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: |
6 |
real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
|
7 |
! (iim, iim, 2:jfiltnu) |
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, allocatable:: matriceun(:, :, :) ! (iim, iim, 2:jfiltnu) |
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, allocatable:: matrinvn(:, :, :) ! (iim, iim, 2:jfiltnu) |
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 |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
18 |
|
! matrice filtre pour les champs situes sur la grille de V ou de Z |
19 |
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|
20 |
! South: |
! South: |
21 |
real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
|
22 |
! (iim, iim, jfiltsu: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, allocatable:: matriceus(:, :, :) ! (iim, iim, jfiltsu:jjm) |
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, allocatable:: matrinvs(:, :, :) ! (iim, iim, jfiltsu:jjm) |
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 |
|
|
32 |
real, allocatable:: matricevs(:, :, :) ! (iim, iim, jfiltsv:jjm) |
real, allocatable:: matricevs(:, :, :) ! (iim, iim, jfiltsv:jjm) |
33 |
|
! matrice filtre pour les champs situes sur la grille de V ou de Z |
34 |
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35 |
contains |
contains |
36 |
|
|
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 |
|
|
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 |
|
! < 1. No filtering at poles. colat0 is to be used when alpha |
46 |
|
! (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 |
53 |
use nr_util, only: pi |
use nr_util, only: pi |
54 |
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55 |
! Local: |
! Local: |
56 |
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57 |
REAL dlatu(jjm) |
REAL dlatu(jjm) |
58 |
REAL rlamda(2: iim) |
REAL rlamda(2:iim) |
59 |
real eignvl(iim) ! eigenvalues sorted in descending order |
real eignvl(iim) ! eigenvalues sorted in descending order (<= 0) |
60 |
REAL cof |
INTEGER i, j, unit |
|
INTEGER i, j, k, unit |
|
61 |
REAL colat0 ! > 0 |
REAL colat0 ! > 0 |
62 |
REAL eignft(iim, iim), coff |
REAL eignft(iim, iim) |
63 |
|
|
64 |
real eignfnu(iim, iim), eignfnv(iim, iim) |
real eignfnu(iim, iim), eignfnv(iim, iim) |
65 |
! eigenfunctions of the discrete laplacian |
! eigenvectors of the discrete second derivative with respect to longitude |
66 |
|
|
67 |
! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
68 |
real coefilu(iim, jjm), coefilv(iim, jjm) |
real coefil(iim) |
|
real coefilu2(iim, jjm), coefilv2(iim, jjm) |
|
69 |
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|
70 |
! Index of the mode from where modes are filtered: |
! Index of the mode from where modes are filtered: |
71 |
integer, allocatable:: modfrstnu(:), modfrstsu(:) |
integer, allocatable:: modfrstnu(:) ! (2:jfiltnu) |
72 |
integer, allocatable:: modfrstnv(:), modfrstsv(:) |
integer, allocatable:: modfrstsu(:) ! (jfiltsu:jjm) |
73 |
|
integer, allocatable:: modfrstnv(:) ! (jfiltnv) |
74 |
|
integer, allocatable:: modfrstsv(:) ! (jfiltsv:jjm) |
75 |
|
|
76 |
!----------------------------------------------------------- |
!----------------------------------------------------------- |
77 |
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79 |
