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ffts.F
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c&FFTS
c&FFTS
subroutine ffts(args,nargs)
c*******************************************************************
c
c Subroutine to handle the command
c
c FFT(xr,xi,nfreqs,nout,isign,zr,zi) or
c
c FFT(x,nfreqs,nout,isign,zr,zi)
c
c
c********************************************************************
c
#include 'tslabc'
character args(nargs)*15,i10*1
integer*2 ickl,icki,ickse
c
c
if(ickl(args(1),npxr,nxr).eq.1) go to 99
nxi=nxr
if(nargs.eq.7) then
if(ickl(args(2),npxi,nxi).eq.1) go to 99
endif
m1=3
if(nargs.eq.6) m1=2
if(icki(args(m1),m1,nfreqs,1,1).eq.1) go to 99
if(nfreqs.gt.min0(nxr,nxi)) then
call error(args,m1,2)
go to 99
endif
m1=m1+1
if(icki(args(m1),m1,nout,0,0).eq.1) go to 99
if(nout.lt.1.or.nout.gt.nfreqs) then
call error(args,m1,2)
go to 99
endif
m1=m1+1
if(icki(args(m1),m1,isign,0,0).eq.1) go to 99
if(isign.ne.1.and.isign.ne.-1) then
call error(args,m1,2)
go to 99
endif
c
c
call movxy(wk,array(nstart(npxr)),4*nfreqs)
if(nargs.eq.7) call movxy(wk(nfreqs+1),array(nstart(npxi)),
1 4*nfreqs)
if(nargs.eq.6) call movct(wk(nfreqs+1),4*nfreqs,char(0))
c
c
if(ickse(2*nfreqs).eq.1) go to 99
call fft(wk,wk(nfreqs+1),nfreqs,nfreqs,nfreqs,isign)
c
c
if(imflag.ne.1) go to 71
imflag=0
write(*,5)
5 format(' Using the Brute Force DFT: It might take a long time')
ns1=nstart(npxr)
iopt=1
ns2=ns1
if(nargs.eq.7) then
iopt=2
ns2=nstart(npxi)
endif
n1=nfreqs+1
n2=n1+nfreqs
n3=n2+nout
c
c
if(ickse(2*nfreqs+2*nout).eq.1) go to 99
call fft1(array(ns1),array(ns2),nfreqs,iopt,isign,nout,
1 wk,wk(n1),wk(n2),wk(n3))
c
c
lab='Real Part of FFT'
m1=m1+1
call ckadda(args(m1),nout,lab,n2,iref)
if(iref.eq.1) go to 99
lab='Imaginary Part of FFT'
m1=m1+1
call ckadda(args(m1),nout,lab,n3,iref)
go to 99
c
c
71 continue
lab='Real Part of FFT'
m1=m1+1
call ckadda(args(m1),nout,lab,1,iref)
if(iref.eq.1) go to 99
lab='Imaginary Part of FFT'
m1=m1+1
call ckadda(args(m1),nout,lab,nfreqs+1,iref)
c
c
99 continue
return
end
c&FFT1
subroutine fft1(a,b,n,iopt,isign,m,cc,ss,zr,zi)
c******************************************************************
c
c Subroutine to do brute force n-point DFT. a and b are
c real and imaginary parts of input, zr and zi are first m points
c of output. If iopt=1 (2), then b is assumed (not assumed)
c to be zeros. isign is 1 or -1 for DFT or IDFT. cc and ss are
c work vectors of length n.
