2 |
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|
3 |
IMPLICIT NONE |
IMPLICIT NONE |
4 |
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|
! North: |
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|
5 |
INTEGER jfiltnu, jfiltnv |
INTEGER jfiltnu, jfiltnv |
6 |
! index of the last scalar line filtered in northern hemisphere |
! index of the last line filtered in northern hemisphere at rlat[uv] |
7 |
|
! latitudes |
|
real, allocatable:: matriceun(:, :, :) ! (iim, iim, 2:jfiltnu) |
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! matrice filtre pour les champs situes sur la grille scalaire |
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real, allocatable:: matrinvn(:, :, :) ! (iim, iim, 2:jfiltnu) |
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! matrice filtre pour les champs situes sur la grille scalaire, pour |
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! le filtre inverse |
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real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
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! matrice filtre pour les champs situes sur la grille de V ou de Z |
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! South: |
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8 |
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|
9 |
integer jfiltsu, jfiltsv |
integer jfiltsu, jfiltsv |
10 |
! index of the first line filtered in southern hemisphere |
! index of the first line filtered in southern hemisphere at |
11 |
|
! rlat[uv] latitudes |
|
real, allocatable:: matriceus(:, :, :) ! (iim, iim, jfiltsu:jjm) |
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! matrice filtre pour les champs situes sur la grille scalaire |
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real, allocatable:: matrinvs(:, :, :) ! (iim, iim, jfiltsu:jjm) |
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! matrice filtre pour les champs situes sur la grille scalaire, pour |
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! le filtre inverse |
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12 |
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13 |
real, allocatable:: matricevs(:, :, :) ! (iim, iim, jfiltsv:jjm) |
! Filtre pour les champs situes sur la grille scalaire (longitudes |
14 |
! matrice filtre pour les champs situes sur la grille de V ou de Z |
! rlonv, latitudes rlatu) : |
15 |
|
real, pointer:: matriceun(:, :, :) ! (iim, iim, jfiltnu - 1) |
16 |
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real, pointer:: matriceus(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
17 |
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|
18 |
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! Filtre pour les champs situes sur la grille scalaire (longitudes |
19 |
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! rlonv, latitudes rlatu), pour le filtre inverse : |
20 |
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real, pointer:: matrinvn(:, :, :) ! (iim, iim, jfiltnu - 1) |
21 |
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real, pointer:: matrinvs(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
22 |
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23 |
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! Filtre pour les champs situes sur la grille de la vorticit\'e |
24 |
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! (longitudes rlonu, latitudes rlatv) |
25 |
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real, pointer:: matricevn(:, :, :) ! (iim, iim, jfiltnv) matrice |
26 |
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real, pointer:: matricevs(:, :, :) ! (iim, iim, jjm - jfiltsv + 1) |
27 |
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|
28 |
contains |
contains |
29 |
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42 |
USE dimens_m, ONLY : iim, jjm |
USE dimens_m, 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 |
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49 |
! Local: |
! Local: |
50 |
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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 (<= 0) |
real eignvl(iim) ! eigenvalues (<= 0) sorted in descending order |
54 |
INTEGER i, j, unit |
INTEGER j, unit |
55 |
REAL colat0 ! > 0 |
REAL colat0 ! > 0 |
56 |
REAL eignft(iim, iim) |
integer j1 ! index of negative latitude closest to the equator |
57 |
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|
58 |
real eignfnu(iim, iim), eignfnv(iim, iim) |
real eignfnu(iim, iim), eignfnv(iim, iim) |
59 |
! eigenvectors of the discrete second derivative with respect to longitude |
! eigenvectors of the discrete second derivative with respect to |
60 |
|
! longitude, at rlon[uv] longitudes |
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! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
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real coefil(iim) |
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! Index of the mode from where modes are filtered: |
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integer, allocatable:: modfrstnu(:) ! (2:jfiltnu) |
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integer, allocatable:: modfrstsu(:) ! (jfiltsu:jjm) |
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integer, allocatable:: modfrstnv(:) ! (jfiltnv) |
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integer, allocatable:: modfrstsv(:) ! (jfiltsv:jjm) |
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61 |
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62 |
!----------------------------------------------------------- |
!----------------------------------------------------------- |
63 |
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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 |
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|
73 |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(- eignvl(2: iim)) |
rlamda = iim / pi / colat0 * grossismx / sqrt(- eignvl(2: iim)) |
74 |
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print *, "1 / rlamda(iim) = ", 1. / rlamda(iim) |
75 |
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! This is demonstrated in the notes but just to be sure: |
76 |
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call assert(rlamda(iim) * colat0 >= 1. - 2. * epsilon(0.), & |
77 |
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"inifilr rlamda(iim) * colat0") |
78 |
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79 |
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call new_unit(unit) |
80 |
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open(unit, file = "modfrst.csv", status = "replace", action = "write") |
81 |
