

def       __a       (   SCREAMING_SNAKE_CASE      )      ->     int:






    '''simple docstring'''
    __UpperCAmelCase									=			0
    for plain_chr in plain_text:
        __UpperCAmelCase									=			(
            ord(SCREAMING_SNAKE_CASE      ) + (hash_value << 6) + (hash_value << 1_6) - hash_value
        )
    return hash_value






import numpy as np


def       __a       (   SCREAMING_SNAKE_CASE      )      ->     Tuple:






    '''simple docstring'''
    __UpperCAmelCase					,     __UpperCAmelCase									=			a.shape
    __UpperCAmelCase									=			min(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
    __UpperCAmelCase									=			np.eye(SCREAMING_SNAKE_CASE      )
    __UpperCAmelCase									=			a.copy()

    for k in range(t - 1      ):
        # select a column of modified matrix A':
        __UpperCAmelCase									=			r[k:, [k]]
        # construct first basis vector
        __UpperCAmelCase									=			np.zeros_like(SCREAMING_SNAKE_CASE      )
        __UpperCAmelCase									=			1.0
        # determine scaling factor
        __UpperCAmelCase									=			np.linalg.norm(SCREAMING_SNAKE_CASE      )
        # construct vector v for Householder reflection
        __UpperCAmelCase									=			x + np.sign(x[0]      ) * alpha * ea
        v /= np.linalg.norm(SCREAMING_SNAKE_CASE      )

        # construct the Householder matrix
        __UpperCAmelCase									=			np.eye(m - k      ) - 2.0 * v @ v.T
        # pad with ones and zeros as necessary
        __UpperCAmelCase									=			np.block([[np.eye(SCREAMING_SNAKE_CASE      ), np.zeros((k, m - k)      )], [np.zeros((m - k, k)      ), q_k]]      )

        __UpperCAmelCase									=			q @ q_k.T
        __UpperCAmelCase									=			q_k @ r

    return q, r


if __name__ == "__main__":
       import doctest

       doctest.testmod()




