cPCG

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R package for solving system of linear equations using (preconditioned) conjugate gradient algorithm, with improved efficiency using C++ Armadillo linear algebra library, and flexibility for user-specified preconditioning method.

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# cPCG: Efficient and Customized Preconditioned Conjugate Gradient Method

An [R package](https://cran.r-project.org/web/packages/cPCG/) to solve system of linear equations using (preconditioned) conjugate gradient algorithm, with improved efficiency using Armadillo templated C++ linear algebra library, and flexibility for userspecified preconditioning method.

# Installation options
Download `cPCG_1.5.5.tar.gz` file [here](https://github.com/styvon/cPCG/blob/master/downloads/cPCG_1.5.5.tar.gz) and build from command line:
```
R CMD INSTALL cPCG_1.5.5.tar.gz
```

Get current development version from github:

```R
devtools::install_github("styvon/cPCG")
```

**NOTE**: Mac OSX users will need to install `OpenMP` in order to compile the package. Check [here](http://thecoatlessprofessor.com/programming/openmp-in-r-on-os-x/) for a solution.

# Functions

## `cgsolve`
Conjugate gradient method for solving system of linear equations Ax = b, where A is symmetric and positive definite, b is a column vector.

```
cgsolve(A, b, float tol = 1e-6, int maxIter = 1000)
```

## `pcgsolve`

When the condition number for A is large, the conjugate gradient (CG) method may fail to converge in a reasonable number of iterations. The Preconditioned Conjugate Gradient (PCG) Method applies a precondition matrix C and approaches the problem by solving C^{-1} A x = {C}^{-1} b where the symmetric and positive-definite matrix C approximates A and C^{-1}A  improves the condition number of A.

```
pcgsolve(A, b, preconditioner = "Jacobi", float tol = 1e-6, int maxIter = 1000)
```

Common choices for the preconditioner include: Jacobi preconditioning, symmetric successive over-relaxation (SSOR), and incomplete Cholesky factorization.

* `Jacobi`: The Jacobi preconditioner is the diagonal of the matrix A, with an assumption that all diagonal elements are non-zero.  
  
* `SSOR`: The symmetric successive over-relaxation preconditioner, implemented as M = (D+L) D^{-1} (D+L)^T.  
  
* `ICC`: The incomplete Cholesky factorization preconditioner.

## `cgsolve_sparseOMP`  *new in v1.5.5*
Sparse matrix with parallelism using OpenMP for conjugate gradient method.

```
# A is a sparse matrix, can be generated using 'Matrix' package function Matrix(..., sparse = TRUE)
cgsolve_sparseOMP(A, b, tol = 1e-6, maxIter = 1000, nThreads=1)
```

## `pcgsolve_sparseOMP` *new in v1.5.5*
Sparse matrix with parallelism using OpenMP for preconditioned conjugate gradient method, Jacobi preconditioner is currently available.

```
# A is a sparse matrix, can be generated using 'Matrix' package function Matrix(..., sparse = TRUE)
pcgsolve_sparseOMP(A, b, preconditioner = "Jacobi", tol = 1e-6, maxIter = 1000, nThreads=1)
```

# Resources

- [User manual](https://github.com/styvon/cPCG/blob/master/docs/manual.pdf)
- [Vignettes](https://github.com/styvon/cPCG/tree/master/vignettes)
- [cPCG: Efficient and Customized Preconditioned Conjugate Gradient Method](https://cran.r-project.org/web/packages/cPCG/cPCG.pdf)

cPCG

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