--- trunk/dyn3d/fxhyp.f 2014/03/05 14:57:53 82 +++ trunk/dyn3d/fxhyp.f 2015/03/20 16:31:06 132 @@ -4,431 +4,227 @@ contains - SUBROUTINE fxhyp(xzoomdeg, grossism, dzooma, tau, rlonm025, xprimm025, & - rlonv, xprimv, rlonu, xprimu, rlonp025, xprimp025, champmin, champmax) + SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025) - ! From LMDZ4/libf/dyn3d/fxhyp.F, v 1.2 2005/06/03 09:11:32 fairhead - - ! Auteur : P. Le Van + ! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 + ! Author: P. Le Van, from formulas by R. Sadourny ! Calcule les longitudes et dérivées dans la grille du GCM pour - ! une fonction f(x) à tangente hyperbolique. - - ! On doit avoir grossism \times dzoom < pi (radians), en longitude. - - USE dimens_m, ONLY: iim - USE paramet_m, ONLY: iip1 + ! une fonction f(x) à dérivée tangente hyperbolique. - INTEGER nmax, nmax2 - PARAMETER (nmax = 30000, nmax2 = 2*nmax) + ! Il vaut mieux avoir : grossismx \times dzoom < pi - LOGICAL scal180 - PARAMETER (scal180 = .TRUE.) + ! Le premier point scalaire pour une grille regulière (grossismx = + ! 1., taux=0., clon=0.) est à - 180 degrés. - ! scal180 = .TRUE. si on veut avoir le premier point scalaire pour - ! une grille reguliere (grossism = 1., tau=0., clon=0.) a -180. degres. - ! sinon scal180 = .FALSE. - - ! ...... arguments d'entree ....... - - REAL xzoomdeg, dzooma, tau, grossism - ! grossism etant le grossissement (= 2 si 2 fois, = 3 si 3 fois, etc.) - ! dzooma etant la distance totale de la zone du zoom - ! tau la raideur de la transition de l'interieur a l'exterieur du zoom - - ! ...... arguments de sortie ...... - - REAL rlonm025(iip1), xprimm025(iip1), rlonv(iip1), xprimv(iip1), & - rlonu(iip1), xprimu(iip1), rlonp025(iip1), xprimp025(iip1) - - ! .... variables locales .... - - REAL dzoom - DOUBLE PRECISION xlon(iip1), xprimm(iip1), xuv - DOUBLE PRECISION xtild(0:nmax2) - DOUBLE PRECISION fhyp(0:nmax2), ffdx, beta, Xprimt(0:nmax2) - DOUBLE PRECISION Xf(0:nmax2), xxpr(0:nmax2) - DOUBLE PRECISION xvrai(iip1), xxprim(iip1) - DOUBLE PRECISION pi, depi, epsilon, xzoom, fa, fb - DOUBLE PRECISION Xf1, Xfi, a0, a1, a2, a3, xi2 - INTEGER i, it, ik, iter, ii, idif, ii1, ii2 - DOUBLE PRECISION xi, xo1, xmoy, xlon2, fxm, Xprimin - DOUBLE PRECISION champmin, champmax, decalx - INTEGER is2 - SAVE is2 - - DOUBLE PRECISION heavyside - - pi = 2. * ASIN(1.) - depi = 2. * pi - epsilon = 1.e-3 - xzoom = xzoomdeg * pi/180. - - decalx = .75 - IF(grossism.EQ.1..AND.scal180) THEN - decalx = 1. - ENDIF - - WRITE(6, *) 'FXHYP scal180, decalx', scal180, decalx - - IF(dzooma.LT.1.) THEN - dzoom = dzooma * depi - ELSEIF(dzooma.LT. 25.) THEN - WRITE(6, *) ' Le param. dzoomx pour fxhyp est trop petit ! L augmenter et relancer ! ' - STOP 1 - ELSE - dzoom = dzooma * pi/180. - ENDIF - - WRITE(6, *) ' xzoom(rad.), grossism, tau, dzoom (radians)' - WRITE(6, 24) xzoom, grossism, tau, dzoom - - DO i = 0, nmax2 - xtild(i) = - pi + FLOAT(i) * depi /nmax2 - ENDDO - - DO i = nmax, nmax2 - - fa = tau* (dzoom/2. - xtild(i)) - fb = xtild(i) * (pi - xtild(i)) - - IF(200.* fb .LT. - fa) THEN - fhyp (i) = - 1. - ELSEIF(200. * fb .LT. fa) THEN - fhyp (i) = 1. - ELSE - IF(ABS(fa).LT.1.e-13.AND.ABS(fb).LT.1.e-13) THEN - IF(200.