2 |
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3 |
IMPLICIT NONE |
IMPLICIT NONE |
4 |
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INTEGER jfiltnu, jfiltsu, jfiltnv, jfiltsv |
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5 |
! North: |
! North: |
6 |
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7 |
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INTEGER jfiltnu, jfiltnv |
8 |
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! index of the last scalar line filtered in northern hemisphere |
9 |
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10 |
real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
11 |
! (iim, iim, 2:jfiltnu) |
! (iim, iim, 2:jfiltnu) |
12 |
|
|
13 |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
14 |
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15 |
! South: |
! South: |
16 |
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17 |
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integer jfiltsu, jfiltsv |
18 |
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! index of the first line filtered in southern hemisphere |
19 |
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20 |
real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
21 |
! (iim, iim, jfiltsu:jjm) |
! (iim, iim, jfiltsu:jjm) |
22 |
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26 |
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27 |
SUBROUTINE inifilr |
SUBROUTINE inifilr |
28 |
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29 |
! 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 |
30 |
! H. Upadhyaya, O. Sharma |
! H. Upadhyaya, O. Sharma |
31 |
|
|
32 |
! This routine computes the eigenfunctions of the laplacian on the |
! This procedure computes the filtering coefficients for scalar |
33 |
! stretched grid, and the filtering coefficients. |
! lines and meridional wind v lines. The modes are filtered from |
34 |
! We designate: |
! modfrst to iim. We filter all those latitude lines where coefil |
35 |
! eignfn eigenfunctions of the discrete laplacian |
! < 1. No filtering at poles. colat0 is to be used when alpha |
36 |
! eigenvl eigenvalues |
! (stretching coefficient) is set equal to zero for the regular |
37 |
! jfiltn index of the last scalar line filtered in NH |
! grid case. |
|
! jfilts index of the first line filtered in SH |
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! modfrst index of the mode from where modes are filtered |
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! modemax maximum number of modes (im) |
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! coefil filtering coefficients (lamda_max * cos(rlat) / lamda) |
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! sdd SQRT(dx) |
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38 |
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! The modes are filtered from modfrst to modemax. |
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USE coefils, ONLY : coefilu, coefilu2, coefilv, coefilv2, eignfnu, & |
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eignfnv, modfrstu, modfrstv |
|
39 |
USE dimens_m, ONLY : iim, jjm |
USE dimens_m, ONLY : iim, jjm |
40 |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
41 |
use inifgn_m, only: inifgn |
use inifgn_m, only: inifgn |
42 |
|
use jumble, only: new_unit |
43 |
use nr_util, only: pi |
use nr_util, only: pi |
44 |
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45 |
! Local: |
! Local: |
|
REAL dlatu(jjm) |
|
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REAL rlamda(2: iim), eignvl(iim) |
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46 |
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47 |
REAL lamdamax, cof |
REAL dlatu(jjm) |
48 |
INTEGER i, j, modemax, imx, k, kf |
REAL rlamda(2: iim) |
49 |
REAL dymin, colat0 |
real eignvl(iim) ! eigenvalues sorted in descending order (<= 0) |
50 |
REAL eignft(iim, iim), coff |
INTEGER i, j, unit |
51 |
