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module inifgn_m |
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! $Header: /home/cvsroot/LMDZ4/libf/filtrez/inifgn.F,v 1.1.1.1 2004/05/19 |
use dimens_m, only: iim |
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! 12:53:09 lmdzadmin Exp $ |
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SUBROUTINE inifgn(dv) |
IMPLICIT NONE |
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! ... H.Upadyaya , O.Sharma ... |
private iim |
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USE dimens_m |
real sddu(iim), sddv(iim) |
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USE paramet_m |
! sdd[uv] = sqrt(2 pi / iim * (derivative of the longitudinal zoom |
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USE comgeom |
! function)(rlon[uv])) |
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USE serre |
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USE coefils |
real unsddu(iim), unsddv(iim) |
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IMPLICIT NONE |
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contains |
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SUBROUTINE inifgn(eignval_v, eignfnu, eignfnv) |
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! From LMDZ4/libf/filtrez/inifgn.F, v 1.1.1.1 2004/05/19 12:53:09 |
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! Authors: H. Upadyaya, O. Sharma |
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! Computes the eigenvalues and eigenvectors of the discrete analog |
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! of the second derivative with respect to longitude. |
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use acc_m, only: acc |
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USE dimens_m, ONLY: iim |
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USE dynetat0_m, ONLY: xprimu, xprimv |
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use numer_rec_95, only: jacobi, eigsrt |
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real, intent(out):: eignval_v(:) ! (iim) |
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! eigenvalues sorted in descending order |
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real, intent(out):: eignfnu(:, :), eignfnv(:, :) ! (iim, iim) eigenvectors |
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! Local: |
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REAL a(iim, iim) ! second derivative, symmetric, elements are angle^{-2} |
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REAL deriv_u(iim, iim), deriv_v(iim, iim) |
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! first derivative at u and v longitudes, elements are angle^{-1} |
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REAL eignval_u(iim) |
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INTEGER i |
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!---------------------------------------------------------------- |
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print *, "Call sequence information: inifgn" |
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sddv = sqrt(xprimv(:iim)) |
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sddu = sqrt(xprimu(:iim)) |
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unsddu = 1. / sddu |
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unsddv = 1. / sddv |
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deriv_u = 0. |
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deriv_u(iim, 1) = unsddu(iim) * unsddv(1) |
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forall (i = 1:iim) deriv_u(i, i) = - unsddu(i) * unsddv(i) |
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forall (i = 1:iim - 1) deriv_u(i, i + 1) = unsddu(i) * unsddv(i + 1) |
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deriv_v = - transpose(deriv_u) |
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a = matmul(deriv_v, deriv_u) ! second derivative at v longitudes |
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CALL jacobi(a, eignval_v, eignfnv) |
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CALL acc(eignfnv) |
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CALL eigsrt(eignval_v, eignfnv) |
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REAL vec(iim, iim), vec1(iim, iim) |
a = matmul(deriv_u, deriv_v) ! second derivative at u longitudes |
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REAL dlonu(iim), dlonv(iim) |
CALL jacobi(a, eignval_u, eignfnu) |
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REAL du(iim), dv(iim), d(iim) |
CALL acc(eignfnu) |
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REAL pi |
CALL eigsrt(eignval_u, eignfnu) |
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INTEGER i, j, k, imm1, nrot |
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EXTERNAL ssum, acc, jacobi |
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! C EXTERNAL eigen |
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REAL ssum |
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imm1 = iim - 1 |
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pi = 2.*asin(1.) |
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DO i = 1, iim |
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dlonu(i) = xprimu(i) |
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dlonv(i) = xprimv(i) |
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END DO |
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DO i = 1, iim |
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sddv(i) = sqrt(dlonv(i)) |
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sddu(i) = sqrt(dlonu(i)) |
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unsddu(i) = 1./sddu(i) |
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unsddv(i) = 1./sddv(i) |
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END DO |
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DO j = 1, iim |
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DO i = 1, iim |
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vec(i, j) = 0. |
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vec1(i, j) = 0. |
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eignfnv(i, j) = 0. |
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eignfnu(i, j) = 0. |
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END DO |
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END DO |
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eignfnv(1, 1) = -1. |
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eignfnv(iim, 1) = 1. |
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DO i = 1, imm1 |
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eignfnv(i+1, i+1) = -1. |
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eignfnv(i, i+1) = 1. |
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END DO |
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DO j = 1, iim |
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DO i = 1, iim |
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eignfnv(i, j) = eignfnv(i, j)/(sddu(i)*sddv(j)) |
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END DO |
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END DO |
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DO j = 1, iim |
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DO i = 1, iim |
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eignfnu(i, j) = -eignfnv(j, i) |
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END DO |
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END DO |
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DO j = 1, iim |
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DO i = 1, iim |
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vec(i, j) = 0.0 |
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vec1(i, j) = 0.0 |
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DO k = 1, iim |
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vec(i, j) = vec(i, j) + eignfnu(i, k)*eignfnv(k, j) |
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vec1(i, j) = vec1(i, j) + eignfnv(i, k)*eignfnu(k, j) |
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END DO |
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END DO |
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END DO |
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CALL jacobi(vec, iim, iim, dv, eignfnv, nrot) |
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CALL acc(eignfnv, d, iim) |
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CALL eigen_sort(dv, eignfnv, iim, iim) |
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CALL jacobi(vec1, iim, iim, du, eignfnu, nrot) |
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CALL acc(eignfnu, d, iim) |
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CALL eigen_sort(du, eignfnu, iim, iim) |
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! c ancienne version avec appels IMSL |
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! CALL MXM(eignfnu,iim,eignfnv,iim,vec,iim) |
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! CALL MXM(eignfnv,iim,eignfnu,iim,vec1,iim) |
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! CALL EVCSF(iim,vec,iim,dv,eignfnv,iim) |
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! CALL acc(eignfnv,d,iim) |
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! CALL eigen(eignfnv,dv) |
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! CALL EVCSF(iim,vec1,iim,du,eignfnu,iim) |
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! CALL acc(eignfnu,d,iim) |
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! CALL eigen(eignfnu,du) |
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RETURN |
END SUBROUTINE inifgn |
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END SUBROUTINE inifgn |
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end module inifgn_m |
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