expm {Matrix}R Documentation

Matrix exponential

Description

Compute the exponential of a matrix.

Usage

expm(x)

Arguments

x an R object that inherits from the Matrix class

Details

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.

Value

The matrix exponential of x.

Author(s)

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.

References

See Also

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))
(e3 <- expm(m3))

[Package Matrix version 0.95-5 Index]