

from typing import Any

import numpy as np
def 						UpperCamelCase_(			snake_case__:  np.ndarray   )       -> 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.
 UpperCAmelCase__				,    UpperCAmelCase__							=				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 						UpperCamelCase_(			snake_case__:  int   )       -> Any:
 UpperCAmelCase__							=				np.random.randn(snake_case__  ,    snake_case__   )
 UpperCAmelCase__							=				np.dot(snake_case__  ,    random_matrix.T   )
 assert _is_matrix_spd(snake_case__   )
 return spd_matrix
def 						UpperCamelCase_(			snake_case__:  np.ndarray  ,    snake_case__:  np.ndarray  ,    snake_case__:  int = 10_00  ,    snake_case__:  float = 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.
 UpperCAmelCase__							=				np.zeros((np.shape(snake_case__   )[0], 1)   )
 UpperCAmelCase__							=				np.copy(snake_case__   )
 UpperCAmelCase__							=				np.copy(snake_case__   )

 # Set initial errors in solution guess and residual.
 UpperCAmelCase__							=				1e9
 UpperCAmelCase__							=				1e9
 UpperCAmelCase__							=				1e9

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

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

  # The main algorithm.

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

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

  # Update variables.
  UpperCAmelCase__							=				np.copy(snake_case__   )
  UpperCAmelCase__							=				np.copy(snake_case__   )
  UpperCAmelCase__							=				np.copy(snake_case__   )

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

 return x
def 						UpperCamelCase_(			)       -> None:
 UpperCAmelCase__							=				3
 UpperCAmelCase__							=				_create_spd_matrix(snake_case__   )
 UpperCAmelCase__							=				np.random.randn(snake_case__  ,    1   )
 UpperCAmelCase__							=				np.dot(snake_case__  ,    snake_case__   )

 # Numpy solution.
 UpperCAmelCase__							=				np.linalg.solve(snake_case__  ,    snake_case__   )

 # Our implementation.
 UpperCAmelCase__							=				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()






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     lowercase						(       unittest.TestCase ,				_UpperCamelCase					):



 '''simple docstring'''


 def   UpperCamelCase__							(self ) ->					List[Any]:






  """simple docstring"""





  UpperCAmelCase__							=				load_tool('translation' )
  self.tool.setup()
  UpperCAmelCase__							=				load_tool('translation'       ,       remote=__a )




 def   UpperCamelCase__							(self ) ->					Optional[int]:






  """simple docstring"""





  UpperCAmelCase__							=				self.tool('Hey, what\'s up?'       ,       src_lang='English'       ,       tgt_lang='French' )
  self.assertEqual(__a       ,       '- Hé, comment ça va?' )




 def   UpperCamelCase__							(self ) ->					Any:






  """simple docstring"""





  UpperCAmelCase__							=				self.remote_tool('Hey, what\'s up?'       ,       src_lang='English'       ,       tgt_lang='French' )
  self.assertEqual(__a       ,       '- Hé, comment ça va?' )




 def   UpperCamelCase__							(self ) ->					Optional[int]:






  """simple docstring"""





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




 def   UpperCamelCase__							(self ) ->					Optional[Any]:






  """simple docstring"""





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




 def   UpperCamelCase__							(self ) ->					Any:






  """simple docstring"""





  UpperCAmelCase__							=				['Hey, what\'s up?', 'English', 'Spanish']
  UpperCAmelCase__							=				self.tool(*__a )

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

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




 def   UpperCamelCase__							(self ) ->					Optional[int]:






  """simple docstring"""





  UpperCAmelCase__							=				['Hey, what\'s up?', 'English', 'Spanish']
  UpperCAmelCase__							=				self.tool(*__a )

  if not isinstance(__a       ,       __a ):
   UpperCAmelCase__							=				[outputs]

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

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




 def   UpperCamelCase__							(self ) ->					Dict:






  """simple docstring"""





  UpperCAmelCase__							=				['Hey, what\'s up?', 'English', 'Spanish']

  UpperCAmelCase__							=				[]

  for _input, input_type in zip(__a       ,       self.tool.inputs ):
   if isinstance(__a       ,       __a ):
    _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
  UpperCAmelCase__							=				self.tool(*__a )

  if not isinstance(__a       ,       __a ):
   UpperCAmelCase__							=				[outputs]

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



