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subroutine dexpm1(ia,n,a,ea,iea,w,iw,ierr)
c
c!purpose
c compute the exponential of a matrix a by the pade's
c approximants(subroutine pade).a block diagonalization
c is performed prior call pade.
c!calling sequence
c subroutine dexpm1(ia,n,a,ea,iea,w,iw,ierr)
c
c integer ia,n,iw,ierr
c double precision a,ea,w
c dimension a(ia,n),ea(iea,n),w(*),iw(*)
c
c ia: the leading dimension of array a.
c n: the order of the matrices a,ea,x,xi .
c a: the real double precision array that contains the n*n matrix a
c ea: the array that contains the n*n exponential of a.
c iea : the leading dimension of array ea
c w : work space array of size: n*(2*ia+2*n+5)
c iw : integer work space array of size 2*n
c ierr: =0 if the prosessus is normal.
c =-1 if n>ia.
c =-2 if the block diagonalization is not possible.
c =-4 if the subroutine dpade can not computes exp(a)
c
c!auxiliary routines
c exp abs sqrt dble real (fortran)
c bdiag (eispack.extension)
c balanc balinv (eispack)
c dmmul (blas.extension)
c pade
c! originator
c j roche laboratoire d'automatique de grenoble
c!
integer ia,n,iw,ierr
double precision a,ea,w
dimension a(ia,*),ea(iea,*),w(*),iw(*)
c internal variables
c
integer i,j,k,ni,nii,ndng
double precision anorm,alpha,bvec,bbvec,rn,zero,c(41)
logical fail
c
common /dcoeff/ c,ndng
data zero /0.0d+0/
ndng=-1
c
ierr=0
kscal=1
kx=kscal+n
kxi=kx+n*ia
ker=kxi+n*ia
kei=ker+n
kw=kei+n
c
kbs=1
kiw=kbs+n
c
if (n.gt.ia) go to 110
c
c balance the matrix a
c
c
c compute the norm one of a.
c
anorm = 0.0d+0
do 20 j=1,n
alpha = zero
do 10 i=1,n
alpha = alpha + abs(a(i,j))
10 continue
if (alpha.gt.anorm) anorm = alpha
20 continue
if (anorm.eq.0.0d0) then
c null matrix special case (Serge Steer 96)
do 21 j=1,n
call dset(n,0.0d+0,ea(j,1),iea)
ea(j,j)=1.0d0
21 continue
return
endif
anorm=max(anorm,1.0d0)
c
c call bdiag whith rmax equal to the norm one of matrix a.
c
call bdiag(ia,n,a,0.0d+0,anorm,w(ker),w(kei),
* iw(kbs),w(kx),w(kxi),w(kscal),1,fail)
if (fail) go to 120
do 25 j=1,n
call dset(n,0.0d+0,ea(j,1),iea)
25 continue
c
c compute the pade's approximants of the block.
c block origin is shifted before calling pade.
c
ni = 1
k = 0
c
c loop on the block.
c
30 k = k + ni
if (k.gt.n) go to 100
ni = iw(kbs-1+k)
if (ni.eq.1) go to 90
nii = k + ni - 1
bvec = zero
do 40 i=k,nii
bvec = bvec + w(ker-1+i)
40 continue
bvec = bvec/dble(real(ni))
do 50 i=k,nii
w(ker-1+i) = w(ker-1+i) - bvec
a(i,i) = a(i,i) - bvec
50 continue
alpha = zero
do 60 i=k,nii
rn = w(ker-1+i)**2 + w(kei-1+i)**2
rn = sqrt(rn)
if (rn.gt.alpha) alpha = rn
60 continue
c
c call pade subroutine.
c
call pade(a(k,k),ia,ni,ea(k,k),iea,alpha,w(kw),iw(kiw),
1 ierr)
if (ierr.lt.0) go to 130
c
c remove the effect of origin shift on the block.
c
bbvec = exp(bvec)
do 80 i=k,nii
do 70 j=k,nii
ea(i,j) = ea(i,j)*bbvec
70 continue
80 continue
go to 30
90 ea(k,k) = exp(a(k,k))
go to 30
c
c end of loop.
c
100 continue
c
c remove the effect of block diagonalization.
c
call dmmul(w(kx),ia,ea,iea,w(kw),n,n,n,n)
call dmmul(w(kw),n,w(kxi),ia,ea,iea,n,n,n)
c
c remove the effects of balance
c
c
c error output
c
go to 130
110 ierr = -1
go to 130
120 ierr = -2
130 continue
return
end
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