| 1 | module regr1_conserv_m |
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| 2 | |
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| 3 | ! Author: Lionel GUEZ |
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| 4 | |
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| 5 | use assert_eq_m, only: assert_eq |
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| 6 | use assert_m, only: assert |
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| 7 | use interpolation, only: locate |
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| 8 | |
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| 9 | implicit none |
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| 10 | |
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| 11 | interface regr1_conserv |
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| 12 | |
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| 13 | ! This generic procedure regrids a piecewise linear function (not |
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| 14 | ! necessarily continuous) by averaging it. This is a conservative |
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| 15 | ! regridding. The regridding operation is done on the first |
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| 16 | ! dimension of the input array. Input are positions of cell |
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| 17 | ! edges. The target grid should be included in the source grid: |
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| 18 | ! no extrapolation is allowed. |
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| 19 | |
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| 20 | ! The only difference between the procedures is the rank of the |
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| 21 | ! first argument. |
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| 22 | |
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| 23 | ! real, intent(in), rank >= 1:: vs ! (ns, ...) |
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| 24 | ! averages of cells of the source grid |
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| 25 | ! vs(is, ...) for [xs(is), xs(is + 1)] |
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| 26 | |
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| 27 | ! real, intent(in):: xs(:) ! (ns + 1) |
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| 28 | ! edges of cells of the source grid, in strictly ascending order |
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| 29 | |
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| 30 | ! real, intent(in):: xt(:) ! (nt + 1) |
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| 31 | ! edges of cells of the target grid, in strictly ascending order |
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| 32 | |
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| 33 | ! real, intent(in), optional, rank >= 1:: slope ! (ns, ...) |
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| 34 | ! same rank as vs |
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| 35 | ! slopes inside cells of the source grid |
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| 36 | ! slope(is, ...) for [xs(is), xs(is + 1)] |
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| 37 | ! If not present, slopes are taken equal to 0. The regridding is |
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| 38 | ! then first order. |
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| 39 | |
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| 40 | ! real, intent(out), rank >= 1:: vt(nt, ...) |
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| 41 | ! has the same rank as vs and slope |
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| 42 | ! averages of cells of the target grid |
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| 43 | ! vt(it, ...) for [xt(it), xt(it + 1)] |
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| 44 | |
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| 45 | ! ns and nt must be >= 1. |
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| 46 | |
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| 47 | ! See notes for explanations on the algorithm and justification |
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| 48 | ! of algorithmic choices. |
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| 49 | |
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| 50 | module procedure regr11_conserv, regr12_conserv, regr13_conserv, & |
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| 51 | regr14_conserv |
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| 52 | end interface regr1_conserv |
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| 53 | |
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| 54 | private |
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| 55 | public regr1_conserv |
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| 56 | |
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| 57 | contains |
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| 58 | |
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| 59 | subroutine regr11_conserv(vs, xs, xt, vt, slope) |
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| 60 | |
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| 61 | ! vs and slope have rank 1. |
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| 62 | |
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| 63 | real, intent(in):: vs(:) |
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| 64 | real, intent(in):: xs(:) |
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| 65 | real, intent(in):: xt(:) |
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| 66 | real, intent(out):: vt(:) |
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| 67 | real, intent(in), optional:: slope(:) |
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| 68 | |
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| 69 | ! Local: |
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| 70 | integer is, it, ns, nt |
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| 71 | logical slope_present |
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| 72 | |
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| 73 | !--------------------------------------------- |
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| 74 | |
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| 75 | ns = assert_eq(size(vs), size(xs) - 1, "regr11_conserv ns") |
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| 76 | nt = assert_eq(size(xt) - 1, size(vt), "regr11_conserv nt") |
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| 77 | |
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| 78 | ! Quick check on sort order: |
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| 79 | call assert(xs(1) < xs(2), "regr11_conserv xs bad order") |
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| 80 | call assert(xt(1) < xt(2), "regr11_conserv xt bad order") |
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| 81 | |
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| 82 | call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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| 83 | "regr11_conserv extrapolation") |
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| 84 | slope_present = present(slope) |
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| 85 | |
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| 86 | is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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| 87 | do it = 1, nt |
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| 88 | ! 1 <= is <= ns |
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| 89 | ! xs(is) <= xt(it) < xs(is + 1) |
