--- trunk/Sources/filtrez/inifgn.f	2015/06/23 15:14:20	151
+++ trunk/Sources/filtrez/inifgn.f	2015/08/24 16:30:33	167
@@ -6,32 +6,43 @@
 
   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 nr_util, only: pi
+    use jumble, only: new_unit
     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 vec(iim, iim), vec1(iim, iim)
-    REAL du(iim)
-    INTEGER i, j, k, nrot
+
+    REAL delta(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, unit
 
     !----------------------------------------------------------------
 
@@ -42,52 +53,27 @@
     unsddu = 1. / sddu
     unsddv = 1. / sddv
 
-    DO j = 1, iim
-       DO i = 1, iim
-          vec(i, j) = 0.
-          vec1(i, j) = 0.
-          eignfnv(i, j) = 0.
-          eignfnu(i, j) = 0.
-       END DO
-    END DO
-
-    eignfnv(1, 1) = - 1.
-    eignfnv(iim, 1) = 1.
-    DO i = 1, iim - 1
-       eignfnv(i+1, i+1) = - 1.
-       eignfnv(i, i+1) = 1.
-    END DO
-
-    DO j = 1, iim
-       DO i = 1, iim
-          eignfnv(i, j) = eignfnv(i, j) / (sddu(i) * sddv(j))
-       END DO
-    END DO
-
-    DO j = 1, iim
-       DO i = 1, iim
-          eignfnu(i, j) = - eignfnv(j, i)
-       END DO
-    END DO
-
-    DO j = 1, iim
-       DO i = 1, iim
-          vec(i, j) = 0.0
-          vec1(i, j) = 0.0
-          DO k = 1, iim
-             vec(i, j) = vec(i, j) + eignfnu(i, k) * eignfnv(k, j)
-             vec1(i, j) = vec1(i, j) + eignfnv(i, k) * eignfnu(k, j)
-          END DO
-       END DO
-    END DO
+    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)
 
-    CALL jacobi(vec, dv, eignfnv, nrot)
+    deriv_v = - transpose(deriv_u)
+
+    delta = matmul(deriv_v, deriv_u) ! second derivative at v longitudes
+    CALL jacobi(delta, eignval_v, eignfnv)
     CALL acc(eignfnv)
-    CALL eigsrt(dv, eignfnv)
+    CALL eigsrt(eignval_v, eignfnv)
 
-    CALL jacobi(vec1, du, eignfnu, nrot)
+    delta = matmul(deriv_u, deriv_v) ! second derivative at u longitudes
+    CALL jacobi(delta, eignval_u, eignfnu)
     CALL acc(eignfnu)
-    CALL eigsrt(du, eignfnu)
+    CALL eigsrt(eignval_u, eignfnu)
+
+    call new_unit(unit)
+    open(unit, file = "inifgn_out.txt", status = "replace", action = "write") 
+    write(unit, fmt = *) '"eignval_v"', eignval_v
+    close(unit)
 
   END SUBROUTINE inifgn