! source file: /Users/csomes/Research/Models/UVic_ESCM/2.9/source/common/filtr.F subroutine filtr (s, im, mm, n, iss) !======================================================================= ! === ! filter fourier analyses the arrays of various === ! physical quantities, then truncates the series and === ! resynthesizes the filtered quantities where: === ! s =the string to be filtered === ! im =the length of s === ! mm =1 (cosine series, deriv at bndry pts=0) === ! =2 ( sine series, bndry pts=0) === ! =3 (full series, cyclic) === ! n =number of waves to keep === ! iss=0 (cant use fourier coefs from previous call) === ! iss>0 (can use fourier coefs from previous call) === !======================================================================= implicit none !--------------------------------------------------------------------- ! define global data !--------------------------------------------------------------------- integer imtx2, ni, imtd2, lqmsum, lhsum, imtx4, imtx8, imtimt integer imp1x2, im, mm, n, iss, imsave, i, imm1, imqc, nmax integer nmaxp1, lcy, lh, lhm1, lqm, l2cy, lcym1, lcyp1, imx2 integer imx4, imx8, nprint, maxind, ncyc, maxndx, npwr, np, j integer ioff1, ioff2, joff, ioff, jbase, ibase real ssm, fimr, cc1, cc2, fnorm, ssum, fim, stemp, fact1 real fact2, genadj include "size.h" include "param.h" include "pconst.h" include "stdunits.h" include "scalar.h" include "switch.h" !--------------------------------------------------------------------- ! define local data and dimension argument arrays !--------------------------------------------------------------------- parameter (imtx2=imt*2,ni=imt) parameter (imtd2=imt/2,lqmsum=imtd2*(imt-imtd2),lhsum=imt*imtp1/2) parameter (imtx4=imt*4,imtx8=imt*8,imtimt=imt*imt) parameter (imp1x2=imtp1*2) integer icbase(imtp1), idbase(imtp1), ind(imtx8), indx(imtx8) common /cfilt_i/ ind, idbase, icbase common /cfilt_i/ imsave, jbase, ibase real*8 cossav(lqmsum) real temp(imtx4), denmsv(lhsum), cosnpi(imt) real cof(imtx8), cosine(imtx8), ftarr(imtimt) real denom(imtx4), s(imt), sprime(imt), circle(4) common /cfilt_d/ cossav common /cfilt_r/ denmsv, cosnpi, ftarr, circle ! data circle /0.,-1.,0.,1./ circle(1) = 0.0 circle(2) = -1.0 circle(3) = 0.0 circle(4) = 1.0 !--------------------------------------------------------------------- ! begin executable code !--------------------------------------------------------------------- if (im.lt.1 .or. mm.lt.1 .or. mm.gt.3 .or. n.lt.0 .or. iss.lt.0) $ then write (stdout,99) im, mm, n, iss write (stderr,99) im, mm, n, iss stop ' filtr 1' endif if (first) then ! this section sets up tables for filter; it must be called once ! per execution of ocean ! note: lqmsum is the sum of (im-1)/2 for im=1,imtp1 ! lhsum is the sum of im-1 for im=1,imtp1 imsave = im ! assemble index array do 100 i=1,imtx8 ind(i) = i 100 continue ! calculate and save all cosines which will be needed ibase = 0 jbase = 0 do 200 im=1,imtp1 fimr = c1/float(im) imm1 = im-1 if (imm1.eq.0) goto 181 do 180 i=1,imm1 denmsv(ibase+i) = c1/(c1-cos(pi*float(i)*fimr)) 180 continue 181 continue idbase(im) = ibase ibase = ibase + imm1 imqc = (im-1)/2 if (imqc .eq. 0) goto 191 do 190 i=1,imqc cossav(jbase+i) = cos(pi*float(i)*fimr) 190 continue 191 continue icbase(im) = jbase jbase = jbase + imqc 200 continue ! calculate adjustments for general fourier case if im=2*n do 300 im=1,imt cosnpi(im) = circle(mod(im-1,4)+1) 300 continue im = imsave endif ! calculate some useful constants if (mm.eq.2 .and. n.eq.0) then do 400 i=1,im s(i) = c0 400 continue goto 3201 endif if (mm .eq. 1) then nmax = n - 1 else nmax = n endif nmaxp1 = nmax + 1 cc1 = p5*float(nmax) + p25 cc2 = float(nmax) + p5 if (mm .eq. 2) then lcy = 2*(im + 1) fnorm = c2/float(im + 1) else lcy = 2*im fnorm = c2/float(im) endif lh = lcy/2 lhm1 = lh - 1 lqm = (lh - 1)/2 l2cy = 2*lcy lcym1 = lcy - 1 lcyp1 = lcy + 1 imx2 = im*2 imx4 = im*4 