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(bv_r, 48 [ 49 deref/2, 50 deref_var/2, 51 determine_active_dec/1, 52 inf/2, 53 iterate_dec/2, 54 sup/2, 55 var_with_def_assign/2 56 ]). 57:- use_module(nf_r, 58 [ 59 {}/1, 60 entailed/1, 61 nf/2, 62 nf_constant/2, 63 repair/2, 64 wait_linear/3 65 ]). 66 67% bb_inf(Ints,Term,Inf) 68% 69% Finds the infimum of Term where the variables Ints are to be integers. 70% The infimum is stored in Inf. 71 72bb_inf(Is,Term,Inf) :- 73 bb_inf(Is,Term,Inf,_,0.001). 74 75bb_inf(Is,Term,Inf,Vertex,Eps) :- 76 nf(Eps,ENf), 77 nf_constant(ENf,EpsN), 78 wait_linear(Term,Nf,bb_inf_internal(Is,Nf,EpsN,Inf,Vertex)). 79 80% --------------------------------------------------------------------- 81 82% bb_inf_internal(Is,Lin,Eps,Inf,Vertex) 83% 84% Finds an infimum Inf for linear expression in normal form Lin, where 85% all variables in Is are to be integers. Eps denotes the margin in which 86% we accept a number as an integer (to deal with rounding errors etc.). 87 88bb_inf_internal(Is,Lin,Eps,_,_) :- 89 bb_intern(Is,IsNf,Eps), 90 nb_delete(prov_opt), 91 repair(Lin,LinR), % bb_narrow ... 92 deref(LinR,Lind), 93 var_with_def_assign(Dep,Lind), 94 determine_active_dec(Lind), 95 bb_loop(Dep,IsNf,Eps), 96 fail. 97bb_inf_internal(_,_,_,Inf,Vertex) :- 98 catch(nb_getval(prov_opt,InfVal-Vertex),_,fail), 99 {Inf =:= InfVal}, 100 nb_delete(prov_opt). 101 102% bb_loop(Opt,Is,Eps) 103% 104% Minimizes the value of Opt where variables Is have to be integer values. 105% Eps denotes the rounding error that is acceptable. This predicate can be 106% backtracked to try different strategies. 107 108bb_loop(Opt,Is,Eps) :- 109 bb_reoptimize(Opt,Inf), 110 bb_better_bound(Inf), 111 vertex_value(Is,Ivs), 112 ( bb_first_nonint(Is,Ivs,Eps,Viol,Floor,Ceiling) 113 -> bb_branch(Viol,Floor,Ceiling), 114 bb_loop(Opt,Is,Eps) 115 ; round_values(Ivs,RoundVertex), 116 nb_setval(prov_opt,Inf-RoundVertex) % new provisional optimum 117 ). 118 119% bb_reoptimize(Obj,Inf) 120% 121% Minimizes the value of Obj and puts the result in Inf. 122% This new minimization is necessary as making a bound integer may yield a 123% different optimum. The added inequalities may also have led to binding. 124 125bb_reoptimize(Obj,Inf) :- 126 var(Obj), 127 iterate_dec(Obj,Inf). 128bb_reoptimize(Obj,Inf) :- 129 nonvar(Obj), 130 Inf = Obj. 131 132% bb_better_bound(Inf) 133% 134% Checks if the new infimum Inf is better than the previous one (if such exists). 135 136bb_better_bound(Inf) :- 137 catch((nb_getval(prov_opt,Inc-_),Inf - Inc < -1.0e-10),_,true). 138 139% bb_branch(V,U,L) 140% 141% Stores that V =< U or V >= L, can be used for different strategies within bb_loop/3. 142 143bb_branch(V,U,_) :- {V =< U}. 144bb_branch(V,_,L) :- {V >= L}. 145 146% vertex_value(Vars,Values) 147% 148% Returns in <Values> the current values of the variables in <Vars>. 149 150vertex_value([],[]). 151vertex_value([X|Xs],[V|Vs]) :- 152 rhs_value(X,V), 153 vertex_value(Xs,Vs). 154 155% rhs_value(X,Value) 156% 157% Returns in <Value> the current value of variable <X>. 