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contains |
contains |
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SUBROUTINE fxhyp(xzoomdeg, grossism, dzooma, tau, rlonm025, xprimm025, & |
SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025) |
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rlonv, xprimv, rlonu, xprimu, rlonp025, xprimp025, champmin, champmax) |
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! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 |
! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 |
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! Author: P. Le Van |
! Author: P. Le Van, from formulas by R. Sadourny |
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! Calcule les longitudes et dérivées dans la grille du GCM pour |
! Calcule les longitudes et dérivées dans la grille du GCM pour |
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! une fonction f(x) à tangente hyperbolique. |
! une fonction f(x) à dérivée tangente hyperbolique. |
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! On doit avoir grossism \times dzoom < pi (radians), en longitude. |
! Il vaut mieux avoir : grossismx \times dzoom < pi |
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USE dimens_m, ONLY: iim |
! Le premier point scalaire pour une grille regulière (grossismx = |
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USE paramet_m, ONLY: iip1 |
! 1., taux=0., clon=0.) est à - 180 degrés. |
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REAL, intent(in):: xzoomdeg |
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REAL, intent(in):: grossism |
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! grossissement (= 2 si 2 fois, = 3 si 3 fois, etc.) |
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REAL, intent(in):: dzooma ! distance totale de la zone du zoom |
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REAL, intent(in):: tau |
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! raideur de la transition de l'intérieur à l'extérieur du zoom |
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! arguments de sortie |
USE dimens_m, ONLY: iim |
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use dynetat0_m, only: clon, grossismx, dzoomx, taux |
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REAL, dimension(iip1):: rlonm025, xprimm025, rlonv, xprimv |
use invert_zoom_x_m, only: invert_zoom_x, nmax |
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real, dimension(iip1):: rlonu, xprimu, rlonp025, xprimp025 |
use nr_util, only: pi, pi_d, twopi, twopi_d, arth |
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use principal_cshift_m, only: principal_cshift |
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use tanh_cautious_m, only: tanh_cautious |
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DOUBLE PRECISION, intent(out):: champmin, champmax |
REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
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real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
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! Local: |
! Local: |
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real rlonm025(iim + 1), rlonp025(iim + 1) |
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INTEGER, PARAMETER:: nmax = 30000, nmax2 = 2*nmax |
REAL dzoom, step |
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real d_rlonv(iim) |
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LOGICAL, PARAMETER:: scal180 = .TRUE. |
DOUBLE PRECISION xtild(0:2 * nmax) |
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! scal180 = .TRUE. si on veut avoir le premier point scalaire pour |
DOUBLE PRECISION fhyp(nmax:2 * nmax), ffdx, beta, Xprimt(0:2 * nmax) |
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! une grille reguliere (grossism = 1., tau=0., clon=0.) a |
DOUBLE PRECISION Xf(0:2 * nmax), xxpr(2 * nmax) |
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! -180. degres. sinon scal180 = .FALSE. |
INTEGER i, is2 |
38 |
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DOUBLE PRECISION, dimension(nmax + 1:2 * nmax):: xmoy, fxm |
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REAL dzoom |
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DOUBLE PRECISION xlon(iip1), xprimm(iip1), xuv |
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DOUBLE PRECISION xtild(0:nmax2) |
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DOUBLE PRECISION fhyp(0:nmax2), ffdx, beta, Xprimt(0:nmax2) |
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DOUBLE PRECISION Xf(0:nmax2), xxpr(0:nmax2) |
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DOUBLE PRECISION xvrai(iip1), xxprim(iip1) |
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DOUBLE PRECISION pi, depi, epsilon, 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, xlon2, fxm, Xprimin |
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DOUBLE PRECISION decalx |
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INTEGER is2 |
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SAVE is2 |
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!---------------------------------------------------------------------- |
!---------------------------------------------------------------------- |
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pi = 2. * ASIN(1.) |
print *, "Call sequence information: fxhyp" |
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depi = 2. * pi |
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epsilon = 1.e-3 |
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xzoom = xzoomdeg * pi/180. |
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decalx = .75 |
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IF (grossism == 1. .AND. scal180) THEN |
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decalx = 1. |
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ENDIF |
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print *, 'FXHYP scal180, decalx', scal180, decalx |
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IF (dzooma.LT.1.) THEN |
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dzoom = dzooma * depi |
