12 |
! Calcule les longitudes et dérivées dans la grille du GCM pour |
! Calcule les longitudes et dérivées dans la grille du GCM pour |
13 |
! une fonction f(x) à dérivée tangente hyperbolique. |
! une fonction f(x) à dérivée tangente hyperbolique. |
14 |
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15 |
! On doit avoir grossismx \times dzoomx < pi (radians) |
! Il vaut mieux avoir : grossismx \times dzoom < pi |
16 |
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17 |
! Le premier point scalaire pour une grille regulière (grossismx = |
! Le premier point scalaire pour une grille regulière (grossismx = |
18 |
! 1., taux=0., clon=0.) est à - 180 degrés. |
! 1., taux = 0., clon = 0.) est à - 180 degrés. |
19 |
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use coefpoly_m, only: coefpoly |
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20 |
USE dimens_m, ONLY: iim |
USE dimens_m, ONLY: iim |
21 |
use nr_util, only: pi_d, twopi_d, arth |
use dynetat0_m, only: clon, grossismx, dzoomx, taux |
22 |
use serre, only: clon, grossismx, dzoomx, taux |
use invert_zoom_x_m, only: invert_zoom_x, nmax |
23 |
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use nr_util, only: pi, pi_d, twopi, twopi_d, arth |
24 |
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use principal_cshift_m, only: principal_cshift |
25 |
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use tanh_cautious_m, only: tanh_cautious |
26 |
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27 |
REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
28 |
real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
29 |
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30 |
! Local: |
! Local: |
31 |
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real rlonm025(iim + 1), rlonp025(iim + 1), d_rlonv(iim) |
32 |
DOUBLE PRECISION champmin, champmax |
REAL dzoom, step |
33 |
real rlonm025(iim + 1), rlonp025(iim + 1) |
DOUBLE PRECISION, dimension(0:nmax):: xtild, fhyp, G, Xf, ffdx |
34 |
INTEGER, PARAMETER:: nmax = 30000, nmax2 = 2 * nmax |
DOUBLE PRECISION beta |
35 |
REAL dzoom |
INTEGER i, is2 |
36 |
DOUBLE PRECISION xlon(iim + 1), xprimm(iim + 1), xuv |
DOUBLE PRECISION xmoy(nmax), fxm(nmax) |
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DOUBLE PRECISION xtild(0:nmax2) |
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DOUBLE PRECISION fhyp(nmax:nmax2), ffdx, beta, Xprimt(0:nmax2) |
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DOUBLE PRECISION Xf(0:nmax2), xxpr(nmax2) |
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DOUBLE PRECISION xvrai(iim + 1), xxprim(iim + 1) |
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DOUBLE PRECISION my_eps, xzoom, fa, fb |
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DOUBLE PRECISION Xf1, Xfi, a0, a1, a2, a3, xi2 |
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INTEGER i, it, ik, iter, ii, idif, ii1, ii2 |
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DOUBLE PRECISION xi, xo1, xmoy, fxm, Xprimin |
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DOUBLE PRECISION decalx |
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INTEGER is2 |
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37 |
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38 |
!---------------------------------------------------------------------- |
!---------------------------------------------------------------------- |
39 |
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40 |
print *, "Call sequence information: fxhyp" |
print *, "Call sequence information: fxhyp" |
41 |
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42 |
my_eps = 1e-3 |
test_grossismx: if (grossismx == 1.) then |
43 |
xzoom = clon * pi_d / 180. |
step = twopi / iim |
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IF (grossismx == 1.) THEN |
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decalx = 1. |
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else |
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decalx = 0.75 |
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END IF |
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44 |
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45 |
IF (dzoomx < 1.) THEN |
xprimm025(:iim) = step |
46 |
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xprimp025(:iim) = step |
47 |
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xprimv(:iim) = step |
48 |
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xprimu(:iim) = step |
49 |
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50 |
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rlonv(:iim) = arth(- pi + clon, step, iim) |
51 |
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rlonm025(:iim) = rlonv(:iim) - 0.25 * step |
52 |
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rlonp025(:iim) = rlonv(:iim) + 0.25 * step |
53 |
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rlonu(:iim) = rlonv(:iim) + 0.5 * step |
54 |
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else test_grossismx |
55 |
dzoom = dzoomx * twopi_d |
dzoom = dzoomx * twopi_d |
56 |
ELSE IF (dzoomx < 25.) THEN |
xtild = arth(0d0, pi_d / nmax, nmax + 1) |
57 |
print *, "dzoomx pour fxhyp est trop petit." |
forall (i = 1:nmax) xmoy(i) = 0.5d0 * (xtild(i-1) + xtild(i)) |
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STOP 1 |
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ELSE |
