


"""simple docstring"""







from typing import Any

import numpy as np
def _A		(		lowercase						):







    """simple docstring"""
    assert np.shape(lowercase						)[0] == np.shape(lowercase						)[1]

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

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

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







    """simple docstring"""
    a											=np.random.randn(lowercase			,       lowercase						)
    a											=np.dot(lowercase			,       random_matrix.T						)
    assert _is_matrix_spd(lowercase						)
    return spd_matrix
def _A		(		lowercase			,       lowercase			,       lowercase = 10_00			,       lowercase = 1E-8			,       ):







    """simple docstring"""
    assert np.shape(lowercase						)[0] == np.shape(lowercase						)[1]
    assert np.shape(lowercase						)[0] == np.shape(lowercase						)[0]
    assert _is_matrix_spd(lowercase						)

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

    # 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(lowercase			,       lowercase						)

        # The main algorithm.

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

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

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

    return x
def _A		(		):







    """simple docstring"""
    a											=3
    a											=_create_spd_matrix(lowercase						)
    a											=np.random.randn(lowercase			,       1						)
    a											=np.dot(lowercase			,       lowercase						)

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

    # Our implementation.
    a											=conjugate_gradient(lowercase			,       lowercase						)

    # 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"""







from __future__ import annotations

import random
import string






class  __A							:






 """simple docstring"""




 def __init__(						self					,       __A = None		)   ->	None:
     a											=passcode or self.__passcode_creator()
     a											=self.__make_key_list()
     a											=self.__make_shift_key()


 def __str__(						self		)   ->	str:
     return "".join(self.__passcode		)


 def  SCREAMING_SNAKE_CASE				(						self					,       __A		)   ->	list[int]:
     for i in range(1					,       len(__A		)					,       2		):
         iterlist[i] *= -1
     return iterlist


 def  SCREAMING_SNAKE_CASE				(						self		)   ->	list[str]:
     a											=string.ascii_letters + string.digits
     a											=[random.choice(__A		) for _ in range(random.randint(10					,       20		)		)]
     return password


 def  SCREAMING_SNAKE_CASE				(						self		)   ->	list[str]:
     a											=(
         string.ascii_letters + string.digits + string.punctuation + ''' \t\n'''
     )

     a											=[]

     # creates points known as breakpoints to break the key_list_options at those
     # points and pivot each substring
     a											=sorted(set(self.__passcode		)		)
     a											=[]

     # algorithm for creating a new shuffled list, keys_l, out of key_list_options
     for i in key_list_options:
         temp_list.extend(__A		)

         # checking breakpoints at which to pivot temporary sublist and add it into
         # keys_l
         if i in breakpoints or i == key_list_options[-1]:
             keys_l.extend(temp_list[::-1]		)
             temp_list.clear()

        # returning a shuffled keys_l to prevent brute force guessing of shift key
     return keys_l


 def  SCREAMING_SNAKE_CASE				(						self		)   ->	int:
     a											=sum(self.__neg_pos([ord(__A		) for x in self.__passcode]		)		)
     return num if num > 0 else len(self.__passcode		)


 def  SCREAMING_SNAKE_CASE				(						self					,       __A		)   ->	str:
     a											=''''''

     # decoding shift like Caesar cipher algorithm implementing negative shift or
     # reverse shift or left shift
     for i in encoded_message:
         a											=self.__key_list.index(__A		)
         decoded_message += self.__key_list[
             (position - self.__shift_key) % -len(self.__key_list		)
         ]

     return decoded_message





 def  SCREAMING_SNAKE_CASE				(						self					,       __A		)   ->	str:
     a											=''''''

     # encoding shift like Caesar cipher algorithm implementing positive shift or
     # forward shift or right shift
     for i in plaintext:
         a											=self.__key_list.index(__A		)
         encoded_message += self.__key_list[
             (position + self.__shift_key) % len(self.__key_list		)
         ]

     return encoded_message

def _A		(		lowercase = "Hello, this is a modified Caesar cipher"						):







    """simple docstring"""
    a											=ShuffledShiftCipher()
    return cipa.decrypt(cipa.encrypt(lowercase						)						)


if __name__ == "__main__":
       import doctest

       doctest.testmod()