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| 90 | if (xt(it + 1) <= xs(is + 1)) then |
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| 91 | vt(it) = mean_lin(xt(it), xt(it + 1)) |
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| 92 | else |
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| 93 | vt(it) = mean_lin(xt(it), xs(is + 1)) * (xs(is + 1) - xt(it)) |
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| 94 | is = is + 1 |
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| 95 | do while (xs(is + 1) < xt(it + 1)) |
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| 96 | ! 1 <= is <= ns - 1 |
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| 97 | vt(it) = vt(it) + (xs(is + 1) - xs(is)) * vs(is) |
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| 98 | is = is + 1 |
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| 99 | end do |
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| 100 | ! 1 <= is <= ns |
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| 101 | vt(it) = (vt(it) + mean_lin(xs(is), xt(it + 1)) * (xt(it + 1) & |
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| 102 | - xs(is))) / (xt(it + 1) - xt(it)) |
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| 103 | end if |
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| 104 | |
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| 105 | if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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| 106 | ! 1 <= is <= ns .or. it == nt |
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| 107 | end do |
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| 108 | |
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| 109 | contains |
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| 110 | |
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| 111 | real function mean_lin(a, b) |
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| 112 | |
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| 113 | ! mean in [a, b] of the linear function in [xs(is), xs(is + 1)] |
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| 114 | |
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| 115 | real, intent(in):: a, b |
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| 116 | |
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| 117 | !--------------------------------------------- |
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| 118 | |
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| 119 | if (slope_present) then |
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| 120 | mean_lin = slope(is) / 2. * (a + b - xs(is) - xs(is + 1)) + vs(is) |
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| 121 | else |
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| 122 | mean_lin = vs(is) |
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| 123 | end if |
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| 124 | |
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| 125 | end function mean_lin |
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| 126 | |
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| 127 | end subroutine regr11_conserv |
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| 128 | |
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| 129 | !******************************************** |
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| 130 | |
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| 131 | subroutine regr12_conserv(vs, xs, xt, vt, slope) |
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| 132 | |
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| 133 | ! vs and slope have rank 2. |
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| 134 | |
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| 135 | real, intent(in):: vs(:, :) |
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| 136 | real, intent(in):: xs(:) |
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| 137 | real, intent(in):: xt(:) |
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| 138 | real, intent(out):: vt(:, :) |
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| 139 | real, intent(in), optional:: slope(:, :) |
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| 140 | |
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| 141 | ! Local: |
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| 142 | integer is, it, ns, nt, n2 |
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| 143 | logical slope_present |
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| 144 | |
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| 145 | !--------------------------------------------- |
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| 146 | |
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| 147 | ns = assert_eq(size(vs, 1), size(xs) - 1, "regr12_conserv ns") |
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| 148 | nt = assert_eq(size(xt) - 1, size(vt, 1), "regr12_conserv nt") |
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| 149 | n2 = assert_eq(size(vs, 2), size(vt, 2), "regr12_conserv n2") |
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| 150 | |
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| 151 | ! Quick check on sort order: |
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| 152 | call assert(xs(1) < xs(2), "regr12_conserv xs bad order") |
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| 153 | call assert(xt(1) < xt(2), "regr12_conserv xt bad order") |
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| 154 | |
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| 155 | call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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| 156 | "regr12_conserv extrapolation") |
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| 157 | slope_present = present(slope) |
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| 158 | |
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| 159 | is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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| 160 | do it = 1, nt |
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| 161 | ! 1 <= is <= ns |
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| 162 | ! xs(is) <= xt(it) < xs(is + 1) |
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| 163 | if (xt(it + 1) <= xs(is + 1)) then |
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| 164 | vt(it, :) = mean_lin(xt(it), xt(it + 1)) |
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| 165 | else |
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| 166 | vt(it, :) = mean_lin(xt(it), xs(is + 1)) * (xs(is + 1) - xt(it)) |
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| 167 | is = is + 1 |
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| 168 | do while (xs(is + 1) < xt(it + 1)) |
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| 169 | ! 1 <= is <= ns - 1 |
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| 170 | vt(it, :) = vt(it, :) + (xs(is + 1) - xs(is)) * vs(is, :) |
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| 171 | is = is + 1 |
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| 172 | end do |
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| 173 | ! 1 <= is <= ns |
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| 174 | vt(it, :) = (vt(it, :) + mean_lin(xs(is), xt(it + 1)) * (xt(it + 1) & |
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| 175 | - xs(is))) / (xt(it + 1) - xt(it)) |
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| 176 | end if |
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| 177 | |
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| 178 | if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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| 179 | ! 1 <= is <= ns .or. it == nt |
