| 4 |
|
|
| 5 |
IMPLICIT NONE |
IMPLICIT NONE |
| 6 |
|
|
| 7 |
private iim, jjm |
private iim, jjm, principal_cshift, invert_zoom_x, funcd |
| 8 |
|
|
| 9 |
INTEGER day_ini |
INTEGER day_ini |
| 10 |
! day number at the beginning of the run, based at value 1 on |
! day number at the beginning of the run, based at value 1 on |
| 29 |
real, protected:: taux, tauy |
real, protected:: taux, tauy |
| 30 |
! raideur de la transition de l'int\'erieur \`a l'ext\'erieur du zoom |
! raideur de la transition de l'int\'erieur \`a l'ext\'erieur du zoom |
| 31 |
|
|
| 32 |
real rlatu(jjm + 1) |
real, protected:: rlatu(jjm + 1) |
| 33 |
! latitudes of points of the "scalar" and "u" grid, in rad |
! latitudes of points of the "scalar" and "u" grid, in rad |
| 34 |
|
|
| 35 |
real rlatv(jjm) |
real, protected:: rlatv(jjm) |
| 36 |
! latitudes of points of the "v" grid, in rad, in decreasing order |
! latitudes of points of the "v" grid, in rad, in decreasing order |
| 37 |
|
|
| 38 |
real rlonu(iim + 1) ! longitudes of points of the "u" grid, in rad |
real, protected:: rlonu(iim + 1) |
| 39 |
|
! longitudes of points of the "u" grid, in rad |
| 40 |
|
|
| 41 |
real rlonv(iim + 1) |
real, protected:: rlonv(iim + 1) |
| 42 |
! longitudes of points of the "scalar" and "v" grid, in rad |
! longitudes of points of the "scalar" and "v" grid, in rad |
| 43 |
|
|
| 44 |
real xprimu(iim + 1), xprimv(iim + 1) |
real, protected:: xprimu(iim + 1), xprimv(iim + 1) |
| 45 |
! 2 pi / iim * (derivative of the longitudinal zoom function)(rlon[uv]) |
! 2 pi / iim * (derivative of the longitudinal zoom function)(rlon[uv]) |
| 46 |
|
|
| 47 |
REAL xprimm025(iim + 1), xprimp025(iim + 1) |
REAL, protected:: xprimm025(iim + 1), xprimp025(iim + 1) |
| 48 |
REAL rlatu1(jjm), rlatu2(jjm), yprimu1(jjm), yprimu2(jjm) |
REAL, protected:: rlatu1(jjm), rlatu2(jjm), yprimu1(jjm), yprimu2(jjm) |
| 49 |
REAL ang0, etot0, ptot0, ztot0, stot0 |
REAL ang0, etot0, ptot0, ztot0, stot0 |
| 50 |
|
INTEGER, PARAMETER, private:: nmax = 30000 |
| 51 |
|
DOUBLE PRECISION, private:: abs_y |
| 52 |
|
|
| 53 |
save |
save |
| 54 |
|
|
| 258 |
|
|
| 259 |
end subroutine read_serre |
end subroutine read_serre |
| 260 |
|
|
| 261 |
|
!******************************************************************** |
| 262 |
|
|
| 263 |
|
SUBROUTINE fyhyp |
| 264 |
|
|
| 265 |
|
! From LMDZ4/libf/dyn3d/fyhyp.F, version 1.2, 2005/06/03 09:11:32 |
| 266 |
|
|
| 267 |
|
! Author: P. Le Van, from analysis by R. Sadourny |
| 268 |
|
|
| 269 |
|
! Define rlatu, rlatv, rlatu2, yprimu2, rlatu1, yprimu1, using |
| 270 |
|
! clat, grossismy, dzoomy, tauy. |
| 271 |
|
|
| 272 |
|
! Calcule les latitudes et dérivées dans la grille du GCM pour une |
| 273 |
|
! fonction f(y) à dérivée tangente hyperbolique. |
| 274 |
|
|
| 275 |
|
! Il vaut mieux avoir : grossismy * dzoom < pi / 2 |
| 276 |
|
|
| 277 |
|
