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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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9 |
! From LMDZ4/libf/dyn3d/fxhyp.F, v 1.2 2005/06/03 09:11:32 fairhead |
! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 |
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! Author: P. Le Van, from formulas by R. Sadourny |
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! Auteur : P. Le Van |
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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. |
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USE dimens_m, ONLY: iim |
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USE paramet_m, ONLY: iip1 |
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INTEGER nmax, nmax2 |
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PARAMETER (nmax = 30000, nmax2 = 2*nmax) |
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LOGICAL scal180 |
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PARAMETER (scal180 = .TRUE.) |
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! scal180 = .TRUE. si on veut avoir le premier point scalaire pour |
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! une grille reguliere (grossism = 1., tau=0., clon=0.) a -180. degres. |
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! sinon scal180 = .FALSE. |
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! ...... arguments d'entree ....... |
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REAL xzoomdeg, dzooma, tau, grossism |
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! grossism etant le grossissement (= 2 si 2 fois, = 3 si 3 fois, etc.) |
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! dzooma etant la distance totale de la zone du zoom |
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! tau la raideur de la transition de l'interieur a l'exterieur du zoom |
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! ...... arguments de sortie ...... |
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REAL rlonm025(iip1), xprimm025(iip1), rlonv(iip1), xprimv(iip1), & |
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rlonu(iip1), xprimu(iip1), rlonp025(iip1), xprimp025(iip1) |
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! .... variables locales .... |
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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 champmin, champmax, decalx |
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INTEGER is2 |
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SAVE is2 |
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DOUBLE PRECISION heavyside |
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pi = 2. * ASIN(1.) |
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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.EQ.1..AND.scal180) THEN |
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decalx = 1. |
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ENDIF |
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WRITE(6, *) '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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WRITE(6, *) ' Le param. dzoomx pour fxhyp est trop petit ! 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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ENDIF |
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WRITE(6, *) ' xzoom(rad.), grossism, tau, dzoom (radians)' |
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WRITE(6, 24) xzoom, grossism, tau, dzoom |
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DO i = 0, nmax2 |
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xtild(i) = - pi + FLOAT(i) * depi /nmax2 |
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ENDDO |
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DO i = nmax, nmax2 |
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fa = tau* (dzoom/2. - xtild(i)) |
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fb = xtild(i) * (pi - xtild(i)) |
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IF(200.* fb .LT. - fa) THEN |
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fhyp (i) = - 1. |
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ELSEIF(200. * fb .LT. fa) THEN |
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fhyp (i) = 1. |
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ELSE |
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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 |
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fhyp (i) = - 1. |
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ELSEIF(200.*fb - fa.LT.1.e-10) THEN |
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fhyp (i) = 1. |
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ENDIF |
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ELSE |
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fhyp (i) = TANH (fa/fb) |
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ENDIF |
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ENDIF |
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IF (xtild(i).EQ. 0.) fhyp(i) = 1. |
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IF (xtild(i).EQ. pi) fhyp(i) = -1. |
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ENDDO |
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!c .... Calcul de beta .... |
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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 = tau* (dzoom/2. - xmoy) |
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fb = xmoy * (pi - xmoy) |
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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 |
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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 |
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fxm = - 1. |
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ELSEIF(200.*fb - fa.LT.1.e-10) THEN |