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dzoom = dzoomx * pi_d / 180. |
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END IF |
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58 |
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59 |
print *, 'dzoom (rad):', dzoom |
! Compute fhyp: |
60 |
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fhyp(1:nmax - 1) = tanh_cautious(taux * (dzoom / 2d0 & |
61 |
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- xtild(1:nmax - 1)), xtild(1:nmax - 1) & |
62 |
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* (pi_d - xtild(1:nmax - 1))) |
63 |
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fhyp(0) = 1d0 |
64 |
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fhyp(nmax) = -1d0 |
65 |
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66 |
xtild = arth(- pi_d, twopi_d / nmax2, nmax2 + 1) |
fxm = tanh_cautious(taux * (dzoom / 2d0 - xmoy), xmoy * (pi_d - xmoy)) |
67 |
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68 |
DO i = nmax, nmax2 |
! Compute \int_0 ^{\tilde x} F: |
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fa = taux * (dzoom / 2. - xtild(i)) |
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fb = xtild(i) * (pi_d - xtild(i)) |
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IF (200. * fb < - fa) THEN |
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fhyp(i) = - 1. |
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ELSE IF (200. * fb < fa) THEN |
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fhyp(i) = 1. |
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ELSE |
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IF (ABS(fa) < 1e-13.AND.ABS(fb) < 1e-13) THEN |
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IF (200. * fb + fa < 1e-10) THEN |
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fhyp(i) = - 1. |
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ELSE IF (200. * fb - fa < 1e-10) THEN |
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fhyp(i) = 1. |
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END IF |
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ELSE |
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fhyp(i) = TANH(fa / fb) |
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END IF |
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END IF |
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IF (xtild(i) == 0.) fhyp(i) = 1. |
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IF (xtild(i) == pi_d) fhyp(i) = -1. |
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END DO |
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69 |
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70 |
! Calcul de beta |
ffdx(0) = 0d0 |
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ffdx = 0. |
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DO i = nmax + 1, nmax2 |
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xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
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fa = taux * (dzoom / 2. - xmoy) |
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fb = xmoy * (pi_d - xmoy) |
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IF (200. * fb < - fa) THEN |
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fxm = - 1. |
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ELSE IF (200. * fb < fa) THEN |
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fxm = 1. |
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ELSE |
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IF (ABS(fa) < 1e-13.AND.ABS(fb) < 1e-13) THEN |
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IF (200. * fb + fa < 1e-10) THEN |
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fxm = - 1. |
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ELSE IF (200. * fb - fa < 1e-10) THEN |
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fxm = 1. |
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END IF |
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ELSE |
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fxm = TANH(fa / fb) |
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END IF |
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END IF |
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IF (xmoy == 0.) fxm = 1. |
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IF (xmoy == pi_d) fxm = -1. |
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ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) |
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END DO |
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71 |
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72 |
beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d) |
DO i = 1, nmax |
73 |
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ffdx(i) = ffdx(i - 1) + fxm(i) * (xtild(i) - xtild(i-1)) |
74 |
IF (2. * beta - grossismx <= 0.) THEN |
END DO |
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print *, 'Attention ! La valeur beta calculée dans fxhyp est mauvaise.' |
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print *, 'Modifier les valeurs de grossismx, taux ou dzoomx et relancer.' |
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STOP 1 |
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END IF |
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! calcul de Xprimt |
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DO i = nmax, nmax2 |
