--- trunk/Sources/filtrez/inifgn.f	2015/06/23 18:26:18	153
+++ trunk/Sources/filtrez/inifgn.f	2015/07/07 17:49:23	154
@@ -6,30 +6,41 @@
 
   private iim
 
-  real sddu(iim), sddv(iim) ! SQRT(dx / di)
-  real unsddu(iim), unsddv(iim)
+  real sddu(iim), sddv(iim) 
+  ! sdd[uv] = sqrt(2 pi / iim * (derivative of the longitudinal zoom
+  ! function)(rlon[uv]))
 
-  real eignfnu(iim, iim), eignfnv(iim, iim)
-  ! eigenfunctions of the discrete laplacian
+  real unsddu(iim), unsddv(iim)
 
 contains
 
-  SUBROUTINE inifgn(dv)
+  SUBROUTINE inifgn(eignval_v, eignfnu, eignfnv)
 
     ! From LMDZ4/libf/filtrez/inifgn.F, v 1.1.1.1 2004/05/19 12:53:09
 
-    ! H. Upadyaya, O. Sharma 
+    ! Authors: H. Upadyaya, O. Sharma
+
+    ! Computes the eigenvalues and eigenvectors of the discrete analog
+    ! of the second derivative with respect to longitude.
 
     use acc_m, only: acc 
     USE dimens_m, ONLY: iim
     USE dynetat0_m, ONLY: xprimu, xprimv
     use numer_rec_95, only: jacobi, eigsrt
 
-    real, intent(out):: dv(:) ! (iim) eigenvalues sorted in descending order
+    real, intent(out):: eignval_v(:) ! (iim)
+    ! eigenvalues sorted in descending order
+
+    real, intent(out):: eignfnu(:, :), eignfnv(:, :) ! (iim, iim) eigenvectors
 
     ! Local:
-    REAL, dimension(iim, iim):: a, b, c
-    REAL du(iim)
+
+    REAL a(iim, iim) ! second derivative, symmetric, elements are angle^{-2}
+
+    REAL deriv_u(iim, iim), deriv_v(iim, iim) 
+    ! first derivative at u and v longitudes, elements are angle^{-1}
+
+    REAL eignval_u(iim)
     INTEGER i
 
     !----------------------------------------------------------------
@@ -41,22 +52,22 @@
     unsddu = 1. / sddu
     unsddv = 1. / sddv
 
-    b = 0.
-    b(iim, 1) = unsddu(iim) * unsddv(1)
-    forall (i = 1:iim) b(i, i) = - unsddu(i) * unsddv(i)
-    forall (i = 1:iim - 1) b(i, i + 1) = unsddu(i) * unsddv(i + 1)
+    deriv_u = 0.
+    deriv_u(iim, 1) = unsddu(iim) * unsddv(1)
+    forall (i = 1:iim) deriv_u(i, i) = - unsddu(i) * unsddv(i)
+    forall (i = 1:iim - 1) deriv_u(i, i + 1) = unsddu(i) * unsddv(i + 1)
 
-    c = - transpose(b)
+    deriv_v = - transpose(deriv_u)
 
-    a = matmul(c, b)
-    CALL jacobi(a, dv, eignfnv)
+    a = matmul(deriv_v, deriv_u) ! second derivative at v longitudes
+    CALL jacobi(a, eignval_v, eignfnv)
     CALL acc(eignfnv)
-    CALL eigsrt(dv, eignfnv)
+    CALL eigsrt(eignval_v, eignfnv)
 
-    a = matmul(b, c)
-    CALL jacobi(a, du, eignfnu)
+    a = matmul(deriv_u, deriv_v) ! second derivative at u longitudes
+    CALL jacobi(a, eignval_u, eignfnu)
     CALL acc(eignfnu)
-    CALL eigsrt(du, eignfnu)
+    CALL eigsrt(eignval_u, eignfnu)
 
   END SUBROUTINE inifgn