imx8 = im*8 ! average incoming array ssum = c0 do 500 i=1,im ssum = ssum + s(i) 500 continue ! mm = 1 derivative must be zero at boundaries (cosine) ! mm = 2 value must be zero at boundaries (sine) ! mm = 3 cyclic boundary conditions (general fourier series) fim = float(im) fimr = c1/fim stemp = ssum*fimr if (n.gt.1 .or. mm.ne.1) goto 601 do 600 i=1,im s(i)=stemp 600 continue go to 3201 601 continue if (mm .ne. 2) then do 700 i=1,im s(i) = s(i) - stemp 700 continue endif if (iss .gt. 0) goto 2501 ! assemble appropriate 1-cycle (2*pi) cosine array ! use stored 1/4 cycle to calculate first 1/2 cycle jbase = icbase(lh) do 800 i=1,lqm cosine(i) = cossav(jbase+i) 800 continue do 900 i=1,lqm cosine(lh-i) = -cossav(jbase+i) 900 continue ! fill in cos(pi/2) if lh is even if (2*(lqm+1) .eq. lh) cosine(lqm+1) = c0 ! fill in cos(pi) in any case cosine(lh) = -c1 ! fill in rest of cycle do 1000 i=1,lh cosine(lh+i) = -cosine(i) 1000 continue ! assemble denominator array ibase = idbase(lh) do 1100 i=1,lhm1 denom(i) = p25*denmsv(ibase+i) 1100 continue denom(lh) = 0.125 do 1200 i=1,lhm1 temp(i) = denom(lh-i) 1200 continue do 1300 i=1,lhm1 denom(lh+i) = temp(i) 1300 continue nprint = 0 denom(lcy) = c0 do 1400 i=lcyp1,imx4 denom(i) = denom(i-lcy) 1400 continue ! assemble appropriate subscript arrays ! calculate needed indices if (mm.eq.3) then fact1 = 2*nmax fact2 = 2*nmaxp1 else fact1 = nmax fact2 = nmaxp1 endif do 1500 i=1,imx4 indx(i) = ind(i)*fact1 1500 continue do 1600 i=1,imx4 indx(imx4+i) = ind(i)*fact2 1600 continue ! calculate parameters for reducing indices maxind = imx4*fact2 ncyc = (maxind-1)/lcy + 1 maxndx = lcy if (maxndx .ge. maxind) goto 1801 do 1700 npwr=1,ncyc+2 maxndx = 2*maxndx if (maxndx .ge. maxind) goto 1701 1700 continue write (stdout,999) write (stderr,999) stop ' filtr 2' 1701 continue do 1800 np=1,npwr maxndx = maxndx/2 do 1790 i=1,imx8 if (indx(i) .gt. maxndx) indx(i) = indx(i) - maxndx 1790 continue 1800 continue 1801 continue ! gather coefficients do 1900 j=1,imx8 cof(j) = cosine(indx(j)) 1900 continue ! assemble transformation array which will filter s if (mm.eq.1) then ! cosine transform ioff1 = lcy ioff2 = lcy + imx4 do 2000 j=1,im joff = (j-1)*imt do 1990 i=1,im ftarr(joff+i) = $ (cof(i-j+ioff1) - cof(i-j+ioff2)) *denom(i-j+ioff1) + $ (cof(i + j - 1) - cof(imx4+i+j-1))*denom(i+j-1) - p5 1990 continue 2000 continue do 2100 j=1,im ftarr(j*imtp1-imt) = ftarr(j*imtp1-imt) + cc1 2100 continue elseif (mm .eq. 2) then ! sine transform ioff1 = lcy ioff2 = lcy + imx4 do 2200 j=1,im joff = (j-1)*imt do 2190 i=1,im ftarr(joff+i) = $ (cof(i-j+ioff1) - cof(i-j+ioff2))*denom(i-j+ioff1) - $ (cof(i + j) - cof(imx4+i+j)) *denom(i+j) 2190 continue 2200 continue do 2300 j=1,im ftarr(j*imtp1-imt) = ftarr(j*imtp1-imt) + cc1 2300 continue elseif (mm.eq.3) then ! general fourier transform if (2*n .eq. im) then genadj = p5 else genadj = c0 endif ioff1 = lcy ioff2 = lcy + imx4 do 2400 j=1,im joff = (j-1)*imt do 2390 i=1,im ftarr(joff+i) = (c2*(cof(i-j+ioff1) - cof(i-j+ioff2))) $ *denom(2*i-2*j+ioff1) - p5 - genadj*cosnpi(i)*cosnpi(j) 2390 continue 2400 continue do 2500 j=1,im ftarr(j*imtp1-imt) = ftarr(j*imtp1-imt) + cc2 2500 continue endif ! filter s 2501 continue do 2600 i=1,im sprime(i) = c0 2600 continue ! note that ftarr(j,i)=ftarr(i,j), so following is legal do 2700 i=1,im ioff = (i-1)*imt do 2690 j=1,im sprime(j) = sprime(j) + s(i)*ftarr(ioff+j) 2690 continue 2700 continue do 2800 i=1,im sprime(i) = fnorm*sprime(i) 2800 continue if (mm.eq.2) then do 2900 i=1,im s(i) = sprime(i) 2900 continue goto 3201 endif ssm = c0 do 3100 i=1,im ssm = ssm + sprime(i) 3100 continue ssm = (ssum-ssm)*fimr do 3200 i=1,im s(i) = ssm+sprime(i) 3200 continue 3201 continue 99 format (/' error => bad argument(s) in call to filtr' $ /' im,mm,n,iss = ',4i10) 999 format (/' error => can not calculate parameters for reducing', $ ' indices in filtr') return end