use coefpoly_m, only: coefpoly, a0, a1, a2, a3 |
| 278 |
|
USE dimensions, only: jjm |
| 279 |
|
use heavyside_m, only: heavyside |
| 280 |
|
|
| 281 |
|
! Local: |
| 282 |
|
|
| 283 |
|
INTEGER, PARAMETER:: nmax=30000, nmax2=2*nmax |
| 284 |
|
REAL dzoom ! distance totale de la zone du zoom (en radians) |
| 285 |
|
DOUBLE PRECISION ylat(jjm + 1), yprim(jjm + 1) |
| 286 |
|
DOUBLE PRECISION yuv |
| 287 |
|
DOUBLE PRECISION, save:: yt(0:nmax2) |
| 288 |
|
DOUBLE PRECISION fhyp(0:nmax2), beta |
| 289 |
|
DOUBLE PRECISION, save:: ytprim(0:nmax2) |
| 290 |
|
DOUBLE PRECISION fxm(0:nmax2) |
| 291 |
|
DOUBLE PRECISION, save:: yf(0:nmax2) |
| 292 |
|
DOUBLE PRECISION yypr(0:nmax2) |
| 293 |
|
DOUBLE PRECISION yvrai(jjm + 1), yprimm(jjm + 1), ylatt(jjm + 1) |
| 294 |
|
DOUBLE PRECISION pi, pis2, epsilon, pisjm |
| 295 |
|
DOUBLE PRECISION yo1, yi, ylon2, ymoy, yprimin |
| 296 |
|
DOUBLE PRECISION yfi, yf1, ffdy |
| 297 |
|
DOUBLE PRECISION ypn |
| 298 |
|
DOUBLE PRECISION, save::deply, y00 |
| 299 |
|
|
| 300 |
|
INTEGER i, j, it, ik, iter, jlat, jjpn |
| 301 |
|
INTEGER, save:: jpn |
| 302 |
|
DOUBLE PRECISION yi2, heavyy0, heavyy0m |
| 303 |
|
DOUBLE PRECISION fa(0:nmax2), fb(0:nmax2) |
| 304 |
|
REAL y0min, y0max |
| 305 |
|
|
| 306 |
|
!------------------------------------------------------------------- |
| 307 |
|
|
| 308 |
|
print *, "Call sequence information: fyhyp" |
| 309 |
|
|
| 310 |
|
pi = 2.*asin(1.) |
| 311 |
|
pis2 = pi/2. |
| 312 |
|
pisjm = pi/real(jjm) |
| 313 |
|
epsilon = 1e-3 |
| 314 |
|
dzoom = dzoomy*pi |
| 315 |
|
|
| 316 |
|
DO i = 0, nmax2 |
| 317 |
|
yt(i) = -pis2 + real(i)*pi/nmax2 |
| 318 |
|
END DO |
| 319 |
|
|
| 320 |
|
heavyy0m = heavyside(-clat) |
| 321 |
|
heavyy0 = heavyside(clat) |
| 322 |
|
y0min = 2.*clat*heavyy0m - pis2 |
| 323 |
|
y0max = 2.*clat*heavyy0 + pis2 |
| 324 |
|
|
| 325 |
|
fa = 999.999 |
| 326 |
|
fb = 999.999 |
| 327 |
|
|
| 328 |
|
DO i = 0, nmax2 |
| 329 |
|
IF (yt(i)<clat) THEN |
| 330 |
|
fa(i) = tauy*(yt(i)-clat + dzoom/2.) |
| 331 |
|
fb(i) = (yt(i)-2.*clat*heavyy0m + pis2)*(clat-yt(i)) |
| 332 |
|
ELSE IF (yt(i)>clat) THEN |
| 333 |
|
fa(i) = tauy*(clat-yt(i) + dzoom/2.) |
| 334 |
|
fb(i) = (2.*clat*heavyy0-yt(i) + pis2)*(yt(i)-clat) |
| 335 |
|
END IF |
| 336 |
|
|
| 337 |
|
IF (200.*fb(i)<-fa(i)) THEN |
| 338 |
|
fhyp(i) = -1. |
| 339 |
|
ELSE IF (200.*fb(i)<fa(i)) THEN |
| 340 |
|
fhyp(i) = 1. |
| 341 |
|
ELSE |
| 342 |
|
fhyp(i) = tanh(fa(i)/fb(i)) |
| 343 |
|
END IF |
| 344 |
|
|
| 345 |
|
IF (yt(i)==clat) fhyp(i) = 1. |
| 346 |
|
IF (yt(i)==y0min .OR. yt(i)==y0max) fhyp(i) = -1. |
| 347 |
|
END DO |
| 348 |
|
|
| 349 |
|
! Calcul de beta |
| 350 |
|
|
| 351 |
|
ffdy = 0. |
| 352 |
|
|
| 353 |
|
DO i = 1, nmax2 |
| 354 |
|
ymoy = 0.5*(yt(i-1) + yt(i)) |
| 355 |
|
IF (ymoy<clat) THEN |
| 356 |
|
fa(i) = tauy*(ymoy-clat + dzoom/2.) |
| 357 |
|
fb(i) = (ymoy-2.*clat*heavyy0m + pis2)*(clat-ymoy) |
| 358 |
