Calculate svds

Use the C++ Spectra solver (same as RSpectra package), in order to compute the largest k values and corresponding singular vectors. Empirically, memory usage is much lower than using irlba::irlba(), likely due to avoiding R garbage creation while solving due to the pure-C++ solver. This documentation is a slightly-edited version of the RSpectra::svds() documentation.

Usage

svds(A, k, nu = k, nv = k, opts = list(), threads=0L, ...)

Arguments

A

The matrix whose truncated SVD is to be computed.

k

Number of singular values requested.

nu

Number of right singular vectors to be computed. This must be between 0 and 'k'. (Must be equal to 'k' for BPCells IterableMatrix)

opts

Control parameters related to computing algorithm. See Details below

threads

Control threads to use calculating mat-vec producs (BPCells specific)

Value

A list with the following components:

d

A vector of the computed singular values.

u

An m by nu matrix whose columns contain the left singular vectors. If nu == 0, NULL will be returned.

v

An n by nv matrix whose columns contain the right singular vectors. If nv == 0, NULL will be returned.

nconv

Number of converged singular values.

niter

Number of iterations used.

nops

Number of matrix-vector multiplications used.

Details

When RSpectra is installed, this function will just add a method to RSpectra::svds() for the IterableMatrix class.

The opts argument is a list that can supply any of the following parameters:

ncv

Number of Lanzcos basis vectors to use. More vectors will result in faster convergence, but with greater memory use. ncv must be satisfy \(k < ncv \le p\) where p = min(m, n). Default is min(p, max(2*k+1, 20)).

tol

Precision parameter. Default is 1e-10.

maxitr

Maximum number of iterations. Default is 1000.

center

Either a logical value (TRUE/FALSE), or a numeric vector of length \(n\). If a vector \(c\) is supplied, then SVD is computed on the matrix \(A - 1c'\), in an implicit way without actually forming this matrix. center = TRUE has the same effect as center = colMeans(A). Default is FALSE. Ignored in BPCells

scale

Either a logical value (TRUE/FALSE), or a numeric vector of length \(n\). If a vector \(s\) is supplied, then SVD is computed on the matrix \((A - 1c')S\), where \(c\) is the centering vector and \(S = diag(1/s)\). If scale = TRUE, then the vector \(s\) is computed as the column norm of \(A - 1c'\). Default is FALSE. Ignored in BPCells

References

Qiu Y, Mei J (2022). RSpectra: Solvers for Large-Scale Eigenvalue and SVD Problems. R package version 0.16-1, https://CRAN.R-project.org/package=RSpectra.