1/* $Id$ 2 3 Part of CPL(R) (Constraint Logic Programming over Reals) 4 5 Author: Leslie De Koninck 6 E-mail: Leslie.DeKoninck@cs.kuleuven.be 7 WWW: http://www.swi-prolog.org 8 http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09 9 Copyright (C): 2004, K.U. Leuven and 10 1992-1995, Austrian Research Institute for 11 Artificial Intelligence (OFAI), 12 Vienna, Austria 13 14 This software is part of Leslie De Koninck's master thesis, supervised 15 by Bart Demoen and daily advisor Tom Schrijvers. It is based on CLP(Q,R) 16 by Christian Holzbaur for SICStus Prolog and distributed under the 17 license details below with permission from all mentioned authors. 18 19 This program is free software; you can redistribute it and/or 20 modify it under the terms of the GNU General Public License 21 as published by the Free Software Foundation; either version 2 22 of the License, or (at your option) any later version. 23 24 This program is distributed in the hope that it will be useful, 25 but WITHOUT ANY WARRANTY; without even the implied warranty of 26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 27 GNU General Public License for more details. 28 29 You should have received a copy of the GNU Lesser General Public 30 License along with this library; if not, write to the Free Software 31 Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 32 33 As a special exception, if you link this library with other files, 34 compiled with a Free Software compiler, to produce an executable, this 35 library does not by itself cause the resulting executable to be covered 36 by the GNU General Public License. This exception does not however 37 invalidate any other reasons why the executable file might be covered by 38 the GNU General Public License. 39*/ 40 41:- module(bb_r, 42 [ 43 bb_inf/3, 44 bb_inf/5, 45 vertex_value/2 46 ]). 47:- use_module(library(error), [type_error/2]). 48:- use_module(bv_r, 49 [ 50 deref/2, 51 deref_var/2, 52 determine_active_dec/1, 53 inf/2, 54 iterate_dec/2, 55 sup/2, 56 var_with_def_assign/2 57 ]). 58:- use_module(nf_r, 59 [ 60 {}/1, 61 entailed/1, 62 nf/2, 63 nf_constant/2, 64 repair/2, 65 wait_linear/3 66 ]). 67 68% bb_inf(Ints,Term,Inf) 69% 70% Finds the infimum of Term where the variables Ints are to be integers. 71% The infimum is stored in Inf. 72 73bb_inf(Is,Term,Inf) :- 74 bb_inf(Is,Term,Inf,_,0.001). 75 76bb_inf(Is,Term,Inf,Vertex,Eps) :- 77 nf(Eps,ENf), 78 nf_constant(ENf,EpsN), 79 wait_linear(Term,Nf,bb_inf_internal(Is,Nf,EpsN,Inf,Vertex)). 80 81% --------------------------------------------------------------------- 82 83% bb_inf_internal(Is,Lin,Eps,Inf,Vertex) 84% 85% Finds an infimum Inf for linear expression in normal form Lin, where 86% all variables in Is are to be integers. Eps denotes the margin in which 87% we accept a number as an integer (to deal with rounding errors etc.). 88 89% The incumbent must survive the backtracking that drives the search, but 90% it must not survive the call itself. It is therefore kept in a mutable 91% term that is local to this call rather than in a global variable, which 92% would clobber a global of the same name in the calling program and would 93% make nested calls interfere. 94 95bb_inf_internal(Is,Lin,Eps,Inf,Vertex) :- 96 State = state(none), 97 ( bb_intern(Is,IsNf,Eps), 98 repair(Lin,LinR), % bb_narrow ... 99 deref(LinR,Lind), 100 var_with_def_assign(Dep,Lind), 101 determine_active_dec(Lind), 102 bb_loop(Dep,IsNf,Eps,State), 103 fail 104 ; arg(1,State,InfVal-Vertex), 105 {Inf =:= InfVal} 106 ). 107 108% bb_loop(Opt,Is,Eps,State) 109% 110% Minimizes the value of Opt where variables Is have to be integer values. 111% Eps denotes the rounding error that is acceptable. This predicate can be 112% backtracked to try different strategies. 113 114bb_loop(Opt,Is,Eps,State) :- 115 bb_reoptimize(Opt,Inf), 116 bb_better_bound(State,Inf), 117 vertex_value(Is,Ivs), 118 ( bb_first_nonint(Is,Ivs,Eps,Viol,Floor,Ceiling) 119 -> bb_branch(Viol,Floor,Ceiling), 120 bb_loop(Opt,Is,Eps,State) 121 ; round_values(Ivs,RoundVertex), 122 nb_setarg(1,State,Inf-RoundVertex) % new provisional optimum 123 ). 