expm {Matrix} | R Documentation |
Compute the exponential of a matrix.
expm(x)
x |
an R object that inherits from the Matrix class |
The exponential of a matrix is defined as the infinite Taylor
series expm(A) = I + A + A^2/2! + A^3/3! + ...
(although this is
definitely not the way to compute it). The method for the
dgeMatrix
class uses Ward's diagonal Pade' approximation with
three step preconditioning.
The matrix exponential of x
.
This is a simple translation of the implementation of the corresponding Octave function contributed to the Octave project by A. Scottedward Hodel A.S.Hodel@Eng.Auburn.EDU.
(m1 <- Matrix(c(1,0,1,1), nc = 2)) (e1 <- expm(m1)) ; e <- exp(1) stopifnot(all.equal(e1@x, c(e,0,e,e), tol = 1e-15)) (m2 <- Matrix(c(-49, -64, 24, 31), nc = 2)) (e2 <- expm(m2)) (m3 <- Matrix(cbind(0,rbind(6*diag(3),0)), nc = 4)) (e3 <- expm(m3))