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| 180 | end do |
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| 181 | |
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| 182 | contains |
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| 183 | |
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| 184 | function mean_lin(a, b) |
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| 185 | |
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| 186 | ! mean in [a, b] of the linear function in [xs(is), xs(is + 1)] |
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| 187 | |
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| 188 | real, intent(in):: a, b |
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| 189 | real mean_lin(n2) |
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| 190 | |
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| 191 | !--------------------------------------------- |
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| 192 | |
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| 193 | if (slope_present) then |
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| 194 | mean_lin = slope(is, :) / 2. * (a + b - xs(is) - xs(is + 1)) & |
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| 195 | + vs(is, :) |
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| 196 | else |
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| 197 | mean_lin = vs(is, :) |
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| 198 | end if |
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| 199 | |
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| 200 | end function mean_lin |
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| 201 | |
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| 202 | end subroutine regr12_conserv |
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| 203 | |
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| 204 | !******************************************** |
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| 205 | |
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| 206 | subroutine regr13_conserv(vs, xs, xt, vt, slope) |
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| 207 | |
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| 208 | ! vs and slope have rank 3. |
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| 209 | |
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| 210 | real, intent(in):: vs(:, :, :) |
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| 211 | real, intent(in):: xs(:) |
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| 212 | real, intent(in):: xt(:) |
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| 213 | real, intent(out):: vt(:, :, :) |
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| 214 | real, intent(in), optional:: slope(:, :, :) |
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| 215 | |
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| 216 | ! Local: |
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| 217 | integer is, it, ns, nt, n2, n3 |
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| 218 | logical slope_present |
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| 219 | |
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| 220 | !--------------------------------------------- |
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| 221 | |
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| 222 | ns = assert_eq(size(vs, 1), size(xs) - 1, "regr13_conserv ns") |
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| 223 | nt = assert_eq(size(xt) - 1, size(vt, 1), "regr13_conserv nt") |
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| 224 | n2 = assert_eq(size(vs, 2), size(vt, 2), "regr13_conserv n2") |
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| 225 | n3 = assert_eq(size(vs, 3), size(vt, 3), "regr13_conserv n3") |
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| 226 | |
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| 227 | ! Quick check on sort order: |
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| 228 | call assert(xs(1) < xs(2), "regr13_conserv xs bad order") |
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| 229 | call assert(xt(1) < xt(2), "regr13_conserv xt bad order") |
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| 230 | |
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| 231 | call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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| 232 | "regr13_conserv extrapolation") |
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| 233 | slope_present = present(slope) |
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| 234 | |
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| 235 | is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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| 236 | do it = 1, nt |
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| 237 | ! 1 <= is <= ns |
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| 238 | ! xs(is) <= xt(it) < xs(is + 1) |
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| 239 | if (xt(it + 1) <= xs(is + 1)) then |
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| 240 | vt(it, :, :) = mean_lin(xt(it), xt(it + 1)) |
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| 241 | else |
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| 242 | vt(it, :, :) = mean_lin(xt(it), xs(is + 1)) * (xs(is + 1) - xt(it)) |
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| 243 | is = is + 1 |
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| 244 | do while (xs(is + 1) < xt(it + 1)) |
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| 245 | ! 1 <= is <= ns - 1 |
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| 246 | vt(it, :, :) = vt(it, :, :) + (xs(is + 1) - xs(is)) * vs(is, :, :) |
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| 247 | is = is + 1 |
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| 248 | end do |
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| 249 | ! 1 <= is <= ns |
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| 250 | vt(it, :, :) = (vt(it, :, :) + mean_lin(xs(is), xt(it + 1)) & |
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| 251 | * (xt(it + 1) - xs(is))) / (xt(it + 1) - xt(it)) |
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| 252 | end if |
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| 253 | |
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| 254 | if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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| 255 | ! 1 <= is <= ns .or. it == nt |
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| 256 | end do |
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| 257 | |
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| 258 | contains |
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| 259 | |
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| 260 | function mean_lin(a, b) |
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| 261 | |
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| 262 | ! mean in [a, b] of the linear function in [xs(is), xs(is + 1)] |
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| 263 | |
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| 264 | real, intent(in):: a, b |
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| 265 | real mean_lin(n2, n3) |
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| 266 | |
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| 267 | !--------------------------------------------- |
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| 268 | |
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| 269 | if (slope_present) then |
