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- subroutine remez1
- c--------------------------------------------------------------------
- c from Ref. [31] of chapter 5
- c in chapter 8
- c--------------------------------------------------------------------
- dimension iext(66),ad(66),alpha(66),x(66),y(66)
- dimension des(1045),grid(1045),wt(1045)
- dimension a(66),p(66),q(66)
- common pi2,ad,dev,x,y,grid,des,wt,alpha,iext,nfcns,ngrid
- common /oops/niter
- itrmax=25
- devl=-1.
- nz=nfcns+1
- nzz=nfcns+2
- niter=0
- 100 continue
- iext(nzz)=ngrid+1
- niter=niter+1
- if(niter.gt.itrmax) goto 400
- do 110 j=1,nz
- jxt=iext(j)
- dtemp=grid(jxt)
- dtemp=cos(dtemp*pi2)
- x(j)=dtemp
- 110 continue
- jet=(nfcns-1)/15+1
- do 120 j=1,nz
- ad(j)=d(j,nz,jet)
- 120 continue
- dnum=0.0
- dden=0.0
- k=1
- do 130 j=1,nz
- l=iext(j)
- dtemp=ad(j)*des(l)
- dnum=dnum+dtemp
- dtemp=k*ad(j)/wt(l)
- dden=dden+dtemp
- k=-k
- 130 continue
- dev=dnum/dden
- nu=1
- if(dev.gt.0.)nu=-1
- dev=-nu*dev
- k=nu
- do 140 j=1,nz
- l=iext(j)
- dtemp=k*dev/wt(l)
- y(j)=des(l)+dtemp
- k=-k
- 140 continue
- if(dev.gt.devl)goto 150
- call ouch
- goto 400
- 150 devl=dev
- jchneg=0
- k1=iext(1)
- knz=iext(nz)
- klow=0
- nut=-nu
- j=1
- 200 if(j.eq.nzz)ynz=comp
- if(j.ge.nzz) goto 300
- kup=iext(j+1)
- l=iext(j)+1
- nut=-nut
- if(j.eq.2)y1=comp
- comp=dev
- if(l.ge.kup) goto 220
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.le.0.)goto 220
- comp=nut*err
- 210 l=l+1
- if(l.ge.kup) goto 215
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.le.0.)goto 215
- comp=nut*err
- goto 210
- 215 iext(j)=l-1
- j=j+1
- klow=l-1
- jchnge=jchnge+1
- goto 200
- 220 l=l-1
- 225 l=l-1
- if(l.le.klow) goto 250
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.gt.0.)goto 230
- if(jchnge.le.0.)goto 225
- goto 260
- 230 comp=nut*err
- 235 l=l-1
- if(l.le.klow) goto 240
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.le.0.)goto 240
- comp=nut*err
- goto 235
- 240 klow=iext(j)
- iext(j)=l+1
- j=j+1
- jchnge=jchnge+1
- goto 200
- 250 l=iext(j)+1
- if(jchnge.gt.0.)goto 215
- 255 l=l+1
- if(l.ge.kup) goto 260
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.le.0.)goto 255
- comp=nut*err
- goto 210
- 260 klow=iext(j)
- j=j+1
- goto 200
- 300 if(j.gt.nzz)goto 320
- if(k1.gt.iext(1)) k1=iext(1)
- if(knz.lt.iext(nz)) knz=iext(nz)
- nut1=nut
- nut=-nu
- l=0
- kup=k1
- comp=ynz*1.00001
- luck=1
- 310 l=l+1
- if(l.ge.kup) goto 315
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.le.0.)goto 310
- comp=nut*err
- j=nzz
- goto 210
- 315 luck=6
- goto 325
- 320 if(luck.gt.9) goto 350
- if(comp.gt.y1) y1=comp
- k1=iext(nzz)
- 325 l=ngrid+1
- klow=knz
- nut=-nut1
- comp=y1*1.00001
- 330 l=l-1
- if(l.le.klow) goto 340
- err=gee(l,nz)
- err=(err-des(l))*wt(l)
- dtemp=nut*err-comp
- if(dtemp.le.0.)goto 330
- j=nzz
- comp=nut*err
- luck=luck+10
- goto 235
- 340 if(luck.eq.6)goto 370
- do 345 j=1,nfcns
- nzzmj=nzz-j
- nzmj=nz-j
- iext(nzzmj)=iext(nzmj)
- 345 continue
- iext(1)=k1
- goto 100
- 350 kn=iext(nzz)
- do 360 j=1,nfcns
- iext(j)=iext(j+1)
- 360 continue
- iext(nz)=kn
- goto 100
- 370 if(jchnge.gt.0) goto 100
- 400 continue
- nm1=nfcns-1
- fsh=1.e-06
- gtemp=grid(1)
- x(nzz)=-2.