|
ELSE IF (ymoy>clat) THEN |
| 359 |
|
fa(i) = tauy*(clat-ymoy + dzoom/2.) |
| 360 |
|
fb(i) = (2.*clat*heavyy0-ymoy + pis2)*(ymoy-clat) |
| 361 |
|
END IF |
| 362 |
|
|
| 363 |
|
IF (200.*fb(i)<-fa(i)) THEN |
| 364 |
|
fxm(i) = -1. |
| 365 |
|
ELSE IF (200.*fb(i)<fa(i)) THEN |
| 366 |
|
fxm(i) = 1. |
| 367 |
|
ELSE |
| 368 |
|
fxm(i) = tanh(fa(i)/fb(i)) |
| 369 |
|
END IF |
| 370 |
|
IF (ymoy==clat) fxm(i) = 1. |
| 371 |
|
IF (ymoy==y0min .OR. yt(i)==y0max) fxm(i) = -1. |
| 372 |
|
ffdy = ffdy + fxm(i)*(yt(i)-yt(i-1)) |
| 373 |
|
END DO |
| 374 |
|
|
| 375 |
|
beta = (grossismy*ffdy-pi)/(ffdy-pi) |
| 376 |
|
|
| 377 |
|
IF (2. * beta - grossismy <= 0.) THEN |
| 378 |
|
print *, 'Attention ! La valeur beta calculee dans la routine fyhyp ' & |
| 379 |
|
// 'est mauvaise. Modifier les valeurs de grossismy, tauy ou ' & |
| 380 |
|
// 'dzoomy et relancer.' |
| 381 |
|
STOP 1 |
| 382 |
|
END IF |
| 383 |
|
|
| 384 |
|
! calcul de Ytprim |
| 385 |
|
|
| 386 |
|
DO i = 0, nmax2 |
| 387 |
|
ytprim(i) = beta + (grossismy-beta)*fhyp(i) |
| 388 |
|
END DO |
| 389 |
|
|
| 390 |
|
! Calcul de Yf |
| 391 |
|
|
| 392 |
|
yf(0) = -pis2 |
| 393 |
|
DO i = 1, nmax2 |
| 394 |
|
yypr(i) = beta + (grossismy-beta)*fxm(i) |
| 395 |
|
END DO |
| 396 |
|
|
| 397 |
|
DO i = 1, nmax2 |
| 398 |
|
yf(i) = yf(i-1) + yypr(i)*(yt(i)-yt(i-1)) |
| 399 |
|
END DO |
| 400 |
|
|
| 401 |
|
! yuv = 0. si calcul des latitudes aux pts. U |
| 402 |
|
! yuv = 0.5 si calcul des latitudes aux pts. V |
| 403 |
|
|
| 404 |
|
loop_ik: DO ik = 1, 4 |
| 405 |
|
IF (ik==1) THEN |
| 406 |
|
yuv = 0. |
| 407 |
|
jlat = jjm + 1 |
| 408 |
|
ELSE IF (ik==2) THEN |
| 409 |
|
yuv = 0.5 |
| 410 |
|
jlat = jjm |
| 411 |
|
ELSE IF (ik==3) THEN |
| 412 |
|
yuv = 0.25 |
| 413 |
|
jlat = jjm |
| 414 |
|
ELSE IF (ik==4) THEN |
| 415 |
|
yuv = 0.75 |
| 416 |
|
jlat = jjm |
| 417 |
|
END IF |
| 418 |
|
|
| 419 |
|
yo1 = 0. |
| 420 |
|
DO j = 1, jlat |
| 421 |
|
yo1 = 0. |
| 422 |
|
ylon2 = -pis2 + pisjm*(real(j) + yuv-1.) |
| 423 |
|
yfi = ylon2 |
| 424 |
|
|
| 425 |
|
it = nmax2 |
| 426 |
|
DO while (it >= 1 .and. yfi < yf(it)) |
| 427 |
|
it = it - 1 |
| 428 |
|
END DO |
| 429 |
|
|
| 430 |
|
yi = yt(it) |
| 431 |
|
IF (it==nmax2) THEN |
| 432 |
|
it = nmax2 - 1 |
| 433 |
|
yf(it + 1) = pis2 |
| 434 |
|
END IF |
| 435 |
|
|
| 436 |
|
! Interpolation entre yi(it) et yi(it + 1) pour avoir Y(yi) |
| 437 |
|
! et Y'(yi) |
| 438 |
|
|
| 439 |
|
CALL coefpoly(yf(it), yf(it + 1), ytprim(it), ytprim(it + 1), & |
| 440 |
|
yt(it), yt(it + 1)) |
| 441 |
|
|
| 442 |
|
yf1 = yf(it) |
| 443 |
|
yprimin = a1 + 2.*a2*yi + 3.*a3*yi*yi |
| 444 |
|
|
| 445 |
|
iter = 1 |
| 446 |
|
DO |
| 447 |
|
yi = yi - (yf1-yfi)/yprimin |
| 448 |
|
IF (abs(yi-yo1)<=epsilon .or. iter == 300) exit |
| 449 |
|
yo1 = yi |
| 450 |
|
yi2 = yi*yi |
| 451 |
|
yf1 = a0 + a1*yi + a2*yi2 + a3*yi2*yi |
| 452 |
|
yprimin = a1 + 2.*a2*yi + 3.*a3*yi2 |
