rexpokit (version 0.26.6.4)

expm: Simple Interface

Description

A simple interface for matrix exponentiation, similar to that found in the Matrix package.

Usage

expm(x, t=1)

Arguments

x

A square matrix.

t

Time value; see details section below. Default value is 1.

Value

The matrix exponential.

Details

This routine computes exp(t*x), where t in a single numeric value, and x is a square matrix and exp refers to the matrix exponential. Formally, the matrix exponential is given by the power series:

\(expm(x) = x/1! + x^2/2! + x^3/3! + \dots\)

where the powers on the matrix correspond to matrix-matrix multiplications.

expm() directly computes the matrix exponential of a dense matrix. The implementation uses an order 6 Pade' approximation with a scaling-and-squaring technique.

References

Sidje RB (1998). "Expokit. A Software Package for Computing Matrix Exponentials." _ACM Trans. Math. Softw._, *24*(1), pp. 130-156. <URL: http://dx.doi.org/10.1145/285861.285868>, <URL: http://dl.acm.org/citation.cfm?id=285868>.

Examples

# NOT RUN {
# Example use:
x <- matrix(1:25, nrow=5)/100

expm(x)
# }