| 1 | !! |
|---|
| 2 | !! ZDF.MATRIXSOLVER |
|---|
| 3 | !! ******************** |
|---|
| 4 | !! |
|---|
| 5 | !! Matrix inversion |
|---|
| 6 | !!---------------------------------------------------------------------- |
|---|
| 7 | !! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 8 | !! |
|---|
| 9 | !! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
|---|
| 10 | !! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
|---|
| 11 | !! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
|---|
| 12 | !! ( ... )( ... ) ( ... ) |
|---|
| 13 | !! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 14 | !! |
|---|
| 15 | !! m is decomposed in the product of an upper and lower triangular |
|---|
| 16 | !! matrix |
|---|
| 17 | !! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 18 | !! The second member is in 2d array zwy |
|---|
| 19 | !! The solution is in 2d array zwx |
|---|
| 20 | !! The 3d arry zwt is a work space array |
|---|
| 21 | !! zwy is used and then used as a work space array : its value is modified! |
|---|
| 22 | !! |
|---|
| 23 | !! N.B. the starting vertical index (ikst) is equal to 1 except for |
|---|
| 24 | !! the resolution of tke matrix where surface tke value is prescribed |
|---|
| 25 | !! so that ikstrt=2. |
|---|
| 26 | !!---------------------------------------------------------------------- |
|---|
| 27 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
|---|
| 28 | !! $Id: zdf.matrixsolver.vopt.h90 1152 2008-06-26 14:11:13Z rblod $ |
|---|
| 29 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
|---|
| 30 | !!---------------------------------------------------------------------- |
|---|
| 31 | |
|---|
| 32 | ikstp1 = ikst + 1 |
|---|
| 33 | ikenm2 = jpk - 2 |
|---|
| 34 | |
|---|
| 35 | DO jj = 2, jpjm1 |
|---|
| 36 | DO ji = fs_2, fs_jpim1 |
|---|
| 37 | zwt(ji,jj,ikst) = zwd(ji,jj,ikst) |
|---|
| 38 | END DO |
|---|
| 39 | END DO |
|---|
| 40 | |
|---|
| 41 | DO jk = ikstp1, jpkm1 |
|---|
| 42 | DO jj = 2, jpjm1 |
|---|
| 43 | DO ji = fs_2, fs_jpim1 |
|---|
| 44 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwt(ji,jj,jk-1) |
|---|
| 45 | END DO |
|---|
| 46 | END DO |
|---|
| 47 | END DO |
|---|
| 48 | |
|---|
| 49 | DO jk = ikstp1, jpkm1 |
|---|
| 50 | DO jj = 2, jpjm1 |
|---|
| 51 | DO ji = fs_2, fs_jpim1 |
|---|
| 52 | zwy(ji,jj,jk) = zwy(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * zwy(ji,jj,jk-1) |
|---|
| 53 | END DO |
|---|
| 54 | END DO |
|---|
| 55 | END DO |
|---|
| 56 | |
|---|
| 57 | DO jj = 2, jpjm1 |
|---|
| 58 | DO ji = fs_2, fs_jpim1 |
|---|
| 59 | zwx(ji,jj,jpkm1) = zwy(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
|---|
| 60 | END DO |
|---|
| 61 | END DO |
|---|
| 62 | |
|---|
| 63 | DO jk = ikenm2, ikst, -1 |
|---|
| 64 | DO jj = 2, jpjm1 |
|---|
| 65 | DO ji = fs_2, fs_jpim1 |
|---|
| 66 | zwx(ji,jj,jk) = ( zwy(ji,jj,jk) - zws(ji,jj,jk) * zwx(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
|---|
| 67 | END DO |
|---|
| 68 | END DO |
|---|
| 69 | END DO |
|---|
