

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 = 1_0_0_0   ,					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()







import requests
from bsa import BeautifulSoup







def a_		(       UpperCamelCase_   :							int   ,					UpperCamelCase_   :							str  )							->   str:







 """simple docstring"""

 lowerCamelCase      						=    (
     'https://www.horoscope.com/us/horoscopes/general/'
     f'''horoscope-general-daily-{day}.aspx?sign={zodiac_sign}'''
 )
 lowerCamelCase      						=    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 :	Dict     				=    int(input('number> ').strip())
     print('choose some day:\n', 'yesterday\n', 'today\n', 'tomorrow\n')
     _lowerCAmelCase :	Optional[Any]     				=    input('enter the day> ')
     _lowerCAmelCase :	int     				=    horoscope(zodiac_sign, day)
     print(horoscope_text)




