01_expm: Simple Interface

In nmatzke/rexpokit: R Wrappers for EXPOKIT; Other Matrix Functions

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.

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.

Value

The matrix exponential.

Author(s)

Drew Schmidt [e-mail]

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: https://dl.acm.org/doi/10.1145/285861.285868>.

Examples

# Example use:
x <- matrix(1:25, nrow=5)/100

expm(x)

nmatzke/rexpokit documentation built on June 29, 2024, 4:46 a.m.