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ELSEIF (dzooma.LT. 25.) THEN |
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print *, "Le paramètre dzoomx pour fxhyp est trop petit. " & |
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// "L'augmenter et relancer." |
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STOP 1 |
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ELSE |
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dzoom = dzooma * pi/180. |
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END IF |
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print *, ' xzoom(rad), grossism, tau, dzoom (rad):' |
test_grossismx: if (grossismx == 1.) then |
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print *, xzoom, grossism, tau, dzoom |
step = twopi / iim |
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DO i = 0, nmax2 |
xprimm025(:iim) = step |
48 |
xtild(i) = - pi + REAL(i) * depi /nmax2 |
xprimp025(:iim) = step |
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ENDDO |
xprimv(:iim) = step |
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xprimu(:iim) = step |
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DO i = nmax, nmax2 |
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52 |
fa = tau* (dzoom/2. - xtild(i)) |
rlonv(:iim) = arth(- pi + clon, step, iim) |
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fb = xtild(i) * (pi - xtild(i)) |
rlonm025(:iim) = rlonv(:iim) - 0.25 * step |
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rlonp025(:iim) = rlonv(:iim) + 0.25 * step |
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IF (200.* fb .LT. - fa) THEN |
rlonu(:iim) = rlonv(:iim) + 0.5 * step |
56 |
fhyp (i) = - 1. |
else test_grossismx |
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ELSEIF (200. * fb .LT. fa) THEN |
dzoom = dzoomx * twopi_d |
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fhyp (i) = 1. |
xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1) |
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ELSE |
forall (i = nmax + 1:2 * nmax) xmoy(i) = 0.5d0 * (xtild(i-1) + xtild(i)) |
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IF (ABS(fa).LT.1.e-13.AND.ABS(fb).LT.1.e-13) THEN |
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IF (200.*fb + fa.LT.1.e-10) THEN |
! Compute fhyp: |
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fhyp (i) = - 1. |
fhyp(nmax + 1:2 * nmax - 1) = tanh_cautious(taux * (dzoom / 2. & |
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ELSEIF (200.*fb - fa.LT.1.e-10) THEN |
- xtild(nmax + 1:2 * nmax - 1)), xtild(nmax + 1:2 * nmax - 1) & |
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fhyp (i) = 1. |
* (pi_d - xtild(nmax + 1:2 * nmax - 1))) |
65 |
ENDIF |
fhyp(nmax) = 1d0 |
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ELSE |
fhyp(2 * nmax) = -1d0 |
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fhyp (i) = TANH (fa/fb) |
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ENDIF |
fxm = tanh_cautious(taux * (dzoom / 2. - xmoy), xmoy * (pi_d - xmoy)) |
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! Calcul de beta |
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ffdx = 0. |
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DO i = nmax + 1, 2 * nmax |
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ffdx = ffdx + fxm(i) * (xtild(i) - xtild(i-1)) |
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END DO |
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print *, "ffdx = ", ffdx |
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beta = (pi_d - grossismx * ffdx) / (pi_d - ffdx) |
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print *, "beta = ", beta |
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IF (2. * beta - grossismx <= 0.) THEN |
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print *, 'Bad choice of grossismx, taux, dzoomx.' |
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print *, 'Decrease dzoomx or grossismx.' |
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STOP 1 |
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END IF |
END IF |
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IF (xtild(i) == 0.) fhyp(i) = 1. |
! calcul de Xprimt |
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IF (xtild(i) == pi) fhyp(i) = -1. |
Xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp |
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END DO |
xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1) |
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! Calcul de beta |
! Calcul de Xf |
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ffdx = 0. |
xxpr(nmax + 1:2 * nmax) = beta + (grossismx - beta) * fxm |
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xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1) |
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DO i = nmax + 1, nmax2 |
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xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
Xf(0) = - pi_d |
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fa = tau* (dzoom/2. - xmoy) |
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fb = xmoy * (pi - xmoy) |
DO i=1, 2 * nmax - 1 |
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Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) |
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IF (200.* fb .LT. - fa) THEN |
END DO |
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fxm = - 1. |
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ELSEIF (200. * fb .LT. fa) THEN |
Xf(2 * nmax) = pi_d |
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fxm = 1. |
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ELSE |
call invert_zoom_x(xf, xtild, Xprimt, rlonm025(:iim), xprimm025(:iim), & |
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IF (ABS(fa).LT.1.e-13.AND.ABS(fb).LT.1.e-13) THEN |
xuv = - 0.25d0) |
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IF (200.*fb + fa.LT.1.e-10) THEN |
call invert_zoom_x(xf, xtild, Xprimt, rlonv(:iim), xprimv(:iim), & |
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fxm = - 1. |
xuv = 0d0) |
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ELSEIF (200.*fb - fa.LT.1.e-10) THEN |