| 453 |
|
END DO |
| 454 |
|
if (abs(yi-yo1) > epsilon) then |
| 455 |
|
print *, 'Pas de solution.', j, ylon2 |
| 456 |
|
STOP 1 |
| 457 |
|
end if |
| 458 |
|
|
| 459 |
|
yprimin = a1 + 2.*a2*yi + 3.*a3*yi*yi |
| 460 |
|
yprim(j) = pi/(jjm*yprimin) |
| 461 |
|
yvrai(j) = yi |
| 462 |
|
END DO |
| 463 |
|
|
| 464 |
|
DO j = 1, jlat - 1 |
| 465 |
|
IF (yvrai(j + 1)<yvrai(j)) THEN |
| 466 |
|
print *, 'Problème avec rlat(', j + 1, ') plus petit que rlat(', & |
| 467 |
|
j, ')' |
| 468 |
|
STOP 1 |
| 469 |
|
END IF |
| 470 |
|
END DO |
| 471 |
|
|
| 472 |
|
print *, 'Reorganisation des latitudes pour avoir entre - pi/2 et pi/2' |
| 473 |
|
|
| 474 |
|
IF (ik==1) THEN |
| 475 |
|
ypn = pis2 |
| 476 |
|
DO j = jjm + 1, 1, -1 |
| 477 |
|
IF (yvrai(j)<=ypn) exit |
| 478 |
|
END DO |
| 479 |
|
|
| 480 |
|
jpn = j |
| 481 |
|
y00 = yvrai(jpn) |
| 482 |
|
deply = pis2 - y00 |
| 483 |
|
END IF |
| 484 |
|
|
| 485 |
|
DO j = 1, jjm + 1 - jpn |
| 486 |
|
ylatt(j) = -pis2 - y00 + yvrai(jpn + j-1) |
| 487 |
|
yprimm(j) = yprim(jpn + j-1) |
| 488 |
|
END DO |
| 489 |
|
|
| 490 |
|
jjpn = jpn |
| 491 |
|
IF (jlat==jjm) jjpn = jpn - 1 |
| 492 |
|
|
| 493 |
|
DO j = 1, jjpn |
| 494 |
|
ylatt(j + jjm + 1-jpn) = yvrai(j) + deply |
| 495 |
|
yprimm(j + jjm + 1-jpn) = yprim(j) |
| 496 |
|
END DO |
| 497 |
|
|
| 498 |
|
! Fin de la reorganisation |
| 499 |
|
|
| 500 |
|
DO j = 1, jlat |
| 501 |
|
ylat(j) = ylatt(jlat + 1-j) |
| 502 |
|
yprim(j) = yprimm(jlat + 1-j) |
| 503 |
|
END DO |
| 504 |
|
|
| 505 |
|
DO j = 1, jlat |
| 506 |
|
yvrai(j) = ylat(j)*180./pi |
| 507 |
|
END DO |
| 508 |
|
|
| 509 |
|
IF (ik==1) THEN |
| 510 |
|
DO j = 1, jjm + 1 |
| 511 |
|
rlatu(j) = ylat(j) |
| 512 |
|
END DO |
| 513 |
|
ELSE IF (ik==2) THEN |
| 514 |
|
DO j = 1, jjm |
| 515 |
|
rlatv(j) = ylat(j) |
| 516 |
|
END DO |
| 517 |
|
ELSE IF (ik==3) THEN |
| 518 |
|
DO j = 1, jjm |
| 519 |
|
rlatu2(j) = ylat(j) |
| 520 |
|
yprimu2(j) = yprim(j) |
| 521 |
|
END DO |
| 522 |
|
ELSE IF (ik==4) THEN |
| 523 |
|
DO j = 1, jjm |
| 524 |
|
rlatu1(j) = ylat(j) |
| 525 |
|
yprimu1(j) = yprim(j) |
| 526 |
|
END DO |
| 527 |
|
END IF |
| 528 |
|
END DO loop_ik |
| 529 |
|
|
| 530 |
|
DO j = 1, jjm |
| 531 |
|
ylat(j) = rlatu(j) - rlatu(j + 1) |
| 532 |
|
END DO |
| 533 |
|
|
| 534 |
|
DO j = 1, jjm |
| 535 |
|
IF (rlatu1(j) <= rlatu2(j)) THEN |
| 536 |
|
print *, 'Attention ! rlatu1 < rlatu2 ', rlatu1(j), rlatu2(j), j |
| 537 |
|
STOP 13 |
| 538 |
|
ENDIF |
| 539 |
|
|
| 540 |
|
IF (rlatu2(j) <= rlatu(j+1)) THEN |
| 541 |
|
print *, 'Attention ! rlatu2 < rlatup1 ', rlatu2(j), rlatu(j+1), j |
| 542 |
|
STOP 14 |
| 543 |
|
ENDIF |
| 544 |
|
|
| 545 |
|
IF (rlatu(j) <= rlatu1(j)) THEN |
| 546 |
|
print *, ' Attention ! rlatu < rlatu1 ', rlatu(j), rlatu1(j), j |
| 547 |
|
STOP 15 |
| 548 |
|
ENDIF |
| 549 |
|
|
| 550 |
|
IF (rlatv(j) <= rlatu2(j)) THEN |
| 551 |
|
