README.Rmd

---
output:
  github_document
---

<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r setup, include = FALSE}
library(knitr)
library(pcg2)

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)

local({
  hook_plot = knit_hooks$get('plot')
  knit_hooks$set(plot = function(x, options) {
    x = paste(x, collapse = '.')
    if (!grepl('\\.svg', x)) return(hook_plot(x, options))
    # read the content of the svg image and write it out without <?xml ... ?>
    paste0('<img src= "./', x, '">')
  })
})
```

# pcg2
[![lifecycle](https://img.shields.io/badge/lifecycle-maturing-blue.svg)](https://www.tidyverse.org/lifecycle/#maturing)
[![Travis build status](https://travis-ci.org/natbprice/pcg2.svg?branch=master)](https://travis-ci.org/natbprice/pcg2)

There are several R packages that implement the preconditioned conjugate 
gradients (pcg) method, but none of them allow for the passage of a function handle
in place of the matrix vector products A\*x. This functionality is available in Matlab
via the [`pcg`](https://www.mathworks.com/help/matlab/ref/pcg.html) function
and in Python via the [`scipy.sparse.linalg.cg`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.cg.html) and [`scipy.sparse.linalg.LinearOperator`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html) functions. This package is a simple implementation
of the pcg method allowing the user to pass a function handle in place of the 
matrix vector product A\*x.

Other pcg packages in R:

* [pcg](https://cran.r-project.org/package=pcg)
* [Rlinsolve](https://cran.r-project.org/package=Rlinsolve)
* [cPCG](https://cran.r-project.org/package=cPCG)


## Installation

The **pcg2** package is currently only available from Github.

```{r, eval = FALSE}
devtools::install_github("natbprice/pcg2")
```

## Example

```{r}
A <- matrix(c(4, 1, 1, 3), nrow = 2)
b <- c(1, 2)
x0 <- c(2, 1)

Ax <- function(x) {
  A %*% x
}

M <- matrix(c(4, 0, 0, 3), nrow = nrow(A))

pcg(Ax, b, M, x0)
```