c
c*******************************************************************
c
dimension a(1),b(1),cc(1),ss(1),zr(1),zi(1)
c
c
on=float(n)
oi=float(isign)
twopi=8.*atan(1.0)
c1=twopi/on
n1=(n/2)+1
cc(1)=1.0
ss(1)=0.0
c
c
jj=n+1
do 10 j=2,n1
jj=jj-1
arg=float(j-1)*c1
cc(j)=cos(arg)
ss(j)=oi*sin(arg)
cc(jj)=cc(j)
10 ss(jj)=-ss(j)
if(2*(n/2).eq.n) ss(n1)=-ss(n1)
c
c
mm=m
iopt1=0
if(iopt.eq.1.and.m.gt.n1) then
mm=n1
iopt1=1
endif
iptev=0
if(2*(n/2).eq.n) iptev=1
c
c
if(iptev.eq.1) ajj=a(n1)
if(iptev.eq.1.and.iopt.eq.2) bjj=b(n1)
jj=n+1
do 15 j=2,n1
jj=jj-1
ajp=a(j)+a(jj)
ajm=a(j)-a(jj)
a(jj)=ajm
15 a(j)=ajp
if(iopt.eq.1) go to 17
jj=n+1
do 16 j=2,n1
jj=jj-1
bjp=b(j)+b(jj)
bjm=b(j)-b(jj)
b(jj)=bjm
16 b(j)=bjp
17 continue
c
c
cc1=0.0
if(iopt.eq.2) cc1=b(1)
c
c
do 40 i=1,mm
c1=a(1)
c2=cc1
ind=1
im1=i-1
jj=n+1
c
if(iopt.eq.1) then
do 30 j=2,n1
jj=jj-1
ind=ind+im1
if(ind.gt.n) ind=ind-n
cci=cc(ind)
ssi=ss(ind)
c1=c1+a(j)*cci
c2=c2+a(jj)*ssi
30 continue
if(iptev.eq.1) c1=c1-ajj*cci
else
do 31 j=2,n1
jj=jj-1
ind=ind+im1
if(ind.gt.n) ind=ind-n
cci=cc(ind)
ssi=ss(ind)
c1=c1+a(j)*cci-b(jj)*ssi
c2=c2+a(jj)*ssi+b(j)*cci
31 continue
if(iptev.eq.1) then
c1=c1-ajj*cci
c2=c2-bjj*cci
endif
endif
zr(i)=c1
zi(i)=c2
40 continue
c
c Unscramble a's and b's:
c
jj=n+1
do 45 j=2,n1
jj=jj-1
ajp=(a(j)+a(jj))/2.
ajm=(a(j)-a(jj))/2.
a(jj)=ajm
45 a(j)=ajp
if(iptev.eq.1) a(n1)=ajj
if(iopt.eq.1) go to 47
jj=n+1
do 46 j=2,n1
jj=jj-1
bjp=(b(j)+b(jj))/2.
bjm=(b(j)-b(jj))/2.
b(jj)=bjm
46 b(j)=bjp
if(iptev.eq.1) b(n1)=bjj
47 continue
c
c
if(iopt1.eq.1) then
jj=n-n1+2
do 50 j=n1+1,m
jj=jj-1
zr(j)=zr(jj)
50 zi(j)=-zi(jj)
endif
c
c
return
end
c&REPL
subroutine repl(args,nargs,vname)
c******************************************************************
c
c Subroutine to handle the command
c
c y=REPLACE(x,xi,rep,nr)
c
c or
c
c y=REPLACE(x,n,iopt,a[,b,c]) iopt=1 (below), 2(above), 3(both)
c 4 (in between)
c 5 (b if le a, c if >a)
c
c*******************************************************************
c
#include 'tslabc'
character args(nargs)*15,vname*15
integer*2 ickl,icki,ickr
c
c
if(ickl(args(1),npx,nx).eq.1) go to 99
if(nargs.eq.4) then
call ckint(args(2),n)
if(n.eq.-999) go to 5
endif
c
c handle second case:
c
if(icki(args(2),2,n,5,nx).eq.1) go to 99
if(icki(args(3),3,iopt,1,1).eq.1) go to 99
if(iopt.gt.5) then
call error(args,3,2)
go to 99
endif
if(iopt.eq.3.and.nargs.ne.5) then
write(*,901)
901 format(' Wrong number of arguments in REPLACE')
imflag=1
go to 99
endif
if(iopt.ge.4.and.nargs.ne.6) then
write(*,901)
imflag=1
go to 99
endif
if(ickr(args(4),4,a,0,0.).eq.1) go to 99
if(iopt.gt.2) then
if(ickr(args(5),5,b,0,0.).eq.1) go to 99
endif
if(iopt.ge.4) then
if(ickr(args(6),6,c,0,0.).eq.1) go to 99
endif
call movxy(wk,array(nstart(npx)),4*n)
if(iopt.eq.1) then
do 1 i=1,n
1 if(wk(i).lt.a) wk(i)=a
go to 7
endif
if(iopt.eq.2) then
do 2 i=1,n
2 if(wk(i).gt.a) wk(i)=a
go to 7
endif
if(iopt.eq.3) then
do 3 i=1,n
if(wk(i).lt.a) wk(i)=a
3 if(wk(i).gt.b) wk(i)=b
go to 7
endif
if(iopt.eq.4) then
do 4 i=1,n
4 if(a.le.wk(i).and.wk(i).le.b) wk(i)=c
go to 7
endif
if(iopt.eq.5) then
do 6 i=1,n
cc=wk(i)
if(cc.le.a) wk(i)=b
6 if(cc.gt.a) wk(i)=c
go to 7
endif
7 lab='Truncated Array'
call ckadda(vname,n,lab,1,iref)
go to 99
c
c handle first case:
c
5 if(ickl(args(2),npxi,nxi).eq.1) go to 99
if(nxi.gt.nx) then
call error(args,2,2)
go to 99
endif
if(icki(args(4),4,nr,1,1).eq.1) go to 99
if(nr.gt.min0(nx,nxi)) then
call error(args,4,2)
go to 99
endif
rep=0.