*fb + fa.LT.1.e-10) THEN - fhyp (i) = - 1. - ELSEIF(200.*fb - fa.LT.1.e-10) THEN - fhyp (i) = 1. - ENDIF + USE dimens_m, ONLY: iim + use invert_zoom_x_m, only: invert_zoom_x, nmax + use nr_util, only: pi, pi_d, twopi, twopi_d, arth + use principal_cshift_m, only: principal_cshift + use serre, only: clon, grossismx, dzoomx, taux + + REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1) + real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1) + + ! Local: + real rlonm025(iim + 1), rlonp025(iim + 1) + REAL dzoom, step + real d_rlonv(iim) + DOUBLE PRECISION xtild(0:2 * nmax) + DOUBLE PRECISION fhyp(nmax:2 * nmax), ffdx, beta, Xprimt(0:2 * nmax) + DOUBLE PRECISION Xf(0:2 * nmax), xxpr(2 * nmax) + DOUBLE PRECISION fa, fb + INTEGER i, is2 + DOUBLE PRECISION xmoy, fxm + + !---------------------------------------------------------------------- + + print *, "Call sequence information: fxhyp" + + test_grossismx: if (grossismx == 1.) then + step = twopi / iim + + xprimm025(:iim) = step + xprimp025(:iim) = step + xprimv(:iim) = step + xprimu(:iim) = step + + rlonv(:iim) = arth(- pi + clon, step, iim) + rlonm025(:iim) = rlonv(:iim) - 0.25 * step + rlonp025(:iim) = rlonv(:iim) + 0.25 * step + rlonu(:iim) = rlonv(:iim) + 0.5 * step + else test_grossismx + dzoom = dzoomx * twopi_d + xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1) + + ! Compute fhyp: + DO i = nmax, 2 * nmax + fa = taux * (dzoom / 2. - xtild(i)) + fb = xtild(i) * (pi_d - xtild(i)) + + IF (200. * fb < - fa) THEN + fhyp(i) = - 1. + ELSE IF (200. * fb < fa) THEN + fhyp(i) = 1. ELSE - fhyp (i) = TANH (fa/fb) - ENDIF - ENDIF - IF (xtild(i).EQ. 0.) fhyp(i) = 1. - IF (xtild(i).EQ. pi) fhyp(i) = -1. - - ENDDO - - !c .... Calcul de beta .... - - ffdx = 0. - - DO i = nmax +1, nmax2 - - xmoy = 0.5 * (xtild(i-1) + xtild(i)) - fa = tau* (dzoom/2. - xmoy) - fb = xmoy * (pi - xmoy) - - IF(200.* fb .LT. - fa) THEN - fxm = - 1. - ELSEIF(200. * fb .LT. fa) THEN - fxm = 1. - ELSE - IF(ABS(fa).LT.1.e-13.AND.ABS(fb).LT.1.e-13) THEN - IF(200.*fb + fa.LT.1.e-10) THEN - fxm = - 1. - ELSEIF(200.*fb - fa.LT.1.e-10) THEN - fxm = 1. - ENDIF + IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN + IF (200. * fb + fa < 1e-10) THEN + fhyp(i) = - 1. + ELSE IF (200. * fb - fa < 1e-10) THEN + fhyp(i) = 1. + END IF + ELSE + fhyp(i) = TANH(fa / fb) + END IF + END IF + + IF (xtild(i) == 0.) fhyp(i) = 1. + IF (xtild(i) == pi_d) fhyp(i) = -1. + END DO + + ! Calcul de beta + + ffdx = 0. + + DO i = nmax + 1, 2 * nmax + xmoy = 0.5 * (xtild(i-1) + xtild(i)) + fa = taux * (dzoom / 2. - xmoy) + fb = xmoy * (pi_d - xmoy) + + IF (200. * fb < - fa) THEN + fxm = - 1. + ELSE IF (200. * fb < fa) THEN + fxm = 1. ELSE - fxm = TANH (fa/fb) - ENDIF - ENDIF - - IF (xmoy.EQ. 0.) fxm = 1. - IF (xmoy.EQ. pi) fxm = -1. - - ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) - - ENDDO - - beta = (grossism * ffdx - pi) / (ffdx - pi) - - IF(2.*beta - grossism.LE. 0.) THEN - WRITE(6, *) ' ** Attention ! La valeur beta calculee dans la routine fxhyp est mauvaise ! ' - WRITE(6, *)'Modifier les valeurs de grossismx, tau ou dzoomx ', & - ' et relancer ! *** ' - STOP 1 - ENDIF - - ! ..... calcul de Xprimt ..... - - - DO i = nmax, nmax2 - Xprimt(i) = beta + (grossism - beta) * fhyp(i) - ENDDO - - DO i = nmax+1, nmax2 - Xprimt(nmax2 - i) = Xprimt(i) - ENDDO - - - ! ..... Calcul de Xf ........ - - Xf(0) = - pi - - DO i = nmax +1, nmax2 - - xmoy = 0.5 * (xtild(i-1) + xtild(i)) - fa = tau* (dzoom/2. - xmoy) - fb = xmoy * (pi - xmoy) + IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN + IF (200. * fb + fa < 1e-10) THEN + fxm = - 1. + ELSE IF (200. * fb - fa < 1e-10) THEN + fxm = 1. + END IF + ELSE + fxm = TANH(fa / fb) + END IF + END IF + + IF (xmoy == 0.) fxm = 1. + IF (xmoy == pi_d) fxm = -1. + + ffdx = ffdx + fxm * (xtild(i) - xtild(i-1)) + END DO + + print *, "ffdx = ", ffdx + beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d) + print *, "beta = ", beta + + IF (2. * beta - grossismx <= 0.) THEN + print *, 'Bad choice of grossismx, taux, dzoomx.' + print *, 'Decrease dzoomx or grossismx.' + STOP 1 + END IF + + ! calcul de Xprimt + Xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp + xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1) + + ! Calcul de Xf + + DO i = nmax + 1, 2 * nmax + xmoy = 0.5 * (xtild(i-1) + xtild(i)) + fa = taux * (dzoom / 2. - xmoy) + fb = xmoy * (pi_d - xmoy) + + IF (200. * fb < - fa) THEN + fxm = - 1. + ELSE IF (200. * fb < fa) THEN + fxm = 1. + ELSE + fxm = TANH(fa / fb) + END IF - IF(200.* fb .LT. - fa) THEN - fxm = - 1. - ELSEIF(200. * fb .LT. fa) THEN - fxm = 1. + IF (xmoy == 0.) fxm = 1. + IF (xmoy == pi_d) fxm = -1. + xxpr(i) = beta + (grossismx - beta) * fxm + END DO + + xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1) + + Xf(0) = - pi_d + + DO i=1, 2 * nmax - 1 + Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) + END DO + + Xf(2 * nmax) = pi_d + + call invert_zoom_x(xf, xtild, Xprimt, rlonm025(:iim), xprimm025(:iim), & + xuv = - 0.25d0) + call invert_zoom_x(xf, xtild, Xprimt, rlonv(:iim), xprimv(:iim), & + xuv = 0d0) + call invert_zoom_x(xf, xtild, Xprimt, rlonu(:iim), xprimu(:iim), & + xuv = 0.5d0) + call invert_zoom_x(xf, xtild, Xprimt, rlonp025(:iim), xprimp025(:iim), & + xuv = 0.25d0) + end if test_grossismx + + is2 = 0 + + IF (MINval(rlonm025(:iim)) < - pi - 0.1 & + .or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN + IF (clon <= 0.) THEN + is2 = 1 + + do while (rlonm025(is2) < - pi .and. is2 < iim) + is2 = is2 + 1 + end do + + if (rlonm025(is2) < - pi) then + print *, 'Rlonm025 plus petit que - pi !' + STOP 1 + end if ELSE - fxm = TANH (fa/fb) - ENDIF + is2 = iim - IF (xmoy.EQ. 0.) fxm = 1. - IF (xmoy.EQ. pi) fxm = -1. - xxpr(i) = beta + (grossism - beta) * fxm - - ENDDO - - DO i = nmax+1, nmax2 - xxpr(nmax2-i+1) = xxpr(i) - ENDDO - - DO i=1, nmax2 - Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1)) - ENDDO - - ! ***************************************************************** - - - ! ..... xuv = 0. si calcul aux pts scalaires ........ - ! ..... xuv = 0.5 si calcul aux pts U ........ - - WRITE(6, 18) - - DO ik = 1, 4 - - IF(ik.EQ.1) THEN - xuv = -0.25 - ELSE IF (ik.EQ.2) THEN - xuv = 0. - ELSE IF (ik.EQ.3) THEN - xuv = 0.50 - ELSE IF (ik.EQ.4) THEN - xuv = 0.25 - ENDIF - - xo1 = 0. - - ii1=1 - ii2=iim - IF(ik.EQ.1.and.grossism.EQ.1.) THEN - ii1 = 2 - ii2 = iim+1 - ENDIF - DO i = ii1, ii2 - - xlon2 = - pi + (FLOAT(i) + xuv - decalx) * depi / FLOAT(iim) - - Xfi = xlon2 - - DO it = nmax2, 0, -1 - IF(Xfi.GE.Xf(it)) GO TO 350 - end DO - - it = 0 - -350 CONTINUE - - ! ...... Calcul de Xf(xi) ...... - - xi = xtild(it) - - IF(it.EQ.nmax2) THEN - it = nmax2 -1 - Xf(it+1) = pi - ENDIF - ! ..................................................................... - - ! Appel de la routine qui calcule les coefficients a0, a1, a2, a3 d'un - ! polynome de degre 3 qui passe par les points (Xf(it), xtild(it)) - ! et (Xf(it+1), xtild(it+1)) - - CALL coefpoly (Xf(it), Xf(it+1), Xprimt(it), Xprimt(it+1), & - xtild(it), xtild(it+1), a0, a1, a2, a3) - - Xf1 = Xf(it) - Xprimin = a1 + 2.* a2 * xi + 3.*a3 * xi *xi - - DO iter = 1, 300 - xi = xi - (Xf1 - Xfi)/ Xprimin - - IF(ABS(xi-xo1).LE.epsilon) GO TO 550 - xo1 = xi - xi2 = xi * xi - Xf1 = a0 + a1 * xi + a2 * xi2 + a3 * xi2 * xi - Xprimin = a1 + 2.* a2 * xi + 3.* a3 * xi2 - end DO - WRITE(6, *) ' Pas de solution ***** ', i, xlon2, iter - STOP 6 -550 CONTINUE - - xxprim(i) = depi/ (FLOAT(iim) * Xprimin) - xvrai(i) = xi + xzoom - - end DO - - IF(ik.EQ.1.and.grossism.EQ.1.) THEN - xvrai(1) = xvrai(iip1)-depi - xxprim(1) = xxprim(iip1) - ENDIF - DO i = 1, iim - xlon(i) = xvrai(i) - xprimm(i) = xxprim(i) - ENDDO - DO i = 1, iim -1 - IF(xvrai(i+1).LT. xvrai(i)) THEN - WRITE(6, *) ' PBS. avec rlonu(', i+1, ') plus petit que rlonu(', i, & - ')' - STOP 7 - ENDIF - ENDDO - - ! ... Reorganisation des longitudes pour les avoir entre - pi et pi .. - ! ........................................................................ - - champmin = 1.e12 - champmax = -1.e12 - DO i = 1, iim - champmin = MIN(champmin, xvrai(i)) - champmax = MAX(champmax, xvrai(i)) - ENDDO - - IF(.not. (champmin .GE.-pi-0.10.and.champmax.LE.pi+0.10)) THEN - WRITE(6, *) 'Reorganisation des longitudes pour avoir entre - pi', & - ' et pi ' - - IF(xzoom.LE.0.) THEN - IF(ik.EQ. 1) THEN - DO i = 1, iim - 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) + do while (rlonm025(is2) > pi .and. is2 > 1) + is2 = is2 - 1 + end do + + if (rlonm025(is2) > pi) then + print *, 'Rlonm025 plus grand que pi !' + STOP 1 + end if + END IF + END IF + + call principal_cshift(is2, rlonm025, xprimm025) + call principal_cshift(is2, rlonv, xprimv) + call principal_cshift(is2, rlonu, xprimu) + call principal_cshift(is2, rlonp025, xprimp025) + + forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i) + print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees" + print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "degrees" + + ! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: + DO i = 1, iim + 1 + IF (rlonp025(i) < rlonv(i)) THEN + print *, 'rlonp025(', i, ') = ', rlonp025(i) + print *, "< rlonv(", i, ") = ", rlonv(i) + STOP 1 + END IF + + IF (rlonv(i) < rlonm025(i)) THEN + print *, 'rlonv(', i, ') = ', rlonv(i) + print *, "< rlonm025(", i, ") = ", rlonm025(i) + STOP 1 + END IF + + IF (rlonp025(i) > rlonu(i)) THEN + print *, 'rlonp025(', i, ') = ', rlonp025(i) + print *, "> rlonu(", i, ") = ", rlonu(i) + STOP 1 + END IF + END DO END SUBROUTINE fxhyp