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**954**- (**download**) (**as text**) (**annotate**)*Wed Sep 28 19:34:31 2005 UTC*(13 years, 10 months ago) by*maechler*File size: 1190 byte(s)

more "Compare" and some "!" methods; expm() for sparse; updated tests

\name{expm} \alias{expm} \alias{expm,dMatrix-method} \alias{expm,dgeMatrix-method} \title{Matrix exponential} \description{ Compute the exponential of a matrix. } \usage{ expm(x) } \arguments{ \item{x}{an \R object that inherits from the \code{dMatrix} class.} } \details{ The exponential of a matrix is defined as the infinite Taylor series \code{expm(A) = I + A + A^2/2! + A^3/3! + ...} (although this is definitely not the way to compute it). The method for the \code{dgeMatrix} class uses Ward's diagonal Pade' approximation with three step preconditioning. } \value{ The matrix exponential of \code{x}. } \references{}%% << FIXME \author{This is a simple translation of the implementation of the corresponding Octave function contributed to the Octave project by A. Scottedward Hodel \email{A.S.Hodel@Eng.Auburn.EDU}. } %\note{} \seealso{\code{\link{Schur}}} \examples{ (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))# sparse! (e3 <- expm(m3)) } \keyword{algebra} \keyword{math}

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