call invert_zoom_x(xf, xtild, Xprimt, rlonu(:iim), xprimu(:iim), & |
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fxm = 1. |
xuv = 0.5d0) |
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ENDIF |
call invert_zoom_x(xf, xtild, Xprimt, rlonp025(:iim), xprimp025(:iim), & |
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ELSE |
xuv = 0.25d0) |
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fxm = TANH (fa/fb) |
end if test_grossismx |
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ENDIF |
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ENDIF |
is2 = 0 |
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IF (xmoy == 0.) fxm = 1. |
IF (MINval(rlonm025(:iim)) < - pi - 0.1 & |
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IF (xmoy == pi) fxm = -1. |
.or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN |
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IF (clon <= 0.) THEN |
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ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) |
is2 = 1 |
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ENDDO |
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beta = (grossism * ffdx - pi) / (ffdx - pi) |
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IF (2.*beta - grossism <= 0.) THEN |
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print *, 'Attention ! La valeur beta calculée dans fxhyp est mauvaise.' |
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print *, 'Modifier les valeurs de grossismx, tau 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 |
do while (rlonm025(is2) < - pi .and. is2 < iim) |
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Xprimt(i) = beta + (grossism - beta) * fhyp(i) |
is2 = is2 + 1 |
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END DO |
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 |
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DO i = nmax + 1, nmax2 |
if (rlonm025(is2) < - pi) then |
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xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
print *, 'Rlonm025 plus petit que - pi !' |
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fa = tau* (dzoom/2. - xmoy) |
STOP 1 |
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fb = xmoy * (pi - xmoy) |
end if |
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IF (200.* fb .LT. - fa) THEN |
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fxm = - 1. |
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ELSEIF (200. * fb .LT. fa) THEN |
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fxm = 1. |
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ELSE |
ELSE |
131 |
fxm = TANH (fa/fb) |
is2 = iim |
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ENDIF |
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IF (xmoy == 0.) fxm = 1. |
do while (rlonm025(is2) > pi .and. is2 > 1) |
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IF (xmoy == pi) fxm = -1. |
is2 = is2 - 1 |
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xxpr(i) = beta + (grossism - beta) * fxm |
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ENDDO |
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DO i = nmax + 1, nmax2 |
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xxpr(nmax2-i + 1) = xxpr(i) |
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ENDDO |
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DO i=1, nmax2 |
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Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) |
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ENDDO |
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! xuv = 0. si calcul aux pts scalaires |
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! xuv = 0.5 si calcul aux pts U |
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print * |
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DO ik = 1, 4 |
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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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ENDIF |
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xo1 = 0. |
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ii1=1 |
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ii2=iim |
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IF (ik == 1.and.grossism == 1.) THEN |
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ii1 = 2 |
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ii2 = iim + 1 |
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ENDIF |
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DO i = ii1, ii2 |
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xlon2 = - pi + (REAL(i) + xuv - decalx) * depi / REAL(iim) |
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Xfi = xlon2 |
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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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end do |
end do |
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! Calcul de Xf(xi) |
if (rlonm025(is2) > pi) then |
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print *, 'Rlonm025 plus grand 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 |
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ENDIF |
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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) <= epsilon .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) > epsilon) then |
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! iter == 300 |
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print *, 'Pas de solution.' |
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print *, i, xlon2 |
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STOP 1 |
STOP 1 |
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end if |
end if |
141 |
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END IF |
142 |
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END IF |
143 |
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144 |
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call principal_cshift(is2, rlonm025, xprimm025) |
145 |