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| 270 | mean_lin = slope(is, :, :) / 2. * (a + b - xs(is) - xs(is + 1)) & |
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| 271 | + vs(is, :, :) |
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| 272 | else |
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| 273 | mean_lin = vs(is, :, :) |
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| 274 | end if |
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| 275 | |
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| 276 | end function mean_lin |
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| 277 | |
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| 278 | end subroutine regr13_conserv |
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| 279 | |
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| 280 | !******************************************** |
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| 281 | |
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| 282 | subroutine regr14_conserv(vs, xs, xt, vt, slope) |
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| 283 | |
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| 284 | ! vs and slope have rank 4. |
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| 285 | |
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| 286 | real, intent(in):: vs(:, :, :, :) |
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| 287 | real, intent(in):: xs(:) |
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| 288 | real, intent(in):: xt(:) |
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| 289 | real, intent(out):: vt(:, :, :, :) |
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| 290 | real, intent(in), optional:: slope(:, :, :, :) |
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| 291 | |
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| 292 | ! Local: |
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| 293 | integer is, it, ns, nt, n2, n3, n4 |
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| 294 | logical slope_present |
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| 295 | |
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| 296 | !--------------------------------------------- |
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| 297 | |
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| 298 | ns = assert_eq(size(vs, 1), size(xs) - 1, "regr14_conserv ns") |
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| 299 | nt = assert_eq(size(xt) - 1, size(vt, 1), "regr14_conserv nt") |
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| 300 | n2 = assert_eq(size(vs, 2), size(vt, 2), "regr14_conserv n2") |
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| 301 | n3 = assert_eq(size(vs, 3), size(vt, 3), "regr14_conserv n3") |
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| 302 | n4 = assert_eq(size(vs, 4), size(vt, 4), "regr14_conserv n4") |
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| 303 | |
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| 304 | ! Quick check on sort order: |
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| 305 | call assert(xs(1) < xs(2), "regr14_conserv xs bad order") |
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| 306 | call assert(xt(1) < xt(2), "regr14_conserv xt bad order") |
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| 307 | |
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| 308 | call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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| 309 | "regr14_conserv extrapolation") |
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| 310 | slope_present = present(slope) |
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| 311 | |
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| 312 | is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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| 313 | do it = 1, nt |
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| 314 | ! 1 <= is <= ns |
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| 315 | ! xs(is) <= xt(it) < xs(is + 1) |
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| 316 | if (xt(it + 1) <= xs(is + 1)) then |
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| 317 | vt(it, :, :, :) = mean_lin(xt(it), xt(it + 1)) |
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| 318 | else |
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| 319 | vt(it, :, :, :) = mean_lin(xt(it), xs(is + 1)) * (xs(is + 1) - xt(it)) |
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| 320 | is = is + 1 |
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| 321 | do while (xs(is + 1) < xt(it + 1)) |
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| 322 | ! 1 <= is <= ns - 1 |
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| 323 | vt(it, :, :, :) = vt(it, :, :, :) + (xs(is + 1) - xs(is)) & |
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| 324 | * vs(is, :, :, :) |
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| 325 | is = is + 1 |
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| 326 | end do |
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| 327 | ! 1 <= is <= ns |
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| 328 | vt(it, :, :, :) = (vt(it, :, :, :) + mean_lin(xs(is), xt(it + 1)) & |
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| 329 | * (xt(it + 1) - xs(is))) / (xt(it + 1) - xt(it)) |
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| 330 | end if |
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| 331 | |
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| 332 | if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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| 333 | ! 1 <= is <= ns .or. it == nt |
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| 334 | end do |
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| 335 | |
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| 336 | contains |
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| 337 | |
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| 338 | function mean_lin(a, b) |
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| 339 | |
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| 340 | ! mean in [a, b] of the linear function in [xs(is), xs(is + 1)] |
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| 341 | |
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| 342 | real, intent(in):: a, b |
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| 343 | real mean_lin(n2, n3, n4) |
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| 344 | |
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| 345 | !--------------------------------------------- |
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| 346 | |
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| 347 | if (slope_present) then |
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| 348 | mean_lin = slope(is, :, :, :) / 2. * (a + b - xs(is) - xs(is + 1)) & |
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| 349 | + vs(is, :, :, :) |
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| 350 | else |
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| 351 | mean_lin = vs(is, :, :, :) |
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| 352 | end if |
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| 353 | |
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| 354 | end function mean_lin |
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| 355 | |
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| 356 | end subroutine regr14_conserv |
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| 357 | |
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| 358 | end module regr1_conserv_m |
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