print *, ' Attention ! rlatv < rlatu2 ', rlatv(j), rlatu2(j), j |
| 552 |
|
STOP 16 |
| 553 |
|
ENDIF |
| 554 |
|
|
| 555 |
|
IF (rlatv(j) >= rlatu1(j)) THEN |
| 556 |
|
print *, ' Attention ! rlatv > rlatu1 ', rlatv(j), rlatu1(j), j |
| 557 |
|
STOP 17 |
| 558 |
|
ENDIF |
| 559 |
|
|
| 560 |
|
IF (rlatv(j) >= rlatu(j)) THEN |
| 561 |
|
print *, ' Attention ! rlatv > rlatu ', rlatv(j), rlatu(j), j |
| 562 |
|
STOP 18 |
| 563 |
|
ENDIF |
| 564 |
|
ENDDO |
| 565 |
|
|
| 566 |
|
print *, 'Latitudes' |
| 567 |
|
print 3, minval(ylat(:jjm)) *180d0/pi, maxval(ylat(:jjm))*180d0/pi |
| 568 |
|
|
| 569 |
|
3 Format(1x, ' Au centre du zoom, la longueur de la maille est', & |
| 570 |
|
' d environ ', f0.2, ' degres ', /, & |
| 571 |
|
' alors que la maille en dehors de la zone du zoom est ', & |
| 572 |
|
"d'environ ", f0.2, ' degres ') |
| 573 |
|
|
| 574 |
|
rlatu(1) = pi / 2. |
| 575 |
|
rlatu(jjm + 1) = -rlatu(1) |
| 576 |
|
|
| 577 |
|
END SUBROUTINE fyhyp |
| 578 |
|
|
| 579 |
|
!******************************************************************** |
| 580 |
|
|
| 581 |
|
SUBROUTINE fxhyp |
| 582 |
|
|
| 583 |
|
! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32 |
| 584 |
|
! Author: P. Le Van, from formulas by R. Sadourny |
| 585 |
|
|
| 586 |
|
! Compute xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025, |
| 587 |
|
! using clon, grossismx, dzoomx, taux. |
| 588 |
|
|
| 589 |
|
! Calcule les longitudes et dérivées dans la grille du GCM pour |
| 590 |
|
! une fonction $x_f(\tilde x)$ à dérivée tangente hyperbolique. |
| 591 |
|
|
| 592 |
|
! Il vaut mieux avoir : grossismx $\times$ delta < pi |
| 593 |
|
|
| 594 |
|
! Le premier point scalaire pour une grille regulière (grossismx = |
| 595 |
|
! 1) avec clon = 0 est à - 180 degrés. |
| 596 |
|
|
| 597 |
|
use nr_util, only: pi, pi_d, twopi, twopi_d, arth, assert, rad_to_deg |
| 598 |
|
|
| 599 |
|
USE dimensions, ONLY: iim |
| 600 |
|
use tanh_cautious_m, only: tanh_cautious |
| 601 |
|
|
| 602 |
|
! Local: |
| 603 |
|
real rlonm025(iim + 1), rlonp025(iim + 1), d_rlonv(iim) |
| 604 |
|
REAL delta, h |
| 605 |
|
DOUBLE PRECISION, dimension(0:nmax):: xtild, fhyp, G, Xf, ffdx |
| 606 |
|
DOUBLE PRECISION beta |
| 607 |
|
INTEGER i, is2 |
| 608 |
|
DOUBLE PRECISION xmoy(nmax), fxm(nmax) |
| 609 |
|
|
| 610 |
|
!---------------------------------------------------------------------- |
| 611 |
|
|
| 612 |
|
print *, "Call sequence information: fxhyp" |
| 613 |
|
|
| 614 |
|
if (grossismx == 1.) then |
| 615 |
|
h = twopi / iim |
| 616 |
|
|
| 617 |
|
xprimm025(:iim) = h |
| 618 |
|
xprimp025(:iim) = h |
| 619 |
|
xprimv(:iim) = h |
| 620 |
|
xprimu(:iim) = h |
| 621 |
|
|
| 622 |
|
rlonv(:iim) = arth(- pi + clon, h, iim) |
| 623 |
|
rlonm025(:iim) = rlonv(:iim) - 0.25 * h |
| 624 |
|
rlonp025(:iim) = rlonv(:iim) + 0.25 * h |
| 625 |
|
rlonu(:iim) = rlonv(:iim) + 0.5 * h |
| 626 |
|
else |
| 627 |
|
