

										# The main algorithm.

										# Update search direction magnitude.
										lowerCAmelCase__									=							np.dot(ra.T  ,		UpperCamelCase_ ) / np.dot(pa.T  ,		UpperCamelCase_ )
										# Update solution guess.
										lowerCAmelCase__									=							xa + alpha * pa
										# Calculate new residual.
										lowerCAmelCase__									=							ra - alpha * w
										# Calculate new Krylov subspace scale.
										lowerCAmelCase__									=							np.dot(r.T  ,		UpperCamelCase_ ) / np.dot(ra.T  ,		UpperCamelCase_ )
										# Calculate new A conjuage search direction.
										lowerCAmelCase__									=							r + beta * pa

										# Calculate errors.
										lowerCAmelCase__									=							np.linalg.norm(r - ra )
										lowerCAmelCase__									=							np.linalg.norm(x - xa )
										lowerCAmelCase__									=							np.maximum(UpperCamelCase_  ,		UpperCamelCase_ )

										# Update variables.
										lowerCAmelCase__									=							np.copy(UpperCamelCase_ )
										lowerCAmelCase__									=							np.copy(UpperCamelCase_ )
										lowerCAmelCase__									=							np.copy(UpperCamelCase_ )

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

					return x







def 					A       ( )   ->    None:







					'''simple docstring'''



					lowerCAmelCase__									=							3
					lowerCAmelCase__									=							_create_spd_matrix(UpperCamelCase_ )
					lowerCAmelCase__									=							np.random.randn(UpperCamelCase_  ,		1 )
					lowerCAmelCase__									=							np.dot(UpperCamelCase_  ,		UpperCamelCase_ )

					# Numpy solution.
					lowerCAmelCase__									=							np.linalg.solve(UpperCamelCase_  ,		UpperCamelCase_ )

					# Our implementation.
					lowerCAmelCase__									=							conjugate_gradient(UpperCamelCase_  ,		UpperCamelCase_ )

					# 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'''

import unittest

from transformers import load_tool
from transformers.tools.agent_types import AGENT_TYPE_MAPPING

from .test_tools_common import ToolTesterMixin, output_types






class 				A       (		unittest.TestCase					, SCREAMING_SNAKE_CASE__      ):





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[Any]							):


				"""simple docstring"""

				lowerCAmelCase__									=							load_tool("translation"							)
				self.tool.setup()
				lowerCAmelCase__									=							load_tool("translation" ,							remote=__magic_name__							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Tuple							):


				"""simple docstring"""

				lowerCAmelCase__									=							self.tool("Hey, what's up?" ,							src_lang="English" ,							tgt_lang="French"							)
				self.assertEqual(__magic_name__ ,							"- Hé, comment ça va?"							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Optional[int]							):


				"""simple docstring"""

				lowerCAmelCase__									=							self.remote_tool("Hey, what's up?" ,							src_lang="English" ,							tgt_lang="French"							)
				self.assertEqual(__magic_name__ ,							"- Hé, comment ça va?"							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[Any]							):


				"""simple docstring"""

				lowerCAmelCase__									=							self.tool(text="Hey, what's up?" ,							src_lang="English" ,							tgt_lang="French"							)
				self.assertEqual(__magic_name__ ,							"- Hé, comment ça va?"							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    int							):


				"""simple docstring"""

				lowerCAmelCase__									=							self.remote_tool(text="Hey, what's up?" ,							src_lang="English" ,							tgt_lang="French"							)
				self.assertEqual(__magic_name__ ,							"- Hé, comment ça va?"							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    int							):


				"""simple docstring"""

				lowerCAmelCase__									=							["Hey, what's up?", "English", "Spanish"]
				lowerCAmelCase__									=							self.tool(*__magic_name__							)

				# There is a single output
				if len(self.tool.outputs							) == 1:
							lowerCAmelCase__									=							[outputs]

				self.assertListEqual(output_types(__magic_name__							) ,							self.tool.outputs							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    str							):


				"""simple docstring"""

				lowerCAmelCase__									=							["Hey, what's up?", "English", "Spanish"]
				lowerCAmelCase__									=							self.tool(*__magic_name__							)

				if not isinstance(__magic_name__ ,							__magic_name__							):
							lowerCAmelCase__									=							[outputs]

				self.assertEqual(len(__magic_name__							) ,							len(self.tool.outputs							)							)

				for output, output_type in zip(__magic_name__ ,							self.tool.outputs							):
							lowerCAmelCase__									=							AGENT_TYPE_MAPPING[output_type]
							self.assertTrue(isinstance(__magic_name__ ,							__magic_name__							)							)







	def 							__SCREAMING_SNAKE_CASE					(   self     :    int							):


				"""simple docstring"""

				lowerCAmelCase__									=							["Hey, what's up?", "English", "Spanish"]

				lowerCAmelCase__									=							[]

				for _input, input_type in zip(__magic_name__ ,							self.tool.inputs							):
							if isinstance(__magic_name__ ,							__magic_name__							):
										_inputs.append([AGENT_TYPE_MAPPING[_input_type](_input							) for _input_type in input_type]							)
							else:
										_inputs.append(AGENT_TYPE_MAPPING[input_type](_input							)							)

        # Should not raise an error
				lowerCAmelCase__									=							self.tool(*__magic_name__							)

				if not isinstance(__magic_name__ ,							__magic_name__							):
							lowerCAmelCase__									=							[outputs]

				self.assertEqual(len(__magic_name__							) ,							len(self.tool.outputs							)							)





