Science Score: 26.0%
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○Scientific vocabulary similarity
Low similarity (10.6%) to scientific vocabulary
Last synced: 10 months ago
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Repository
Quadratic forms in R
Basic Info
- Host: GitHub
- Owner: RobinHankin
- Language: R
- Default Branch: master
- Size: 155 KB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 1
- Releases: 0
Created about 2 years ago
· Last pushed 11 months ago
Metadata Files
Readme
Changelog
README.Rmd
---
title: "Quadratic forms in R: the `quadform` package"
output: github_document
---
```{r setup, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
```
# 
[](https://cran.r-project.org/package=quadform)
Quadratic forms are polynomials with all terms of degree 2. Given a
column vector ${\mathbf x}=(x_1,\ldots,x_n)^\top$ and an $n\times n$
matrix $M$ then the function
$f\colon\mathbb{R}^n\longrightarrow\mathbb{R}$ given by $f({\mathbf
x})=x^TMx$ is a quadratic form; we extend to complex vectors by
mapping ${\mathbf z}=(z_1,\ldots, z_n)^\top$ to ${\mathbf
z}^*M{\mathbf z}$, where $z^*$ means the complex conjugate of $z^T$.
These are implemented in the package with `quad.form(M,x)` which is
essentially
`quad.form <- function(M,x){crossprod(crossprod(M, Conj(x)), x)}.`
This is preferable to `t(x) %*% M %*% x` on several grounds. Firstly,
it streamlines and simplifies code; secondly, it is more efficient;
and thirdly it handles the complex case consistently. The package
includes similar functionality for other related expressions.
The main motivation for the package is nicer code. For example, the
`emulator` package has to manipulate the following expression:
\[
\left[H_x-H^\top A^{-1}U\right]^\top
\left[H^\top\left(H^\top A^{-1}H\right)^{-1}H\right]
\left[H_x-H^\top A^{-1}U\right].
\]
Direct R idiom would be:
```
t(Hx - t(H) %*% solve(A) %*% U) %*% t(H) %*% solve(t(H) %*% solve(A) %*% H) %*% H %*% (Hx - t(H) %*% solve(A) %*% U)
```
But `quadform` idiom is:
```
quad.form(quad.form.inv(quad.form.inv(A,H),H), Hx - quad3.form.inv(A,H,U))
```
and in terse form becomes:
```
qf(qfi(qfi(A,H),H), Hx - q3fi(A,H,U))
```
which is certainly shorter, arguably more elegant, and possibly faster.
The package is maintained on
[github](https://github.com/RobinHankin/quadform).
Owner
- Name: Robin Hankin
- Login: RobinHankin
- Kind: user
- Location: Auckland
- Company: AUT
- Repositories: 30
- Profile: https://github.com/RobinHankin
pushing the boundaries of R in non-statistical contexts
GitHub Events
Total
- Push event: 3
Last Year
- Push event: 3
Packages
- Total packages: 1
-
Total downloads:
- cran 229 last-month
- Total dependent packages: 0
- Total dependent repositories: 0
- Total versions: 2
- Total maintainers: 1
cran.r-project.org: quadform
Efficient Evaluation of Quadratic Forms
- Homepage: https://github.com/RobinHankin/quadform
- Documentation: http://cran.r-project.org/web/packages/quadform/quadform.pdf
- License: GPL-2 | GPL-3 [expanded from: GPL]
-
Latest release: 0.0-2
published about 2 years ago
Rankings
Dependent packages count: 28.0%
Dependent repos count: 36.0%
Average: 49.7%
Downloads: 85.1%
Maintainers (1)
Last synced:
10 months ago
Dependencies
DESCRIPTION
cran
- R >= 3.0.1 depends
- mathjaxr * imports
- testthat * suggests