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trunk/Sources/filtrez/inifilr.f revision 154 by guez, Tue Jul 7 17:49:23 2015 UTC trunk/filtrez/inifilr.f revision 265 by guez, Tue Mar 20 09:35:59 2018 UTC
# Line 2  module inifilr_m Line 2  module inifilr_m
2    
3    IMPLICIT NONE    IMPLICIT NONE
4    
5    INTEGER jfiltnu, jfiltsu, jfiltnv, jfiltsv    INTEGER jfiltnu, jfiltnv
6    ! jfiltn index of the last scalar line filtered in NH    ! index of the last line filtered in northern hemisphere at rlat[uv]
7    ! jfilts index of the first line filtered in SH    ! latitudes
8    
9    ! North:    integer jfiltsu, jfiltsv
10    real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :)    ! index of the first line filtered in southern hemisphere at
11    ! (iim, iim, 2:jfiltnu)    ! rlat[uv] latitudes
12    
13    real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv)    ! Filtre pour les champs situes sur la grille scalaire (longitudes
14      ! rlonv, latitudes rlatu) :
15    ! South:    real, pointer:: matriceun(:, :, :) ! (iim, iim, jfiltnu - 1)
16    real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :)    real, pointer:: matriceus(:, :, :) ! (iim, iim, jjm - jfiltsu + 1)
17    ! (iim, iim, jfiltsu:jjm)  
18      ! Filtre pour les champs situes sur la grille scalaire (longitudes
19    real, allocatable:: matricevs(:, :, :) ! (iim, iim, jfiltsv:jjm)    ! rlonv, latitudes rlatu), pour le filtre inverse :
20      real, pointer:: matrinvn(:, :, :) ! (iim, iim, jfiltnu - 1)
21      real, pointer:: matrinvs(:, :, :) ! (iim, iim, jjm - jfiltsu + 1)
22    
23      ! Filtre pour les champs situes sur la grille de la vorticit\'e
24      ! (longitudes rlonu, latitudes rlatv)
25      real, pointer:: matricevn(:, :, :) ! (iim, iim, jfiltnv) matrice
26      real, pointer:: matricevs(:, :, :) ! (iim, iim, jjm - jfiltsv + 1)
27    
28  contains  contains
29    
30    SUBROUTINE inifilr    SUBROUTINE inifilr
31    
32      ! From filtrez/inifilr.F, version 1.1.1.1 2004/05/19 12:53:09      ! From filtrez/inifilr.F, version 1.1.1.1, 2004/05/19 12:53:09
33      ! H. Upadhyaya, O. Sharma      ! H. Upadhyaya, O. Sharma
34    
35      ! This routine computes the eigenfunctions of the laplacian on the      ! This procedure computes the filtering coefficients for scalar
36      ! stretched grid, and the filtering coefficients. The modes are      ! lines and meridional wind v lines. The modes are filtered from
37      ! filtered from modfrst to iim.      ! modfrst to iim. We filter all those latitude lines where coefil
38        ! < 1. No filtering at poles. colat0 is to be used when alpha
39        ! (stretching coefficient) is set equal to zero for the regular
40        ! grid case.
41    
42      USE dimens_m, ONLY : iim, jjm      USE dimensions, ONLY : iim, jjm
43      USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx      USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx
44      use inifgn_m, only: inifgn      use inifgn_m, only: inifgn
45        use inifilr_hemisph_m, only: inifilr_hemisph
46      use jumble, only: new_unit      use jumble, only: new_unit
47      use nr_util, only: pi      use nr_util, only: pi, ifirstloc, assert
48    
49      ! Local:      ! Local:
50    
51      REAL dlatu(jjm)      REAL dlatu(jjm)
52      REAL rlamda(2: iim)      REAL rlamda(2:iim) ! > 0, in descending order
53      real eignvl(iim) ! eigenvalues sorted in descending order      real eignvl(iim) ! eigenvalues (<= 0) sorted in descending order
54      REAL cof      INTEGER j, unit
     INTEGER i, j, k, unit  
55      REAL colat0 ! > 0      REAL colat0 ! > 0
56      REAL eignft(iim, iim), coff      integer j1 ! index of negative latitude closest to the equator
57    
58      real eignfnu(iim, iim), eignfnv(iim, iim)      real eignfnu(iim, iim), eignfnv(iim, iim)
59      ! eigenfunctions of the discrete laplacian      ! eigenvectors of the discrete second derivative with respect to
60        ! longitude, at rlon[uv] longitudes
     ! Filtering coefficients (lamda_max * cos(rlat) / lamda):  
     real coefilu(iim, jjm), coefilv(iim, jjm)  
     real coefilu2(iim, jjm), coefilv2(iim, jjm)  
   