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|
80 |
CALL inifgn(eignvl, eignfnu, eignfnv) |
CALL inifgn(eignvl, eignfnu, eignfnv) |
81 |
|
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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 |
|
|
! NO FILTERING AT POLES |
|
|
! colat0 is to be used when alpha (stretching coefficient) |
|
|
! is set equal to zero for the regular grid case |
|
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|
82 |
! Calcul de colat0 |
! Calcul de colat0 |
83 |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
84 |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
85 |
PRINT *, 'colat0 = ', colat0 |
PRINT *, 'colat0 = ', colat0 |
86 |
|
|
87 |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(abs(eignvl(2: iim))) |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(- eignvl(2: iim)) |
88 |
|
|
89 |
! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv |
! D\'etermination de jfilt[ns][uv] : |
90 |
|
|
91 |
jfiltnu = (jjm + 1) / 2 |
jfiltnu = (jjm + 1) / 2 |
92 |
do while (cos(rlatu(jfiltnu)) >= colat0 & |
do while (cos(rlatu(jfiltnu)) >= colat0 & |
131 |
PRINT *, 'jfiltnv =', jfiltnv |
PRINT *, 'jfiltnv =', jfiltnv |
132 |
PRINT *, 'jfiltsv =', jfiltsv |
PRINT *, 'jfiltsv =', jfiltsv |
133 |
|
|
134 |
! Determination de coefilu, coefilv, modfrst[ns][uv]: |
! D\'etermination de modfrst[ns][uv] : |
135 |
|
|
136 |
allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
137 |
allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
|
coefilu = 0. |
|
|
coefilv = 0. |
|
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coefilu2 = 0. |
|
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coefilv2 = 0. |
|
138 |
|
|
139 |
DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
140 |
modfrstnu(j) = 2 |
modfrstnu(j) = 2 |
142 |
.and. modfrstnu(j) <= iim - 1) |
.and. modfrstnu(j) <= iim - 1) |
143 |
modfrstnu(j) = modfrstnu(j) + 1 |
modfrstnu(j) = modfrstnu(j) + 1 |
144 |
end do |
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 |
|
145 |
END DO |
END DO |
146 |
|
|
147 |
DO j = 1, jfiltnv |
DO j = 1, jfiltnv |
150 |
.and. modfrstnv(j) <= iim - 1) |
.and. modfrstnv(j) <= iim - 1) |
151 |
modfrstnv(j) = modfrstnv(j) + 1 |
modfrstnv(j) = modfrstnv(j) + 1 |
152 |
end do |
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. |
|
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coefilv2(k, j) = cof**2 - 1. |
|
|
end DO |
|
|
end if |
|
153 |
end DO |
end DO |
154 |
|
|
155 |
DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
158 |
.and. modfrstsu(j) <= iim - 1) |
.and. modfrstsu(j) <= iim - 1) |
159 |
modfrstsu(j) = modfrstsu(j) + 1 |
modfrstsu(j) = modfrstsu(j) + 1 |
160 |
end do |
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. |
|
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end DO |
|
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end if |
|
161 |
end DO |
end DO |
162 |
|
|
163 |
DO j = jfiltsv, jjm |
DO j = jfiltsv, jjm |
166 |
.and. modfrstsv(j) <= iim - 1) |
.and. modfrstsv(j) <= iim - 1) |
167 |
modfrstsv(j) = modfrstsv(j) + 1 |
modfrstsv(j) = modfrstsv(j) + 1 |
168 |
end do |
end do |
|
|
|
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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 |
|
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end if |