124 125% bb_reoptimize(Obj,Inf) 126% 127% Minimizes the value of Obj and puts the result in Inf. 128% This new minimization is necessary as making a bound integer may yield a 129% different optimum. The added inequalities may also have led to binding. 130 131bb_reoptimize(Obj,Inf) :- 132 ( var(Obj) 133 -> iterate_dec(Obj,Inf) 134 ; Inf = Obj 135 ). 136 137% bb_better_bound(State,Inf) 138% 139% Checks if the new infimum Inf is better than the previous one (if such exists). 140 141bb_better_bound(State,Inf) :- 142 arg(1,State,Best), 143 ( Best = Inc-_ 144 -> Inf - Inc < -1.0e-10 145 ; true 146 ). 147 148% bb_branch(V,U,L) 149% 150% Stores that V =< U or V >= L, can be used for different strategies within bb_loop/3. 151 152bb_branch(V,U,_) :- {V =< U}. 153bb_branch(V,_,L) :- {V >= L}. 154 155% vertex_value(Vars,Values) 156% 157% Returns in <Values> the current values of the variables in <Vars>. 158 159vertex_value([],[]). 160vertex_value([X|Xs],[V|Vs]) :- 161 rhs_value(X,V), 162 vertex_value(Xs,Vs). 163 164% rhs_value(X,Value) 165% 166% Returns in <Value> the current value of variable <X>. 167 168rhs_value(Xn,Value) :- 169 ( nonvar(Xn) 170 -> Value = Xn 171 ; var(Xn) 172 -> deref_var(Xn,Xd), 173 Xd = [I,R|_], 174 Value is R+I 175 ). 176 177% bb_first_nonint(Ints,Rhss,Eps,Viol,Floor,Ceiling) 178% 179% Finds the first variable in Ints which doesn't have an active integer bound. 180% Rhss contain the Rhs (R + I) values corresponding to the variables. 181% The first variable that hasn't got an active integer bound, is returned in 182% Viol. The floor and ceiling of its actual bound is returned in Floor and Ceiling. 183 184bb_first_nonint([I|Is],[Rhs|Rhss],Eps,Viol,F,C) :- 185 ( Floor is floor(Rhs+1.0e-10), 186 Ceiling is ceiling(Rhs-1.0e-10), 187 Eps - min(Rhs-Floor,Ceiling-Rhs) < -1.0e-10 188 -> Viol = I, 189 F = Floor, 190 C = Ceiling 191 ; bb_first_nonint(Is,Rhss,Eps,Viol,F,C) 192 ). 193 194% round_values([X|Xs],[Xr|Xrs]) 195% 196% Rounds of the values of the first list into the second list. 197 198round_values([],[]). 199round_values([X|Xs],[Y|Ys]) :- 200 Y is round(X), 201 round_values(Xs,Ys). 202 203% bb_intern([X|Xs],[Xi|Xis],Eps) 204% 205% Turns the elements of the first list into integers into the second 206% list via bb_intern/4. 207 208bb_intern([],[],_). 209bb_intern([X|Xs],[Xi|Xis],Eps) :- 210 nf(X,Xnf), 211 bb_intern(Xnf,Xi,X,Eps), 212 bb_intern(Xs,Xis,Eps). 213 214 215% bb_intern(Nf,X,Term,Eps) 216% 217% Makes sure that Term which is normalized into Nf, is integer. 218% X contains the possibly changed Term. If Term is a variable, 219% then its bounds are hightened or lowered to the next integer. 220% Otherwise, it is checked it Term is integer. 221 222bb_intern([],X,_,_) :- 223 !, 224 X = 0.0. 225bb_intern([v(I,[])],X,_,Eps) :- 226 !, 227 X = I, 228 min(I-floor(I+1e-010),ceiling(I-1e-010)-I) - Eps < 1e-010. 229bb_intern([v(One,[V^1])],X,_,_) :- 230 Test is One - 1.0, 231 Test =< 1e-010, 232 Test >= -1e-010, 233 !, 234 V = X, 235 bb_narrow_lower(X), 236 bb_narrow_upper(X). 237bb_intern(_,_,Term,_) :- 238 type_error(var, Term). 239 240% bb_narrow_lower(X) 241% 242% Narrows the lower bound so that it is an integer bound. 243% We do this by finding the infimum of X and asserting that X 244% is larger than the first integer larger or equal to the infimum 245% (second integer if X is to be strict larger than the first integer). 246 247bb_narrow_lower(X) :- 248 ( inf(X,Inf) 249 -> Bound is ceiling(Inf-1.0e-10), 250 ( entailed(X > Bound) 251 -> {X >= Bound+1} 252 ; {X >= Bound} 253 ) 254 ; true 255 ). 256 257% bb_narrow_upper(X) 258% 259% See bb_narrow_lower/1. This predicate handles the upper bound. 260 261bb_narrow_upper(X) :- 262 ( sup(X,Sup) 263 -> Bound is floor(Sup+1.0e-10), 264 ( entailed(X < Bound) 265 -> {X =< Bound-1} 266 ; {X =< Bound} 267 ) 268 ; true 269 ). 270 271 /******************************* 272 * SANDBOX * 273 *******************************/ 274:- multifile 275 sandbox:safe_primitive/1. 276 277sandbox:safe_primitive(bb_r:bb_inf(_,_,_)). 278sandbox:safe_primitive(bb_r:bb_inf(_,_,_,_,_))