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fxm = 1. |
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ENDIF |
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ELSE |
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fxm = TANH (fa/fb) |
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ENDIF |
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ENDIF |
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IF (xmoy.EQ. 0.) fxm = 1. |
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IF (xmoy.EQ. pi) fxm = -1. |
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ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) |
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ENDDO |
! Il vaut mieux avoir : grossismx \times dzoom < pi |
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beta = (grossism * ffdx - pi) / (ffdx - pi) |
! Le premier point scalaire pour une grille regulière (grossismx = |
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! 1., taux = 0., clon = 0.) est à - 180 degrés. |
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IF(2.*beta - grossism.LE. 0.) THEN |
USE dimens_m, ONLY: iim |
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WRITE(6, *) ' ** Attention ! La valeur beta calculee dans la routine fxhyp est mauvaise ! ' |
use dynetat0_m, only: clon, grossismx, dzoomx, taux |
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WRITE(6, *)'Modifier les valeurs de grossismx, tau ou dzoomx ', & |
use invert_zoom_x_m, only: invert_zoom_x, nmax |
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' et relancer ! *** ' |
use nr_util, only: pi, pi_d, twopi, twopi_d, arth |
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STOP 1 |
use principal_cshift_m, only: principal_cshift |
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ENDIF |
use tanh_cautious_m, only: tanh_cautious |
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! ..... calcul de Xprimt ..... |
REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) |
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real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) |
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DO i = nmax, nmax2 |
! Local: |
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Xprimt(i) = beta + (grossism - beta) * fhyp(i) |
real rlonm025(iim + 1), rlonp025(iim + 1), d_rlonv(iim) |
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ENDDO |
REAL dzoom, step |
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DOUBLE PRECISION, dimension(0:nmax):: xtild, fhyp, G, Xf |
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DO i = nmax+1, nmax2 |
DOUBLE PRECISION ffdx, beta |
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Xprimt(nmax2 - i) = Xprimt(i) |
INTEGER i, is2 |
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ENDDO |
DOUBLE PRECISION xxpr(nmax - 1), xmoy(nmax), fxm(nmax) |
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!---------------------------------------------------------------------- |
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! ..... Calcul de Xf ........ |
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print *, "Call sequence information: fxhyp" |
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Xf(0) = - pi |
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test_grossismx: if (grossismx == 1.) then |
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DO i = nmax +1, nmax2 |
step = twopi / iim |
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xmoy = 0.5 * (xtild(i-1) + xtild(i)) |
xprimm025(:iim) = step |
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fa = tau* (dzoom/2. - xmoy) |
xprimp025(:iim) = step |
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fb = xmoy * (pi - xmoy) |
xprimv(:iim) = step |
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xprimu(:iim) = step |
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IF(200.* fb .LT. - fa) THEN |
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fxm = - 1. |
rlonv(:iim) = arth(- pi + clon, step, iim) |
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ELSEIF(200. * fb .LT. fa) THEN |
rlonm025(:iim) = rlonv(:iim) - 0.25 * step |
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fxm = 1. |
rlonp025(:iim) = rlonv(:iim) + 0.25 * step |
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rlonu(:iim) = rlonv(:iim) + 0.5 * step |
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else test_grossismx |
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dzoom = dzoomx * twopi_d |
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xtild = arth(0d0, pi_d / nmax, nmax + 1) |
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forall (i = 1:nmax) xmoy(i) = 0.5d0 * (xtild(i-1) + xtild(i)) |
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! Compute fhyp: |
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fhyp(1:nmax - 1) = tanh_cautious(taux * (dzoom / 2. & |
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- xtild(1:nmax - 1)), xtild(1:nmax - 1) & |
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* (pi_d - xtild(1:nmax - 1))) |
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fhyp(0) = 1d0 |
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fhyp(nmax) = -1d0 |
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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 = 1, 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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80 |
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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 |
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G = beta + (grossismx - beta) * fhyp |
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! Calcul de Xf |
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xxpr = beta + (grossismx - beta) * fxm(:nmax - 1) |
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Xf(0) = 0d0 |
