





import numpy as np






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							List[Any]			):
		SCREAMING_SNAKE_CASE__		,  SCREAMING_SNAKE_CASE__								=					a.shape
		SCREAMING_SNAKE_CASE__								=					min(UpperCamelCase__    ,      UpperCamelCase__			)
		SCREAMING_SNAKE_CASE__								=					np.eye(UpperCamelCase__			)
		SCREAMING_SNAKE_CASE__								=					a.copy()

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

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

				SCREAMING_SNAKE_CASE__								=					q @ q_k.T
				SCREAMING_SNAKE_CASE__								=					q_k @ r

		return q, r


if __name__ == "__main__":
	import doctest

	doctest.testmod()






import unittest

from transformers import is_torch_available, load_tool

from .test_tools_common import ToolTesterMixin


if is_torch_available():
	import torch




class      UpperCamelCase_				(   unittest.TestCase ,     UpperCamelCase__			):


							def    _snake_case     (							self			:Dict						)      ->      Union[str, Any]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=					load_tool("""speech-to-text"""						)
									self.tool.setup()


							def    _snake_case     (							self			:str						)      ->      Union[str, Any]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=					self.tool(torch.ones(3000						)						)
									self.assertEqual(__A							, """ you"""						)


							def    _snake_case     (							self			:Union[str, Any]						)      ->      Union[str, Any]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=					self.tool(audio=torch.ones(3000						)						)
									self.assertEqual(__A							, """ you"""						)