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private iim |
private iim |
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real sddu(iim), sddv(iim) ! SQRT(dx / di) |
real sddu(iim), sddv(iim) |
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real unsddu(iim), unsddv(iim) |
! sdd[uv] = sqrt(2 pi / iim * (derivative of the longitudinal zoom |
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! function)(rlon[uv])) |
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real eignfnu(iim, iim), eignfnv(iim, iim) |
real unsddu(iim), unsddv(iim) |
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! eigenfunctions of the discrete laplacian |
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contains |
contains |
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SUBROUTINE inifgn(dv) |
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 |
! From LMDZ4/libf/filtrez/inifgn.F, v 1.1.1.1 2004/05/19 12:53:09 |
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! H. Upadyaya, O. Sharma |
! 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 |
use acc_m, only: acc |
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USE dimens_m, ONLY: iim |
USE dimens_m, ONLY: iim |
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USE dynetat0_m, ONLY: xprimu, xprimv |
USE dynetat0_m, ONLY: xprimu, xprimv |
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use jumble, only: new_unit |
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use numer_rec_95, only: jacobi, eigsrt |
use numer_rec_95, only: jacobi, eigsrt |
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real, intent(out):: dv(:) ! (iim) eigenvalues sorted in descending order |
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: |
! Local: |
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REAL, dimension(iim, iim):: a, b, c |
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REAL du(iim) |
REAL delta(iim, iim) ! second derivative, symmetric, elements are angle^{-2} |
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INTEGER i |
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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, unit |
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!---------------------------------------------------------------- |
!---------------------------------------------------------------- |
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unsddu = 1. / sddu |
unsddu = 1. / sddu |
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unsddv = 1. / sddv |
unsddv = 1. / sddv |
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b = 0. |
deriv_u = 0. |
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b(iim, 1) = unsddu(iim) * unsddv(1) |
deriv_u(iim, 1) = unsddu(iim) * unsddv(1) |
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forall (i = 1:iim) b(i, i) = - unsddu(i) * unsddv(i) |
forall (i = 1:iim) deriv_u(i, i) = - unsddu(i) * unsddv(i) |
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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) |
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c = - transpose(b) |
deriv_v = - transpose(deriv_u) |
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a = matmul(c, b) |
delta = matmul(deriv_v, deriv_u) ! second derivative at v longitudes |
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CALL jacobi(a, dv, eignfnv) |
CALL jacobi(delta, eignval_v, eignfnv) |
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CALL acc(eignfnv) |
CALL acc(eignfnv) |
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CALL eigsrt(dv, eignfnv) |
CALL eigsrt(eignval_v, eignfnv) |
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a = matmul(b, c) |
delta = matmul(deriv_u, deriv_v) ! second derivative at u longitudes |
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CALL jacobi(a, du, eignfnu) |
CALL jacobi(delta, eignval_u, eignfnu) |
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CALL acc(eignfnu) |
CALL acc(eignfnu) |
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CALL eigsrt(du, eignfnu) |
CALL eigsrt(eignval_u, eignfnu) |
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call new_unit(unit) |
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open(unit, file = "inifgn_out.txt", status = "replace", action = "write") |
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write(unit, fmt = *) '"eignval_v"', eignval_v |
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close(unit) |
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END SUBROUTINE inifgn |
END SUBROUTINE inifgn |
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