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DO i = 1, nmax - 1 |
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Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) |
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END DO |
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Xf(nmax) = pi_d |
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call invert_zoom_x(xf, xtild, G, rlonm025(:iim), xprimm025(:iim), & |
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xuv = - 0.25d0) |
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call invert_zoom_x(xf, xtild, G, rlonv(:iim), xprimv(:iim), xuv = 0d0) |
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call invert_zoom_x(xf, xtild, G, rlonu(:iim), xprimu(:iim), xuv = 0.5d0) |
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call invert_zoom_x(xf, xtild, G, rlonp025(:iim), xprimp025(:iim), & |
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xuv = 0.25d0) |
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end if test_grossismx |
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107 |
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is2 = 0 |
108 |
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109 |
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IF (MINval(rlonm025(:iim)) < - pi - 0.1 & |
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.or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN |
111 |
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IF (clon <= 0.) THEN |
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is2 = 1 |
113 |
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114 |
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do while (rlonm025(is2) < - pi .and. is2 < iim) |
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is2 = is2 + 1 |
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end do |
117 |
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118 |
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if (rlonm025(is2) < - pi) then |
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print *, 'Rlonm025 plus petit que - pi !' |
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STOP 1 |
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end if |
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ELSE |
ELSE |
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fxm = TANH (fa/fb) |
is2 = iim |
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ENDIF |
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IF (xmoy.EQ. 0.) fxm = 1. |
do while (rlonm025(is2) > pi .and. is2 > 1) |
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IF (xmoy.EQ. pi) fxm = -1. |
is2 = is2 - 1 |
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xxpr(i) = beta + (grossism - beta) * fxm |
end do |
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ENDDO |
if (rlonm025(is2) > pi) then |
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print *, 'Rlonm025 plus grand que pi !' |
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DO i = nmax+1, nmax2 |
STOP 1 |
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xxpr(nmax2-i+1) = xxpr(i) |
end if |
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ENDDO |
END IF |
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END IF |
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DO i=1, nmax2 |
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Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) |
call principal_cshift(is2, rlonm025, xprimm025) |
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ENDDO |
call principal_cshift(is2, rlonv, xprimv) |
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call principal_cshift(is2, rlonu, xprimu) |
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! ***************************************************************** |
call principal_cshift(is2, rlonp025, xprimp025) |
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141 |
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forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i) |
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! ..... xuv = 0. si calcul aux pts scalaires ........ |
print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" |
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! ..... xuv = 0.5 si calcul aux pts U ........ |
print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" |
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WRITE(6, 18) |
! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: |
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DO i = 1, iim + 1 |
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DO ik = 1, 4 |
IF (rlonp025(i) < rlonv(i)) THEN |
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print *, 'rlonp025(', i, ') = ', rlonp025(i) |
149 |
IF(ik.EQ.1) THEN |
print *, "< rlonv(", i, ") = ", rlonv(i) |
150 |
xuv = -0.25 |
STOP 1 |
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ELSE IF (ik.EQ.2) THEN |
END IF |
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xuv = 0. |
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ELSE IF (ik.EQ.3) THEN |
IF (rlonv(i) < rlonm025(i)) THEN |
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xuv = 0.50 |
print *, 'rlonv(', i, ') = ', rlonv(i) |
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ELSE IF (ik.EQ.4) THEN |
print *, "< rlonm025(", i, ") = ", rlonm025(i) |
156 |
xuv = 0.25 |
STOP 1 |
157 |
ENDIF |
END IF |
158 |
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xo1 = 0. |
IF (rlonp025(i) > rlonu(i)) THEN |
160 |
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print *, 'rlonp025(', i, ') = ', rlonp025(i) |
161 |
ii1=1 |
print *, "> rlonu(", i, ") = ", rlonu(i) |
162 |
ii2=iim |
STOP 1 |
163 |
IF(ik.EQ.1.and.grossism.EQ.1.) THEN |
END IF |
164 |
ii1 = 2 |
END DO |
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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 + (FLOAT(i) + xuv - decalx) * depi / FLOAT(iim) |
