expm: Matrix exponential

Description

Compute the exponential of a matrix.

Usage

expm(x)

Arguments

an Robject that inherits from the dMatrix class.

Value

The matrix exponential of x.

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.

References

http://en.wikipedia.org/wiki/Matrix_exponential

Cleve Moler and Charles Van Loan (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45, 1, 3--49. Eric W. Weisstein et al. (1999) Matrix Exponential. From MathWorld, http://mathworld.wolfram.com/MatrixExponential.html

Examples

Run this code

(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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