2 |
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3 |
IMPLICIT NONE |
IMPLICIT NONE |
4 |
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INTEGER jfiltnu, jfiltsu, jfiltnv, jfiltsv |
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! jfiltn index of the last scalar line filtered in NH |
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! jfilts index of the first line filtered in SH |
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5 |
! North: |
! North: |
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real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
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! (iim, iim, 2:jfiltnu) |
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6 |
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7 |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
INTEGER jfiltnu, jfiltnv |
8 |
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! index of the last scalar line filtered in northern hemisphere |
9 |
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10 |
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real, pointer:: matriceun(:, :, :) ! (iim, iim, jfiltnu - 1) |
11 |
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! matrice filtre pour les champs situes sur la grille scalaire |
12 |
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13 |
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real, pointer:: matrinvn(:, :, :) ! (iim, iim, jfiltnu - 1) |
14 |
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! matrice filtre pour les champs situes sur la grille scalaire, pour |
15 |
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! le filtre inverse |
16 |
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17 |
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real, pointer:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
18 |
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! matrice filtre pour les champs situes sur la grille de V ou de Z |
19 |
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20 |
! South: |
! South: |
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real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
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! (iim, iim, jfiltsu:jjm) |
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21 |
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22 |
real, allocatable:: matricevs(:, :, :) ! (iim, iim, jfiltsv:jjm) |
integer jfiltsu, jfiltsv |
23 |
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! index of the first line filtered in southern hemisphere |
24 |
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25 |
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real, pointer:: matriceus(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
26 |
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! matrice filtre pour les champs situes sur la grille scalaire |
27 |
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28 |
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real, pointer:: matrinvs(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
29 |
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! matrice filtre pour les champs situes sur la grille scalaire, pour |
30 |
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! le filtre inverse |
31 |
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32 |
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real, pointer:: matricevs(:, :, :) ! (iim, iim, jjm - jfiltsv + 1) |
33 |
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! matrice filtre pour les champs situes sur la grille de V ou de Z |
34 |
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35 |
contains |
contains |
36 |
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37 |
SUBROUTINE inifilr |
SUBROUTINE inifilr |
38 |
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39 |
! 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 |
40 |
! H. Upadhyaya, O. Sharma |
! H. Upadhyaya, O. Sharma |
41 |
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42 |
! This routine computes the eigenfunctions of the laplacian on the |
! This procedure computes the filtering coefficients for scalar |
43 |
! stretched grid, and the filtering coefficients. The modes are |
! lines and meridional wind v lines. The modes are filtered from |
44 |
! filtered from modfrst to iim. |
! modfrst to iim. We filter all those latitude lines where coefil |
45 |
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! < 1. No filtering at poles. colat0 is to be used when alpha |
46 |
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! (stretching coefficient) is set equal to zero for the regular |
47 |
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! grid case. |
48 |
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49 |
USE dimens_m, ONLY : iim, jjm |
USE dimens_m, ONLY : iim, jjm |
50 |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
51 |
use inifgn_m, only: inifgn |
use inifgn_m, only: inifgn |
52 |
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use inifilr_hemisph_m, only: inifilr_hemisph |
53 |
use jumble, only: new_unit |
use jumble, only: new_unit |
54 |
use nr_util, only: pi |
use nr_util, only: pi, ifirstloc |
55 |
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56 |
! Local: |
! Local: |
57 |
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58 |
REAL dlatu(jjm) |
REAL dlatu(jjm) |
59 |
REAL rlamda(2: iim) |
REAL rlamda(2:iim) ! > 0, in descending order |
60 |
real eignvl(iim) ! eigenvalues sorted in descending order |
real eignvl(iim) ! eigenvalues sorted in descending order (<= 0) |
61 |
REAL cof |
INTEGER j, unit |
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INTEGER i, j, k, unit |
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62 |
REAL colat0 ! > 0 |
REAL colat0 ! > 0 |
63 |
REAL eignft(iim, iim), coff |
integer j1 ! index of smallest positive latitude |
64 |
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65 |
real eignfnu(iim, iim), eignfnv(iim, iim) |
real eignfnu(iim, iim), eignfnv(iim, iim) |
66 |
! eigenfunctions of the discrete laplacian |
! eigenvectors of the discrete second derivative with respect to longitude |
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! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
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real coefilu(iim, jjm), coefilv(iim, jjm) |
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real coefilu2(iim, jjm), coefilv2(iim, jjm) |
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! Index of the mode from where modes are filtered: |
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integer, allocatable:: modfrstnu(:), modfrstsu(:) |
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integer, allocatable:: modfrstnv(:), modfrstsv(:) |
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67 |
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68 |
!----------------------------------------------------------- |
!----------------------------------------------------------- |
69 |
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71 |
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72 |
CALL inifgn(eignvl, eignfnu, eignfnv) |
CALL inifgn(eignvl, eignfnu, eignfnv) |
73 |
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! compute eigenvalues and eigenfunctions |
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! compute the filtering coefficients for scalar lines and |
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! meridional wind v-lines |
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! we filter all those latitude lines where coefil < 1 |
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! NO FILTERING AT POLES |
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! colat0 is to be used when alpha (stretching coefficient) |