call cklist(args(3),xlist,numarr,nprep)
if(nprep.ne.-999) then
iptr=1
nrep=nend(nprep)-nstart(nprep)+1
if(nr.gt.nrep) then
call error(args,4,2)
go to 99
endif
go to 10
endif
iptr=0
if(ickr(args(3),3,rep,0,0.).eq.1) go to 99
c
c
10 nsxi=nstart(npxi)-1
if(iptr.eq.1) nxr=nstart(nprep)-1
call movxy(wk,array(nstart(npx)),4*nx)
do 20 i=1,nr
ii=array(nsxi+i)
if(ii.lt.1.or.ii.gt.nx) then
write(*,15)
15 format(' Index outside range of array')
imflag=1
go to 99
endif
wk(ii)=rep
if(iptr.eq.1) wk(ii)=array(nxr+i)
20 continue
c
c
lab='Array from REPLACE'
call ckadda(vname,nx,lab,1,iref)
c
c
99 continue
return
end
c&PARCOR
subroutine parcor(args,nargs,vname)
c******************************************************************
c
c Subroutine to handle the command
c
c part=PARCORR(x,n,m) or
c
c part=PARCORR(x,n,m,rvar)
c
c*******************************************************************
c
#include 'tslabc'
character args(nargs)*15,vname*15
double precision inprod
integer*2 ickl,ickse
c
c
if(ickl(args(1),npx,nx).eq.1) go to 99
call ckint(args(2),n)
if(n.lt.1.or.n.gt.nx) then
call error(args,2,2)
go to 99
endif
call ckint(args(3),m)
if(m.lt.1.or.m.gt.n-1) then
call error(args,3,2)
go to 99
endif
c
c
npm=n+m
nws=2*(n+m)+2*m
if(ickse(nws).eq.1) go to 99
n4=4*n
npm2=2*npm
npm24=4*npm2
call movct(wk,npm24,char(0))
call movxy(wk,array(nstart(npx)),n4)
call movxy(wk(npm+2),array(nstart(npx)),n4)
r0=inprod(wk(1),wk(1),n)/float(n)
rvar=r0
do 120 i=1,m
c
c get partial :
c
top=2.*inprod(wk(1),wk(npm+1),npm)
bot=inprod(wk(1),wk(1),npm)+inprod(wk(npm+1),wk(npm+1),npm)
part=top/bot
if(part.le.-1.) part=-.9999
if(part.ge.1.) part=.9999
wk(npm2+i)=part
rvar=rvar*(1.-part*part)
wk(npm2+m+i)=rvar
c
c shift :
c
do 160 j=1,npm-1
i1=npm-j+1
i2=i1-1
ni1=npm+i1
ni2=npm+i2
temp=wk(ni1)
wk(ni1)=wk(ni2)-part*wk(i2)
160 wk(i1)=wk(i1)-part*temp
wk(1)=wk(1)-part*wk(npm+1)
wk(npm+1)=0.0
c
c end recursion :
c
120 continue
c
c
lab='Partial Autocorrelations'
call ckadda(vname,m,lab,npm2+1,iref)
if(iref.eq.1.or.nargs.eq.3) go to 99
lab='Residual Variances'
call ckadda(args(4),m,lab,npm2+m+1,iref)
c
c
99 continue
return
end
c&DNSITY
subroutine dnsity(args,nargs)
c*******************************************************************
c
c Subroutine to handle the command
c
c DENSITY(x,nobs,rbins,npts,kern,y,fy)
c
c*******************************************************************
c
#include 'tslabc'
character args(nargs)*15
integer*2 ickl,icki,ickse
pi=4.*atan(1.0)
c
c
if(ickl(args(1),npx,nx).eq.1) go to 99
call ckint(args(2),nobs)
if(nobs.lt.2.or.nobs.gt.nx) then
call error(args,2,2)
go to 99
endif
call ckreal(args(3),rbins)