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call principal_cshift(is2, rlonv, xprimv) |
146 |
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call principal_cshift(is2, rlonu, xprimu) |
147 |
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call principal_cshift(is2, rlonp025, xprimp025) |
148 |
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149 |
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forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i) |
150 |
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print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" |
151 |
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print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" |
152 |
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153 |
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! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: |
154 |
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DO i = 1, iim + 1 |
155 |
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IF (rlonp025(i) < rlonv(i)) THEN |
156 |
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print *, 'rlonp025(', i, ') = ', rlonp025(i) |
157 |
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print *, "< rlonv(", i, ") = ", rlonv(i) |
158 |
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STOP 1 |
159 |
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END IF |
160 |
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161 |
xxprim(i) = depi/ (REAL(iim) * Xprimin) |
IF (rlonv(i) < rlonm025(i)) THEN |
162 |
xvrai(i) = xi + xzoom |
print *, 'rlonv(', i, ') = ', rlonv(i) |
163 |
end DO |
print *, "< rlonm025(", i, ") = ", rlonm025(i) |
164 |
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STOP 1 |
165 |
IF (ik == 1.and.grossism == 1.) THEN |
END IF |
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xvrai(1) = xvrai(iip1)-depi |
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xxprim(1) = xxprim(iip1) |
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ENDIF |
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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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ENDDO |
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DO i = 1, iim -1 |
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IF (xvrai(i + 1).LT. xvrai(i)) THEN |
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print *, 'Problème avec rlonu(', i + 1, & |
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') plus petit que rlonu(', i, ')' |
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STOP 1 |
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ENDIF |
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ENDDO |
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! Reorganisation des longitudes pour les avoir entre - pi et pi |
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166 |
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167 |
champmin = 1.e12 |
IF (rlonp025(i) > rlonu(i)) THEN |
168 |
champmax = -1.e12 |
print *, 'rlonp025(', i, ') = ', rlonp025(i) |
169 |
DO i = 1, iim |
print *, "> rlonu(", i, ") = ", rlonu(i) |
170 |
champmin = MIN(champmin, xvrai(i)) |
STOP 1 |
171 |
champmax = MAX(champmax, xvrai(i)) |
END IF |
172 |
ENDDO |
END DO |
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IF (.not. (champmin >= -pi-0.10.and.champmax <= pi + 0.10)) THEN |
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print *, 'Reorganisation des longitudes pour avoir entre - pi', & |
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' 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 .and. i < iim) |
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i = i + 1 |
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end do |
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if (xvrai(i) < - pi) then |
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print *, ' PBS. 1 ! 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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ENDIF |
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IF (is2.NE. 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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ENDDO |
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DO ii = 1, is2 -1 |
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xlon (ii + iim-is2 + 1) = xvrai(ii) + depi |
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xprimm(ii + iim-is2 + 1) = xxprim(ii) |
|
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ENDDO |
|
|
ENDIF |
|
|
ELSE |
|
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IF (ik == 1) THEN |
|
|
i = iim |
|
|
|
|
|
do while (xvrai(i) > pi .and. i > 1) |
|
|
i = i - 1 |
|
|
end do |
|
|
|
|
|
if (xvrai(i) > pi) then |
|
|
print *, ' PBS. 2 ! Xvrai plus grand que pi ! ' |
|
|
STOP 1 |
|
|
end if |
|
|
|
|
|
is2 = i |
|
|
ENDIF |
|
|
idif = iim -is2 |
|
|
DO ii = 1, is2 |
|
|
xlon (ii + idif) = xvrai(ii) |
|
|
xprimm(ii + idif) = xxprim(ii) |
|
|
ENDDO |
|
|
DO ii = 1, idif |
|
|
xlon (ii) = xvrai (ii + is2) - depi |
|
|
xprimm(ii) = xxprim(ii + is2) |
|
|
ENDDO |
|
|
ENDIF |
|
|
ENDIF |
|
|
|
|
|
! Fin de la reorganisation |
|
|
|
|
|
xlon (iip1) = xlon(1) + depi |
|
|
xprimm(iip1) = xprimm (1) |
|
|
|
|
|
DO i = 1, iim + 1 |
|
|
xvrai(i) = xlon(i)*180./pi |
|
|
ENDDO |
|
|
|
|
|
IF (ik == 1) THEN |
|
|
DO i = 1, iim + 1 |
|
|
rlonm025(i) = xlon(i) |
|
|
xprimm025(i) = xprimm(i) |
|
|
ENDDO |
|
|
ELSE IF (ik == 2) THEN |
|
|
DO i = 1, iim + 1 |
|
|
rlonv(i) = xlon(i) |
|
|
xprimv(i) = xprimm(i) |
|
|
ENDDO |
|
|
ELSE IF (ik == 3) THEN |
|
|
DO i = 1, iim + 1 |
|
|
rlonu(i) = xlon(i) |
|
|
xprimu(i) = xprimm(i) |
|
|
ENDDO |
|
|
ELSE IF (ik == 4) THEN |
|
|
DO i = 1, iim + 1 |
|
|
rlonp025(i) = xlon(i) |
|
|
xprimp025(i) = xprimm(i) |
|
|
ENDDO |
|
|
ENDIF |
|
|
end DO |
|
|
|
|
|
print * |
|
|
|
|
|
DO i = 1, iim |
|
|
xlon(i) = rlonv(i + 1) - rlonv(i) |
|
|
ENDDO |
|
|
champmin = 1.e12 |
|
|
champmax = -1.e12 |
|
|
DO i = 1, iim |
|
|
champmin = MIN(champmin, xlon(i)) |
|
|
champmax = MAX(champmax, xlon(i)) |
|
|
ENDDO |
|
|
champmin = champmin * 180./pi |
|
|
champmax = champmax * 180./pi |
|
173 |
|
|
174 |
END SUBROUTINE fxhyp |
END SUBROUTINE fxhyp |
175 |
|
|