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module regr1_step_av_m |
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|
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implicit none |
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|
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interface regr1_step_av |
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|
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! Each procedure regrids a step function by averaging it. |
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! The regridding operation is done on the first dimension of the |
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! input array. |
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! Source grid contains edges of steps. |
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! Target grid contains positions of cell edges. |
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! The target grid should be included in the source grid: no |
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! extrapolation is allowed. |
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! The difference between the procedures is the rank of the first argument. |
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|
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module procedure regr11_step_av, regr12_step_av, regr13_step_av |
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end interface |
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|
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private |
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public regr1_step_av |
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|
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contains |
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|
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function regr11_step_av(vs, xs, xt) result(vt) |
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|
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! "vs" has rank 1. |
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|
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use nrutil, only: assert_eq, assert |
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use interpolation, only: locate |
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|
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real, intent(in):: vs(:) ! values of steps on the source grid |
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! (Step "is" is between "xs(is)" and "xs(is + 1)".) |
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|
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real, intent(in):: xs(:) |
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! (edges of of steps on the source grid, in strictly increasing order) |
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|
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real, intent(in):: xt(:) |
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! (edges of cells of the target grid, in strictly increasing order) |
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|
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real vt(size(xt) - 1) ! average values on the target grid |
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! (Cell "it" is between "xt(it)" and "xt(it + 1)".) |
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|
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! Variables local to the procedure: |
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integer is, it, ns, nt |
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real left_edge |
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|
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!--------------------------------------------- |
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|
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ns = assert_eq(size(vs), size(xs) - 1, "regr11_step_av ns") |
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nt = size(xt) - 1 |
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! Quick check on sort order: |
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call assert(xs(1) < xs(2), "regr11_step_av xs bad order") |
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call assert(xt(1) < xt(2), "regr11_step_av xt bad order") |
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|
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call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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"regr11_step_av extrapolation") |
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|
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is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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do it = 1, nt |
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! 1 <= is <= ns |
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! xs(is) <= xt(it) < xs(is + 1) |
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! Compute "vt(it)": |
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left_edge = xt(it) |
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vt(it) = 0. |
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do while (xs(is + 1) < xt(it + 1)) |
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! 1 <= is <= ns - 1 |
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vt(it) = vt(it) + (xs(is + 1) - left_edge) * vs(is) |
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is = is + 1 |
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left_edge = xs(is) |
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end do |
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! 1 <= is <= ns |
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vt(it) = (vt(it) + (xt(it + 1) - left_edge) * vs(is)) & |
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/ (xt(it + 1) - xt(it)) |
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if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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! 1 <= is <= ns .or. it == nt |
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end do |
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|
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end function regr11_step_av |
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|
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!******************************************** |
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|
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function regr12_step_av(vs, xs, xt) result(vt) |
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|
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! "vs" has rank 2. |
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|
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use nrutil, only: assert_eq, assert |
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use interpolation, only: locate |
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|
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real, intent(in):: vs(:, :) ! values of steps on the source grid |
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! (Step "is" is between "xs(is)" and "xs(is + 1)".) |
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|
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real, intent(in):: xs(:) |
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! (edges of steps on the source grid, in strictly increasing order) |
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|
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real, intent(in):: xt(:) |
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! (edges of cells of the target grid, in strictly increasing order) |
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|
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real vt(size(xt) - 1, size(vs, 2)) ! average values on the target grid |
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! (Cell "it" is between "xt(it)" and "xt(it + 1)".) |
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|
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! Variables local to the procedure: |
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integer is, it, ns, nt |
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real left_edge |
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|
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!--------------------------------------------- |
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|
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ns = assert_eq(size(vs, 1), size(xs) - 1, "regr12_step_av ns") |
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nt = size(xt) - 1 |
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|
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! Quick check on sort order: |
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call assert(xs(1) < xs(2), "regr12_step_av xs bad order") |
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call assert(xt(1) < xt(2), "regr12_step_av xt bad order") |
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|
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call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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"regr12_step_av extrapolation") |
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|
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is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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do it = 1, nt |
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! 1 <= is <= ns |
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! xs(is) <= xt(it) < xs(is + 1) |
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! Compute "vt(it, :)": |
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left_edge = xt(it) |
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vt(it, :) = 0. |
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do while (xs(is + 1) < xt(it + 1)) |
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! 1 <= is <= ns - 1 |
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vt(it, :) = vt(it, :) + (xs(is + 1) - left_edge) * vs(is, :) |
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is = is + 1 |
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left_edge = xs(is) |
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end do |
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! 1 <= is <= ns |
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vt(it, :) = (vt(it, :) + (xt(it + 1) - left_edge) * vs(is, :)) & |
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/ (xt(it + 1) - xt(it)) |
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if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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! 1 <= is <= ns .or. it == nt |
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end do |
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|
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end function regr12_step_av |
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|
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!******************************************** |
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|
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function regr13_step_av(vs, xs, xt) result(vt) |
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|
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! "vs" has rank 3. |
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|
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use nrutil, only: assert_eq, assert |
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use interpolation, only: locate |
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|
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real, intent(in):: vs(:, :, :) ! values of steps on the source grid |
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! (Step "is" is between "xs(is)" and "xs(is + 1)".) |
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|
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real, intent(in):: xs(:) |
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! (edges of steps on the source grid, in strictly increasing order) |
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|
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real, intent(in):: xt(:) |
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! (edges of cells of the target grid, in strictly increasing order) |
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|
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real vt(size(xt) - 1, size(vs, 2), size(vs, 3)) |
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! (average values on the target grid) |
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! (Cell "it" is between "xt(it)" and "xt(it + 1)".) |
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|
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! Variables local to the procedure: |
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integer is, it, ns, nt |
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real left_edge |
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|
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!--------------------------------------------- |
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|
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ns = assert_eq(size(vs, 1), size(xs) - 1, "regr13_step_av ns") |
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nt = size(xt) - 1 |
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|
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! Quick check on sort order: |
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call assert(xs(1) < xs(2), "regr13_step_av xs bad order") |
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call assert(xt(1) < xt(2), "regr13_step_av xt bad order") |
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|
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call assert(xs(1) <= xt(1) .and. xt(nt + 1) <= xs(ns + 1), & |
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"regr13_step_av extrapolation") |
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|
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is = locate(xs, xt(1)) ! 1 <= is <= ns, because we forbid extrapolation |
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do it = 1, nt |
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! 1 <= is <= ns |
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! xs(is) <= xt(it) < xs(is + 1) |
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! Compute "vt(it, :, :)": |
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left_edge = xt(it) |
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vt(it, :, :) = 0. |
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do while (xs(is + 1) < xt(it + 1)) |
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! 1 <= is <= ns - 1 |
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vt(it, :, :) = vt(it, :, :) + (xs(is + 1) - left_edge) * vs(is, :, :) |
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is = is + 1 |
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left_edge = xs(is) |
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end do |
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! 1 <= is <= ns |
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vt(it, :, :) = (vt(it, :, :) & |
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+ (xt(it + 1) - left_edge) * vs(is, :, :)) / (xt(it + 1) - xt(it)) |
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if (xs(is + 1) == xt(it + 1)) is = is + 1 |
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! 1 <= is <= ns .or. it == nt |
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end do |
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|
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end function regr13_step_av |
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|
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end module regr1_step_av_m |
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