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 | !! OPA 8.5, LODYC-IPSL (2002) |
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27 | !!---------------------------------------------------------------------- |
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28 | |
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29 | ikstp1 = ikst + 1 |
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30 | ikenm2 = jpk - 2 |
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31 | DO ji = 2, jpim1 |
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32 | zwt(ji,ikst) = zwd(ji,ikst) |
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33 | END DO |
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34 | DO jk = ikstp1, jpkm1 |
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35 | DO ji = 2, jpim1 |
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36 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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37 | END DO |
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38 | END DO |
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39 | DO ji = 2, jpim1 |
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40 | zwz(ji,ikst) = zwy(ji,ikst) |
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41 | END DO |
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42 | DO jk = ikstp1, jpkm1 |
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43 | DO ji = 2, jpim1 |
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44 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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45 | END DO |
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46 | END DO |
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47 | DO ji = 2, jpim1 |
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48 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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49 | END DO |
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50 | DO jk = ikenm2, ikst, -1 |
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51 | DO ji = 2, jpim1 |
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52 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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53 | END DO |
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54 | END DO |
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55 | |
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