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IMPLICIT NONE |
IMPLICIT NONE |
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INTEGER jfiltnu, jfiltsu, jfiltnv, jfiltsv |
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! jfiltn index of the last scalar line filtered in NH |
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! jfilts index of the first line filtered in SH |
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! North: |
! North: |
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INTEGER jfiltnu, jfiltnv |
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! index of the last scalar line filtered in northern hemisphere |
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real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
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! (iim, iim, 2:jfiltnu) |
! (iim, iim, 2:jfiltnu) |
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real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
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! South: |
! South: |
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integer jfiltsu, jfiltsv |
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! index of the first line filtered in southern hemisphere |
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real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
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! (iim, iim, jfiltsu:jjm) |
! (iim, iim, jfiltsu:jjm) |
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SUBROUTINE inifilr |
SUBROUTINE inifilr |
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! From filtrez/inifilr.F, version 1.1.1.1 2004/05/19 12:53:09 |
! From filtrez/inifilr.F, version 1.1.1.1, 2004/05/19 12:53:09 |
30 |
! H. Upadhyaya, O. Sharma |
! H. Upadhyaya, O. Sharma |
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! This routine computes the eigenfunctions of the laplacian on the |
! This procedure computes the filtering coefficients for scalar |
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! stretched grid, and the filtering coefficients. The modes are |
! lines and meridional wind v lines. The modes are filtered from |
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! filtered from modfrst to iim. |
! modfrst to iim. We filter all those latitude lines where coefil |
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! < 1. No filtering at poles. colat0 is to be used when alpha |
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! (stretching coefficient) is set equal to zero for the regular |
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! grid case. |
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USE dimens_m, ONLY : iim, jjm |
USE dimens_m, ONLY : iim, jjm |
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USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
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use nr_util, only: pi |
use nr_util, only: pi |
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! Local: |
! Local: |
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REAL dlatu(jjm) |
REAL dlatu(jjm) |
48 |
REAL rlamda(2: iim) |
REAL rlamda(2: iim) |
49 |
real eignvl(iim) ! eigenvalues sorted in descending order |
real eignvl(iim) ! eigenvalues sorted in descending order (<= 0) |
50 |
REAL cof |
INTEGER i, j, unit |
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INTEGER i, j, k, unit |
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REAL colat0 ! > 0 |
REAL colat0 ! > 0 |
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REAL eignft(iim, iim), coff |
REAL eignft(iim, iim) |
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real eignfnu(iim, iim), eignfnv(iim, iim) |
real eignfnu(iim, iim), eignfnv(iim, iim) |
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! eigenfunctions of the discrete laplacian |
! eigenvectors of the discrete second derivative with respect to longitude |
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! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
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real coefilu(iim, jjm), coefilv(iim, jjm) |
real, allocatable:: coefilnu(:, :) ! (iim, 2:jfiltnu) |
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real coefilu2(iim, jjm), coefilv2(iim, jjm) |
real, allocatable:: coefilsu(:, :) ! (iim, jfiltsu:jjm) |
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real, allocatable:: coefilnv(:, :) ! (iim, jfiltnv) |
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real, allocatable:: coefilsv(:, :) ! (iim, jfiltsv:jjm) |
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! Index of the mode from where modes are filtered: |
! Index of the mode from where modes are filtered: |
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integer, allocatable:: modfrstnu(:), modfrstsu(:) |
integer, allocatable:: modfrstnu(:) ! (2:jfiltnu) |
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integer, allocatable:: modfrstnv(:), modfrstsv(:) |
integer, allocatable:: modfrstsu(:) ! (jfiltsu:jjm) |
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integer, allocatable:: modfrstnv(:) ! (jfiltnv) |
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integer, allocatable:: modfrstsv(:) ! (jfiltsv:jjm) |
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!----------------------------------------------------------- |