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REAL colat0 ! > 0 |
52 |
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REAL eignft(iim, iim) |
53 |
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54 |
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real eignfnu(iim, iim), eignfnv(iim, iim) |
55 |
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! eigenvectors of the discrete second derivative with respect to longitude |
56 |
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57 |
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! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
58 |
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real, allocatable:: coefilnu(:, :) ! (iim, 2:jfiltnu) |
59 |
|
real, allocatable:: coefilsu(:, :) ! (iim, jfiltsu:jjm) |
60 |
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real, allocatable:: coefilnv(:, :) ! (iim, jfiltnv) |
61 |
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real, allocatable:: coefilsv(:, :) ! (iim, jfiltsv:jjm) |
62 |
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63 |
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! Index of the mode from where modes are filtered: |
64 |
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integer, allocatable:: modfrstnu(:) ! (2:jfiltnu) |
65 |
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integer, allocatable:: modfrstsu(:) ! (jfiltsu:jjm) |
66 |
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integer, allocatable:: modfrstnv(:) ! (jfiltnv) |
67 |
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integer, allocatable:: modfrstsv(:) ! (jfiltsv:jjm) |
68 |
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69 |
!----------------------------------------------------------- |
!----------------------------------------------------------- |
70 |
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71 |
print *, "Call sequence information: inifilr" |
print *, "Call sequence information: inifilr" |
72 |
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73 |
CALL inifgn(eignvl) |
CALL inifgn(eignvl, eignfnu, eignfnv) |
|
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PRINT *, 'EIGNVL ' |
|
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PRINT "(1X, 5E13.6)", eignvl |
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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) |
|
|
! is set equal to zero for the regular grid case |
|
74 |
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|
75 |
! Calcul de colat0 |
! Calcul de colat0 |
76 |
|
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
77 |
DO j = 1, jjm |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
|
dlatu(j) = rlatu(j) - rlatu(j+1) |
|
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END DO |
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dymin = dlatu(1) |
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DO j = 2, jjm |
|
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dymin = min(dymin, dlatu(j)) |
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END DO |
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colat0 = min(0.5, dymin / minval(xprimu(:iim))) |
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|
78 |
PRINT *, 'colat0 = ', colat0 |
PRINT *, 'colat0 = ', colat0 |
79 |
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|
80 |
lamdamax = iim / (pi * colat0 / grossismx) |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(- eignvl(2: iim)) |
|
rlamda = lamdamax / sqrt(abs(eignvl(2: iim))) |
|
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DO j = 1, jjm |
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DO i = 1, iim |
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coefilu(i, j) = 0. |
|
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coefilv(i, j) = 0. |
|
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coefilu2(i, j) = 0. |
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coefilv2(i, j) = 0. |
|
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end DO |
