| 1 | !! |
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| 2 | !! ZDF.MATRIXSOLVER |
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| 3 | !! ******************** |
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| 4 | !! |
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| 5 | !! Matrix inversion |
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| 6 | !!---------------------------------------------------------------------- |
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| 7 | !! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 8 | !! |
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| 9 | !! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 10 | !! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 11 | !! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 12 | !! ( ... )( ... ) ( ... ) |
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| 13 | !! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 14 | !! |
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| 15 | !! m is decomposed in the product of an upper and lower triangular |
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| 16 | !! matrix |
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| 17 | !! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 18 | !! The second member is in 2d array zwy |
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| 19 | !! The solution is in 2d array zwx |
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| 20 | !! The 2d arry zwt and zwz are work space arrays |
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| 21 | !! |
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| 22 | !! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 23 | !! the resolution of tke matrix where surface tke value is prescribed |
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| 24 | !! so that ikstrt=2. |
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| 25 | !!---------------------------------------------------------------------- |
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| 26 | !!---------------------------------------------------------------------- |
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| 27 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| 28 | !! $Id: zdf.matrixsolver.h90 1152 2008-06-26 14:11:13Z rblod $ |
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| 29 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 30 | !!---------------------------------------------------------------------- |
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| 31 | |
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| 32 | ikstp1 = ikst + 1 |
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| 33 | ikenm2 = jpk - 2 |
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| 34 | DO ji = 2, jpim1 |
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| 35 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 36 | END DO |
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| 37 | DO jk = ikstp1, jpkm1 |
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| 38 | DO ji = 2, jpim1 |
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| 39 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 40 | END DO |
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| 41 | END DO |
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| 42 | DO ji = 2, jpim1 |
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| 43 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 44 | END DO |
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| 45 | DO jk = ikstp1, jpkm1 |
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| 46 | DO ji = 2, jpim1 |
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| 47 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 48 | END DO |
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| 49 | END DO |
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| 50 | DO ji = 2, jpim1 |
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| 51 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 52 | END DO |
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| 53 | DO jk = ikenm2, ikst, -1 |
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| 54 | DO ji = 2, jpim1 |
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| 55 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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| 56 | END DO |
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| 57 | END DO |
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| 58 | |
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