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Xprimt(i) = beta + (grossismx - beta) * fhyp(i) |
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END DO |
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DO i = nmax + 1, nmax2 |
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Xprimt(nmax2 - i) = Xprimt(i) |
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END DO |
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! Calcul de Xf |
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Xf(0) = - pi_d |
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75 |
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76 |
DO i = nmax + 1, nmax2 |
print *, "ffdx(nmax) = ", ffdx(nmax) |
77 |
xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
beta = (pi_d - grossismx * ffdx(nmax)) / (pi_d - ffdx(nmax)) |
78 |
fa = taux * (dzoom / 2. - xmoy) |
print *, "beta = ", beta |
79 |
fb = xmoy * (pi_d - xmoy) |
|
80 |
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IF (2d0 * beta - grossismx <= 0d0) THEN |
81 |
IF (200. * fb < - fa) THEN |
print *, 'Bad choice of grossismx, taux, dzoomx.' |
82 |
fxm = - 1. |
print *, 'Decrease dzoomx or grossismx.' |
83 |
ELSE IF (200. * fb < fa) THEN |
STOP 1 |
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fxm = 1. |
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ELSE |
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fxm = TANH(fa / fb) |
|
84 |
END IF |
END IF |
85 |
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86 |
IF (xmoy == 0.) fxm = 1. |
G = beta + (grossismx - beta) * fhyp |
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IF (xmoy == pi_d) fxm = -1. |
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xxpr(i) = beta + (grossismx - beta) * fxm |
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END DO |
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87 |
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88 |
xxpr(:nmax) = xxpr(nmax2:nmax + 1:- 1) |
Xf(:nmax - 1) = beta * xtild(:nmax - 1) + (grossismx - beta) & |
89 |
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* ffdx(:nmax - 1) |
90 |
DO i=1, nmax2 |
Xf(nmax) = pi_d |
91 |
Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) |
|
92 |
END DO |
call invert_zoom_x(xf, xtild, G, rlonm025(:iim), xprimm025(:iim), & |
93 |
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xuv = - 0.25d0) |
94 |
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call invert_zoom_x(xf, xtild, G, rlonv(:iim), xprimv(:iim), xuv = 0d0) |
95 |
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call invert_zoom_x(xf, xtild, G, rlonu(:iim), xprimu(:iim), xuv = 0.5d0) |
96 |
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call invert_zoom_x(xf, xtild, G, rlonp025(:iim), xprimp025(:iim), & |
97 |
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xuv = 0.25d0) |
98 |
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end if test_grossismx |
99 |
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100 |
is2 = 0 |
is2 = 0 |
101 |
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102 |
loop_ik: DO ik = 1, 4 |
IF (MINval(rlonm025(:iim)) < - pi - 0.1 & |
103 |
! xuv = 0. si calcul aux points scalaires |
.or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN |
104 |
! xuv = 0.5 si calcul aux points U |
IF (clon <= 0.) THEN |
105 |
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is2 = 1 |
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IF (ik == 1) THEN |
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xuv = -0.25 |
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ELSE IF (ik == 2) THEN |
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xuv = 0. |
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ELSE IF (ik == 3) THEN |
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xuv = 0.50 |
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ELSE IF (ik == 4) THEN |
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xuv = 0.25 |
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END IF |
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xo1 = 0. |
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106 |
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107 |
IF (ik == 1 .and. grossismx == 1.) THEN |
do while (rlonm025(is2) < - pi .and. is2 < iim) |
108 |
ii1 = 2 |
is2 = is2 + 1 |
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ii2 = iim + 1 |
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else |
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ii1=1 |
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ii2=iim |
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END IF |
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DO i = ii1, ii2 |
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Xfi = - pi_d + (REAL(i) + xuv - decalx) * twopi_d / REAL(iim) |
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it = nmax2 |
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do while (xfi < xf(it) .and. it >= 1) |
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it = it - 1 |
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109 |
end do |
end do |
110 |
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111 |
! Calcul de Xf(xi) |
if (rlonm025(is2) < - pi) then |
112 |
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print *, 'Rlonm025 plus petit que - pi !' |
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xi = xtild(it) |