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END DO |
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! Determination de jfiltnu, jfiltnv, jfiltsu, jfiltsv |
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modemax = iim |
|
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imx = iim |
|
81 |
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82 |
PRINT *, 'TRUNCATION AT ', imx |
! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv |
83 |
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|
84 |
DO j = 2, jjm / 2 + 1 |
jfiltnu = (jjm + 1) / 2 |
85 |
IF (cos(rlatu(j)) / colat0 < 1. & |
do while (cos(rlatu(jfiltnu)) >= colat0 & |
86 |
.and. rlamda(imx) * cos(rlatu(j)) < 1.) jfiltnu = j |
.or. rlamda(iim) * cos(rlatu(jfiltnu)) >= 1.) |
87 |
|
jfiltnu = jfiltnu - 1 |
88 |
IF (cos(rlatu(jjm - j + 2)) / colat0 < 1. & |
end do |
89 |
.and. rlamda(imx) * cos(rlatu(jjm - j + 2)) < 1.) & |
|
90 |
jfiltsu = jjm - j + 2 |
jfiltsu = jjm / 2 + 2 |
91 |
END DO |
do while (cos(rlatu(jfiltsu)) >= colat0 & |
92 |
|
.or. rlamda(iim) * cos(rlatu(jfiltsu)) >= 1.) |
93 |
DO j = 1, jjm/2 |
jfiltsu = jfiltsu + 1 |
94 |
cof = cos(rlatv(j))/colat0 |
end do |
95 |
IF (cof < 1.) THEN |
|
96 |
IF (rlamda(imx)*cos(rlatv(j)) < 1.) jfiltnv = j |
jfiltnv = jjm / 2 |
97 |
END IF |
do while ((cos(rlatv(jfiltnv)) >= colat0 & |
98 |
|
.or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) .and. jfiltnv >= 2) |
99 |
cof = cos(rlatv(jjm-j+1))/colat0 |
jfiltnv = jfiltnv - 1 |
100 |
IF (cof < 1.) THEN |
end do |
101 |
IF (rlamda(imx)*cos(rlatv(jjm-j+1)) < 1.) jfiltsv = jjm - j + 1 |
|
102 |
END IF |
if (cos(rlatv(jfiltnv)) >= colat0 & |
103 |
END DO |
.or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) then |
104 |
|
! {jfiltnv == 1} |
105 |
IF (jfiltnu <= 0) jfiltnu = 1 |
PRINT *, 'Could not find jfiltnv.' |
|
IF (jfiltnu > jjm/2+1) THEN |
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PRINT *, 'jfiltnu en dehors des valeurs acceptables ', jfiltnu |
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STOP 1 |
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END IF |
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IF (jfiltsu <= 0) jfiltsu = 1 |
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IF (jfiltsu > jjm + 1) THEN |
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PRINT *, 'jfiltsu en dehors des valeurs acceptables ', jfiltsu |
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STOP 1 |
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END IF |
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IF (jfiltnv <= 0) jfiltnv = 1 |
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IF (jfiltnv > jjm/2) THEN |
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PRINT *, 'jfiltnv en dehors des valeurs acceptables ', jfiltnv |
|
106 |
STOP 1 |
STOP 1 |
107 |
END IF |
END IF |
108 |
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|
109 |
IF (jfiltsv <= 0) jfiltsv = 1 |
jfiltsv = (jjm + 1)/ 2 + 1 |
110 |
IF (jfiltsv > jjm) THEN |
do while ((cos(rlatv(jfiltsv)) >= colat0 & |
111 |
PRINT *, 'jfiltsv en dehors des valeurs acceptables ', jfiltsv |
.or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) .and. jfiltsv <= jjm - 1) |
112 |
|
jfiltsv = jfiltsv + 1 |
113 |
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end do |
114 |
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115 |
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IF (cos(rlatv(jfiltsv)) >= colat0 & |
116 |
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.or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) THEN |
117 |
|
! {jfiltsv == jjm} |
118 |
|
PRINT *, 'Could not find jfiltsv.' |
119 |
STOP 1 |
STOP 1 |
120 |
END IF |
END IF |
121 |
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|
122 |
PRINT *, 'jfiltnv jfiltsv jfiltnu jfiltsu ', jfiltnv, jfiltsv, jfiltnu, & |
PRINT *, 'jfiltnu =', jfiltnu |
123 |
jfiltsu |
PRINT *, 'jfiltsu =', jfiltsu |
124 |
|
PRINT *, 'jfiltnv =', jfiltnv |
