qrSVD: Wrapper for `svd`, which uses random preconditioning to restart when svd fails to converge

Description

In order to generate the SVD of the matrix x, qrSVD calls genQ to generate a random orthonormal matrix, and uses this random matrix to precondition x. The svd of the preconditioned matrix is calculated, and adjusted to account for the preconditioning process in order to find svd(x).

Usage

qrSVD(x, lim_attempts = 50, warning_type = "silent",
  warning_file = "qrSVD_warnings.txt", ...)

Value

Solves $s v d (x) = U D V^{'}$ , where $U$ is an matrix containing the left singular vectors of $x$ , $D$ is a diagonal matrix containing the singular values of $x$ ; and $V$ is a matrix containing the right singular vectors of $x$ (output follows the same notation convention as the svd function).

qrSVD will attempt the standard svd function before preconditioning the matrix $x$ .

Arguments

x: a matrix to calculate the svd for
lim_attempts: the number of tries to randomly precondition x. We generally find that one preconditioning attempt is sufficient.
warning_type: controls whether the user should be told if an orthogonal preconditioning matrix is required, or if svd gives warnings. 'silent' ignores these warnings, 'print' prints the warning to the console, and 'file' saves the warnings in a text file.
warning_file: gives the location of a file to print warnings to, if warning_type is set to 'file'.
...: parameters passed to svd, such as nv and nu.

Examples

Run this code

x <-matrix(rnorm(3*5),nrow=3,ncol=5)
svdx <- qrSVD(x)
svdx

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