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dekker.one
1/*
2 * Function fzn_piecewise_linear_base creates
3 * interval representation of x,
4 * which is reusable if we have several pwls
5 * on the same set of breakpoints
6 */
7function array[int, int] of var 0.0..1.0: fzn_piecewise_linear_base(
8 var float: x, array[int] of float: xi) ::promise_total =
9 let {
10 set of int: is = index_set(xi),
11 set of int: is_1 = is diff { max(is) },
12 array[is_1] of var 0.0..1.0: s, %% Segment variables
13 array[is_1] of var 0..1: f,
14 constraint 1 == sum(f),
15 constraint forall(i in is_1)(f[i] >= s[i]),
16 constraint x == sum(i in is_1)(xi[i] * f[i] + (xi[i+1]-xi[i]) * s[i]),
17 } in
18 array2d(is_1, 1..2, f++s);
19
20predicate fzn_piecewise_linear(var float: x, var float: y,
21 array[int] of float: xi, array[int] of float: vi) =
22 let {
23 set of int: is = index_set(xi),
24 constraint assert(is == index_set(vi) /\ 0<card(is),
25 "fzn_pwl: index sets unequal or empty"),
26 set of int: is_1 = is diff { max(is) },
27 array[int, int] of var float: fs = fzn_piecewise_linear_base(x, xi),
28 } in
29 y == sum(i in is_1)(vi[i] * fs[i, 1] + (vi[i+1]-vi[i]) * fs[i, 2])
30 ;
31
32%-----------------------------------------------------------------------------%