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Select n_samples integers from the set [0, n_population) without replacement. Parameters ---------- n_population : int The size of the set to sample from. n_samples : int The number of integer to sample. random_state : int, RandomState instance or None, default=None If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. method : {"auto", "tracking_selection", "reservoir_sampling", "pool"}, default='auto' If method == "auto", the ratio of n_samples / n_population is used to determine which algorithm to use: If ratio is between 0 and 0.01, tracking selection is used. If ratio is between 0.01 and 0.99, numpy.random.permutation is used. If ratio is greater than 0.99, reservoir sampling is used. The order of the selected integers is undefined. If a random order is desired, the selected subset should be shuffled. If method =="tracking_selection", a set based implementation is used which is suitable for `n_samples` <<< `n_population`. If method == "reservoir_sampling", a reservoir sampling algorithm is used which is suitable for high memory constraint or when O(`n_samples`) ~ O(`n_population`). The order of the selected integers is undefined. If a random order is desired, the selected subset should be shuffled. If method == "pool", a pool based algorithm is particularly fast, even faster than the tracking selection method. However, a vector containing the entire population has to be initialized. If n_samples ~ n_population, the reservoir sampling method is faster. Returns ------- out : ndarray of shape (n_samples,) The sampled subsets of integer. The subset of selected integer might not be randomized, see the method argument. Examples -------- >>> from sklearn.utils.random import sample_without_replacement >>> sample_without_replacement(10, 5, random_state=42) array([8, 1, 5, 0, 7]) Sample integers without replacement. Select n_samples integers from the set [0, n_population) without replacement. Time complexity of O((n_population - n_samples) * O(np.random.randint) + n_samples) Space complexity of O(n_samples) Parameters ---------- n_population : int The size of the set to sample from. n_samples : int The number of integer to sample. random_state : int, RandomState instance or None, default=None If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Returns ------- out : ndarray of shape (n_samples,) The sampled subsets of integer. The order of the items is not necessarily random. Use a random permutation of the array if the order of the items has to be randomized. Sample integers without replacement. Select n_samples integers from the set [0, n_population) without replacement. Time complexity: O(n_population + O(np.random.randint) * n_samples) Space complexity of O(n_population + n_samples). Parameters ---------- n_population : int The size of the set to sample from. n_samples : int The number of integer to sample. random_state : int, RandomState instance or None, default=None If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Returns ------- out : ndarray of shape (n_samples,) The sampled subsets of integer. Sample integers without replacement. Select n_samples integers from the set [0, n_population) without replacement. Time complexity: - Worst-case: unbounded - Average-case: O(O(np.random.randint) * \sum_{i=1}^n_samples 1 / (1 - i / n_population))) <= O(O(np.random.randint) * n_population * ln((n_population - 2) /(n_population - 1 - n_samples))) <= O(O(np.random.randint) * n_population * 1 / (1 - n_samples / n_population)) Space complexity of O(n_samples) in a python set. Parameters ---------- n_population : int The size of the set to sample from. n_samples : int The number of integer to sample. random_state : int, RandomState instance or None, default=None If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Returns ------- out : ndarray of shape (n_samples,) The sampled subsets of integer. Check that input are consistent for sample_without_replacement Random utility function ======================= This module complements missing features of ``numpy.random``. 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