use new matrix functionality
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Vítor Santos Costa
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b64965f22c
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e19b58cf53
129
library/gecode/clp_examples/3jugs.yap
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129
library/gecode/clp_examples/3jugs.yap
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@ -0,0 +1,129 @@
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% Example with matrices,based on:
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%
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% Three jugs problem in Minzinc modelled as a shortest path problem.
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%
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% Problem from Taha "Introduction to Operations Research", page 245
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%
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% Model created by Hakan Kjellerstrand, hakank@bonetmail.com
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% See also my MiniZinc page: http://www.hakank.org/minizinc
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%
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% VSC: had to transpose the matrix, and change the constraints....
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%
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:- style_check( all ).
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:- use_module(library(gecode/clpfd)).
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:- use_module(library(maplist)).
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:- use_module(library(lists)).
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main :-
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problem(Z, X, InFlow, OutFlow, N),
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out(Z, X, InFlow, OutFlow, N),
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fail.
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main.
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problem(Z, X, InFlow, OutFlow, N) :-
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N = 15,
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Start = 1,
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End = 15,
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M = 999,
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d( M, DD ),
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D = array[1..N,1..N] of DD, % distance
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RHS = array[1..N] of _, % requirements (right hand statement)
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X = array[1..N, 1..N] of 0..1, % the resulting matrix, 1 if connected, 0 else
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OutFlow = array[1..N] of 0..1,
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InFlow = array[1..N] of 0..1,
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% objective to minimize
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Z in 0..M,
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Z #= sum( [I in 1..N, J in 1..N] where D[I,J]<M,
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D[I,J]*X[I,J]),
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% solve minimize z;
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% alternative solve statements which may give faster solution
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%solve :: int_search([ x[i,j] | i,j in 1..n], first_fail, indomain_min, complete) minimize z;
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% solve minimize z;
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minimize(Z),
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% constraint
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for(I in 1..N,
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( I == Start ->
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RHS[I] <== 1 ;
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I == End ->
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RHS[I] <== -1 ;
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RHS[I] <== 0 )
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),
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% must be larger than 0??
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for( [I in 1..N, J in 1..N],
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( D[J,I] = M ->
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X[J,I] #= 0 ;
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true )
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),
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% outflow constraint
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for(I in 1..N,
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OutFlow[I] #= sum(J in 1..N where D[J,I]<M, X[J,I])
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),
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% inflow constraint
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for(J in 1..N,
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InFlow[J] #= sum(I in 1..N where D[J,I]<M, X[J,I])
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),
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% inflow = outflow
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for(I in 1..N, OutFlow[I]-InFlow[I]#=RHS[I]),
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% labeling
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labeling( [], X).
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% data
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d(M, [
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M, 1, M, M, M, M, M, M, 1, M, M, M, M, M, M,
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M, M, 1, M, M, M, M, M, M, M, M, M, M, M, M,
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M, M, M, 1, M, M, M, M, 1, M, M, M, M, M, M,
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M, M, M, M, 1, M, M, M, M, M, M, M, M, M, M,
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M, M, M, M, M, 1, M, M, 1, M, M, M, M, M, M,
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M, M, M, M, M, M, 1, M, M, M, M, M, M, M, M,
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M, M, M, M, M, M, M, 1, 1, M, M, M, M, M, M,
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M, M, M, M, M, M, M, M, M, M, M, M, M, M, 1,
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M, M, M, M, M, M, M, M, M, 1, M, M, M, M, M,
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M, 1, M, M, M, M, M, M, M, M, 1, M, M, M, M,
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M, M, M, M, M, M, M, M, M, M, M, 1, M, M, M,
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M, 1, M, M, M, M, M, M, M, M, M, M, 1, M, M,
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M, M, M, M, M, M, M, M, M, M, M, M, M, 1, M,
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M, 1, M, M, M, M, M, M, M, M, M, M, M, M, 1,
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M, M, M, M, M, M, M, M, M, M, M, M, M, M, M
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]).
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/*
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% shows the result matrix
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output [
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if i = 1 /\ j = 1 then
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"z: " ++ show(z) ++ "\n" ++
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"inFlow: " ++ show(inFlow) ++ "\n" ++ "outFlow: " ++ show(outFlow) ++ "\n" ++
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" 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5\n"
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else "" endif ++
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if j = 1 then show(i) ++ " : " else "" endif ++
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show(x[i,j]) ++ if j = n then "\n" else " " endif
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| i in 1..n, j in 1..n
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];
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*/
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out(Cost, Ts, Ins, Out, N) :-
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format('cost = ~d~n', [Cost]),
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InsL <== list(Ins),
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OutL <== list(Out),
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format('Inputs =', []), maplist(out, InsL), nl,
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format('Outputs =', []), maplist(out, OutL), nl,
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format('transitions =~n', []),
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for(I in 1..N, outl(Ts[_,I]) ).
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outl( X ) :-
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L <== X, % evaluate matrix notation to Prolog lists.
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format(' ', []),
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maplist(out, L), nl.
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out(0) :- format(' .', []).
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out(1) :- format(' 1', []).
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Binary file not shown.
@ -7,6 +7,7 @@
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op(730, yfx, #\),
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op(720, yfx, #/\),
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op(710, fy, #\),
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op(705, xfx, where),
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op(700, xfx, #>),
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op(700, xfx, #<),
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op(700, xfx, #>=),
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@ -34,6 +35,7 @@
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all_distinct/1,
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all_distinct/2,
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maximize/1,
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minimize/1,
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sum/3,
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lex_chain/1,
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minimum/2,
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@ -69,7 +71,17 @@
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:- use_module(library(gecode)).
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:- use_module(library(maplist)).
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:- reexport(library(matrix), [(<==)/2, for/2, for/4]).
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:- reexport(library(matrix), [(<==)/2, for/2, for/4, of/2]).
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% build array of constraints
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%
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matrix:array_extension(_.._ , clpfd:build).
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build( I..J, _, Size, L) :-
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length( L, Size ),
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L ins I..J.
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matrix:rhs_opaque(X) :- constraint(X).
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constraint( (_ #> _) ).
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constraint( (_ #< _) ).
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@ -119,7 +131,6 @@ constraint( fd_size(_, _) ). %2,
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constraint( fd_dom(_, _) ). %2
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process_constraints((B0,B1), (NB0, NB1), Env) :-
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process_constraints(B0, NB0, Env),
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process_constraints(B1, NB1, Env).
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@ -284,14 +295,21 @@ in_dfa( Xs, S0, Ts, Fs ) :-
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labeling(_Opts, Xs) :-
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get_home(Space-Map),
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maplist(ll(Map), Xs, NXs),
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Space += branch(NXs, 'INT_VAR_SIZE_MIN', 'INT_VAL_MIN').
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check( Xs, X1s ),
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( X1s == [] -> true ;
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maplist(ll(Map), X1s, NXs),
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Space += branch(NXs, 'INT_VAR_SIZE_MIN', 'INT_VAL_MIN') ).
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maximize(V) :-
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get_home(Space-Map),
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l(V, I, Map),
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Space += maximize(I).
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minimize(V) :-
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get_home(Space-Map),
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l(V, I, Map),
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Space += minimize(I).
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extensional_constraint( Tuples, TupleSet) :-
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TupleSet := tupleset( Tuples ).
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@ -303,7 +321,11 @@ check(V, NV) :-
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( var(V) -> V = NV ;
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number(V) -> V = NV ;
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is_list(V) -> maplist(check, V, NV) ;
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V = sum(_,_) -> V = NV ;
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V = '[]'(Indx, Mat) -> NV <== '[]'(Indx, Mat) ;
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V = '$matrix'(_, _, _, _, C) -> C =.. [_|L], maplist(check, L, NV) ;
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V = A+B -> check(A,NA), check(B, NB), NV = NB+NA ;
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V = A-B -> check(A,NA), check(B, NB), NV = NB-NA ;
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arith(V, _) -> V =.. [C|L], maplist(check, L, NL), NV =.. [C|NL] ).
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post( ( A #= B), Env, Reify) :-
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@ -318,6 +340,12 @@ post( ( A #>= B), Env, Reify) :-
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post( rel( A, (#>=), B), Env, Reify).
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post( ( A #=< B), Env, Reify) :-
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post( rel( A, (#=<), B), Env, Reify).
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% [X,Y,Z] #<
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post( rel( A, Op), Space-Map, Reify):-
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( var( A ) -> l(A, IA, Map) ; checklist( var, A ) -> maplist(ll(Map), A, IA ) ),
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gecode_arith_op( Op, GOP ),
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(var(Reify) -> Space += rel(IA, GOP) ;
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Space += rel(IA, GOP, Reify) ).
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% X #< Y
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% X #< 2
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post( rel( A, Op, B), Space-Map, Reify):-
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@ -328,11 +356,6 @@ post( rel( A, Op, B), Space-Map, Reify):-
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(var(Reify) -> Space += rel(IA, GOP, IB) ;
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Space += rel(IA, GOP, IB, Reify) ).
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post( rel( A, Op), Space-Map, Reify):-
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( var( A ) -> l(A, IA, Map) ; checklist( var, A ) -> maplist(ll(Map), A, IA ) ),
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gecode_arith_op( Op, GOP ),
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(var(Reify) -> Space += rel(IA, GOP) ;
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Space += rel(IA, GOP, Reify) ).
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% 2 #\= B
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post( rel( A, Op, B), Space-Map, Reify):-
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var(B), integer(A), !,
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@ -340,6 +363,7 @@ post( rel( A, Op, B), Space-Map, Reify):-
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gecode_arith_op( Op, GOP ),
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(var(Reify) -> Space += rel(A, GOP, IB) ;
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Space += rel(A, GOP, IB, Reify) ).
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% sum([A,B,C]) #= X
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post( rel( sum(L), Op, Out), Space-Map, Reify):-
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checklist( var, L ),
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@ -351,6 +375,40 @@ post( rel( sum(L), Op, Out), Space-Map, Reify):-
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Space += linear(IL, GOP, IOut);
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Space += linear(IL, GOP, IOut, Reify)
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).
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% X #= sum([A,B,C])
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post( rel( Out, Op, sum(L)), Space-Map, Reify):-
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checklist( var, L ),
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( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ), !,
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var(Out), !,
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maplist(ll(Map), [Out|L], [IOut|IL] ),
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gecode_arith_op( Op, GOP ),
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(var(Reify) ->
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Space += linear(IL, GOP, IOut);
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Space += linear(IL, GOP, IOut, Reify)
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).
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% sum([I in 0..N-1, M[I]]) #= X
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post( rel( sum(For, Cond), Op, Out), Space-Map, Reify):-
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( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ), !,
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cond2list( For, Cond, Cs, L),
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maplist(ll(Map), [Out|L], [IOut|IL] ),
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gecode_arith_op( Op, GOP ),
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(L = [] -> true ;
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var(Reify) ->
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Space += linear(Cs, IL, GOP, IOut);
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Space += linear(Cs, IL, GOP, IOut, Reify)
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).
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post( rel( Out, Op, sum(For, Cond)), Space-Map, Reify):-
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( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ), !,
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cond2list( For, Cond, Cs, L),
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maplist(ll(Map), [Out|L], [IOut|IL] ),
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gecode_arith_op( Op, GOP ),
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(L = [] -> true ;
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var(Reify) ->
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Space += linear(Cs, IL, GOP, IOut);
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Space += linear(Cs, IL, GOP, IOut, Reify)
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).
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% [A,B,C,D] #< 3
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post( rel( A, Op, B ), Space-Map, Reify):-
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checklist( var, A ), !,
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@ -374,7 +432,7 @@ post( rel( A, Op, B), Space-Map, Reify):-
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(var(Reify) -> Space += rel(IL, GOP, IB) ;
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Space += rel(IL, GOP, IB, Reify) ).
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post( rel(A, Op, B), Space-Map, Reify):-
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( nonvar(A), ( A = _+_ ; A = _-_ ) ;
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( nonvar(A), ( A = _+_ ; A = _-_ ) ;
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nonvar(B), ( B = _ + _ ; B = _-_) ), !,
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linearize(A, 1, As, Bs, CAs, CBs, 0, A0, Space-Map),
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linearize(B, -1, Bs, [], CBs, [], A0, B0, Space-Map),
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@ -532,7 +590,6 @@ arith(min(_,_), min).
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arith(max(_,_), max).
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arith((_ * _), times).
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arith((_ / _), div).
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arith((_ mod _), mod).
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% replace abs(min(A,B)-max(A,B)) by
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% min(A,B,A1), max(A,B,A2), linear([1,-1],[A1,B1],=,A3), abs(A3,AN)
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@ -809,6 +866,17 @@ intvar(Map, V) :-
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get_home(Home) :-
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b_getval(gecode_space, Home).
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cond2list((List where Goal), El, Cs, Vs) :- !,
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for( List, add_el(Goal, El), ([])-([]), Cs-Vs ).
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cond2list(List, El, Cs, Vs) :- !,
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for( List, add_el(true, El), ([])-([]), Cs-Vs ).
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add_el(G0, El, Cs-Vs, [C|Cs]-[V|Vs]) :-
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call(G0), !,
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E <== El,
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( var(E) -> C = 1, E = V ; E = C*V, integer(C), var(V) -> true ; E = V*C, integer(C), var(V) ).
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add_el(_G0, _El, Cs-Vs, Cs-Vs).
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m(NV, OV, NA, NB, Vs) :-
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var(Vs), !,
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Vs = [v(NV,OV,NA,NB)|_].
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