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IF (it == nmax2) THEN |
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it = nmax2 -1 |
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Xf(it + 1) = pi_d |
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END IF |
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! Appel de la routine qui calcule les coefficients a0, a1, |
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! a2, a3 d'un polynome de degre 3 qui passe par les points |
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! (Xf(it), xtild(it)) et (Xf(it + 1), xtild(it + 1)) |
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CALL coefpoly(Xf(it), Xf(it + 1), Xprimt(it), Xprimt(it + 1), & |
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xtild(it), xtild(it + 1), a0, a1, a2, a3) |
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Xf1 = Xf(it) |
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Xprimin = a1 + 2. * a2 * xi + 3. * a3 * xi * xi |
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iter = 1 |
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do |
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xi = xi - (Xf1 - Xfi) / Xprimin |
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IF (ABS(xi - xo1) <= my_eps .or. iter == 300) exit |
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xo1 = xi |
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xi2 = xi * xi |
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Xf1 = a0 + a1 * xi + a2 * xi2 + a3 * xi2 * xi |
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Xprimin = a1 + 2. * a2 * xi + 3. * a3 * xi2 |
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end DO |
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if (ABS(xi - xo1) > my_eps) then |
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! iter == 300 |
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print *, 'Pas de solution.' |
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print *, i, xfi |
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113 |
STOP 1 |
STOP 1 |
114 |
end if |
end if |
115 |
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ELSE |
116 |
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is2 = iim |
117 |
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118 |
xxprim(i) = twopi_d / (REAL(iim) * Xprimin) |
do while (rlonm025(is2) > pi .and. is2 > 1) |
119 |
xvrai(i) = xi + xzoom |
is2 = is2 - 1 |
120 |
end DO |
end do |
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IF (ik == 1 .and. grossismx == 1.) THEN |
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xvrai(1) = xvrai(iim + 1)-twopi_d |
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xxprim(1) = xxprim(iim + 1) |
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END IF |
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DO i = 1, iim |
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xlon(i) = xvrai(i) |
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xprimm(i) = xxprim(i) |
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END DO |
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121 |
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122 |
DO i = 1, iim -1 |
if (rlonm025(is2) > pi) then |
123 |
IF (xvrai(i + 1) < xvrai(i)) THEN |
print *, 'Rlonm025 plus grand que pi !' |
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print *, 'rlonu(', i + 1, ') < rlonu(', i, ')' |
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124 |
STOP 1 |
STOP 1 |
125 |
END IF |
end if |
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END DO |
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IF (.not. (MINval(xvrai(:iim)) >= - pi_d - 0.1 & |
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.and. MAXval(xvrai(:iim)) <= pi_d + 0.1)) THEN |
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print *, & |
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'Réorganisation des longitudes pour les avoir entre - pi et pi' |
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IF (xzoom <= 0.) THEN |
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IF (ik == 1) THEN |
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i = 1 |
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do while (xvrai(i) < - pi_d .and. i < iim) |
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i = i + 1 |
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end do |
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if (xvrai(i) < - pi_d) then |
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print *, 'Xvrai plus petit que - pi !' |
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STOP 1 |
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end if |
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is2 = i |
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END IF |
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IF (is2 /= 1) THEN |
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DO ii = is2, iim |
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xlon(ii-is2 + 1) = xvrai(ii) |
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xprimm(ii-is2 + 1) = xxprim(ii) |
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END DO |
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DO ii = 1, is2 -1 |
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xlon(ii + iim-is2 + 1) = xvrai(ii) + twopi_d |
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xprimm(ii + iim-is2 + 1) = xxprim(ii) |
