fastQR (version 1.1.4)

qr_lse_Qy: Compute Qy for a least-squares problem

Description

Computes the product \(Q y\), where \(Q\) is the orthogonal matrix from the QR decomposition of the design matrix \(X\).

Usage

qr_lse_Qy(X, y)

Value

a numeric vector equal to \(Q y\).

Arguments

X

numeric matrix of dimension \(n \times p\).

y

numeric response vector of length \(n\).

Details

The QR decomposition of \(X\) is computed internally, and the orthogonal matrix \(Q\) is never formed explicitly. The product \(Q y\) is evaluated efficiently using Householder reflectors.

This function is intended as a convenience wrapper for least-squares computations when the explicit QR factors are not required.

Examples

set.seed(1)
n <- 10; p <- 4
X <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)

res1 <- fastQR::qr_lse_Qy(X, y)

## reference computation
res2 <- base::qr.Q(base::qr(X), complete = TRUE) %*% y

max(abs(res1 - drop(res2)))