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gragusa / lyapunov

Solve discrete time sylvester equation in R
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Description

lyapunov is a R package for solving the discrete time Lyapunov equation:

lyapunov

This kind of equation arise in the context of Kalman Filter, and specifically to initialize the variance of the states in the linear filter.

The package provides a single command dlyap. The simple code below describes the interface, which is similar to Matlab's.

M <- c(135.2810,    7.8288,   14.0392,    7.2220,
       7.8288,  100.5310,  -17.6854,  -12.2728,
      14.0392,  -17.6854,  103.4842,    4.5037,
       7.2220,  -12.2728,    4.5037,   88.2638)
M = matrix(M, 4, 4)

## Solve AXA' - X + Q = 0
dlyap(A = M, Q = diag(4))

## Solve AXA' - EXE' + Q = 0
dlyap(A = M, Q = diag(4), E = crossprod(M))

lyapunov is a simple wrapper to Algorithm 705 from the Collected Algorithms from ACM, TRANSACTIONS ON MATHEMATICAL SOFTWARE, VOL. 18, NO. 2, PP. 232-238.75.

Installation

To install the package:

library(devtools)
devtools::install_github("gragusa/lyapunov")

You need development tools installed.