"""simple docstring"""




from typing import Any

import numpy as np






def 	UpperCAmelCase       (						UpperCamelCase__					):






							"""simple docstring"""





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

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

							# Get eigenvalues and eignevectors for a symmetric matrix.
							A__						  =				np.linalg.eigh(__lowerCamelCase					)

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






def 	UpperCAmelCase       (						UpperCamelCase__					):






							"""simple docstring"""





							A__						  =				np.random.randn(__lowerCamelCase							,     __lowerCamelCase					)
							A__						  =				np.dot(__lowerCamelCase							,     random_matrix.T					)
							assert _is_matrix_spd(__lowerCamelCase					)
							return spd_matrix






def 	UpperCAmelCase       (						UpperCamelCase__							,     UpperCamelCase__							,     UpperCamelCase__ = 1_000							,     UpperCamelCase__ = 1E-8							,     ):






							"""simple docstring"""





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

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

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

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

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

														# The main algorithm.

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

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

														# Update variables.
														A__						  =				np.copy(__lowerCamelCase					)
														A__						  =				np.copy(__lowerCamelCase					)
														A__						  =				np.copy(__lowerCamelCase					)

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

							return x






def 	UpperCAmelCase       (						):






							"""simple docstring"""





							A__						  =				3
							A__						  =				_create_spd_matrix(__lowerCamelCase					)
							A__						  =				np.random.randn(__lowerCamelCase							,     1					)
							A__						  =				np.dot(__lowerCamelCase							,     __lowerCamelCase					)

							# Numpy solution.
							A__						  =				np.linalg.solve(__lowerCamelCase							,     __lowerCamelCase					)

							# Our implementation.
							A__						  =				conjugate_gradient(__lowerCamelCase							,     __lowerCamelCase					)

							# 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 os






def  _UpperCAmelCase						( )		->Tuple:


 '''simple docstring'''
 snake_case :			Dict							=   0
 snake_case :			int							=   0
 with open(os.path.dirname(__lowerCamelCase							) + '''/p022_names.txt'''							) as file:
  snake_case :			int							=   str(file.readlines()[0]							)
  snake_case :			Any							=   name.replace('''"'''			,  ''''''							).split(''','''							)

 name.sort()
 for i in range(len(__lowerCamelCase							)							):
  for j in name[i]:
   temp_sum += ord(__lowerCamelCase							) - ord('''A'''							) + 1
  total_sum += (i + 1) * temp_sum
  snake_case :			List[Any]							=   0
 return total_sum


if __name__ == "__main__":
  print(solution())