delta = dzoomx * twopi_d |
| 628 |
|
xtild = arth(0d0, pi_d / nmax, nmax + 1) |
| 629 |
|
forall (i = 1:nmax) xmoy(i) = 0.5d0 * (xtild(i-1) + xtild(i)) |
| 630 |
|
|
| 631 |
|
! Compute fhyp: |
| 632 |
|
fhyp(1:nmax - 1) = tanh_cautious(taux * (delta / 2d0 & |
| 633 |
|
- xtild(1:nmax - 1)), xtild(1:nmax - 1) & |
| 634 |
|
* (pi_d - xtild(1:nmax - 1))) |
| 635 |
|
fhyp(0) = 1d0 |
| 636 |
|
fhyp(nmax) = -1d0 |
| 637 |
|
|
| 638 |
|
fxm = tanh_cautious(taux * (delta / 2d0 - xmoy), xmoy * (pi_d - xmoy)) |
| 639 |
|
|
| 640 |
|
! Compute \int_0 ^{\tilde x} F: |
| 641 |
|
|
| 642 |
|
ffdx(0) = 0d0 |
| 643 |
|
|
| 644 |
|
DO i = 1, nmax |
| 645 |
|
ffdx(i) = ffdx(i - 1) + fxm(i) * (xtild(i) - xtild(i-1)) |
| 646 |
|
END DO |
| 647 |
|
|
| 648 |
|
print *, "ffdx(nmax) = ", ffdx(nmax) |
| 649 |
|
beta = (pi_d - grossismx * ffdx(nmax)) / (pi_d - ffdx(nmax)) |
| 650 |
|
print *, "beta = ", beta |
| 651 |
|
|
| 652 |
|
IF (2d0 * beta - grossismx <= 0d0) THEN |
| 653 |
|
print *, 'Bad choice of grossismx, taux, dzoomx.' |
| 654 |
|
print *, 'Decrease dzoomx or grossismx.' |
| 655 |
|
STOP 1 |
| 656 |
|
END IF |
| 657 |
|
|
| 658 |
|
G = beta + (grossismx - beta) * fhyp |
| 659 |
|
|
| 660 |
|
Xf(:nmax - 1) = beta * xtild(:nmax - 1) + (grossismx - beta) & |
| 661 |
|
* ffdx(:nmax - 1) |
| 662 |
|
Xf(nmax) = pi_d |
| 663 |
|
|
| 664 |
|
call invert_zoom_x(beta, xf, xtild, G, rlonm025(:iim), xprimm025(:iim), & |
| 665 |
|
xuv = - 0.25d0) |
| 666 |
|
call invert_zoom_x(beta, xf, xtild, G, rlonv(:iim), xprimv(:iim), & |
| 667 |
|
xuv = 0d0) |
| 668 |
|
call invert_zoom_x(beta, xf, xtild, G, rlonu(:iim), xprimu(:iim), & |
| 669 |
|
xuv = 0.5d0) |
| 670 |
|
call invert_zoom_x(beta, xf, xtild, G, rlonp025(:iim), xprimp025(:iim), & |
| 671 |
|
xuv = 0.25d0) |
| 672 |
|
end if |
| 673 |
|
|
| 674 |
|
is2 = 0 |
| 675 |
|
|
| 676 |
|
IF (MINval(rlonm025(:iim)) < - pi - 0.1 & |
| 677 |
|
.or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN |
| 678 |
|
IF (clon <= 0.) THEN |
| 679 |
|
is2 = 1 |
| 680 |
|
|
| 681 |
|
do while (rlonm025(is2) < - pi .and. is2 < iim) |
| 682 |
|
is2 = is2 + 1 |
| 683 |
|
end do |
| 684 |
|
|
| 685 |
|
call assert(rlonm025(is2) >= - pi, & |
| 686 |
|
"fxhyp -- rlonm025 should be >= - pi") |
| 687 |
|
ELSE |
| 688 |
|
is2 = iim |
| 689 |
|
|
| 690 |
|
do while (rlonm025(is2) > pi .and. is2 > 1) |
| 691 |
|
is2 = is2 - 1 |
| 692 |
|
end do |
| 693 |
|
|
| 694 |
|
if (rlonm025(is2) > pi) then |
| 695 |
|
print *, 'Rlonm025 plus grand que pi !' |
| 696 |
|
STOP 1 |
| 697 |
|
end if |
| 698 |
|
END IF |
| 699 |
|
END IF |
| 700 |
|
|
| 701 |
|
call principal_cshift(is2, rlonm025, xprimm025) |
| 702 |
|
call principal_cshift(is2, rlonv, xprimv) |
| 703 |
|
call principal_cshift(is2, rlonu, xprimu) |
| 704 |
|
call principal_cshift(is2, rlonp025, xprimp025) |
| 705 |
|
|
| 706 |
|
forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i) |