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write(unit, fmt = *) '"rlat (degrees)" modfrst' ! title line |
82 |
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83 |
! D\'etermination de jfilt[ns][uv] : |
j1 = ifirstloc(rlatu <= 0.) |
84 |
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|
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 |
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|
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} |
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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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105 |
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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 |
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! D\'etermination de modfrst[ns][uv] : |
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allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
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allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
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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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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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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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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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END DO |
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call new_unit(unit) |
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open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
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write(unit, fmt = *) '"EIGNVL"', eignvl |
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close(unit) |
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open(unit, file = "modfrstnu.csv", status = "replace", action = "write") |
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write(unit, fmt = *) '"rlatu (degrees north)" modfrstnu ' & |
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|
// '"rlamda(modfrstnu) * cos(rlatu) < 1"' |
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|
DO j = 2, jfiltnu |
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|
write(unit, fmt = *) rlatu(j) / pi * 180., modfrstnu(j), & |
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|
rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1 |
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end DO |
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close(unit) |
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open(unit, file = "modfrstnv.csv", status = "replace", action = "write") |
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write(unit, fmt = *) '"rlatv (degrees north)" modfrstnv ' & |
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// '"rlamda(modfrstnv) * cos(rlatv) < 1"' |
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|
DO j = 1, jfiltnv |
|
|
write(unit, fmt = *) rlatv(j) / pi * 180., modfrstnv(j), & |
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|
rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1 |
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|
end DO |
|
|
close(unit) |
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open(unit, file = "modfrstsu.csv", status = "replace", action = "write") |
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write(unit, fmt = *) '"rlatu (degrees north)" modfrstsu ' & |
|
|
// '"rlamda(modfrstsu) * cos(rlatu) < 1"' |
|
|
DO j = jfiltsu, jjm |
|
|
write(unit, fmt = *) rlatu(j) / pi * 180., modfrstsu(j), & |
|
|
rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1 |
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|
end DO |
|
|
close(unit) |
|
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|
|
|
open(unit, file = "modfrstsv.csv", status = "replace", action = "write") |
|
|
write(unit, fmt = *) '"rlatv (degrees north)" modfrstsv ' & |
|
|
// '"rlamda(modfrstsv) * cos(rlatv) < 1"' |
|
|
DO j = jfiltsv, jjm |
|
|
write(unit, fmt = *) rlatv(j) / pi * 180., modfrstsv(j), & |
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rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1 |
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end DO |
|
|
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 matriceu et matrinv |
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DO j = 2, jfiltnu |
|
|
if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
|
|
DO i = modfrstnu(j), iim |
|
|
coefil(i) = rlamda(i) * cos(rlatu(j)) - 1. |
|
|
end DO |
|
|
|
|
|
eignft(:modfrstnu(j) - 1, :) = 0. |
|
|
|
|
|
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) * coefil(i) |
|
|
matriceun(:, :, j) = matmul(eignfnv, eignft) |
|
|
|
|
|
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) & |
|
|
* coefil(i) / (1. + coefil(i)) |
|
|
matrinvn(:, :, j) = matmul(eignfnv, eignft) |
|
|
else |
|
|
matriceun(:, :, j) = 0. |
|
|
matrinvn(:, :, j) = 0. |
|
|
end if |
|
|
END DO |
|
|
|
|
|
DO j = jfiltsu, jjm |
|
|
if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
|
|
DO i = modfrstsu(j), iim |
|
|
coefil(i) = rlamda(i) * cos(rlatu(j)) - 1. |
|
|
end DO |
|
|
|
|
|
eignft(:modfrstsu(j) - 1, :) = 0. |
|
|
|
|
|
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) * coefil(i) |
|
|
matriceus(:, :, j) = matmul(eignfnv, eignft) |
|
|
|
|
|
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) & |
|
|
* coefil(i) / (1. + coefil(i)) |
|
|
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
|
|
else |
|
|
matriceus(:, :, j) = 0. |
|
|
matrinvs(:, :, j) = 0. |
|
|
end if |
|
|
END DO |
|
|
|
|
|
! Calcul de matricev |
|
|
|
|
|
DO j = 1, jfiltnv |
|
|
if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
|
|
DO i = modfrstnv(j), iim |
|
|
coefil(i) = rlamda(i) * cos(rlatv(j)) - 1. |
|
|
end DO |
|
|
|
|
|
eignft(:modfrstnv(j) - 1, :) = 0. |
|
|
forall (i = modfrstnv(j):iim) eignft(i, :) = eignfnu(:, i) * coefil(i) |
|
|
matricevn(:, :, j) = matmul(eignfnu, eignft) |
|
|
else |
|
|
matricevn(:, :, j) = 0. |
|
|
end if |
|
|
END DO |
|
|
|
|
|
DO j = jfiltsv, jjm |
|
|
if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
|
|
DO i = modfrstsv(j), iim |
|
|
coefil(i) = rlamda(i) * cos(rlatv(j)) - 1. |
|
|
end DO |
|
|
|
|
|
eignft(:modfrstsv(j) - 1, :) = 0. |
|
|
forall (i = modfrstsv(j):iim) eignft(i, :) = eignfnu(:, i) * coefil(i) |
|
|
matricevs(:, :, j) = matmul(eignfnu, eignft) |
|
|
else |
|
|
matricevs(:, :, j) = 0. |
|
|
end if |
|
|
END DO |
|
|
|
|
112 |
END SUBROUTINE inifilr |
END SUBROUTINE inifilr |
113 |
|
|
114 |
end module inifilr_m |
end module inifilr_m |