randPedPCA (version 1.0.1)

hutchpp: Hutch++ trace estimation

Description

Hutch++ trace estimation

Usage

hutchpp(
  B,
  num_queries = 10,
  sketch_frac = 2/3,
  center = FALSE,
  oraculum = oraculumLi
)

Value

An estimate of A's trace - numeric

Arguments

B

An object related to the matrix A for which the trace is to be estimated

num_queries

Number of random vectors to draw

sketch_frac

Hutch++ detail

center

Whether or not to implicitly centre

oraculum

The oracle function to use

Details

The Hutch++ algorithm (Meyer et al. 2021, https://doi.org/10.48550/arXiv.2010.09649) estimates the trace of a matrix A by evaluating matrix vector products of A and (sub-gaussian) random vectors. This is used on a matrix B which is related to A through some function. The oracle function has to be chosen so that oracle(B, G) returns the product A the oracle function is set to work on a pedigree's L inverse matrix. But this implementation is general and should work - given a custom oracle function - on other input too.

In the context of pedigree PCA, this is used to estimate the trace of an (implicitly) centred additive relationship matrix.

There logical parameter center allows for a pedigree's L matrix to be (implicitly) centred. This is important because centring changes the total variance of the data and thus the trace of A.

Examples

hutchpp(pedLInv)
hutchpp(pedLInv, center=TRUE)