     ! Index of the mode from where modes are filtered:  
     integer, allocatable:: modfrstnu(:), modfrstsu(:)  
     integer, allocatable:: modfrstnv(:), modfrstsv(:)  
61    
62      !-----------------------------------------------------------      !-----------------------------------------------------------
63    
# Line 61  contains Line 65  contains
65    
66      CALL inifgn(eignvl, eignfnu, eignfnv)      CALL inifgn(eignvl, eignfnu, eignfnv)
67    
     ! compute eigenvalues and eigenfunctions  
     ! compute the filtering coefficients for scalar lines and  
     ! meridional wind v-lines  
     ! we filter all those latitude lines where coefil < 1  
     ! NO FILTERING AT POLES  
     ! colat0 is to be used when alpha (stretching coefficient)  
     ! is set equal to zero for the regular grid case  
   
68      ! Calcul de colat0      ! Calcul de colat0
69      forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1)      forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1)
70      colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim)))      colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim)))
71      PRINT *, 'colat0 = ', colat0      PRINT *, 'colat0 = ', colat0
72    
73      rlamda = iim / (pi * colat0 / grossismx) / sqrt(abs(eignvl(2: iim)))      rlamda = iim / pi / colat0 * grossismx / sqrt(- eignvl(2: iim))
74        print *, "1 / rlamda(iim) = ", 1. / rlamda(iim)
75        ! This is demonstrated in the notes but just to be sure:
76        call assert(rlamda(iim) * colat0 >= 1. - 2. * epsilon(0.), &
77             "inifilr rlamda(iim) * colat0")
78    
79        call new_unit(unit)
80        open(unit, file = "modfrst.csv", status = "replace", action = "write")
81        write(unit, fmt = *) '"rlat (degrees)" modfrst' ! title line
82    
83      ! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv      j1 = ifirstloc(rlatu <= 0.)
84    
85      jfiltnu = (jjm + 1) / 2      call inifilr_hemisph(rlatu(j1 - 1:2:- 1), rlamda, unit, eignfnv, jfiltnu, &
86      do while (cos(rlatu(jfiltnu)) >= colat0 &           matriceun, matrinvn)
87           .or. rlamda(iim) * cos(rlatu(jfiltnu)) >= 1.)      jfiltnu = j1 - jfiltnu
88         jfiltnu = jfiltnu - 1      matriceun = matriceun(:, :, jfiltnu - 1:1:- 1)
89      end do      matrinvn = matrinvn(:, :, jfiltnu - 1:1:- 1)
90    
91      jfiltsu = jjm / 2 + 2      call inifilr_hemisph(- rlatu(j1:jjm), rlamda, unit, eignfnv, jfiltsu, &
92      do while (cos(rlatu(jfiltsu)) >= colat0 &           matriceus, matrinvs)
93           .or. rlamda(iim) * cos(rlatu(jfiltsu)) >= 1.)      jfiltsu = j1 - 1 + jfiltsu
94         jfiltsu = jfiltsu + 1  
95      end do      j1 = ifirstloc(rlatv <= 0.)
96    
97      jfiltnv = jjm / 2      call inifilr_hemisph(rlatv(j1 - 1:1:- 1), rlamda, unit, eignfnu, jfiltnv, &
98      do while ((cos(rlatv(jfiltnv)) >= colat0 &           matricevn)
99           .or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) .and. jfiltnv >= 2)      jfiltnv = j1 - jfiltnv
100         jfiltnv = jfiltnv - 1      matricevn = matricevn(:, :, jfiltnv:1:- 1)
101      end do  
102        call inifilr_hemisph(- rlatv(j1:jjm), rlamda, unit, eignfnu, jfiltsv, &
103      if (cos(rlatv(jfiltnv)) >= colat0 &           matricevs)
104           .or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) then      jfiltsv = j1 - 1 + jfiltsv
        ! {jfiltnv == 1}  
        PRINT *, 'Could not find jfiltnv.'  
        STOP 1  
     END IF  
   