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Xfi = xlon2 |
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DO it = nmax2, 0, -1 |
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IF(Xfi.GE.Xf(it)) GO TO 350 |
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end DO |
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it = 0 |
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350 CONTINUE |
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! ...... Calcul de Xf(xi) ...... |
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xi = xtild(it) |
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IF(it.EQ.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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! ..................................................................... |
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! Appel de la routine qui calcule les coefficients a0, a1, a2, a3 d'un |
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! polynome de degre 3 qui passe par les points (Xf(it), xtild(it)) |
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! 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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DO iter = 1, 300 |
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xi = xi - (Xf1 - Xfi)/ Xprimin |
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IF(ABS(xi-xo1).LE.epsilon) GO TO 550 |
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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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WRITE(6, *) ' Pas de solution ***** ', i, xlon2, iter |
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STOP 6 |
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550 CONTINUE |
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xxprim(i) = depi/ (FLOAT(iim) * Xprimin) |
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xvrai(i) = xi + xzoom |
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end DO |
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IF(ik.EQ.1.and.grossism.EQ.1.) THEN |
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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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WRITE(6, *) ' PBS. avec rlonu(', i+1, ') plus petit que rlonu(', i, & |
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')' |
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STOP 7 |
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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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! ........................................................................ |
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champmin = 1.e12 |
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champmax = -1.e12 |
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DO i = 1, iim |
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champmin = MIN(champmin, xvrai(i)) |
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champmax = MAX(champmax, xvrai(i)) |
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ENDDO |
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IF(.not. (champmin .GE.-pi-0.10.and.champmax.LE.pi+0.10)) THEN |
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WRITE(6, *) 'Reorganisation des longitudes pour avoir entre - pi', & |
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' et pi ' |
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IF(xzoom.LE.0.) THEN |
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IF(ik.EQ. 1) THEN |
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DO i = 1, iim |
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|
IF(xvrai(i).GE. - pi) GO TO 80 |
|
|
ENDDO |
|
|
WRITE(6, *) ' PBS. 1 ! Xvrai plus petit que - pi ! ' |
|
|
STOP 8 |
|
|
80 CONTINUE |
|
|
is2 = i |
|
|
ENDIF |
|
|
|
|
|
IF(is2.NE. 1) THEN |
|
|
DO ii = is2, iim |
|
|
xlon (ii-is2+1) = xvrai(ii) |
|
|
xprimm(ii-is2+1) = xxprim(ii) |
|
|
ENDDO |
|
|
DO ii = 1, is2 -1 |
|
|
xlon (ii+iim-is2+1) = xvrai(ii) + depi |
|
|
xprimm(ii+iim-is2+1) = xxprim(ii) |
|
|
ENDDO |
|
|
ENDIF |
|
|
ELSE |
|
|
IF(ik.EQ.1) THEN |
|
|
DO i = iim, 1, -1 |
|
|
IF(xvrai(i).LE. pi) GO TO 90 |
|
|
ENDDO |
|
|
WRITE(6, *) ' PBS. 2 ! Xvrai plus grand que pi ! ' |
|
|
STOP 9 |
|
|
90 CONTINUE |
|
|
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.EQ.1) THEN |
|
|
! WRITE(6, *) ' XLON aux pts. V-0.25 apres (en deg.) ' |
|
|
! WRITE(6, 18) |
|
|
! WRITE(6, 68) xvrai |
|
|
! WRITE(6, *) ' XPRIM k ', ik |
|
|
! WRITE(6, 566) xprimm |
|
|
|
|
|
DO i = 1, iim +1 |
|
|
rlonm025(i) = xlon(i) |
|
|
xprimm025(i) = xprimm(i) |
|
|
ENDDO |
|
|
ELSE IF(ik.EQ.2) THEN |
|
|
! WRITE(6, 18) |
|
|
! WRITE(6, *) ' XLON aux pts. V apres (en deg.) ' |
|
|
! WRITE(6, 68) xvrai |
|
|
! WRITE(6, *) ' XPRIM k ', ik |
|
|
! WRITE(6, 566) xprimm |
|
|
|
|
|
DO i = 1, iim + 1 |
|
|
rlonv(i) = xlon(i) |
|
|
xprimv(i) = xprimm(i) |
|
|
ENDDO |
|
|
|
|
|
ELSE IF(ik.EQ.3) THEN |
|
|
! WRITE(6, 18) |
|
|
! WRITE(6, *) ' XLON aux pts. U apres (en deg.) ' |
|
|
! WRITE(6, 68) xvrai |
|
|
! WRITE(6, *) ' XPRIM ik ', ik |
|
|
! WRITE(6, 566) xprimm |
|
|
|
|
|
DO i = 1, iim + 1 |
|
|
rlonu(i) = xlon(i) |
|
|
xprimu(i) = xprimm(i) |
|
|
ENDDO |
|
|
|
|
|
ELSE IF(ik.EQ.4) THEN |
|
|
! WRITE(6, 18) |
|
|
! WRITE(6, *) ' XLON aux pts. V+0.25 apres (en deg.) ' |
|
|
! WRITE(6, 68) xvrai |
|
|
! WRITE(6, *) ' XPRIM ik ', ik |
|
|
! WRITE(6, 566) xprimm |
|
|
|
|
|
DO i = 1, iim + 1 |
|
|
rlonp025(i) = xlon(i) |
|
|
xprimp025(i) = xprimm(i) |
|
|
ENDDO |
|
|
|
|
|
ENDIF |
|
|
|
|
|
end DO |
|
|
|
|
|
WRITE(6, 18) |
|
|
|
|
|
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 |
|
|
|
|
|
18 FORMAT(/) |
|
|
24 FORMAT(2x, 'Parametres xzoom, gross, tau, dzoom pour fxhyp ', 4f8.3) |
|
|
68 FORMAT(1x, 7f9.2) |
|
|
566 FORMAT(1x, 7f9.4) |
|
165 |
|
|
166 |
END SUBROUTINE fxhyp |
END SUBROUTINE fxhyp |
167 |
|
|