expAtv: Compute Matrix Exponential exp(A t) * v directly
In expm: Matrix Exponential, Log, 'etc'

View source: R/expm_vec.R

expAtv

R Documentation

Compute Matrix Exponential exp(A t) * v directly

Description

Compute \exp(A t) * v directly, without evaluating \exp(A).

Usage

expAtv(A, v, t = 1,
       method = "Sidje98",
       rescaleBelow = 1e-6,
       tol = 1e-07, btol = 1e-07, m.max = 30, mxrej = 10,
       verbose = getOption("verbose"))

Arguments

`A`	n x n matrix
`v`	n - vector
`t`	number (scalar);

`method`	a string indicating the method to be used; there's only one currently; we would like to add newer ones.
`rescaleBelow`	if `norm(A,"I")` is smaller than `rescaleBelow`, rescale `A` to norm 1 and `t` such that A t remains unchanged. This step is in addition to Sidje's original algorithm and easily seen to be necessary even in simple cases (e.g., n = 3).
`tol, btol`	tolerances; these are tuning constants of the "Sidje1998" method which the user should typically not change.
`m.max, mxrej`	integer constants you should only change if you know what you're doing
`verbose`	flag indicating if the algorithm should be verbose..

Value

a list with components

eAtv

.....fixme...

Author(s)

Ravi Varadhan, Johns Hopkins University; Martin Maechler (cosmetic, generalization to sparse matrices; rescaling (see rescaleBelow).

References

Roger B. Sidje (1998) EXPOKIT: Software Package for Computing Matrix Exponentials. ACM - Transactions On Mathematical Software 24(1), 130–156.

((NOT yet available!))
Al-Mohy, A. and Higham, N. (2011). Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. SIAM Journal on Scientific Computing, 33(2), 488–511.

Examples

source(system.file("demo", "exact-fn.R", package = "expm"))
##-> rnilMat() ; xct10
set.seed(1)
(s5 <- Matrix(m5 <- rnilMat(5))); v <- c(1,6:9)
(em5 <- expm(m5))
r5  <- expAtv(m5, v)
r5. <- expAtv(s5, v)
stopifnot(all.equal(r5, r5., tolerance = 1e-14),
          all.equal(c(em5 %*% v), r5$eAtv))

v <- 10:1
with(xct10, all.equal(expm(m), expm))
all.equal(c(xct10$expm %*% v),
          expAtv(xct10$m, v)$eAtv)

expm documentation built on Jan. 9, 2023, 5:11 p.m.