+++ /dev/null
-c===========================================================================
-c
-c This file is part of TISEAN
-c
-c Copyright (c) 1998-2007 Rainer Hegger, Holger Kantz, Thomas Schreiber
-c
-c TISEAN is free software; you can redistribute it and/or modify
-c it under the terms of the GNU General Public License as published by
-c the Free Software Foundation; either version 2 of the License, or
-c (at your option) any later version.
-c
-c TISEAN is distributed in the hope that it will be useful,
-c but WITHOUT ANY WARRANTY; without even the implied warranty of
-c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-c GNU General Public License for more details.
-c
-c You should have received a copy of the GNU General Public License
-c along with TISEAN; if not, write to the Free Software
-c Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
-c
-c===========================================================================
-c nonlinear noise reduction
-c see H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, Cambridge
-c University Press (1997,2004)
-c authors T. Schreiber, H. Kantz, R. Hegger (1998) based on earlier versions
-c===========================================================================
- parameter(nx=100000)
- dimension x(nx), x0(nx), xc(nx)
- character*72 file, fout
- data imax/1/
- data iverb/1/
-
- call whatido("nonlinear noise reduction (see also: noise)",iverb)
- m=imust("m")
- nq=m-imust("q")
- eps=fmust("r",eps)
- kmin=imust("k")
- imax=ican("i",imax)
- nmax=ican("l",nx)
- nexcl=ican("x",0)
- jcol=ican("c",0)
- isout=igetout(fout,iverb)
-
- call nthstring(1,file)
- call readfile(nmax,x,nexcl,jcol,file,iverb)
- if(file.eq."-") file="stdin"
- if(isout.eq.1) call addsuff(fout,file,"_")
-
- do 10 n=1,nmax
- 10 x0(n)=x(n)
- do 20 it=1,imax
- call clean(nmax,x,xc,m,kmin,nq,eps,iverb)
- if(fout.ne." ".or.isout.eq.1.or.it.eq.imax) then
- if(isout.eq.1) call suffix(fout,"c")
- call outfile(fout,iunit,iverb)
- do 30 n=1,nmax
- 30 write(iunit,*) xc(n), x0(n)-xc(n)
- if(iunit.ne.istdout()) close(iunit)
- if(iv_io(iverb).eq.1) call writereport(nmax,fout)
- endif
- eps=0
- do 40 n=1,nmax
- eps=eps+(xc(n)-x(n))**2
- 40 x(n)=xc(n)
- eps=sqrt(eps/nmax)
- 20 if(iv_io(iverb).eq.1)
- . write(istderr(),*) 'New diameter of neighbourhoods is ', eps
- end
-
- subroutine usage()
-c usage message
-
- call whatineed(
- . "-m# -q# -r# -k# [-i# -o outfile -l# -x# -c# -V# -h] file")
- call popt("m","embedding dimension")
- call popt("q","dimension of manifold")
- call popt("r","radius of neighbourhoods")
- call popt("k","minimal number of neighbours")
- call popt("i","number of iterations (1)")
- call popt("l","number of values to be read (all)")
- call popt("x","number of values to be skipped (0)")
- call popt("c","column to be read (1 or file,#)")
- call pout("file_c, file_cc (etc.)")
- call pall()
- call ptext("Verbosity levels (add what you want):")
- call ptext(" 1 = input/output" )
- call ptext(" 2 = state of neighbour search")
- write(istderr(),'()')
- stop
- end
-
- subroutine clean(nmax,y,yc,m,kmin,nq,d,iverb)
- parameter(im=100,ii=100000000,nx=100000,mm=15,small=0.0001)
- dimension y(nmax),yc(nmax),r(mm),ju(nx),c(mm,mm),cm(mm),
- . jh(0:im*im),jpntr(nx),nlist(nx), zcm(mm,nx)
-
- if(nmax.gt.nx.or.m.gt.mm) stop "clean: make mm/nx larger."
- sr=2*small+m-2 ! ${\rm tr}(1/r)=1$
- do 10 i=1,m
- r(i)=sr
- 10 if(i.eq.m.or.i.eq.1) r(i)=sr/small
- do 20 i=1,nmax
- 20 yc(i)=y(i)
- do 30 istep=1,2
- eps=d
- iu=nmax-m+1
- do 40 i=1,iu
- 40 ju(i)=i+m-1
- 1 call base(nmax,y,1,m,jh,jpntr,eps)
- iunp=0
- do 50 nn=1,iu ! find neighbours
- n=ju(nn)
- call neigh(nmax,y,y,n,nmax,1,m,jh,jpntr,eps,nlist,nfound)
- if(nfound.lt.kmin) then ! not enough neighbours found
- iunp=iunp+1 ! mark for next sweep
- ju(iunp)=n
- else ! fine: enough neighbours
- do 90 i=1,m ! centre of mass vector
- s=0
- do 100 np=1,nfound
- 100 s=s+y(nlist(np)-m+i)
- 90 cm(i)=s/nfound
- if(istep.eq.1) then ! just store centre of mass
- do 110 i=1,m
- 110 zcm(i,n)=cm(i)
- else
- do 120 i=1,m ! corrected centre of mass vector
- s=0
- do 130 np=1,nfound
- 130 s=s+zcm(i,nlist(np))
- 120 cm(i)=2*cm(i)-s/nfound
- do 140 i=1,m ! compute covariance matrix
- do 140 j=i,m
- s=0
- do 150 np=1,nfound
- jm=nlist(np)-m
- 150 s=s+(y(jm+i)-cm(i))*(y(jm+j)-cm(j))
- c(i,j)=r(i)*r(j)*s/nfound
- 140 c(j,i)=c(i,j)
- call eigen(c,m) ! find eigenvectors (decreasing)
- do 160 i=1,m
- s=0
- do 170 iq=m-nq+1,m
- do 170 j=1,m
- 170 s=s+(y(n-m+j)-cm(j))*c(i,iq)*c(j,iq)*r(j)
- 160 yc(n-m+i)=yc(n-m+i)-s/r(i)/r(i)
- endif
- endif
- 50 continue
- iu=iunp
- if(iv_uncorr(iverb).eq.1)
- . write(istderr(),*) "With ", eps, iunp, " uncorrected"
- eps=eps*sqrt(2.)
- 30 if(iunp.ne.0) goto 1
- end
-
-c driver for diagonalisation routines
-c see H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, Cambridge
-c University Press (1997)
-c Copyright (C) T. Schreiber (1997)
-
- subroutine eigen(c,kk)
- parameter(md=15)
- dimension c(md,md),d(md),w1(md),w2(md),z(md,md)
- if(kk.gt.md) stop "eigen: make md larger."
-
- call rs(md,kk,c,d,1,z,w1,w2,ierr)
- do 10 i=1,kk
- do 10 j=1,kk
- 10 c(i,j)=z(i,kk+1-j)
- end
-
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