158 159rhs_value(Xn,Value) :- 160 ( nonvar(Xn) 161 -> Value = Xn 162 ; var(Xn) 163 -> deref_var(Xn,Xd), 164 Xd = [I,R|_], 165 Value is R+I 166 ). 167 168% bb_first_nonint(Ints,Rhss,Eps,Viol,Floor,Ceiling) 169% 170% Finds the first variable in Ints which doesn't have an active integer bound. 171% Rhss contain the Rhs (R + I) values corresponding to the variables. 172% The first variable that hasn't got an active integer bound, is returned in 173% Viol. The floor and ceiling of its actual bound is returned in Floor and Ceiling. 174 175bb_first_nonint([I|Is],[Rhs|Rhss],Eps,Viol,F,C) :- 176 ( Floor is floor(Rhs+1.0e-10), 177 Ceiling is ceiling(Rhs-1.0e-10), 178 Eps - min(Rhs-Floor,Ceiling-Rhs) < -1.0e-10 179 -> Viol = I, 180 F = Floor, 181 C = Ceiling 182 ; bb_first_nonint(Is,Rhss,Eps,Viol,F,C) 183 ). 184 185% round_values([X|Xs],[Xr|Xrs]) 186% 187% Rounds of the values of the first list into the second list. 188 189round_values([],[]). 190round_values([X|Xs],[Y|Ys]) :- 191 Y is round(X), 192 round_values(Xs,Ys). 193 194% bb_intern([X|Xs],[Xi|Xis],Eps) 195% 196% Turns the elements of the first list into integers into the second 197% list via bb_intern/4. 198 199bb_intern([],[],_). 200bb_intern([X|Xs],[Xi|Xis],Eps) :- 201 nf(X,Xnf), 202 bb_intern(Xnf,Xi,X,Eps), 203 bb_intern(Xs,Xis,Eps). 204 205 206% bb_intern(Nf,X,Term,Eps) 207% 208% Makes sure that Term which is normalized into Nf, is integer. 209% X contains the possibly changed Term. If Term is a variable, 210% then its bounds are hightened or lowered to the next integer. 211% Otherwise, it is checked it Term is integer. 212 213bb_intern([],X,_,_) :- 214 !, 215 X = 0.0. 216bb_intern([v(I,[])],X,_,Eps) :- 217 !, 218 X = I, 219 min(I-floor(I+1e-010),ceiling(I-1e-010)-I) - Eps < 1e-010. 220bb_intern([v(One,[V^1])],X,_,_) :- 221 Test is One - 1.0, 222 Test =< 1e-010, 223 Test >= -1e-010, 224 !, 225 V = X, 226 bb_narrow_lower(X), 227 bb_narrow_upper(X). 228bb_intern(_,_,Term,_) :- 229 throw(instantiation_error(bb_inf(Term,_,_),1)). 230 231% bb_narrow_lower(X) 232% 233% Narrows the lower bound so that it is an integer bound. 234% We do this by finding the infimum of X and asserting that X 235% is larger than the first integer larger or equal to the infimum 236% (second integer if X is to be strict larger than the first integer). 237 238bb_narrow_lower(X) :- 239 ( inf(X,Inf) 240 -> Bound is ceiling(Inf-1.0e-10), 241 ( entailed(X > Bound) 242 -> {X >= Bound+1} 243 ; {X >= Bound} 244 ) 245 ; true 246 ). 247 248% bb_narrow_upper(X) 249% 250% See bb_narrow_lower/1. This predicate handles the upper bound. 251 252bb_narrow_upper(X) :- 253 ( sup(X,Sup) 254 -> Bound is floor(Sup+1.0e-10), 255 ( entailed(X < Bound) 256 -> {X =< Bound-1} 257 ; {X =< Bound} 258 ) 259 ; true 260 ). 261 262 /******************************* 263 * SANDBOX * 264 *******************************/ 265:- multifile 266 sandbox:safe_primitive/1. 267 268sandbox:safe_primitive(bb_r:bb_inf(_,_,_)). 269sandbox:safe_primitive(bb_r:bb_inf(_,_,_,_,_))