/[lmdze]/trunk/filtrez/inifgn.f
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revision 140 by guez, Fri Jun 5 18:58:06 2015 UTC revision 161 by guez, Fri Jul 24 14:27:59 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)    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)
   ! eignfn 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
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 nr_util, only: pi      use numer_rec_95, only: jacobi, eigsrt
30      use numer_rec_95, only: jacobi  
31        real, intent(out):: eignval_v(:) ! (iim)
32        ! eigenvalues sorted in descending order
33    
34      real, intent(out):: dv(iim)      real, intent(out):: eignfnu(:, :), eignfnv(:, :) ! (iim, iim) eigenvectors
35    
36      ! Local:      ! Local:
     REAL vec(iim, iim), vec1(iim, iim)  
     REAL du(iim)  
     real d(iim)  
     INTEGER i, j, k, nrot  
37    
38      EXTERNAL acc      REAL delta(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
45    
46      !----------------------------------------------------------------      !----------------------------------------------------------------
47    
48        print *, "Call sequence information: inifgn"
49    
50      sddv = sqrt(xprimv(:iim))      sddv = sqrt(xprimv(:iim))
51      sddu = sqrt(xprimu(:iim))      sddu = sqrt(xprimu(:iim))
52      unsddu = 1. / sddu      unsddu = 1. / sddu
53      unsddv = 1. / sddv      unsddv = 1. / sddv
54    
55      DO j = 1, iim      deriv_u = 0.
56         DO i = 1, iim      deriv_u(iim, 1) = unsddu(iim) * unsddv(1)
57            vec(i, j) = 0.      forall (i = 1:iim) deriv_u(i, i) = - unsddu(i) * unsddv(i)
58            vec1(i, j) = 0.      forall (i = 1:iim - 1) deriv_u(i, i + 1) = unsddu(i) * unsddv(i + 1)
59            eignfnv(i, j) = 0.  
60            eignfnu(i, j) = 0.      deriv_v = - transpose(deriv_u)
61         END DO  
62      END DO      delta = matmul(deriv_v, deriv_u) ! second derivative at v longitudes
63        CALL jacobi(delta, eignval_v, eignfnv)
64      eignfnv(1, 1) = - 1.      CALL acc(eignfnv)
65      eignfnv(iim, 1) = 1.      CALL eigsrt(eignval_v, eignfnv)
66      DO i = 1, iim - 1  
67         eignfnv(i+1, i+1) = - 1.      delta = matmul(deriv_u, deriv_v) ! second derivative at u longitudes
68         eignfnv(i, i+1) = 1.      CALL jacobi(delta, eignval_u, eignfnu)
69      END DO      CALL acc(eignfnu)
70        CALL eigsrt(eignval_u, eignfnu)
     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  
   
     CALL jacobi(vec, dv, eignfnv, nrot)  
     CALL acc(eignfnv, d, iim)  
     CALL eigen_sort(dv, eignfnv, iim, iim)  
   
     CALL jacobi(vec1, du, eignfnu, nrot)  
     CALL acc(eignfnu, d, iim)  
     CALL eigen_sort(du, eignfnu, iim, iim)  
71    
72    END SUBROUTINE inifgn    END SUBROUTINE inifgn
73    
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