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Expokit is a software package by Roger B. Sidje that provides matrix exponential routines for small dense or very large sparse matrices, real or complex.
Expokit is free for non-commercial use.
The following function provides a Fortran 90 interface for computing (削除) (追記) (追記ここまで) for a dense, square, real matrix via Expokit:\\mathrm{e}^{tH} (削除ここまで)
! double precision kind constant
integer, parameter :: dp = kind(1.d0)
! Calculate exp(t*H) for an N-by-N matrix H using Expokit.
function expm(t, H) result(expH)
real(dp), intent(in) :: t
real(dp), dimension(:,:), intent(in) :: H
real(dp), dimension(size(H,1),size(H,2)) :: expH
! Expokit variables
external :: DGPADM
integer, parameter :: ideg = 6
real(dp), dimension(4*size(H,1)*size(H,2) + ideg + 1) :: wsp
integer, dimension(size(H,1)) :: iwsp
integer :: iexp, ns, iflag, n
if (size(H,1) /= size(H,2)) then
stop 'expm: matrix must be square'
end if
n = size(H,1)
call DGPADM(ideg, n, t, H, n, wsp, size(wsp,1), iwsp, iexp, ns, iflag)
expH = reshape(wsp(iexp:iexp+n*n-1), shape(expH))
end function expm