





"""simple docstring"""





from typing import Any

import numpy as np


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						np.ndarray      ):







      '''simple docstring'''




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

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

      # Get eigenvalues and eignevectors for a symmetric matrix.
      lowerCAmelCase						,		lowerCAmelCase  						=	np.linalg.eigh(SCREAMING_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__							(  SCREAMING_SNAKE_CASE					:						int      ):







      '''simple docstring'''




      lowerCAmelCase  						=	np.random.randn(SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE      )
      lowerCAmelCase  						=	np.dot(SCREAMING_SNAKE_CASE							,						random_matrix.T      )
      assert _is_matrix_spd(SCREAMING_SNAKE_CASE      )
      return spd_matrix


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						np.ndarray							,						SCREAMING_SNAKE_CASE					:						np.ndarray							,						SCREAMING_SNAKE_CASE					:						int = 10_00							,						SCREAMING_SNAKE_CASE					:						float = 1e-8							,						):







      '''simple docstring'''




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

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

      # 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(SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE      )

            # The main algorithm.

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

            # Update variables.
            lowerCAmelCase  						=	np.copy(SCREAMING_SNAKE_CASE      )
            lowerCAmelCase  						=	np.copy(SCREAMING_SNAKE_CASE      )
            lowerCAmelCase  						=	np.copy(SCREAMING_SNAKE_CASE      )

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

      return x


def       UpperCAmelCase__							(  ):







      '''simple docstring'''




      lowerCAmelCase  						=	3
      lowerCAmelCase  						=	_create_spd_matrix(SCREAMING_SNAKE_CASE      )
      lowerCAmelCase  						=	np.random.randn(SCREAMING_SNAKE_CASE							,						1      )
      lowerCAmelCase  						=	np.dot(SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE      )

      # Numpy solution.
      lowerCAmelCase  						=	np.linalg.solve(SCREAMING_SNAKE_CASE							,						SCREAMING_SNAKE_CASE      )

      # Our implementation.
      lowerCAmelCase  						=	conjugate_gradient(SCREAMING_SNAKE_CASE							,						SCREAMING_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"""





import unittest
from dataclasses import dataclass
from typing import Optional

from transformers.utils import ModelOutput

@dataclass
class 		lowercase ( _UpperCAmelCase ):
      _SCREAMING_SNAKE_CASE         =				42
      _SCREAMING_SNAKE_CASE         =				None
      _SCREAMING_SNAKE_CASE         =				None







class 		lowercase ( unittest.TestCase ):





      def    _snake_case      (	self			)		->					Optional[Any]:
            lowerCAmelCase  						=	ModelOutputTest(a=30			)
            self.assertEqual(x.a				,						30			)
            self.assertIsNone(x.b			)
            self.assertIsNone(x.c			)
            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	x.d





      def    _snake_case      (	self			)		->					Optional[Any]:
            lowerCAmelCase  						=	ModelOutputTest(a=30				,						b=10			)
            self.assertEqual(x[0]				,						30			)
            self.assertEqual(x[1]				,						10			)
            self.assertEqual(x[:2]				,						(30, 10)			)
            self.assertEqual(x[:]				,						(30, 10)			)

            lowerCAmelCase  						=	ModelOutputTest(a=30				,						c=10			)
            self.assertEqual(x[0]				,						30			)
            self.assertEqual(x[1]				,						10			)
            self.assertEqual(x[:2]				,						(30, 10)			)
            self.assertEqual(x[:]				,						(30, 10)			)





      def    _snake_case      (	self			)		->					Tuple:
            lowerCAmelCase  						=	ModelOutputTest(a=30				,						b=10			)
            self.assertEqual(x["""a"""]				,						30			)
            self.assertEqual(x["""b"""]				,						10			)
            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	x["""c"""]

            lowerCAmelCase  						=	ModelOutputTest(a=30				,						c=10			)
            self.assertEqual(x["""a"""]				,						30			)
            self.assertEqual(x["""c"""]				,						10			)
            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	x["""b"""]





      def    _snake_case      (	self			)		->					Union[str, Any]:
            lowerCAmelCase  						=	ModelOutputTest(a=30			)
            self.assertEqual(list(x.keys()			)				,						["""a"""]			)
            self.assertEqual(list(x.values()			)				,						[30]			)
            self.assertEqual(list(x.items()			)				,						[("""a""", 30)]			)
            self.assertEqual(list(lowercase			)				,						["""a"""]			)

            lowerCAmelCase  						=	ModelOutputTest(a=30				,						b=10			)
            self.assertEqual(list(x.keys()			)				,						["""a""", """b"""]			)
            self.assertEqual(list(x.values()			)				,						[30, 10]			)
            self.assertEqual(list(x.items()			)				,						[("""a""", 30), ("""b""", 10)]			)
            self.assertEqual(list(lowercase			)				,						["""a""", """b"""]			)

            lowerCAmelCase  						=	ModelOutputTest(a=30				,						c=10			)
            self.assertEqual(list(x.keys()			)				,						["""a""", """c"""]			)
            self.assertEqual(list(x.values()			)				,						[30, 10]			)
            self.assertEqual(list(x.items()			)				,						[("""a""", 30), ("""c""", 10)]			)
            self.assertEqual(list(lowercase			)				,						["""a""", """c"""]			)

            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	x.update({"""d""": 20}			)
            with self.assertRaises(lowercase			):
                  del x["a"]
            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	x.pop("""a"""			)
            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	x.setdefault("""d"""				,						32			)





      def    _snake_case      (	self			)		->					Dict:
            lowerCAmelCase  						=	ModelOutputTest(a=30			)
            lowerCAmelCase  						=	10
            self.assertEqual(x.a				,						10			)
            self.assertEqual(x["""a"""]				,						10			)





      def    _snake_case      (	self			)		->					List[str]:
            lowerCAmelCase  						=	ModelOutputTest(a=30			)
            lowerCAmelCase  						=	10
            self.assertEqual(x.a				,						10			)
            self.assertEqual(x["""a"""]				,						10			)





      def    _snake_case      (	self			)		->					str:
            lowerCAmelCase  						=	ModelOutputTest({"""a""": 30, """b""": 10}			)
            self.assertEqual(list(x.keys()			)				,						["""a""", """b"""]			)
            self.assertEqual(x.a				,						30			)
            self.assertEqual(x.b				,						10			)





      def    _snake_case      (	self			)		->					Dict:
            lowerCAmelCase  						=	ModelOutputTest([("""a""", 30), ("""b""", 10)]			)
            self.assertEqual(list(x.keys()			)				,						["""a""", """b"""]			)
            self.assertEqual(x.a				,						30			)
            self.assertEqual(x.b				,						10			)

            with self.assertRaises(lowercase			):
                  lowerCAmelCase  						=	ModelOutputTest([("""a""", 30), (10, 10)]			)

            lowerCAmelCase  						=	ModelOutputTest(a=(30, 30)			)
            self.assertEqual(list(x.keys()			)				,						["""a"""]			)
            self.assertEqual(x.a				,						(30, 30)			)