125 |
! Determination de coefilu, coefilv, n=modfrstu, modfrstv |
PRINT *, 'jfiltsv =', jfiltsv |
126 |
|
|
127 |
DO j = 1, jjm |
! D\'etermination de coefil[ns][uv], modfrst[ns][uv]: |
128 |
modfrstu(j) = iim |
|
129 |
modfrstv(j) = iim |
allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
130 |
END DO |
allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
131 |
|
allocate(coefilnu(iim, 2:jfiltnu), coefilsu(iim, jfiltsu:jjm)) |
132 |
|
allocate(coefilnv(iim, jfiltnv), coefilsv(iim, jfiltsv:jjm)) |
133 |
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|
134 |
|
coefilnu = 0. |
135 |
|
coefilnv = 0. |
136 |
|
coefilsu = 0. |
137 |
|
coefilsv = 0. |
138 |
|
|
139 |
DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
140 |
DO k = 2, modemax |
modfrstnu(j) = 2 |
141 |
cof = rlamda(k) * cos(rlatu(j)) |
do while (rlamda(modfrstnu(j)) * cos(rlatu(j)) >= 1. & |
142 |
IF (cof < 1.) exit |
.and. modfrstnu(j) <= iim - 1) |
143 |
end DO |
modfrstnu(j) = modfrstnu(j) + 1 |
144 |
if (k == modemax + 1) cycle |
end do |
145 |
modfrstu(j) = k |
|
146 |
|
if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
147 |
kf = modfrstu(j) |
DO i = modfrstnu(j), iim |
148 |
DO k = kf, modemax |
coefilnu(i, j) = rlamda(i) * cos(rlatu(j)) - 1. |
149 |
cof = rlamda(k)*cos(rlatu(j)) |
end DO |
150 |
coefilu(k, j) = cof - 1. |
end if |
|
coefilu2(k, j) = cof*cof - 1. |
|
|
end DO |
|
151 |
END DO |
END DO |
152 |
|
|
153 |
DO j = 1, jfiltnv |
DO j = 1, jfiltnv |
154 |
DO k = 2, modemax |
modfrstnv(j) = 2 |
155 |
cof = rlamda(k)*cos(rlatv(j)) |
do while (rlamda(modfrstnv(j)) * cos(rlatv(j)) >= 1. & |
156 |
IF (cof < 1.) exit |
.and. modfrstnv(j) <= iim - 1) |
157 |
end DO |
modfrstnv(j) = modfrstnv(j) + 1 |
158 |
if (k == modemax + 1) cycle |
end do |
159 |
modfrstv(j) = k |
|
160 |
|
if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
161 |
kf = modfrstv(j) |
DO i = modfrstnv(j), iim |
162 |
DO k = kf, modemax |
coefilnv(i, j) = rlamda(i) * cos(rlatv(j)) - 1. |
163 |
cof = rlamda(k)*cos(rlatv(j)) |
end DO |
164 |
coefilv(k, j) = cof - 1. |
end if |
|
coefilv2(k, j) = cof*cof - 1. |
|
|
end DO |
|
165 |
end DO |
end DO |
166 |
|
|
167 |
DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
168 |
DO k = 2, modemax |
modfrstsu(j) = 2 |
169 |
cof = rlamda(k)*cos(rlatu(j)) |
do while (rlamda(modfrstsu(j)) * cos(rlatu(j)) >= 1. & |
170 |
IF (cof < 1.) exit |
.and. modfrstsu(j) <= iim - 1) |
171 |
end DO |
modfrstsu(j) = modfrstsu(j) + 1 |
172 |
if (k == modemax + 1) cycle |
end do |
173 |
modfrstu(j) = k |
|
174 |
|
if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
175 |
kf = modfrstu(j) |
DO i = modfrstsu(j), iim |
176 |
DO k = kf, modemax |
coefilsu(i, j) = rlamda(i) * cos(rlatu(j)) - 1. |
177 |
cof = rlamda(k)*cos(rlatu(j)) |
end DO |
178 |
coefilu(k, j) = cof - 1. |
end if |
|
coefilu2(k, j) = cof*cof - 1. |
|
|
end DO |
|
179 |
end DO |
end DO |
180 |
|
|
181 |
DO j = jfiltsv, jjm |
DO j = jfiltsv, jjm |
182 |
DO k = 2, modemax |
modfrstsv(j) = 2 |
183 |
cof = rlamda(k)*cos(rlatv(j)) |
do while (rlamda(modfrstsv(j)) * cos(rlatv(j)) >= 1. & |
184 |
IF (cof < 1.) exit |
.and. modfrstsv(j) <= iim - 1) |
185 |
end DO |
modfrstsv(j) = modfrstsv(j) + 1 |
186 |
if (k == modemax + 1) cycle |
end do |
187 |
modfrstv(j) = k |
|
188 |
|
if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
189 |
kf = modfrstv(j) |
DO i = modfrstsv(j), iim |
190 |
DO k = kf, modemax |
coefilsv(i, j) = rlamda(i) * cos(rlatv(j)) - 1. |
191 |
cof = rlamda(k)*cos(rlatv(j)) |
end DO |
192 |
coefilv(k, j) = cof - 1. |
end if |
193 |
coefilv2(k, j) = cof*cof - 1. |
END DO |
194 |
end DO |
|
195 |
END DO |
call new_unit(unit) |
196 |
|
open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
197 |
IF (jfiltnv>=jjm/2 .OR. jfiltnu>=jjm/2) THEN |
write(unit, fmt = *) '"EIGNVL"', eignvl |
198 |
IF (jfiltnv == jfiltsv) jfiltsv = 1 + jfiltnv |
write(unit, fmt = *) '"modfrstnu"', modfrstnu |
199 |
IF (jfiltnu == jfiltsu) jfiltsu = 1 + jfiltnu |
