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View of /pkg/man/expm.Rd

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Revision 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
\title{Matrix exponential}
  Compute the exponential of a matrix.
  \item{x}{an \R object that inherits from the \code{dMatrix} class.}
  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.
  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
(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))
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