Skip to contents

Stochastic diagonal estimation

Source: R/trace.R
diag_est.Rd

Estimates the diagonal of a matrix that is available only through products \(A X\), using the XDiag estimator, which applies the same low-rank-plus-correction and leave-one-out ideas as trace_est().

Usage

diag_est(A, m, n = NULL, adjoint = NULL)

Arguments

A

A square matrix, a function computing \(A X\) for a matrix \(X\), or a lazy kernel from kernel_matrix().

m

Number of matrix-vector products to spend.

n

Dimension of \(A\). Required only when A is a function.

adjoint

For a non-symmetric A given as a function, a function computing \(A^\top X\). When omitted, A is assumed symmetric.

Value

A numeric vector of length \(n\).

References

Epperly, E. N., Tropp, J. A. & Webber, R. J. (2024) XTrace: making the most of every sample in stochastic trace estimation. SIAM Journal on Matrix Analysis and Applications 45, 1-23. doi:10.1137/23m1548323

See also

trace_est()

Examples

set.seed(1)
U <- qr.Q(qr(matrix(rnorm(200 * 200), 200)))
A <- U %*% diag((1:200)^-1.5) %*% t(U)
est <- diag_est(A, m = 60)
cor(est, diag(A))
#> [1] 0.996457