if(rbins.lt.0..or.rbins.gt.float(nobs)) then
call error(args,3,2)
go to 99
endif
if(icki(args(4),4,npts,0,0).eq.1) go to 99
if(iabs(npts).lt.2) then
call error(args,4,2)
go to 99
endif
iptdet=0
if(npts.lt.0) then
iptdet=1
npts=-npts
if(ickl(args(6),npy,ny).eq.1) go to 99
if(npts.gt.ny) then
call error(args,6,1)
go to 99
endif
call movxy(wk,array(nstart(npy)),4*npts)
do 1 i=1,npts-1
if(wk(i).gt.wk(i+1)) then
call error(args,6,2)
go to 99
endif
1 continue
endif
call ckint(args(5),iopt)
if(iopt.lt.1.or.iopt.gt.7) then
call error(args,5,2)
go to 99
endif
if(ickse(npts).eq.1) go to 99
if(ickse(2*npts+nobs).eq.1) go to 99
c
c
call movxy(wk,array(nstart(npx)),4*nobs)
call qsort(nobs,wk)
xmin=wk(1)
xmax=wk(nobs)
rx=xmax-xmin
if(rx.lt.1.e-20) then
write(*,10)
10 format(' Range of Data less than 1.e-20')
imflag=1
go to 99
endif
if(rbins.eq.0.) then
call xbars2(wk,nobs,xbar,s2)
ot=1./3.
if(iopt.gt.1) ot=1./5.
rbins=(rx*(float(nobs)**ot)/(3.5*sqrt(s2)))+1.
endif
bw=(rx/rbins)/2.
onh=float(nobs)*bw
yinc=rx/float(npts-1)
nobsp=nobs+npts
c
c
j1=1
do 100 i=1,npts
if(iptdet.eq.1) y=array(nstart(npy)+i-1)
if(iptdet.eq.0) y=xmin+float(i-1)*yinc
yl=y-bw
yu=y+bw
do 20 j=j1,nobs
if(wk(j).ge.yl.and.wk(j).le.yu) go to 30
20 continue
nin=0
go to 60
30 nin=1
j1=j
if(j.eq.nobs) go to 60
do 40 k=j+1,nobs
if(wk(k).gt.yu) go to 50
40 nin=nin+1
50 continue
60 call smooth(wk(j1),nin,y,bw,onh,iopt,pi,fy)
wk(nobs+i)=y
wk(nobsp+i)=fy
100 continue
c
c
lab='y'
call ckadda(args(6),npts,lab,nobs+1,iref)
if(iref.eq.1) go to 99
lab='f(y)'
call ckadda(args(7),npts,lab,nobsp+1,iref)
c
c
99 continue
return
end
c&SMOOTH
subroutine smooth(x,nin,y,bw,onh,iopt,pi,fy)
c*******************************************************************
c
c Subroutine to find fy using a kernel function in dnsity
c
c********************************************************************
c
dimension x(1)
c
fy=0.
if(nin.eq.0) go to 99
if(iopt.eq.1) then
fy=.5*float(nin)/onh
go to 99
endif
if(iopt.eq.2) then
do 10 i=1,nin
u=(y-x(i))/bw
10 fy=fy+(1.+cos(pi*u))/2.
fy=fy/onh
go to 99
endif
if(iopt.eq.3) then
do 20 i=1,nin
u=(y-x(i))/bw
20 fy=fy+.75*(1.-u*u)
fy=fy/onh
go to 99
endif
if(iopt.eq.4) then
do 30 i=1,nin
u=(y-x(i))/bw
30 fy=fy+.9375*(1.-u*u)**2
fy=fy/onh
go to 99
endif
if(iopt.eq.5) then
do 40 i=1,nin
u=(y-x(i))/bw
40 fy=fy+(1.-abs(u))
fy=fy/onh
go to 99
endif
if(iopt.eq.6) then
do 50 i=1,nin
u=(y-x(i))/bw
50 fy=fy+1.012339*exp(-pi*u*u)
fy=fy/onh
go to 99
endif
if(iopt.eq.7) then
do 60 i=1,nin
u=(y-x(i))/bw
au=abs(u)
if(au.le..5) fy=fy+1.333-8.*(u*u-au**3)
if(au.gt..5) fy=fy+2.6667*(1.-au)**3
60 continue
fy=fy/onh
go to 99
endif
c
c
99 continue
return
end