|
169 |
END DO |
END DO |
170 |
|
|
171 |
call new_unit(unit) |
call new_unit(unit) |
172 |
|
|
173 |
open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
174 |
write(unit, fmt = *) '"EIGNVL"', eignvl |
write(unit, fmt = *) '"EIGNVL"', eignvl |
175 |
write(unit, fmt = *) '"modfrstnu"', modfrstnu |
close(unit) |
176 |
write(unit, fmt = *) '"modfrstsu"', modfrstsu |
|
177 |
write(unit, fmt = *) '"modfrstnv"', modfrstnv |
open(unit, file = "modfrstnu.csv", status = "replace", action = "write") |
178 |
write(unit, fmt = *) '"modfrstsv"', modfrstsv |
write(unit, fmt = *) '"rlatu (degrees north)" modfrstnu ' & |
179 |
|
// '"rlamda(modfrstnu) * cos(rlatu) < 1"' |
180 |
|
DO j = 2, jfiltnu |
181 |
|
write(unit, fmt = *) rlatu(j) / pi * 180., modfrstnu(j), & |
182 |
|
rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1 |
183 |
|
end DO |
184 |
|
close(unit) |
185 |
|
|
186 |
|
open(unit, file = "modfrstnv.csv", status = "replace", action = "write") |
187 |
|
write(unit, fmt = *) '"rlatv (degrees north)" modfrstnv ' & |
188 |
|
// '"rlamda(modfrstnv) * cos(rlatv) < 1"' |
189 |
|
DO j = 1, jfiltnv |
190 |
|
write(unit, fmt = *) rlatv(j) / pi * 180., modfrstnv(j), & |
191 |
|
rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1 |
192 |
|
end DO |
193 |
|
close(unit) |
194 |
|
|
195 |
|
open(unit, file = "modfrstsu.csv", status = "replace", action = "write") |
196 |
|
write(unit, fmt = *) '"rlatu (degrees north)" modfrstsu ' & |
197 |
|
// '"rlamda(modfrstsu) * cos(rlatu) < 1"' |
198 |
|
DO j = jfiltsu, jjm |
199 |
|
write(unit, fmt = *) rlatu(j) / pi * 180., modfrstsu(j), & |
200 |
|
rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1 |
201 |
|
end DO |
202 |
|
close(unit) |
203 |
|
|
204 |
|
open(unit, file = "modfrstsv.csv", status = "replace", action = "write") |
205 |
|
write(unit, fmt = *) '"rlatv (degrees north)" modfrstsv ' & |
206 |
|
// '"rlamda(modfrstsv) * cos(rlatv) < 1"' |
207 |
|
DO j = jfiltsv, jjm |
208 |
|
write(unit, fmt = *) rlatv(j) / pi * 180., modfrstsv(j), & |
209 |
|
rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1 |
210 |
|
end DO |
211 |
close(unit) |
close(unit) |
212 |
|
|
213 |
allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu)) |
allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu)) |
215 |
allocate(matricevs(iim, iim, jfiltsv:jjm)) |
allocate(matricevs(iim, iim, jfiltsv:jjm)) |
216 |
allocate(matriceus(iim, iim, jfiltsu:jjm), matrinvs(iim, iim, jfiltsu:jjm)) |
allocate(matriceus(iim, iim, jfiltsu:jjm), matrinvs(iim, iim, jfiltsu:jjm)) |
217 |
|
|
218 |
! Calcul de la matrice filtre 'matriceu' pour les champs situes |
! Calcul de matriceu et matrinv |
|
! sur la grille scalaire |
|
219 |
|
|
220 |
DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
221 |
DO i = 1, iim |
if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
222 |
IF (i < modfrstnu(j)) then |
DO i = modfrstnu(j), iim |
223 |
coff = 0. |
coefil(i) = rlamda(i) * cos(rlatu(j)) - 1. |
224 |
else |
end DO |
225 |
coff = coefilu(i, j) |
|
226 |
end IF |
eignft(:modfrstnu(j) - 1, :) = 0. |
227 |
eignft(i, :) = eignfnv(:, i) * coff |
|
228 |
END DO |
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) * coefil(i) |
229 |
matriceun(:, :, j) = matmul(eignfnv, eignft) |
matriceun(:, :, j) = matmul(eignfnv, eignft) |
