/[lmdze]/trunk/filtrez/inifgn.f
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revision 153 by guez, Tue Jun 23 18:26:18 2015 UTC revision 154 by guez, Tue Jul 7 17:49:23 2015 UTC
# Line 6  module inifgn_m Line 6  module inifgn_m
6    
7    private iim    private iim
8    
9    real sddu(iim), sddv(iim) ! SQRT(dx / di)    real sddu(iim), sddv(iim)
10    real unsddu(iim), unsddv(iim)    ! sdd[uv] = sqrt(2 pi / iim * (derivative of the longitudinal zoom
11      ! function)(rlon[uv]))
12    
13    real eignfnu(iim, iim), eignfnv(iim, iim)    real unsddu(iim), unsddv(iim)
   ! eigenfunctions of the discrete laplacian  
14    
15  contains  contains
16    
17    SUBROUTINE inifgn(dv)    SUBROUTINE inifgn(eignval_v, eignfnu, eignfnv)
18    
19      ! From LMDZ4/libf/filtrez/inifgn.F, v 1.1.1.1 2004/05/19 12:53:09      ! From LMDZ4/libf/filtrez/inifgn.F, v 1.1.1.1 2004/05/19 12:53:09
20    
21      ! H. Upadyaya, O. Sharma      ! Authors: H. Upadyaya, O. Sharma
22    
23        ! Computes the eigenvalues and eigenvectors of the discrete analog
24        ! of the second derivative with respect to longitude.
25    
26      use acc_m, only: acc      use acc_m, only: acc
27      USE dimens_m, ONLY: iim      USE dimens_m, ONLY: iim
28      USE dynetat0_m, ONLY: xprimu, xprimv      USE dynetat0_m, ONLY: xprimu, xprimv
29      use numer_rec_95, only: jacobi, eigsrt      use numer_rec_95, only: jacobi, eigsrt
30    
31      real, intent(out):: dv(:) ! (iim) eigenvalues sorted in descending order      real, intent(out):: eignval_v(:) ! (iim)
32        ! eigenvalues sorted in descending order
33    
34        real, intent(out):: eignfnu(:, :), eignfnv(:, :) ! (iim, iim) eigenvectors
35    
36      ! Local:      ! Local:
37      REAL, dimension(iim, iim):: a, b, c  
38      REAL du(iim)      REAL a(iim, iim) ! second derivative, symmetric, elements are angle^{-2}
39    
40        REAL deriv_u(iim, iim), deriv_v(iim, iim)
41        ! first derivative at u and v longitudes, elements are angle^{-1}
42    
43        REAL eignval_u(iim)
44      INTEGER i      INTEGER i
45    
46      !----------------------------------------------------------------      !----------------------------------------------------------------
# Line 41  contains Line 52  contains
52      unsddu = 1. / sddu      unsddu = 1. / sddu
53      unsddv = 1. / sddv      unsddv = 1. / sddv
54    
55      b = 0.      deriv_u = 0.
56      b(iim, 1) = unsddu(iim) * unsddv(1)      deriv_u(iim, 1) = unsddu(iim) * unsddv(1)
57      forall (i = 1:iim) b(i, i) = - unsddu(i) * unsddv(i)      forall (i = 1:iim) deriv_u(i, i) = - unsddu(i) * unsddv(i)
58      forall (i = 1:iim - 1) b(i, i + 1) = unsddu(i) * unsddv(i + 1)      forall (i = 1:iim - 1) deriv_u(i, i + 1) = unsddu(i) * unsddv(i + 1)
59    
60      c = - transpose(b)      deriv_v = - transpose(deriv_u)
61    
62      a = matmul(c, b)      a = matmul(deriv_v, deriv_u) ! second derivative at v longitudes
63      CALL jacobi(a, dv, eignfnv)      CALL jacobi(a, eignval_v, eignfnv)
64      CALL acc(eignfnv)      CALL acc(eignfnv)
65      CALL eigsrt(dv, eignfnv)      CALL eigsrt(eignval_v, eignfnv)
66    
67      a = matmul(b, c)      a = matmul(deriv_u, deriv_v) ! second derivative at u longitudes
68      CALL jacobi(a, du, eignfnu)      CALL jacobi(a, eignval_u, eignfnu)
69      CALL acc(eignfnu)      CALL acc(eignfnu)
70      CALL eigsrt(du, eignfnu)      CALL eigsrt(eignval_u, eignfnu)
71    
72    END SUBROUTINE inifgn    END SUBROUTINE inifgn
73    
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