



from typing import Any

import numpy as np


def 						UpperCAmelCase__   (   UpperCAmelCase__			:Optional[int]       ):






 '''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.
 a							=		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 						UpperCAmelCase__   (   UpperCAmelCase__			:Union[str, Any]       ):






 '''simple docstring'''

 a							=		np.random.randn(_UpperCAmelCase			,       _UpperCAmelCase       )
 a							=		np.dot(_UpperCAmelCase			,       random_matrix.T       )
 assert _is_matrix_spd(_UpperCAmelCase       )
 return spd_matrix


def 						UpperCAmelCase__   (   UpperCAmelCase__			:Optional[Any]			,       UpperCAmelCase__			:Union[str, Any]			,       UpperCAmelCase__			:Tuple = 10_00			,       UpperCAmelCase__			:int = 1E-8			,       ):






 '''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.
 a							=		np.zeros((np.shape(_UpperCAmelCase       )[0], 1)       )
 a							=		np.copy(_UpperCAmelCase       )
 a							=		np.copy(_UpperCAmelCase       )

 # 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(_UpperCAmelCase			,       _UpperCAmelCase       )

  # The main algorithm.

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

  # Update variables.
  a							=		np.copy(_UpperCAmelCase       )
  a							=		np.copy(_UpperCAmelCase       )
  a							=		np.copy(_UpperCAmelCase       )

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

 return x


def 						UpperCAmelCase__   (   ):






 '''simple docstring'''

 a							=		3
 a							=		_create_spd_matrix(_UpperCAmelCase       )
 a							=		np.random.randn(_UpperCAmelCase			,       1       )
 a							=		np.dot(_UpperCAmelCase			,       _UpperCAmelCase       )

 # Numpy solution.
 a							=		np.linalg.solve(_UpperCAmelCase			,       _UpperCAmelCase       )

 # Our implementation.
 a							=		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 requests
from bsa import BeautifulSoup





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_    :			Optional[int]									=    (
      'https://www.horoscope.com/us/horoscopes/general/'
      f"""horoscope-general-daily-{day}.aspx?sign={zodiac_sign}"""
  )
  A_    :			List[Any]									=    BeautifulSoup(requests.get(_UpperCAmelCase   ).content					,   'html.parser'   )
  return soup.find('div'					,   class_='main-horoscope'   ).p.text


if __name__ == "__main__":
   print('Daily Horoscope. \n')
   print(
       'enter your Zodiac sign number:\n',
       '1. Aries\n',
       '2. Taurus\n',
       '3. Gemini\n',
       '4. Cancer\n',
       '5. Leo\n',
       '6. Virgo\n',
       '7. Libra\n',
       '8. Scorpio\n',
       '9. Sagittarius\n',
       '10. Capricorn\n',
       '11. Aquarius\n',
       '12. Pisces\n',
   )
   lowerCamelCase_	:		Any         =   int(input('number> ').strip())
   print('choose some day:\n', 'yesterday\n', 'today\n', 'tomorrow\n')
   lowerCamelCase_	:		int         =   input('enter the day> ')
   lowerCamelCase_	:		List[Any]         =   horoscope(zodiac_sign, day)
   print(horoscope_text)