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! is set equal to zero for the regular grid case |
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74 |
! Calcul de colat0 |
! Calcul de colat0 |
75 |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
76 |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
77 |
PRINT *, 'colat0 = ', colat0 |
PRINT *, 'colat0 = ', colat0 |
78 |
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79 |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(abs(eignvl(2: iim))) |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(- eignvl(2: iim)) |
80 |
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call new_unit(unit) |
81 |
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open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
82 |
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write(unit, fmt = *) '"EIGNVL"', eignvl |
83 |
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close(unit) |
84 |
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open(unit, file = "modfrst.csv", status = "replace", action = "write") |
85 |
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write(unit, fmt = *) '"rlat (degrees)" modfrst' ! title line |
86 |
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87 |
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! D\'etermination de jfilt[ns][uv] : |
88 |
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89 |
! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv |
j1 = jjm + 1 - ifirstloc(rlatu(jjm:1:- 1) >= 0.) |
90 |
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91 |
jfiltnu = (jjm + 1) / 2 |
call inifilr_hemisph(rlatu(j1:2:- 1), colat0, rlamda, unit, eignfnv, & |
92 |
do while (cos(rlatu(jfiltnu)) >= colat0 & |
jfiltnu, matriceun, matrinvn) |
93 |
.or. rlamda(iim) * cos(rlatu(jfiltnu)) >= 1.) |
jfiltnu = j1 + 1 - jfiltnu |
94 |
jfiltnu = jfiltnu - 1 |
matriceun = matriceun(:, :, jfiltnu - 1:1:- 1) |
95 |
end do |
matrinvn = matrinvn(:, :, jfiltnu - 1:1:- 1) |
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jfiltsu = jjm / 2 + 2 |
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do while (cos(rlatu(jfiltsu)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatu(jfiltsu)) >= 1.) |
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jfiltsu = jfiltsu + 1 |
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end do |
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jfiltnv = jjm / 2 |
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do while ((cos(rlatv(jfiltnv)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) .and. jfiltnv >= 2) |
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jfiltnv = jfiltnv - 1 |
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end do |
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if (cos(rlatv(jfiltnv)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) then |
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! {jfiltnv == 1} |
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PRINT *, 'Could not find jfiltnv.' |
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STOP 1 |
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END IF |
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jfiltsv = (jjm + 1)/ 2 + 1 |
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do while ((cos(rlatv(jfiltsv)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) .and. jfiltsv <= jjm - 1) |
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jfiltsv = jfiltsv + 1 |
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end do |
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IF (cos(rlatv(jfiltsv)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) THEN |
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! {jfiltsv == jjm} |
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PRINT *, 'Could not find jfiltsv.' |
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STOP 1 |
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END IF |
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96 |
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97 |
PRINT *, 'jfiltnu =', jfiltnu |
call inifilr_hemisph(- rlatu(j1 + 1:jjm), colat0, rlamda, unit, eignfnv, & |
98 |
PRINT *, 'jfiltsu =', jfiltsu |
jfiltsu, matriceus, matrinvs) |
99 |
PRINT *, 'jfiltnv =', jfiltnv |
jfiltsu = j1 + jfiltsu |
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PRINT *, 'jfiltsv =', jfiltsv |
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100 |
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101 |
! Determination de coefilu, coefilv, modfrst[ns][uv]: |
j1 = jjm + 1 - ifirstloc(rlatv(jjm:1:- 1) >= 0.) |
102 |
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103 |
allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
call inifilr_hemisph(rlatv(j1:1:- 1), colat0, rlamda, unit, eignfnu, & |
104 |
allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
jfiltnv, matricevn) |
105 |
coefilu = 0. |
jfiltnv = j1 + 1 - jfiltnv |
106 |
coefilv = 0. |
matricevn = matricevn(:, :, jfiltnv:1:- 1) |
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coefilu2 = 0. |
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coefilv2 = 0. |
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DO j = 2, jfiltnu |
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modfrstnu(j) = 2 |
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do while (rlamda(modfrstnu(j)) * cos(rlatu(j)) >= 1. & |
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.and. modfrstnu(j) <= iim - 1) |
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modfrstnu(j) = modfrstnu(j) + 1 |
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end do |
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if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
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DO k = modfrstnu(j), iim |
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cof = rlamda(k) * cos(rlatu(j)) |
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coefilu(k, j) = cof - 1. |
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coefilu2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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END DO |
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DO j = 1, jfiltnv |
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modfrstnv(j) = 2 |
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do while (rlamda(modfrstnv(j)) * cos(rlatv(j)) >= 1. & |
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.and. modfrstnv(j) <= iim - 1) |
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modfrstnv(j) = modfrstnv(j) + 1 |
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end do |
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if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
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DO k = modfrstnv(j), iim |
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cof = rlamda(k) * cos(rlatv(j)) |
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coefilv(k, j) = cof - 1. |
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coefilv2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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end DO |
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DO j = jfiltsu, jjm |
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modfrstsu(j) = 2 |
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do while (rlamda(modfrstsu(j)) * cos(rlatu(j)) >= 1. & |
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.and. modfrstsu(j) <= iim - 1) |
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modfrstsu(j) = modfrstsu(j) + 1 |
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end do |
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if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
