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 function and in Python via the scipy.sparse.linalg.cg and scipy.sparse.linalg.LinearOperator 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
• Rlinsolve
• cPCG

Installation

The pcg2 package is currently only available from Github.

devtools::install_github("natbprice/pcg2")

Example

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)
#> $x
#>            [,1]
#> [1,] 0.09090909
#> [2,] 0.63636364
#> 
#> $resid
#> [1] 2.220446e-16
#> 
#> $iter
#> [1] 3