     jfiltsv = (jjm + 1)/ 2 + 1  
     do while ((cos(rlatv(jfiltsv)) >= colat0 &  
          .or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) .and. jfiltsv <= jjm - 1)  
        jfiltsv = jfiltsv + 1  
     end do  
   
     IF (cos(rlatv(jfiltsv)) >= colat0 &  
          .or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) THEN  
        ! {jfiltsv == jjm}  
        PRINT *, 'Could not find jfiltsv.'  
        STOP 1  
     END IF  
105    
106        close(unit)
107      PRINT *, 'jfiltnu =', jfiltnu      PRINT *, 'jfiltnu =', jfiltnu
108      PRINT *, 'jfiltsu =', jfiltsu      PRINT *, 'jfiltsu =', jfiltsu
109      PRINT *, 'jfiltnv =', jfiltnv      PRINT *, 'jfiltnv =', jfiltnv
110      PRINT *, 'jfiltsv =', jfiltsv      PRINT *, 'jfiltsv =', jfiltsv
111    
     ! Determination de coefilu, coefilv, modfrst[ns][uv]:  
   
     allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm))  
     allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm))  
     coefilu = 0.  
     coefilv = 0.  
     coefilu2 = 0.  
     coefilv2 = 0.  
   
     DO j = 2, jfiltnu  
        modfrstnu(j) = 2  
        do while (rlamda(modfrstnu(j)) * cos(rlatu(j)) >= 1. &  
             .and. modfrstnu(j) <= iim - 1)  
           modfrstnu(j) = modfrstnu(j) + 1  
        end do  
   
        if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then  
           DO k = modfrstnu(j), iim  
              cof = rlamda(k) * cos(rlatu(j))  
              coefilu(k, j) = cof - 1.  
              coefilu2(k, j) = cof**2 - 1.  
           end DO  
        end if  
     END DO  
   
     DO j = 1, jfiltnv  
        modfrstnv(j) = 2  
        do while (rlamda(modfrstnv(j)) * cos(rlatv(j)) >= 1. &  
             .and. modfrstnv(j) <= iim - 1)  
           modfrstnv(j) = modfrstnv(j) + 1  
        end do  
   
        if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then  
           DO k = modfrstnv(j), iim  
              cof = rlamda(k) * cos(rlatv(j))  
              coefilv(k, j) = cof - 1.  
              coefilv2(k, j) = cof**2 - 1.  
           end DO  
        end if  
     end DO  
   
     DO j = jfiltsu, jjm  
        modfrstsu(j) = 2  
        do while (rlamda(modfrstsu(j)) * cos(rlatu(j)) >= 1. &  
             .and. modfrstsu(j) <= iim - 1)  
           modfrstsu(j) = modfrstsu(j) + 1  
        end do  
   
        if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then  
           DO k = modfrstsu(j), iim  
              cof = rlamda(k) * cos(rlatu(j))  
              coefilu(k, j) = cof - 1.  
              coefilu2(k, j) = cof**2 - 1.  
           end DO  
        end if  
     end DO  
   