!----------------------------------------------------------- |
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CALL inifgn(eignvl, eignfnu, eignfnv) |
CALL inifgn(eignvl, eignfnu, eignfnv) |
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! compute eigenvalues and eigenfunctions |
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! compute the filtering coefficients for scalar lines and |
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! meridional wind v-lines |
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! we filter all those latitude lines where coefil < 1 |
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! NO FILTERING AT POLES |
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! colat0 is to be used when alpha (stretching coefficient) |
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! is set equal to zero for the regular grid case |
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! Calcul de colat0 |
! Calcul de colat0 |
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forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
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colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
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PRINT *, 'colat0 = ', colat0 |
PRINT *, 'colat0 = ', colat0 |
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rlamda = iim / (pi * colat0 / grossismx) / sqrt(abs(eignvl(2: iim))) |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(- eignvl(2: iim)) |
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! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv |
! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv |
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PRINT *, 'jfiltnv =', jfiltnv |
PRINT *, 'jfiltnv =', jfiltnv |
125 |
PRINT *, 'jfiltsv =', jfiltsv |
PRINT *, 'jfiltsv =', jfiltsv |
126 |
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! Determination de coefilu, coefilv, modfrst[ns][uv]: |
! D\'etermination de coefil[ns][uv], modfrst[ns][uv]: |
128 |
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allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
130 |
allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
131 |
coefilu = 0. |
allocate(coefilnu(iim, 2:jfiltnu), coefilsu(iim, jfiltsu:jjm)) |
132 |
coefilv = 0. |
allocate(coefilnv(iim, jfiltnv), coefilsv(iim, jfiltsv:jjm)) |
133 |
coefilu2 = 0. |
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134 |
coefilv2 = 0. |
coefilnu = 0. |
135 |
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coefilnv = 0. |
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coefilsu = 0. |
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coefilsv = 0. |
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139 |
DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
140 |
modfrstnu(j) = 2 |
modfrstnu(j) = 2 |
144 |
end do |
end do |
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146 |
if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
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DO k = modfrstnu(j), iim |
DO i = modfrstnu(j), iim |
148 |
cof = rlamda(k) * cos(rlatu(j)) |
coefilnu(i, j) = rlamda(i) * cos(rlatu(j)) - 1. |
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coefilu(k, j) = cof - 1. |
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coefilu2(k, j) = cof**2 - 1. |
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end DO |
end DO |
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end if |
end if |
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END DO |
END DO |
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end do |
end do |
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if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
161 |
DO k = modfrstnv(j), iim |
DO i = modfrstnv(j), iim |
162 |
cof = rlamda(k) * cos(rlatv(j)) |
coefilnv(i, j) = rlamda(i) * cos(rlatv(j)) - 1. |
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coefilv(k, j) = cof - 1. |
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coefilv2(k, j) = cof**2 - 1. |
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end DO |
end DO |
164 |
end if |
end if |
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end DO |
end DO |
172 |
end do |
end do |
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if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
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DO k = modfrstsu(j), iim |
DO i = modfrstsu(j), iim |
176 |
cof = rlamda(k) * cos(rlatu(j)) |
coefilsu(i, j) = rlamda(i) * cos(rlatu(j)) - 1. |
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coefilu(k, j) = cof - 1. |
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coefilu2(k, j) = cof**2 - 1. |
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end DO |
end DO |
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end if |
end if |
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end DO |
end DO |
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end do |
end do |
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if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
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DO k = modfrstsv(j), iim |
DO i = modfrstsv(j), iim |
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cof = rlamda(k) * cos(rlatv(j)) |
coefilsv(i, j) = rlamda(i) * cos(rlatv(j)) - 1. |
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coefilv(k, j) = cof - 1. |
