


def 			__lowerCAmelCase       (SCREAMING_SNAKE_CASE   )->    Optional[int]:




      """simple docstring"""

      snake_case_			= snake_case_			= 0
      for letter in data:
            snake_case_			= (hash_ << 4) + ord(lowercase_   )
            snake_case_			= hash_ & 0XF000_0000
            if x != 0:
                  hash_ ^= x >> 24
            hash_ &= ~x
      return hash_


if __name__ == "__main__":
   import doctest

   doctest.testmod()





'''simple docstring'''







import numpy as np






def 						_lowercase						(      lowercase_    ):



		'''simple docstring'''







		_snake_case			,       _snake_case      			=			a.shape
		_snake_case      			=			min(lowercase_		,				lowercase_    )
		_snake_case      			=			np.eye(lowercase_    )
		_snake_case      			=			a.copy()

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

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

				_snake_case      			=			q @ q_k.T
				_snake_case      			=			q_k @ r

		return q, r


if __name__ == "__main__":
						import doctest

						doctest.testmod()





