vp.randla.rp_cholesky

Randomly pivoted Cholesky: F with A ~ F F^T.

Part of the distribution vipyr; it runs from a checkout of the repository. Planned on PyPI as pip install vipyr.

Signature

vp.randla.rp_cholesky(A, k, seed)

Parameters

A : ndarray[float64], required

k : int, required

seed : int, required

Returns

A frozen RpCholeskyResult. Iterating it gives the fields below in order; it also has params, tests, log and check().

F : ndarray[float64]

The n by k factor, with A approximately F F^T.

Raises

TypeError

An argument of the wrong type, or an unknown keyword.

vipyr.VivBuildError

An ImportError: no C compiler, or the program's C does not build.

Examples

import numpy as np
import vipyr as vp
x = np.linspace(0.0, 1.0, 300)
K = np.exp(-0.5 * (x[:, None] - x[None, :]) ** 2 / 0.05**2)
r = vp.randla.rp_cholesky(A=K, k=40, seed=7)
print(np.trace(K) - np.sum(r.F * r.F))   # the trace error
assert r.check()

5.254628842976672e-05

Each example ran as written when these pages were generated, and the output shown is what it printed.

Checked against

Reference

lib/randla/check_ref.py: on a Gaussian kernel of 500 points (bandwidth 0.05), the trace error tr(A - F F^T) at k = 40 is below the best rank-20 approximation's.

Source

• Viv: lib/randla/api.viv
• The defs it reaches and the calls between them: map of the code