Function compression_matrix

dask/array/linalg.py:655–743

Randomly sample matrix to find most active subspace This compression matrix returned by this algorithm can be used to compute both the QR decomposition and the Singular Value Decomposition. Parameters ---------- data: Array q: int Size of the desired subspace (t

(
    data,
    q,
    iterator="power",
    n_power_iter=0,
    n_oversamples=10,
    seed=None,
    compute=False,
)

def compression_matrix(
    data,
    q,
    iterator="power",
    n_power_iter=0,
    n_oversamples=10,
    seed=None,
    compute=False,
):
    """Randomly sample matrix to find most active subspace

    This compression matrix returned by this algorithm can be used to
    compute both the QR decomposition and the Singular Value
    Decomposition.

    Parameters
    ----------
    data: Array
    q: int
        Size of the desired subspace (the actual size will be bigger,
        because of oversampling, see ``da.linalg.compression_level``)
    iterator: {'power', 'QR'}, default='power'
        Define the technique used for iterations to cope with flat
        singular spectra or when the input matrix is very large.
    n_power_iter: int
        Number of power iterations, useful when the singular values
        decay slowly. Error decreases exponentially as `n_power_iter`
        increases. In practice, set `n_power_iter` <= 4.
    n_oversamples: int, default=10
        Number of oversamples used for generating the sampling matrix.
        This value increases the size of the subspace computed, which is more
        accurate at the cost of efficiency.  Results are rarely sensitive to this choice
        though and in practice a value of 10 is very commonly high enough.
    compute : bool
        Whether or not to compute data at each use.
        Recomputing the input while performing several passes reduces memory
        pressure, but means that we have to compute the input multiple times.
        This is a good choice if the data is larger than memory and cheap to
        recreate.

    References
    ----------
    N. Halko, P. G. Martinsson, and J. A. Tropp.
    Finding structure with randomness: Probabilistic algorithms for
    constructing approximate matrix decompositions.
    SIAM Rev., Survey and Review section, Vol. 53, num. 2,
    pp. 217-288, June 2011
    https://arxiv.org/abs/0909.4061
    """
    if iterator not in ["power", "QR"]:
        raise ValueError(
            f"Iterator '{iterator}' not valid, must one one of ['power', 'QR']"
        )
    m, n = data.shape
    comp_level = compression_level(min(m, n), q, n_oversamples=n_oversamples)
    if isinstance(seed, RandomState):
        state = seed
    else: