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dekker.one
1int: w = 4;
2int: h = 4;
3
4% arraydec
5set of int: HEIGHT = 0..h;
6set of int: CHEIGHT = 1..h-1;
7set of int: WIDTH = 0..w;
8set of int: CWIDTH = 1..w-1;
9array[HEIGHT,WIDTH] of var float: t; % temperature at point (i,j)
10var float: left; % left edge temperature
11var float: right; % right edge temperature
12var float: top; % top edge temperature
13var float: bottom; % bottom edge temperature
14
15% equation
16% Laplace equation: each internal temp. is average of its neighbours
17constraint forall(i in CHEIGHT, j in CWIDTH)(
18 4.0*t[i,j] = t[i-1,j] + t[i,j-1] + t[i+1,j] + t[i,j+1]);
19% sides
20% edge constraints
21constraint forall(i in CHEIGHT)(t[i,0] = left);
22constraint forall(i in CHEIGHT)(t[i,w] = right);
23constraint forall(j in CWIDTH)(t[0,j] = top);
24constraint forall(j in CWIDTH)(t[h,j] = bottom);
25% corners
26% corner constraints
27constraint t[0,0]=0.0;
28constraint t[0,w]=0.0;
29constraint t[h,0]=0.0;
30constraint t[h,w]=0.0;
31left = 0.0;
32right = 0.0;
33top = 100.0;
34bottom = 0.0;
35
36solve satisfy;
37
38output [ show_float(6, 2, t[i,j]) ++
39 if j == w then "\n" else " " endif |
40 i in HEIGHT, j in WIDTH
41];