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END DO |
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END IF |
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ELSE |
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IF (ik == 1) THEN |
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i = iim |
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do while (xvrai(i) > pi_d .and. i > 1) |
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i = i - 1 |
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end do |
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if (xvrai(i) > pi_d) then |
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print *, 'Xvrai plus grand que pi !' |
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STOP 1 |
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end if |
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is2 = i |
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END IF |
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idif = iim -is2 |
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DO ii = 1, is2 |
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xlon(ii + idif) = xvrai(ii) |
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xprimm(ii + idif) = xxprim(ii) |
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END DO |
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DO ii = 1, idif |
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xlon(ii) = xvrai(ii + is2) - twopi_d |
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xprimm(ii) = xxprim(ii + is2) |
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END DO |
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END IF |
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END IF |
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xlon(iim + 1) = xlon(1) + twopi_d |
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xprimm(iim + 1) = xprimm(1) |
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DO i = 1, iim + 1 |
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xvrai(i) = xlon(i) * 180. / pi_d |
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END DO |
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IF (ik == 1) THEN |
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DO i = 1, iim + 1 |
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rlonm025(i) = xlon(i) |
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xprimm025(i) = xprimm(i) |
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END DO |
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ELSE IF (ik == 2) THEN |
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rlonv = xlon |
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xprimv = xprimm |
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ELSE IF (ik == 3) THEN |
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DO i = 1, iim + 1 |
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rlonu(i) = xlon(i) |
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xprimu(i) = xprimm(i) |
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END DO |
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ELSE IF (ik == 4) THEN |
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rlonp025 = xlon |
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xprimp025 = xprimm |
|
126 |
END IF |
END IF |
127 |
end DO loop_ik |
END IF |
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print * |
|
128 |
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129 |
DO i = 1, iim |
call principal_cshift(is2, rlonm025, xprimm025) |
130 |
xlon(i) = rlonv(i + 1) - rlonv(i) |
call principal_cshift(is2, rlonv, xprimv) |
131 |
END DO |
call principal_cshift(is2, rlonu, xprimu) |
132 |
champmin = 1e12 |
call principal_cshift(is2, rlonp025, xprimp025) |
133 |
champmax = -1e12 |
|
134 |
DO i = 1, iim |
forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i) |
135 |
champmin = MIN(champmin, xlon(i)) |
print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" |
136 |
champmax = MAX(champmax, xlon(i)) |
print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" |
|
END DO |
|
|
champmin = champmin * 180. / pi_d |
|
|
champmax = champmax * 180. / pi_d |
|
137 |
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138 |
|
! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: |
139 |
DO i = 1, iim + 1 |
DO i = 1, iim + 1 |
140 |
IF (rlonp025(i) < rlonv(i)) THEN |
IF (rlonp025(i) < rlonv(i)) THEN |
141 |
print *, ' Attention ! rlonp025 < rlonv', i |
print *, 'rlonp025(', i, ') = ', rlonp025(i) |
142 |
|
print *, "< rlonv(", i, ") = ", rlonv(i) |
143 |
STOP 1 |
STOP 1 |
144 |
END IF |
END IF |
145 |
|
|
146 |
IF (rlonv(i) < rlonm025(i)) THEN |
IF (rlonv(i) < rlonm025(i)) THEN |
147 |
print *, ' Attention ! rlonm025 > rlonv', i |
print *, 'rlonv(', i, ') = ', rlonv(i) |
148 |
|
print *, "< rlonm025(", i, ") = ", rlonm025(i) |
149 |
STOP 1 |
STOP 1 |
150 |
END IF |
END IF |
151 |
|
|
156 |
END IF |
END IF |
157 |
END DO |
END DO |
158 |
|
|
|
print *, ' Longitudes ' |
|
|
print 3, champmin, champmax |
|
|
|
|
|
3 Format(1x, ' Au centre du zoom, la longueur de la maille est', & |
|
|
' d environ ', f0.2, ' degres ', /, & |
|
|
' alors que la maille en dehors de la zone du zoom est ', & |
|
|
"d'environ ", f0.2, ' degres ') |
|
|
|
|
159 |
END SUBROUTINE fxhyp |
END SUBROUTINE fxhyp |
160 |
|
|
161 |
end module fxhyp_m |
end module fxhyp_m |