     DO j = jfiltsv, jjm  
        modfrstsv(j) = 2  
        do while (rlamda(modfrstsv(j)) * cos(rlatv(j)) >= 1. &  
             .and. modfrstsv(j) <= iim - 1)  
           modfrstsv(j) = modfrstsv(j) + 1  
        end do  
   
        if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then  
           DO k = modfrstsv(j), iim  
              cof = rlamda(k) * cos(rlatv(j))  
              coefilv(k, j) = cof - 1.  
              coefilv2(k, j) = cof**2 - 1.  
           end DO  
        end if  
     END DO  
   
     call new_unit(unit)  
     open(unit, file = "inifilr_out.txt", status = "replace", action = "write")  
     write(unit, fmt = *) '"EIGNVL"', eignvl  
     write(unit, fmt = *) '"modfrstnu"', modfrstnu  
     write(unit, fmt = *) '"modfrstsu"', modfrstsu  
     write(unit, fmt = *) '"modfrstnv"', modfrstnv  
     write(unit, fmt = *) '"modfrstsv"', modfrstsv  
     close(unit)  
   
     allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu))  
     allocate(matricevn(iim, iim, jfiltnv))  
     allocate(matricevs(iim, iim, jfiltsv:jjm))  
     allocate(matriceus(iim, iim, jfiltsu:jjm), matrinvs(iim, iim, jfiltsu:jjm))  
   
     ! Calcul de la matrice filtre 'matriceu' pour les champs situes  
     ! sur la grille scalaire  
   
     DO j = 2, jfiltnu  
        DO i = 1, iim  
           IF (i < modfrstnu(j)) then  
              coff = 0.  
           else  
              coff = coefilu(i, j)  
           end IF  
           eignft(i, :) = eignfnv(:, i) * coff  
        END DO  
        matriceun(:, :, j) = matmul(eignfnv, eignft)  
     END DO  
   
     DO j = jfiltsu, jjm  
        DO i = 1, iim  
           IF (i < modfrstsu(j)) then  
              coff = 0.  
           else  
              coff = coefilu(i, j)  
           end IF  
           eignft(i, :) = eignfnv(:, i) * coff  
        END DO  
        matriceus(:, :, j) = matmul(eignfnv, eignft)  
     END DO  
   
     ! Calcul de la matrice filtre 'matricev' pour les champs situes  
     ! sur la grille de V ou de Z  
   
     DO j = 1, jfiltnv  
        DO i = 1, iim  
           IF (i < modfrstnv(j)) then  
              coff = 0.  
           else  
              coff = coefilv(i, j)  
           end IF  
           eignft(i, :) = eignfnu(:, i) * coff  
        END DO  
        matricevn(:, :, j) = matmul(eignfnu, eignft)  
     END DO  
   
     DO j = jfiltsv, jjm  
        DO i = 1, iim  
           IF (i < modfrstsv(j)) then  
              coff = 0.  
           else  
              coff = coefilv(i, j)  
           end IF  
           eignft(i, :) = eignfnu(:, i) * coff  
        END DO  
        matricevs(:, :, j) = matmul(eignfnu, eignft)  
     END DO  
   
     ! Calcul de la matrice filtre 'matrinv' pour les champs situes  
     ! sur la grille scalaire , pour le filtre inverse  
   
     DO j = 2, jfiltnu  
        DO i = 1, iim  
           IF (i < modfrstnu(j)) then  
              coff = 0.  
           else  
              coff = coefilu(i, j) / (1. + coefilu(i, j))  
           end IF  
           eignft(i, :) = eignfnv(:, i) * coff  
        END DO  
        matrinvn(:, :, j) = matmul(eignfnv, eignft)  
     END DO  
   
     DO j = jfiltsu, jjm  
        DO i = 1, iim  
           IF (i < modfrstsu(j)) then  
              coff = 0.  
           else  
              coff = coefilu(i, j) / (1. + coefilu(i, j))  
           end IF  
           eignft(i, :) = eignfnv(:, i) * coff  
        END DO  
        matrinvs(:, :, j) = matmul(eignfnv, eignft)  
     END DO  
   
112    END SUBROUTINE inifilr    END SUBROUTINE inifilr
113    
114  end module inifilr_m  end module inifilr_m
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