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coefilv2(k, j) = cof**2 - 1. |
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end DO |
end DO |
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end if |
end if |
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END DO |
END DO |
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! sur la grille scalaire |
! sur la grille scalaire |
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DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
213 |
DO i = 1, iim |
eignft(:modfrstnu(j) - 1, :) = 0. |
214 |
IF (i < modfrstnu(j)) then |
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) & |
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coff = 0. |
* coefilnu(i, j) |
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else |
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coff = coefilu(i, j) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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matriceun(:, :, j) = matmul(eignfnv, eignft) |
matriceun(:, :, j) = matmul(eignfnv, eignft) |
217 |
END DO |
END DO |
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DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
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DO i = 1, iim |
eignft(:modfrstsu(j) - 1, :) = 0. |
221 |
IF (i < modfrstsu(j)) then |
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) & |
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coff = 0. |
* coefilsu(i, j) |
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else |
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coff = coefilu(i, j) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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223 |
matriceus(:, :, j) = matmul(eignfnv, eignft) |
matriceus(:, :, j) = matmul(eignfnv, eignft) |
224 |
END DO |
END DO |
225 |
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! sur la grille de V ou de Z |
! sur la grille de V ou de Z |
228 |
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DO j = 1, jfiltnv |
DO j = 1, jfiltnv |
230 |
DO i = 1, iim |
eignft(:modfrstnv(j) - 1, :) = 0. |
231 |
IF (i < modfrstnv(j)) then |
forall (i = modfrstnv(j): iim) eignft(i, :) = eignfnu(:, i) & |
232 |
coff = 0. |
* coefilnv(i, j) |
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else |
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coff = coefilv(i, j) |
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end IF |
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eignft(i, :) = eignfnu(:, i) * coff |
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END DO |
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matricevn(:, :, j) = matmul(eignfnu, eignft) |
matricevn(:, :, j) = matmul(eignfnu, eignft) |
234 |
END DO |
END DO |
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DO j = jfiltsv, jjm |
DO j = jfiltsv, jjm |
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DO i = 1, iim |
eignft(:modfrstsv(j) - 1, :) = 0. |
238 |
IF (i < modfrstsv(j)) then |
forall (i = modfrstsv(j):iim) eignft(i, :) = eignfnu(:, i) & |
239 |
coff = 0. |
* coefilsv(i, j) |
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else |
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coff = coefilv(i, j) |
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end IF |
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eignft(i, :) = eignfnu(:, i) * coff |
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END DO |
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matricevs(:, :, j) = matmul(eignfnu, eignft) |
matricevs(:, :, j) = matmul(eignfnu, eignft) |
241 |
END DO |
END DO |
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! sur la grille scalaire , pour le filtre inverse |
! sur la grille scalaire , pour le filtre inverse |
245 |
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DO j = 2, jfiltnu |
DO j = 2, jfiltnu |
247 |
DO i = 1, iim |
eignft(:modfrstnu(j) - 1, :) = 0. |
248 |
IF (i < modfrstnu(j)) then |
forall (i = modfrstnu(j):iim) eignft(i, :) = eignfnv(:, i) & |
249 |
coff = 0. |
* coefilnu(i, j) / (1. + coefilnu(i, j)) |
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else |
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coff = coefilu(i, j) / (1. + coefilu(i, j)) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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matrinvn(:, :, j) = matmul(eignfnv, eignft) |
matrinvn(:, :, j) = matmul(eignfnv, eignft) |
251 |
END DO |
END DO |
252 |
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253 |
DO j = jfiltsu, jjm |
DO j = jfiltsu, jjm |
254 |
DO i = 1, iim |
eignft(:modfrstsu(j) - 1, :) = 0. |
255 |
IF (i < modfrstsu(j)) then |
forall (i = modfrstsu(j):iim) eignft(i, :) = eignfnv(:, i) & |
256 |
coff = 0. |
* coefilsu(i, j) / (1. + coefilsu(i, j)) |
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else |
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coff = coefilu(i, j) / (1. + coefilu(i, j)) |
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end IF |
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eignft(i, :) = eignfnv(:, i) * coff |
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END DO |
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257 |
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
258 |
END DO |
END DO |
259 |
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