- cn=2*nfcns-1
- delf=1./cn
- l=1
- kkk=0
- if(grid(1).le..01.and.grid(ngrid).gt.0.49) kkk=1
- if(nfcns.le.3)kkk=1
- if(kkk.eq.1)goto 405
- dtemp=cos(pi2*grid(1))
- dnum=cos(pi2*grid(ngrid))
- aa=2./(dtemp-dnum)
- bb=-(dtemp+dnum)/(dtemp-dnum)
- 405 continue
- do 430 j=1,nfcns
- ft=j-1
- ft=ft*delf
- xt=cos(pi2*ft)
- if(kkk.eq.1)goto 410
- xt=(xt-bb)/aa
- xt1=sqrt(1.-xt*xt)
- ft=atan2(xt1,xt)/pi2
- 410 xe=x(l)
- if(xt.gt.xe)goto 420
- if((xe-xt).lt.fsh)goto 415
- l=l+1
- goto 410
- 415 a(j)=y(l)
- goto 425
- 420 if((xt-xe).lt.fsh)goto 415
- grid(1)=ft
- a(j)=gee(1,nz)
- 425 if(l.gt.1)l=l-1
- 430 continue
- grid(1)=gtemp
- dden=pi2/cn
- do 510 j=1,nfcns
- dtemp=0.
- dnum=j-1
- dnum=dnum*dden
- if(nm1.lt.1)goto 505
- do 500 k=1,nm1
- dak=a(k+1)
- dk=k
- dtemp=dtemp+dak*cos(dnum*dk)
- 500 continue
- 505 dtemp=dtemp*2.+a(1)
- alpha(j)=dtemp
- 510 continue
- do 550 j=2,nfcns
- alpha(j)=alpha(j)*2./cn
- 550 continue
- alpha(1)=alpha(1)/cn
- if(kkk.eq.1) goto 545
- p(1)=2.*alpha(nfcns)*bb+alpha(nm1)
- p(2)=2.*alpha(nfcns)*aa
- q(1)=alpha(nfcns-2)-alpha(nfcns)
- do 540 j=2,nm1
- if(j.lt.nm1) goto 515
- aa=.5*aa
- bb=.5*bb
- 515 continue
- p(j+1)=0.
- do 520 k=1,j
- a(k)=p(k)
- p(k)=2.*bb*a(k)
- 520 continue
- p(2)=p(2)+a(1)*2.*aa
- jm1=j-1
- do 525 k=1,jm1
- p(k)=p(k)+q(k)+aa*a(k+1)
- 525 continue
- jp1=j+1
- do 530 k=3,jp1
- p(k)=p(k)+aa*a(k-1)
- 530 continue
- if(j.eq.nm1) goto 540
- do 535 k=1,j
- q(k)=-a(k)
- 535 continue
- nf1j=nfcns-j-1
- q(1)=q(1)+alpha(nf1j)
- 540 continue
- do 543 j=1,nfcns
- alpha(j)=p(j)
- 543 continue
- 545 continue
- if(nfcns.gt.3) return
- alpha(nfcns+1)=0.0
- alpha(nfcns+2)=0.0
- return
- end
- c----------------------------------------------------------------------
- function d(k,n,m)
- dimension iext(66),ad(66),alpha(66),x(66),y(66)
- dimension des(1045),grid(1045),wt(1045)
- common pi2,ad,dev,x,y,grid,des,wt,alpha,iext,nfcns,ngrid
- d=1.
- q=x(k)
- do 3 l=1,m
- do 2 j=l,n,m
- if(j-k)1,2,1
- 1 d=2.*d*(q-x(j))
- 2 continue
- 3 continue
- d=1./d
- return
- end
- c----------------------------------------------------------------------
- function gee(k,n)
- dimension iext(66),ad(66),alpha(66),x(66),y(66)
- dimension des(1045),grid(1045),wt(1045)
- c double precision ad,dev,x,y,p12,p,c,d,xf
- common pi2,ad,dev,x,y,grid,des,wt,alpha,iext,nfcns,ngrid
- p=0.0
- xf=grid(k)
- xf=cos(pi2*xf)
- d1=0.
- do 1 j=1,n
- c=xf-x(j)
- c=ad(j)/c
- d1=d1+c
- p=p+c*y(j)
- 1 continue
- gee=p/d1
- return
- end
- c----------------------------------------------------------------------
- subroutine ouch
- common /oops/niter
- return
- end
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发表于 2006-8-12 07:40
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