| 707 |
|
print *, "Minimum longitude step:", MINval(d_rlonv) * rad_to_deg, "degrees" |
| 708 |
|
print *, "Maximum longitude step:", MAXval(d_rlonv) * rad_to_deg, "degrees" |
| 709 |
|
|
| 710 |
|
! Check that rlonm025 <= rlonv <= rlonp025 <= rlonu: |
| 711 |
|
DO i = 1, iim + 1 |
| 712 |
|
IF (rlonp025(i) < rlonv(i)) THEN |
| 713 |
|
print *, 'rlonp025(', i, ') = ', rlonp025(i) |
| 714 |
|
print *, "< rlonv(", i, ") = ", rlonv(i) |
| 715 |
|
STOP 1 |
| 716 |
|
END IF |
| 717 |
|
|
| 718 |
|
IF (rlonv(i) < rlonm025(i)) THEN |
| 719 |
|
print *, 'rlonv(', i, ') = ', rlonv(i) |
| 720 |
|
print *, "< rlonm025(", i, ") = ", rlonm025(i) |
| 721 |
|
STOP 1 |
| 722 |
|
END IF |
| 723 |
|
|
| 724 |
|
IF (rlonp025(i) > rlonu(i)) THEN |
| 725 |
|
print *, 'rlonp025(', i, ') = ', rlonp025(i) |
| 726 |
|
print *, "> rlonu(", i, ") = ", rlonu(i) |
| 727 |
|
STOP 1 |
| 728 |
|
END IF |
| 729 |
|
END DO |
| 730 |
|
|
| 731 |
|
END SUBROUTINE fxhyp |
| 732 |
|
|
| 733 |
|
!******************************************************************** |
| 734 |
|
|
| 735 |
|
subroutine principal_cshift(is2, xlon, xprimm) |
| 736 |
|
|
| 737 |
|
! Add or subtract 2 pi so that xlon is near [-pi, pi], then cshift |
| 738 |
|
! so that xlon is in ascending order. Make the same cshift on |
| 739 |
|
! xprimm. Use clon. In this module to avoid circular dependency. |
| 740 |
|
|
| 741 |
|
use nr_util, only: twopi |
| 742 |
|
|
| 743 |
|
USE dimensions, ONLY: iim |
| 744 |
|
|
| 745 |
|
integer, intent(in):: is2 |
| 746 |
|
real, intent(inout):: xlon(:), xprimm(:) ! (iim + 1) |
| 747 |
|
|
| 748 |
|
!----------------------------------------------------- |
| 749 |
|
|
| 750 |
|
if (is2 /= 0) then |
| 751 |
|
IF (clon <= 0.) THEN |
| 752 |
|
IF (is2 /= 1) THEN |
| 753 |
|
xlon(:is2 - 1) = xlon(:is2 - 1) + twopi |
| 754 |
|
xlon(:iim) = cshift(xlon(:iim), shift = is2 - 1) |
| 755 |
|
xprimm(:iim) = cshift(xprimm(:iim), shift = is2 - 1) |
| 756 |
|
END IF |
| 757 |
|
else |
| 758 |
|
xlon(is2 + 1:iim) = xlon(is2 + 1:iim) - twopi |
| 759 |
|
xlon(:iim) = cshift(xlon(:iim), shift = is2) |
| 760 |
|
xprimm(:iim) = cshift(xprimm(:iim), shift = is2) |
| 761 |
|
end IF |
| 762 |
|
end if |
| 763 |
|
|
| 764 |
|
xlon(iim + 1) = xlon(1) + twopi |
| 765 |
|
xprimm(iim + 1) = xprimm(1) |
| 766 |
|
|
| 767 |
|
end subroutine principal_cshift |
| 768 |
|
|
| 769 |
|
!********************************************************************** |
| 770 |
|
|
| 771 |
|
subroutine invert_zoom_x(beta, xf, xtild, G, xlon, xprim, xuv) |
| 772 |
|
|
| 773 |
|
! Using clon and grossismx. In this module to avoid circular dependency. |
| 774 |
|
|
| 775 |
|
use coefpoly_m, only: coefpoly, a1, a2, a3 |
| 776 |
|
USE dimensions, ONLY: iim |
| 777 |
|
use nr_util, only: pi_d, twopi_d |
| 778 |
|
use numer_rec_95, only: hunt, rtsafe |
| 779 |
|
|
| 780 |
|
DOUBLE PRECISION, intent(in):: beta, Xf(0:), xtild(0:), G(0:) ! (0:nmax) |
