




'''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()











'''simple docstring'''







def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 9 / 5) + 32						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) + 273.15						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 9 / 5) + 491.67						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) - 32) * 5 / 9						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(((float(lowercase_  ) - 32) * 5 / 9) + 273.15						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) + 459.67						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) - 273.15						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(((float(lowercase_  ) - 273.15) * 9 / 5) + 32						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 9 / 5)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) - 491.67) * 5 / 9						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round(float(lowercase_  ) - 459.67						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 5 / 9)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 1.25 + 273.15)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 2.25 + 32)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 1.25)						,							lowercase_  )






def 		_lowercase		(     lowercase_						,							lowercase_ = 2  ):



		'''simple docstring'''







		return round((float(lowercase_  ) * 2.25 + 32 + 459.67)						,							lowercase_  )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





