lqr

• Version: 0.1-0
• Status:
• License:
• Author: Drew Schmidt

A streamlined interface for carefully optimized, high-performance access to the QR and LQ orthogonal factorizations. L and R are lower and upper triangular matrices respectively, and Q is an orthogonal matrix.

You can read more about the QR factorization here and the LQ factorization here.

Installation

The development version is maintained on GitHub, and can easily be installed by any of the packages that offer installations from GitHub:

### Pick your preference
devtools::install_github("wrathematics/lqr")
ghit::install_github("wrathematics/lqr")
remotes::install_github("wrathematics/lqr")

Example Usage

You can compute Q and/or R via QR() and L and/or Q via LQ(). If m>>n then you should use QR and for m<<n use LQ. For example:

library(lqr)
m <- 3
n <- 10
x <- matrix(rnorm(m*n), m, n)

lq <- LQ(x)
## List of 2
##  $ Q: num [1:3, 1:10] -0.3805 -0.3031 -0.0648 0.0017 -0.2542 ...
##  $ L: num [1:3, 1:3] 3.5771 0.2538 0.0454 0 2.5589 ...

all.equal(lq$L %*% lq$Q, x)
## [1] TRUE

Benchmarks

library(lqr)
library(rbenchmark)

rqr <- function(x)
{
  tmp <- qr(x, LAPACK=TRUE)
  list(Q=qr.Q(tmp), R=qr.R(tmp))
}

cols <- cols <- c("test", "replications", "elapsed", "relative")
reps <- 25

m = 5000
n = 1000
x = matrix(rnorm(m*n), m, n)

benchmark(QR(x), rqr(x), replications=reps, columns=cols)
##     test replications elapsed relative
## 1  QR(x)           25  15.135    1.000
## 2 rqr(x)           25  53.302    3.522

OpenBLAS with 4 threads on a 4 core 2nd generation Intel Core i5 were used for this benchmark.

Several other benchmarks can be found in the inst/benchmarks/ subdirectory of the source tree for the package. The above was based on the benchmark found in the file qr.r, but with a larger problem size. The supplied benchmarks are small and should complete reasonably quickly. However, the performance of lqr scales up somewhat (relative to base R) as problem sizes grow.