




import numpy as np
def  snake_case_					(		SCREAMING_SNAKE_CASE_    )      ->			Union[str, Any]:
							lowercase__ ,       lowercase__  :	Union[str, Any]        =							a.shape
							lowercase__  :	str        =							min(SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )
							lowercase__  :	List[Any]        =							np.eye(SCREAMING_SNAKE_CASE_    )
							lowercase__  :	Union[str, Any]        =							a.copy()

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

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

														lowercase__  :	List[str]        =							q @ q_k.T
														lowercase__  :	Optional[int]        =							q_k @ r

							return q, r


if __name__ == "__main__":
						import doctest

						doctest.testmod()





import numpy as np
def  snake_case_					(		SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )      ->			int:
							lowercase__  :	str        =							n_draws * class_counts / class_counts.sum()
							# floored means we don't overshoot n_samples, but probably undershoot
							lowercase__  :	Union[str, Any]        =							np.floor(SCREAMING_SNAKE_CASE_    )
							# we add samples according to how much "left over" probability
							# they had, until we arrive at n_samples
							lowercase__  :	Tuple        =							int(n_draws - floored.sum()    )
							if need_to_add > 0:
														lowercase__  :	Union[str, Any]        =							continuous - floored
														lowercase__  :	Optional[Any]        =							np.sort(np.unique(SCREAMING_SNAKE_CASE_    )    )[::-1]
														# add according to remainder, but break ties
														# randomly to avoid biases
														for value in values:
																					((lowercase__) ,       )  :	Optional[Any]        =							np.where(remainder == value    )
																					# if we need_to_add less than what's in inds
																					# we draw randomly from them.
																					# if we need to add more, we add them all and
																					# go to the next value
																					lowercase__  :	Dict        =							min(len(SCREAMING_SNAKE_CASE_    )    ,SCREAMING_SNAKE_CASE_    )
																					lowercase__  :	Any        =							rng.choice(SCREAMING_SNAKE_CASE_    ,size=SCREAMING_SNAKE_CASE_    ,replace=SCREAMING_SNAKE_CASE_    )
																					floored[inds] += 1
																					need_to_add -= add_now
																					if need_to_add == 0:
																												break
							return floored.astype(np.intaa    )




def  snake_case_					(		SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_=10    )      ->			List[str]:
							lowercase__ ,       lowercase__  :	int        =							np.unique(SCREAMING_SNAKE_CASE_    ,return_inverse=SCREAMING_SNAKE_CASE_    )
							lowercase__  :	int        =							classes.shape[0]
							lowercase__  :	Union[str, Any]        =							np.bincount(SCREAMING_SNAKE_CASE_    )
							if np.min(SCREAMING_SNAKE_CASE_    ) < 2:
														raise ValueError("Minimum class count error"    )
							if n_train < n_classes:
														raise ValueError(
														    "The train_size = %d should be greater or " "equal to the number of classes = %d" % (n_train, n_classes)    )
							if n_test < n_classes:
														raise ValueError(
														    "The test_size = %d should be greater or " "equal to the number of classes = %d" % (n_test, n_classes)    )
							lowercase__  :	List[Any]        =							np.split(np.argsort(SCREAMING_SNAKE_CASE_    ,kind="mergesort"    )    ,np.cumsum(SCREAMING_SNAKE_CASE_    )[:-1]    )
							for _ in range(SCREAMING_SNAKE_CASE_    ):
														lowercase__  :	str        =							approximate_mode(SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )
														lowercase__  :	int        =							class_counts - n_i
														lowercase__  :	int        =							approximate_mode(SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )

														lowercase__  :	Tuple        =							[]
														lowercase__  :	int        =							[]

														for i in range(SCREAMING_SNAKE_CASE_    ):
																					lowercase__  :	Union[str, Any]        =							rng.permutation(class_counts[i]    )
																					lowercase__  :	List[Any]        =							class_indices[i].take(SCREAMING_SNAKE_CASE_    ,mode="clip"    )
																					train.extend(perm_indices_class_i[: n_i[i]]    )
																					test.extend(perm_indices_class_i[n_i[i] : n_i[i] + t_i[i]]    )
														lowercase__  :	Tuple        =							rng.permutation(SCREAMING_SNAKE_CASE_    )
														lowercase__  :	Dict        =							rng.permutation(SCREAMING_SNAKE_CASE_    )

														yield train, test