/
roots.F
259 lines (259 loc) · 5.2 KB
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roots.F
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c&ROOTS
c&RTPOLY
subroutine rtpoly(args,nargs)
c******************************************************************
c
c Subroutine to handle the command
c
c ROOTSPOLY(rr,ri,np,a)
c
c
c******************************************************************
c
#include 'tslabc'
character args(nargs)*15
integer*2 ickl
c
c
if(ickl(args(1),nprr,nrr).eq.1) go to 99
if(ickl(args(2),npri,nri).eq.1) go to 99
call ckint(args(3),np)
if(np.lt.1.or.np.gt.min0(nrr,nri)) then
call error(args,3,2)
go to 99
endif
c
c
n1=nstart(nprr)
n2=nstart(npri)
np4=4*np
call movxy(wk,array(n1),np4)
call movxy(wk(np+1),array(n2),np4)
do 5 i=1,np
if(abs(wk(i)).lt.1.e-20.and.abs(wk(np+i)).lt.1.e-20) then
write(*,6)
6 format(' One of the roots is too small')
imflag=1
go to 99
endif
5 continue
n1=np+1
n2=n1+np
n3=n2+np
n4=n3+2*(np+1)
n5=n4+2*(np+1)
call rtar(wk,wk(n1),np,wk(n2),wk(n3),wk(n4),wk(n5),iwk)
c
c
lab='Polynomial Coefficients'
call ckadda(args(4),np,lab,n2,iref)
c
c
99 continue
return
end
c&RTAR
subroutine rtar(rr,ri,n,alpha,r,c,cf,j)
c****************************************************************
c
c subroutine to find the coefficients of a polynomial given it zeros
c
c********************************************************************
c
complex r(1),c(1),pr,sum,cone
dimension rr(n),ri(n),alpha(n),cf(1),j(1)
c
c
cone=cmplx(1.0,0.)
nn=n+1
do 10 i=1,n
10 r(i)=cone/cmplx(rr(i),ri(i))
cf(nn)=1.
do 14 m=1,n
sum=cmplx(0.0,0.0)
l=1
j(1)=1
go to 2
1 j(l)=j(l)+1
2 if(l-m) 3,5,50
3 mm=m-1
do 4 i=l,mm
ii=i+1
4 j(ii)=j(i)+1
5 pr=cmplx(1.0,0.0)
do 7 i=1,m
ick=j(i)
7 pr=-pr*r(ick)
sum=sum+pr
do 6 i=1,m
l=m-i+1
if(j(l)-n+m-l) 1,6,50
6 continue
mp=n-m+1
14 cf(mp)=real(sum)
do 15 i=1,n
nn=n-i+1
15 alpha(i)=cf(nn)
return
50 ier=1
return
end
c&POLYRT
subroutine polyrt(args,nargs)
c******************************************************************
c
c Subroutine to handle the command
c
c POLYROOTS(a,a0,np,maxit,rootr,rooti,ier)
c
c roots of polynomial a0 + a(1)x + a(2)x**2 + ... + a(np)x**np
c
c******************************************************************
c
#include 'tslabc'
character args(nargs)*15
integer*2 ickl,ickr,icki
c
if(ickl(args(1),npa,na).eq.1) go to 99
if(ickr(args(2),2,a0,0,0.).eq.1) go to 99
if(icki(args(3),3,np,1,1).eq.1) go to 99
if(np.gt.na.or.np.gt.1000) then
call error(args,3,2)
go to 99
endif
if(icki(args(4),4,maxit,1,1).eq.1) go to 99
if(maxit.gt.1000) then
call error(args,4,2)
go to 99
endif
c
c
wk(1)=a0
call movxy(wk(2),array(nstart(npa)),4*np)
nn=2*(np+1)
n1=np+2
n2=n1+nn
n3=n2+nn
n4=n3+nn
n5=n4+np
call proots(wk,np,maxit,wk(n1),wk(n2),wk(n3),wk(n4),wk(n5),ier)
c
c
call ckaddi(args(7),ier,iref)
if(ier.eq.1) then
write(*,10)
10 format(' Convergence not reached in POLYROOT')
imflag=1
go to 99
endif
if(iref.eq.1) go to 99
lab='Real Part of Polynomial Roots'
call ckadda(args(5),np,lab,n4,iref)
if(iref.eq.1) go to 99
lab='Imaginary Part of Polynomial Roots'
call ckadda(args(6),np,lab,n5,iref)
c
c
99 continue
return
end
c&PROOTS
subroutine proots(ra,np,maxit,a,a1,roots,rr,ri,ier)
c*****************************************************************
c
c calculate roots of a(1)+a(2)z+a(3)z**2+...+a(np+1)z**np
c
c*****************************************************************
c
dimension ra(1),rr(1),ri(1)
complex a(1),a1(1),roots(1),x,b,c
c
c
eps=1.e-6
do 1 i=1,np+1
a(i)=ra(i)
1 a1(i)=a(i)
do 3 j=np,1,-1
x=cmplx(0.,0.)
call root1(a1,j,x,eps,0,maxit,ier)
if(ier.eq.1) go to 99
if(abs(aimag(x)).le.2.*eps**2*abs(real(x))) x=cmplx(real(x),0.)
roots(j)=x
b=a1(j+1)
do 2 jj=j,1,-1
c=a1(jj)
a1(jj)=b
2 b=x*b+c
3 continue
do 4 j=1,np
call root1(a,np,roots(j),eps,1,maxit,ier)
4 if(ier.eq.1) go to 99
do 6 j=2,np
x=roots(j)
do 5 i=j-1,1,-1
if(real(roots(i)).le.real(x)) go to 10
roots(i+1)=roots(i)
5 continue
i=0
10 roots(i+1)=x
6 continue
do 20 i=1,np
rr(i)=real(roots(i))
20 ri(i)=aimag(roots(i))
99 continue
return
end
c&ROOT1
subroutine root1(a,np,x,eps,iopt,maxit,ier)
c********************************************************************
c
c calculate one root.
c
c********************************************************************
c
complex a(1),x,dx,x1,b,d,f,g,h,sq,gp,gm,g2,zero
c
c
ier=0
zero=cmplx(0.,0.)
if(iopt.eq.1) then
dxold=cabs(x)
npol=0
endif
do 2 it=1,maxit
b=a(np+1)
d=zero
f=zero
do 1 j=np,1,-1
f=x*f+d
d=x*d+b
1 b=x*b+a(j)
if(cabs(b).le.1.e-15) then
dx=zero
else if(cabs(d).le.1.e-15.and.cabs(f).le.1.e-15) then
dx=cmplx(cabs(b/a(np+1))**(1./np),0.)
else
g=d/b
g2=g*g
h=g2-2.*f/b
sq=csqrt((np-1)*(np*h-g2))
gp=g+sq
gm=g-sq
if(cabs(gp).lt.cabs(gm)) gp=gm
dx=np/gp
endif
x1=x-dx
if(x.eq.x1) return
x=x1
if(iopt.eq.1) then
npol=npol+1
cdx=cabs(dx)
if(npol.gt.9.and.cdx.ge.dxold) return
dxold=cdx
else
if(cabs(dx).le.eps*cabs(x)) return
endif
2 continue
ier=1
return
end