230 |
|
|
231 |
|
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) & |
232 |
|
* coefil(i) / (1. + coefil(i)) |
233 |
|
matrinvn(:, :, j) = matmul(eignfnv, eignft) |
234 |
|
else |
235 |
|
matriceun(:, :, j) = 0. |
236 |
|
matrinvn(:, :, j) = 0. |
237 |
|
end if |
238 |
END DO |
END DO |
239 |
|
|
240 |
DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
241 |
DO i = 1, iim |
if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
242 |
IF (i < modfrstsu(j)) then |
DO i = modfrstsu(j), iim |
243 |
coff = 0. |
coefil(i) = rlamda(i) * cos(rlatu(j)) - 1. |
244 |
else |
end DO |
|
coff = coefilu(i, j) |
|
|
end IF |
|
|
eignft(i, :) = eignfnv(:, i) * coff |
|
|
END DO |
|
|
matriceus(:, :, j) = matmul(eignfnv, eignft) |
|
|
END DO |
|
245 |
|
|
246 |
! Calcul de la matrice filtre 'matricev' pour les champs situes |
eignft(:modfrstsu(j) - 1, :) = 0. |
|
! sur la grille de V ou de Z |
|
247 |
|
|
248 |
DO j = 1, jfiltnv |
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) * coefil(i) |
249 |
DO i = 1, iim |
matriceus(:, :, j) = matmul(eignfnv, eignft) |
|
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 |
|
250 |
|
|
251 |
DO j = jfiltsv, jjm |
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) & |
252 |
DO i = 1, iim |
* coefil(i) / (1. + coefil(i)) |
253 |
IF (i < modfrstsv(j)) then |
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
254 |
coff = 0. |
else |
255 |
else |
matriceus(:, :, j) = 0. |
256 |
coff = coefilv(i, j) |
matrinvs(:, :, j) = 0. |
257 |
end IF |
end if |
|
eignft(i, :) = eignfnu(:, i) * coff |
|
|
END DO |
|
|
matricevs(:, :, j) = matmul(eignfnu, eignft) |
|
258 |
END DO |
END DO |
259 |
|
|
260 |
! Calcul de la matrice filtre 'matrinv' pour les champs situes |
! Calcul de matricev |
|
! sur la grille scalaire , pour le filtre inverse |
|
261 |
|
|
262 |
DO j = 2, jfiltnu |
DO j = 1, jfiltnv |
263 |
DO i = 1, iim |
if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
264 |
IF (i < modfrstnu(j)) then |
DO i = modfrstnv(j), iim |
265 |
coff = 0. |
coefil(i) = rlamda(i) * cos(rlatv(j)) - 1. |
266 |
else |
end DO |
267 |
coff = coefilu(i, j) / (1. + coefilu(i, j)) |
|
268 |
end IF |
eignft(:modfrstnv(j) - 1, :) = 0. |
269 |
eignft(i, :) = eignfnv(:, i) * coff |
forall (i = modfrstnv(j):iim) eignft(i, :) = eignfnu(:, i) * coefil(i) |
270 |
END DO |
matricevn(:, :, j) = matmul(eignfnu, eignft) |
271 |
matrinvn(:, :, j) = matmul(eignfnv, eignft) |
else |
272 |
|
matricevn(:, :, j) = 0. |
273 |
|
end if |
274 |
END DO |
END DO |
275 |
|
|
276 |
DO j = jfiltsu, jjm |
DO j = jfiltsv, jjm |
277 |
DO i = 1, iim |
if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
278 |
IF (i < modfrstsu(j)) then |
DO i = modfrstsv(j), iim |
279 |
coff = 0. |
coefil(i) = rlamda(i) * cos(rlatv(j)) - 1. |
280 |
else |
end DO |
281 |
coff = coefilu(i, j) / (1. + coefilu(i, j)) |
|
282 |
end IF |
eignft(:modfrstsv(j) - 1, :) = 0. |
283 |
eignft(i, :) = eignfnv(:, i) * coff |
forall (i = modfrstsv(j):iim) eignft(i, :) = eignfnu(:, i) * coefil(i) |
284 |
END DO |
matricevs(:, :, j) = matmul(eignfnu, eignft) |
285 |
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
else |
286 |
|
matricevs(:, :, j) = 0. |
287 |
|
end if |
288 |
END DO |
END DO |
289 |
|
|
290 |
END SUBROUTINE inifilr |
END SUBROUTINE inifilr |