Description Usage Arguments Details Value Note Author(s) References See Also Examples
Compute the exponential of a matrix.
1  expm(x)

x 
a matrix, typically inheriting from the

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.
The matrix exponential of x
.
The expm package contains newer (partly faster and more
accurate) algorithms for expm()
and includes
logm
and sqrtm
.
This is a translation of the implementation of the corresponding Octave function contributed to the Octave project by A. Scottedward Hodel A.S.Hodel@Eng.Auburn.EDU. A bug in there has been fixed by Martin Maechler.
https://en.wikipedia.org/wiki/Matrix_exponential
Cleve Moler and Charles Van Loan (2003) Nineteen dubious ways to compute the exponential of a matrix, twentyfive years later. SIAM Review 45, 1, 3â€“49.
Eric W. Weisstein et al. (1999) Matrix Exponential. From MathWorld, https://mathworld.wolfram.com/MatrixExponential.html
Schur
; additionally,
expm
, logm
, etc in package expm.
1 2 3 4 5 6 7 
2 x 2 Matrix of class "dtrMatrix"
[,1] [,2]
[1,] 1 1
[2,] . 1
2 x 2 Matrix of class "dtrMatrix"
[,1] [,2]
[1,] 2.718282 2.718282
[2,] . 2.718282
2 x 2 Matrix of class "dgeMatrix"
[,1] [,2]
[1,] 49 24
[2,] 64 31
2 x 2 Matrix of class "dgeMatrix"
[,1] [,2]
[1,] 0.7357588 0.5518191
[2,] 1.4715176 1.1036382
4 x 4 sparse Matrix of class "dtCMatrix"
[1,] . 6 . .
[2,] . . 6 .
[3,] . . . 6
[4,] . . . .
4 x 4 Matrix of class "dtrMatrix"
[,1] [,2] [,3] [,4]
[1,] 1 6 18 36
[2,] . 1 6 18
[3,] . . 1 6
[4,] . . . 1
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