expAtv {expm} 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.

expm

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)


[Package expm version 0.999-9 Index]