| 781 |
|
|
| 782 |
|
real, intent(out):: xlon(:), xprim(:) ! (iim) |
| 783 |
|
|
| 784 |
|
DOUBLE PRECISION, intent(in):: xuv |
| 785 |
|
! between - 0.25 and 0.5 |
| 786 |
|
! 0. si calcul aux points scalaires |
| 787 |
|
! 0.5 si calcul aux points U |
| 788 |
|
|
| 789 |
|
! Local: |
| 790 |
|
DOUBLE PRECISION Y |
| 791 |
|
DOUBLE PRECISION h ! step of the uniform grid |
| 792 |
|
integer i, it |
| 793 |
|
|
| 794 |
|
DOUBLE PRECISION xvrai(iim), Gvrai(iim) |
| 795 |
|
! intermediary variables because xlon and xprim are single precision |
| 796 |
|
|
| 797 |
|
!------------------------------------------------------------------ |
| 798 |
|
|
| 799 |
|
print *, "Call sequence information: invert_zoom_x" |
| 800 |
|
it = 0 ! initial guess |
| 801 |
|
h = twopi_d / iim |
| 802 |
|
|
| 803 |
|
DO i = 1, iim |
| 804 |
|
Y = - pi_d + (i + xuv - 0.75d0) * h |
| 805 |
|
! - pi <= y < pi |
| 806 |
|
abs_y = abs(y) |
| 807 |
|
|
| 808 |
|
! Distinguish boundaries in order to avoid roundoff error. |
| 809 |
|
! funcd should be exactly equal to 0 at xtild(it) or xtild(it + |
| 810 |
|
! 1) and could be very small with the wrong sign so rtsafe |
| 811 |
|
! would fail. |
| 812 |
|
if (abs_y == 0d0) then |
| 813 |
|
xvrai(i) = 0d0 |
| 814 |
|
gvrai(i) = grossismx |
| 815 |
|
else if (abs_y == pi_d) then |
| 816 |
|
xvrai(i) = pi_d |
| 817 |
|
gvrai(i) = 2d0 * beta - grossismx |
| 818 |
|
else |
| 819 |
|
call hunt(xf, abs_y, it, my_lbound = 0) |
| 820 |
|
! {0 <= it <= nmax - 1} |
| 821 |
|
|
| 822 |
|
! Calcul de xvrai(i) et Gvrai(i) |
| 823 |
|
CALL coefpoly(Xf(it), Xf(it + 1), G(it), G(it + 1), xtild(it), & |
| 824 |
|
xtild(it + 1)) |
| 825 |
|
xvrai(i) = rtsafe(funcd, xtild(it), xtild(it + 1), xacc = 1d-6) |
| 826 |
|
Gvrai(i) = a1 + xvrai(i) * (2d0 * a2 + xvrai(i) * 3d0 * a3) |
| 827 |
|
end if |
| 828 |
|
|
| 829 |
|
if (y < 0d0) xvrai(i) = - xvrai(i) |
| 830 |
|
end DO |
| 831 |
|
|
| 832 |
|
DO i = 1, iim -1 |
| 833 |
|
IF (xvrai(i + 1) < xvrai(i)) THEN |
| 834 |
|
print *, 'xvrai(', i + 1, ') < xvrai(', i, ')' |
| 835 |
|
STOP 1 |
| 836 |
|
END IF |
| 837 |
|
END DO |
| 838 |
|
|
| 839 |
|
xlon = xvrai + clon |
| 840 |
|
xprim = h / Gvrai |
| 841 |
|
|
| 842 |
|
end subroutine invert_zoom_x |
| 843 |
|
|
| 844 |
|
!********************************************************************** |
| 845 |
|
|
| 846 |
|
SUBROUTINE funcd(x, fval, fderiv) |
| 847 |
|
|
| 848 |
|
use coefpoly_m, only: a0, a1, a2, a3 |
| 849 |
|
|
| 850 |
|
DOUBLE PRECISION, INTENT(IN):: x |
| 851 |
|
DOUBLE PRECISION, INTENT(OUT):: fval, fderiv |
| 852 |
|
|
| 853 |
|
fval = a0 + x * (a1 + x * (a2 + x * a3)) - abs_y |
| 854 |
|
fderiv = a1 + x * (2d0 * a2 + x * 3d0 * a3) |
| 855 |
|
|
| 856 |
|
END SUBROUTINE funcd |
| 857 |
|
|
| 858 |
end module dynetat0_m |
end module dynetat0_m |
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