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subroutine wexpm1(n,ar,ai,ia,ear,eai,iea,w,iw,ierr)
c
c!purpose
c compute the exponential of a complex matrix a by the pade's
c approximants(subroutine pade).a block diagonalization
c is performed prior call pade.
c!calling sequence
c subroutine wexpm1(n,ar,ai,ia,ear,eai,iea,w,iw,ierr)
c
c integer ia,n,iw,ierr
c double precision ar,ai,ear,eai,w
c dimension ar(ia,n),ai(ia,n),ear(iea,n),eai(iea,n),w(*),iw(*)
c
c n: the order of the matrices a,ea, .
c ar,ai :the array that contains :the n*n matrix a
c ia: the leading dimension of array a.
c ear,eai: the array that contains the n*n exponential of a.
c iea :the leading dimension of ea
c w : work space array of size: n*(4*ia+4*n+7)
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 cos sin exp abs sqrt dble real (fortran)
c wbdiag wbalin (eispack.extension)
c cbal (eispack)
c wmmul (blas.extension)
c wpade
c! originator
c S Steer INRIA from dexpm1:
c j roche laboratoire d'automatique de grenoble
c!
c Copyright INRIA
integer ia,n,iw,ierr
double precision ar,ai,ear,eai,w
dimension ar(ia,n),ai(ia,n),ear(iea,n),eai(iea,n),w(*),iw(*)
c internal variables
c
integer i,j,k,ni,nii,ndng
double precision anorm,alpha,bvecr,bveci,bbvec,rn,zero,c(41)
logical fail
c
common /dcoeff/ c,ndng
c
data zero /0.0d+0/
ndng=-1
c
ierr=0
nn=n*n
kscal=1
kxr=kscal+n
kxi=kxr+n*ia
kyr=kxi+n*ia
kyi=kyr+n*ia
ker=kyi+n*ia
kei=ker+n
kw=kei+n
c
kbs=1
kpvt=kbs+n
c
if (n.gt.ia) go to 110
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(ar(i,j)) + abs(ai(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,ear(j,1),iea)
call dset(n,0.0d+0,eai(j,1),iea)
ear(j,j)=1.0d0
21 continue
return
endif
anorm=max(anorm,1.0d0)
c
c call wbdiag whith rmax equal to the norm one of matrix a.
c
call wbdiag(ia,n,ar,ai,anorm,w(ker),w(kei),
* iw(kbs),w(kxr),w(kxi),w(kyr),w(kyi),w(kscal),1,fail)
if (fail) go to 120
c
c clear matrix ea
do 25 j=1,n
call dset(n,0.0d+0,ear(j,1),iea)
call dset(n,0.0d+0,eai(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
bvecr = zero
bveci = zero
do 40 i=k,nii
bvecr = bvecr + w(ker-1+i)
bveci = bveci + w(kei-1+i)
40 continue
bvecr = bvecr/dble(real(ni))
bveci = bveci/dble(real(ni))
do 50 i=k,nii
w(ker-1+i) = w(ker-1+i) - bvecr
w(kei-1+i) = w(kei-1+i) - bveci
ar(i,i) = ar(i,i) - bvecr
ai(i,i) = ai(i,i) - bveci
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 wpade(ar(k,k),ai(k,k),ia,ni,ear(k,k),eai(k,k),iea,
* alpha,w(kw),iw(kpvt),ierr)
if (ierr.lt.0) go to 130
c
c remove the effect of origin shift on the block.
c
bbvec = exp(bvecr)
bvecr=bbvec*cos(bveci)
bveci=bbvec*sin(bveci)
do 80 i=k,nii
do 70 j=k,nii
bbvec = ear(i,j)*bvecr - eai(i,j)*bveci
eai(i,j) = ear(i,j)*bveci + eai(i,j)*bvecr
ear(i,j) = bbvec
70 continue
80 continue
go to 30
90 bbvec=exp(ar(k,k))
ear(k,k) = bbvec * cos(ai(k,k))
eai(k,k) = bbvec * sin(ai(k,k))
go to 30
c
c end of loop.
c
100 continue
c
c remove the effect of block diagonalization.
c
call wmmul(w(kxr),w(kxi),ia,ear,eai,iea,w(kw),w(kw+nn),n,n,n,n)
call wmmul(w(kw),w(kw+nn),n,w(kyr),w(kyi),ia,ear,eai,iea,n,n,n)
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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