

"""simple docstring"""




import numpy as np
def    __SCREAMING_SNAKE_CASE						(						lowercase__      ):
					"""simple docstring"""
					A			,    A			=					a.shape
					A			=					min(UpperCamelCase__			,							UpperCamelCase__      )
					A			=					np.eye(UpperCamelCase__      )
					A			=					a.copy()

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

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

										A			=					q @ q_k.T
										A			=					q_k @ r

					return q, r


if __name__ == "__main__":
	import doctest

	doctest.testmod()












def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							str			):
		SCREAMING_SNAKE_CASE__								=					SCREAMING_SNAKE_CASE__								=					0
		for letter in data:
				SCREAMING_SNAKE_CASE__								=					(hash_ << 4) + ord(UpperCamelCase__			)
				SCREAMING_SNAKE_CASE__								=					hash_ & 0XF_0_0_0_0_0_0_0
				if x != 0:
						hash_ ^= x >> 24
				hash_ &= ~x
		return hash_


if __name__ == "__main__":
	import doctest

	doctest.testmod()