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DO k = modfrstsu(j), iim |
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cof = rlamda(k) * cos(rlatu(j)) |
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coefilu(k, j) = cof - 1. |
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coefilu2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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end DO |
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DO j = jfiltsv, jjm |
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modfrstsv(j) = 2 |
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do while (rlamda(modfrstsv(j)) * cos(rlatv(j)) >= 1. & |
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.and. modfrstsv(j) <= iim - 1) |
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modfrstsv(j) = modfrstsv(j) + 1 |
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end do |
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if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
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DO k = modfrstsv(j), iim |
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cof = rlamda(k) * cos(rlatv(j)) |
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coefilv(k, j) = cof - 1. |
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coefilv2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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END DO |
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107 |
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108 |
call new_unit(unit) |
call inifilr_hemisph(- rlatv(j1 + 1:jjm), colat0, rlamda, unit, eignfnu, & |
109 |
open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
jfiltsv, matricevs) |
110 |
write(unit, fmt = *) '"EIGNVL"', eignvl |
jfiltsv = j1 + jfiltsv |
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write(unit, fmt = *) '"modfrstnu"', modfrstnu |
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write(unit, fmt = *) '"modfrstsu"', modfrstsu |
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write(unit, fmt = *) '"modfrstnv"', modfrstnv |
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write(unit, fmt = *) '"modfrstsv"', modfrstsv |
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close(unit) |
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111 |
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112 |
allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu)) |
close(unit) |
113 |
allocate(matricevn(iim, iim, jfiltnv)) |
PRINT *, 'jfiltnu =', jfiltnu |
114 |
allocate(matricevs(iim, iim, jfiltsv:jjm)) |
PRINT *, 'jfiltsu =', jfiltsu |
115 |
allocate(matriceus(iim, iim, jfiltsu:jjm), matrinvs(iim, iim, jfiltsu:jjm)) |
PRINT *, 'jfiltnv =', jfiltnv |
116 |
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PRINT *, 'jfiltsv =', jfiltsv |
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! Calcul de la matrice filtre 'matriceu' pour les champs situes |
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! sur la grille scalaire |
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DO j = 2, jfiltnu |
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DO i = 1, iim |
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IF (i < modfrstnu(j)) then |
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coff = 0. |
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else |
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coff = coefilu(i, j) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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matriceun(:, :, j) = matmul(eignfnv, eignft) |
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END DO |
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DO j = jfiltsu, jjm |
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DO i = 1, iim |
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IF (i < modfrstsu(j)) then |
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coff = 0. |
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else |
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coff = coefilu(i, j) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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matriceus(:, :, j) = matmul(eignfnv, eignft) |
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END DO |
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! Calcul de la matrice filtre 'matricev' pour les champs situes |
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! sur la grille de V ou de Z |
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DO j = 1, jfiltnv |
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DO i = 1, iim |
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IF (i < modfrstnv(j)) then |
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coff = 0. |
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else |
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coff = coefilv(i, j) |
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end IF |
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eignft(i, :) = eignfnu(:, i) * coff |
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END DO |
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matricevn(:, :, j) = matmul(eignfnu, eignft) |
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END DO |
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DO j = jfiltsv, jjm |
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DO i = 1, iim |
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IF (i < modfrstsv(j)) then |
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coff = 0. |
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else |
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coff = coefilv(i, j) |
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end IF |
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eignft(i, :) = eignfnu(:, i) * coff |
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END DO |
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matricevs(:, :, j) = matmul(eignfnu, eignft) |
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END DO |
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! Calcul de la matrice filtre 'matrinv' pour les champs situes |
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! sur la grille scalaire , pour le filtre inverse |
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DO j = 2, jfiltnu |
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DO i = 1, iim |
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IF (i < modfrstnu(j)) then |
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coff = 0. |
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else |
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coff = coefilu(i, j) / (1. + coefilu(i, j)) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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matrinvn(:, :, j) = matmul(eignfnv, eignft) |
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END DO |
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DO j = jfiltsu, jjm |
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DO i = 1, iim |
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IF (i < modfrstsu(j)) then |
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coff = 0. |
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else |
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coff = coefilu(i, j) / (1. + coefilu(i, j)) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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matrinvs(:, :, j) = matmul(eignfnv, eignft) |
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END DO |
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117 |
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118 |
END SUBROUTINE inifilr |
END SUBROUTINE inifilr |
119 |
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