/scikit-learn

# sklearn.utils.extmath.randomized_range_finder

`sklearn.utils.extmath.randomized_range_finder(A, size, n_iter, power_iteration_normalizer=’auto’, random_state=None)` [source]

Computes an orthonormal matrix whose range approximates the range of A.

Parameters: `A : 2D array` The input data matrix `size : integer` Size of the return array `n_iter : integer` Number of power iterations used to stabilize the result `power_iteration_normalizer : ‘auto’ (default), ‘QR’, ‘LU’, ‘none’` Whether the power iterations are normalized with step-by-step QR factorization (the slowest but most accurate), ‘none’ (the fastest but numerically unstable when `n_iter` is large, e.g. typically 5 or larger), or ‘LU’ factorization (numerically stable but can lose slightly in accuracy). The ‘auto’ mode applies no normalization if `n_iter` <= 2 and switches to LU otherwise. New in version 0.18. `random_state : int, RandomState instance or None, optional (default=None)` The seed of the pseudo random number generator to use when shuffling the data. 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`. `Q : 2D array` A (size x size) projection matrix, the range of which approximates well the range of the input matrix A.

#### Notes

Follows Algorithm 4.3 of Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions Halko, et al., 2009 (arXiv:909) http://arxiv.org/pdf/0909.4061

An implementation of a randomized algorithm for principal component analysis A. Szlam et al. 2014