--- trunk/Sources/dyn3d/invert_zoom_x.f	2015/06/17 16:40:24	148
+++ trunk/dyn3d/invert_zoom_x.f	2018/03/20 09:35:59	265
@@ -3,18 +3,21 @@
   implicit none
 
   INTEGER, PARAMETER:: nmax = 30000
+  DOUBLE PRECISION abs_y
+
+  private abs_y, funcd
 
 contains
 
-  subroutine invert_zoom_x(xf, xtild, G, xlon, xprim, xuv)
+  subroutine invert_zoom_x(beta, xf, xtild, G, xlon, xprim, xuv)
 
-    use coefpoly_m, only: coefpoly
-    USE dimens_m, ONLY: iim
-    use dynetat0_m, only: clon
+    use coefpoly_m, only: coefpoly, a1, a2, a3
+    USE dimensions, ONLY: iim
+    use dynetat0_m, only: clon, grossismx
     use nr_util, only: pi_d, twopi_d
-    use numer_rec_95, only: hunt
+    use numer_rec_95, only: hunt, rtsafe
 
-    DOUBLE PRECISION, intent(in):: Xf(0:), xtild(0:), G(0:) ! (0:nmax)
+    DOUBLE PRECISION, intent(in):: beta, Xf(0:), xtild(0:), G(0:) ! (0:nmax)
 
     real, intent(out):: xlon(:), xprim(:) ! (iim)
 
@@ -24,49 +27,43 @@
     ! 0.5 si calcul aux points U
 
     ! Local:
-    DOUBLE PRECISION Y, abs_y, a0, a1, a2, a3
-    integer i, it, iter
-    real, parameter:: my_eps = 1e-6
-
-    real xo1, Xf1
-    real xvrai(iim), Gvrai(iim) 
-    ! intermediary variables because xlon and xprim are simple precision
+    DOUBLE PRECISION Y
+    DOUBLE PRECISION h ! step of the uniform grid
+    integer i, it
+
+    DOUBLE PRECISION xvrai(iim), Gvrai(iim) 
+    ! intermediary variables because xlon and xprim are single precision
 
     !------------------------------------------------------------------
 
+    print *, "Call sequence information: invert_zoom_x"
     it = 0 ! initial guess
+    h = twopi_d / iim
 
     DO i = 1, iim
-       Y = - pi_d + (i + xuv - 0.75d0) * twopi_d / iim
+       Y = - pi_d + (i + xuv - 0.75d0) * h
        ! - pi <= y < pi
        abs_y = abs(y)
 
-       call hunt(xf, abs_y, it, my_lbound = 0)
-       ! {0 <= it <= nmax - 1}
-
-       ! Calcul de xvrai(i) et Gvrai(i)
-
-       CALL coefpoly(Xf(it), Xf(it + 1), G(it), G(it + 1), xtild(it), &
-            xtild(it + 1), a0, a1, a2, a3)
-       xvrai(i) = xtild(it)
-       Xf1 = Xf(it)
-       Gvrai(i) = G(it)
-       xo1 = xvrai(i)
-       iter = 1
-
-       do
-          xvrai(i) = xvrai(i) - (Xf1 - abs_y) / Gvrai(i)
-          IF (ABS(xvrai(i) - xo1) <= my_eps .or. iter == 300) exit
-          xo1 = xvrai(i)
-          Xf1 = a0 + xvrai(i) * (a1 + xvrai(i) * (a2 + xvrai(i) * a3))
+       ! Distinguish boundaries in order to avoid roundoff error.
+       ! funcd should be exactly equal to 0 at xtild(it) or xtild(it +
+       ! 1) and could be very small with the wrong sign so rtsafe
+       ! would fail.
+       if (abs_y == 0d0) then
+          xvrai(i) = 0d0
+          gvrai(i) = grossismx
+       else if (abs_y == pi_d) then
+          xvrai(i) = pi_d
+          gvrai(i) = 2d0 * beta - grossismx
+       else
+          call hunt(xf, abs_y, it, my_lbound = 0)
+          ! {0 <= it <= nmax - 1}
+
+          ! Calcul de xvrai(i) et Gvrai(i)
+          CALL coefpoly(Xf(it), Xf(it + 1), G(it), G(it + 1), xtild(it), &
+               xtild(it + 1))
+          xvrai(i) = rtsafe(funcd, xtild(it), xtild(it + 1), xacc = 1d-6)
           Gvrai(i) = a1 + xvrai(i) * (2d0 * a2 + xvrai(i) * 3d0 * a3)
-       end DO
-
-       if (ABS(xvrai(i) - xo1) > my_eps) then
-          ! iter == 300
-          print *, 'Pas de solution.'
-          print *, i, abs_y
-          STOP 1
        end if
 
        if (y < 0d0) xvrai(i) = - xvrai(i)
@@ -80,8 +77,22 @@
     END DO
 
     xlon = xvrai + clon
-    xprim = twopi_d / (iim * Gvrai)
+    xprim = h / Gvrai
 
   end subroutine invert_zoom_x
 
+  !**********************************************************************
+
+  SUBROUTINE funcd(x, fval, fderiv)
+
+    use coefpoly_m, only: a0, a1, a2, a3
+
+    DOUBLE PRECISION, INTENT(IN):: x
+    DOUBLE PRECISION, INTENT(OUT):: fval, fderiv
+
+    fval = a0 + x * (a1 + x * (a2 + x * a3)) - abs_y
+    fderiv = a1 + x * (2d0 * a2 + x * 3d0 * a3)
+
+  END SUBROUTINE funcd
+
 end module invert_zoom_x_m