





'''simple docstring'''

from typing import Any

import numpy as np





def lowerCamelCase						(					__lowerCamelCase			:   np.ndarray   )						->bool:
    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.
    _SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE     =      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 lowerCamelCase						(					__lowerCamelCase			:   int   )						->Any:
    _SCREAMING_SNAKE_CASE     =      np.random.randn(__lowerCamelCase ,	__lowerCamelCase   )
    _SCREAMING_SNAKE_CASE     =      np.dot(__lowerCamelCase ,	random_matrix.T   )
    assert _is_matrix_spd(__lowerCamelCase   )
    return spd_matrix





def lowerCamelCase						(					__lowerCamelCase			:   np.ndarray ,	__lowerCamelCase			:   np.ndarray ,	__lowerCamelCase			:   int = 1000 ,	__lowerCamelCase			:   float = 1e-8 ,	)						->Any:
    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.
    _SCREAMING_SNAKE_CASE     =      np.zeros((np.shape(__lowerCamelCase   )[0], 1)   )
    _SCREAMING_SNAKE_CASE     =      np.copy(__lowerCamelCase   )
    _SCREAMING_SNAKE_CASE     =      np.copy(__lowerCamelCase   )

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

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

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

        # The main algorithm.

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

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

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

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

    return x





def lowerCamelCase						(					)						->None:
    _SCREAMING_SNAKE_CASE     =      3
    _SCREAMING_SNAKE_CASE     =      _create_spd_matrix(__lowerCamelCase   )
    _SCREAMING_SNAKE_CASE     =      np.random.randn(__lowerCamelCase ,	1   )
    _SCREAMING_SNAKE_CASE     =      np.dot(__lowerCamelCase ,	__lowerCamelCase   )

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

    # Our implementation.
    _SCREAMING_SNAKE_CASE     =      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()










'''simple docstring'''

def lowerCamelCase						(					__lowerCamelCase			:   int   )						->int:
    barcode //= 10  # exclude the last digit
    _SCREAMING_SNAKE_CASE     =      False
    _SCREAMING_SNAKE_CASE     =      0

    # extract and check each digit
    while barcode != 0:
        _SCREAMING_SNAKE_CASE     =      1 if checker else 3
        s += mult * (barcode % 10)
        barcode //= 10
        _SCREAMING_SNAKE_CASE     =      not checker

    return (10 - (s % 10)) % 10





def lowerCamelCase						(					__lowerCamelCase			:   int   )						->bool:
    return len(str(__lowerCamelCase   )   ) == 13 and get_check_digit(__lowerCamelCase   ) == barcode % 10





def lowerCamelCase						(					__lowerCamelCase			:   str   )						->int:
    if str(__lowerCamelCase   ).isalpha():
        _SCREAMING_SNAKE_CASE     =      F'Barcode \'{barcode}\' has alphabetic characters.'
        raise ValueError(__lowerCamelCase   )
    elif int(__lowerCamelCase   ) < 0:
        raise ValueError("""The entered barcode has a negative value. Try again."""   )
    else:
        return int(__lowerCamelCase   )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      lowercase_         =			get_barcode(input("""Barcode: """).strip())

      if is_valid(barcode):
            print(f"""'{barcode}' is a valid barcode.""")
      else:
            print(f"""'{barcode}' is NOT a valid barcode.""")