write(unit, fmt = *) '"modfrstsu"', modfrstsu |
200 |
|
write(unit, fmt = *) '"modfrstnv"', modfrstnv |
201 |
PRINT *, 'jfiltnv jfiltsv jfiltnu jfiltsu', jfiltnv, jfiltsv, jfiltnu, & |
write(unit, fmt = *) '"modfrstsv"', modfrstsv |
202 |
jfiltsu |
close(unit) |
|
END IF |
|
|
|
|
|
PRINT *, 'Modes premiers v ' |
|
|
PRINT 334, modfrstv |
|
|
PRINT *, 'Modes premiers u ' |
|
|
PRINT 334, modfrstu |
|
203 |
|
|
204 |
allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu)) |
allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu)) |
205 |
allocate(matricevn(iim, iim, jfiltnv)) |
allocate(matricevn(iim, iim, jfiltnv)) |
210 |
! sur la grille scalaire |
! sur la grille scalaire |
211 |
|
|
212 |
DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
213 |
DO i = 1, iim |
eignft(:modfrstnu(j) - 1, :) = 0. |
214 |
IF (i < modfrstu(j)) then |
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) & |
215 |
coff = 0. |
* coefilnu(i, j) |
|
else |
|
|
coff = coefilu(i, j) |
|
|
end IF |
|
|
eignft(i, :) = eignfnv(:, i)*coff |
|
|
END DO |
|
216 |
matriceun(:, :, j) = matmul(eignfnv, eignft) |
matriceun(:, :, j) = matmul(eignfnv, eignft) |
217 |
END DO |
END DO |
218 |
|
|
219 |
DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
220 |
DO i = 1, iim |
eignft(:modfrstsu(j) - 1, :) = 0. |
221 |
IF (i < modfrstu(j)) then |
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) & |
222 |
coff = 0. |
* coefilsu(i, j) |
|
else |
|
|
coff = coefilu(i, j) |
|
|
end IF |
|
|
eignft(i, :) = eignfnv(:, i) * coff |
|
|
END DO |
|
223 |
matriceus(:, :, j) = matmul(eignfnv, eignft) |
matriceus(:, :, j) = matmul(eignfnv, eignft) |
224 |
END DO |
END DO |
225 |
|
|
227 |
! sur la grille de V ou de Z |
! sur la grille de V ou de Z |
228 |
|
|
229 |
DO j = 1, jfiltnv |
DO j = 1, jfiltnv |
230 |
DO i = 1, iim |
eignft(:modfrstnv(j) - 1, :) = 0. |
231 |
IF (i < modfrstv(j)) then |
forall (i = modfrstnv(j): iim) eignft(i, :) = eignfnu(:, i) & |
232 |
coff = 0. |
* coefilnv(i, j) |
|
else |
|
|
coff = coefilv(i, j) |
|
|
end IF |
|
|
eignft(i, :) = eignfnu(:, i)*coff |
|
|
END DO |
|
233 |
matricevn(:, :, j) = matmul(eignfnu, eignft) |
matricevn(:, :, j) = matmul(eignfnu, eignft) |
234 |
END DO |
END DO |
235 |
|
|
236 |
DO j = jfiltsv, jjm |
DO j = jfiltsv, jjm |
237 |
DO i = 1, iim |
eignft(:modfrstsv(j) - 1, :) = 0. |
238 |
IF (i < modfrstv(j)) then |
forall (i = modfrstsv(j):iim) eignft(i, :) = eignfnu(:, i) & |
239 |
coff = 0. |
* coefilsv(i, j) |
|
else |
|
|
coff = coefilv(i, j) |
|
|
end IF |
|
|
eignft(i, :) = eignfnu(:, i)*coff |
|
|
END DO |
|
240 |
matricevs(:, :, j) = matmul(eignfnu, eignft) |
matricevs(:, :, j) = matmul(eignfnu, eignft) |
241 |
END DO |
END DO |
242 |
|
|
244 |
! sur la grille scalaire , pour le filtre inverse |
! sur la grille scalaire , pour le filtre inverse |
245 |
|
|
246 |
DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
247 |
DO i = 1, iim |
eignft(:modfrstnu(j) - 1, :) = 0. |
248 |
IF (i < modfrstu(j)) then |
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) & |
249 |
coff = 0. |
* coefilnu(i, j) / (1. + coefilnu(i, j)) |
|
else |
|
|
coff = coefilu(i, j)/(1.+coefilu(i, j)) |
|
|
end IF |
|
|
eignft(i, :) = eignfnv(:, i)*coff |
|
|
END DO |
|
250 |
matrinvn(:, :, j) = matmul(eignfnv, eignft) |
matrinvn(:, :, j) = matmul(eignfnv, eignft) |
251 |
END DO |
END DO |
252 |
|
|
253 |
DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
254 |
DO i = 1, iim |
eignft(:modfrstsu(j) - 1, :) = 0. |
255 |
IF (i < modfrstu(j)) then |
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) & |
256 |
coff = 0. |
* coefilsu(i, j) / (1. + coefilsu(i, j)) |
|
else |
|
|
coff = coefilu(i, j)/(1.+coefilu(i, j)) |
|
|
end IF |
|
|
eignft(i, :) = eignfnv(:, i)*coff |
|
|
END DO |
|
257 |
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
258 |
END DO |
END DO |
259 |
|
|
|
334 FORMAT (1X, 24I3) |
|
|
|
|
260 |
END SUBROUTINE inifilr |
END SUBROUTINE inifilr |
261 |
|
|
262 |
end module inifilr_m |
end module inifilr_m |