1282 lines
35 KiB
Perl
1282 lines
35 KiB
Perl
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/* $Id$
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Part of CLP(Q) (Constraint Logic Programming over Rationals)
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Author: Leslie De Koninck
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E-mail: Leslie.DeKoninck@cs.kuleuven.be
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WWW: http://www.swi-prolog.org
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http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09
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Copyright (C): 2006, K.U. Leuven and
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1992-1995, Austrian Research Institute for
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Artificial Intelligence (OFAI),
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Vienna, Austria
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This software is based on CLP(Q,R) by Christian Holzbaur for SICStus
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Prolog and distributed under the license details below with permission from
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all mentioned authors.
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This program is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public License
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as published by the Free Software Foundation; either version 2
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of the License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, write to the Free Software
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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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As a special exception, if you link this library with other files,
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compiled with a Free Software compiler, to produce an executable, this
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library does not by itself cause the resulting executable to be covered
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by the GNU General Public License. This exception does not however
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invalidate any other reasons why the executable file might be covered by
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the GNU General Public License.
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*/
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:- module(ineq_q,
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[
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ineq/4,
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ineq_one/4,
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ineq_one_n_n_0/1,
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ineq_one_n_p_0/1,
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ineq_one_s_n_0/1,
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ineq_one_s_p_0/1
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]).
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:- use_module(bv_q,
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[
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backsubst/3,
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backsubst_delta/4,
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basis_add/2,
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dec_step/2,
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deref/2,
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determine_active_dec/1,
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determine_active_inc/1,
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export_binding/1,
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get_or_add_class/2,
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inc_step/2,
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lb/3,
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pivot_a/4,
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rcbl_status/6,
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reconsider/1,
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same_class/2,
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solve/1,
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ub/3,
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unconstrained/4,
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var_intern/3,
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var_with_def_intern/4
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]).
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:- use_module(store_q,
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[
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add_linear_11/3,
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add_linear_ff/5,
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normalize_scalar/2
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]).
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% ineq(H,I,Nf,Strictness)
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%
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% Solves the inequality Nf < 0 or Nf =< 0 where Nf is in normal form
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% and H and I are the homogene and inhomogene parts of Nf.
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ineq([],I,_,Strictness) :- ineq_ground(Strictness,I).
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ineq([v(K,[X^1])|Tail],I,Lin,Strictness) :-
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ineq_cases(Tail,I,Lin,Strictness,X,K).
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ineq_cases([],I,_,Strictness,X,K) :- % K*X + I < 0 or K*X + I =< 0
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ineq_one(Strictness,X,K,I).
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ineq_cases([_|_],_,Lin,Strictness,_,_) :-
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deref(Lin,Lind), % Id+Hd =< 0
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Lind = [Inhom,_|Hom],
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ineq_more(Hom,Inhom,Lind,Strictness).
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% ineq_ground(Strictness,I)
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%
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% Checks whether a grounded inequality I < 0 or I =< 0 is satisfied.
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ineq_ground(strict,I) :- I < 0.
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ineq_ground(nonstrict,I) :- I =< 0.
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% ineq_one(Strictness,X,K,I)
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%
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% Solves the inequality K*X + I < 0 or K*X + I =< 0
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ineq_one(strict,X,K,I) :-
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( K > 0
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-> ( I =:= 0
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-> ineq_one_s_p_0(X) % K*X < 0, K > 0 => X < 0
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; Inhom is I rdiv K,
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ineq_one_s_p_i(X,Inhom) % K*X + I < 0, K > 0 => X + I/K < 0
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)
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; ( I =:= 0
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-> ineq_one_s_n_0(X) % K*X < 0, K < 0 => -X < 0
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; Inhom is -I rdiv K,
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ineq_one_s_n_i(X,Inhom) % K*X + I < 0, K < 0 => -X - I/K < 0
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)
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).
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ineq_one(nonstrict,X,K,I) :-
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( K > 0
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-> ( I =:= 0
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-> ineq_one_n_p_0(X) % K*X =< 0, K > 0 => X =< 0
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; Inhom is I rdiv K,
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ineq_one_n_p_i(X,Inhom) % K*X + I =< 0, K > 0 => X + I/K =< 0
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)
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; ( I =:= 0
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-> ineq_one_n_n_0(X) % K*X =< 0, K < 0 => -X =< 0
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; Inhom is -I rdiv K,
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ineq_one_n_n_i(X,Inhom) % K*X + I =< 0, K < 0 => -X - I/K =< 0
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)
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).
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% --------------------------- strict ----------------------------
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% ineq_one_s_p_0(X)
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%
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% Solves the inequality X < 0
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ineq_one_s_p_0(X) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!, % old variable, this is deref
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_s_p_0(OrdX,X,Ix)
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).
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ineq_one_s_p_0(X) :- % new variable, nothing depends on it
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var_intern(t_u(0),X,1). % put a strict inactive upperbound on the variable
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% ineq_one_s_n_0(X)
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%
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% Solves the inequality X > 0
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ineq_one_s_n_0(X) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!,
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_s_n_0(OrdX,X,Ix)
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).
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ineq_one_s_n_0(X) :-
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var_intern(t_l(0),X,2). % puts a strict inactive lowerbound on the variable
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% ineq_one_s_p_i(X,I)
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%
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% Solves the inequality X < -I
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ineq_one_s_p_i(X,I) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!,
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_s_p_i(OrdX,I,X,Ix)
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).
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ineq_one_s_p_i(X,I) :-
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Bound is -I,
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var_intern(t_u(Bound),X,1). % puts a strict inactive upperbound on the variable
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% ineq_one_s_n_i(X,I)
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%
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% Solves the inequality X > I
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ineq_one_s_n_i(X,I) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!,
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_s_n_i(OrdX,I,X,Ix)
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).
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ineq_one_s_n_i(X,I) :- var_intern(t_l(I),X,2). % puts a strict inactive lowerbound on the variable
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% ineq_one_old_s_p_0(Hom,X,Inhom)
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%
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% Solves the inequality X < 0 where X has linear equation Hom + Inhom
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ineq_one_old_s_p_0([],_,Ix) :- Ix < 0. % X = I: Ix < 0
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ineq_one_old_s_p_0([l(Y*Ky,_)|Tail],X,Ix) :-
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( Tail = [] % X = K*Y + I
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-> Bound is -Ix rdiv Ky,
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update_indep(strict,Y,Ky,Bound) % X < 0, X = K*Y + I => Y < -I/K or Y > -I/K (depending on K)
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; Tail = [_|_]
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-> get_attr(X,itf,Att),
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arg(2,Att,type(Type)),
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arg(3,Att,strictness(Old)),
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arg(4,Att,lin(Lin)),
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udus(Type,X,Lin,0,Old) % update strict upperbound
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).
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% ineq_one_old_s_p_0(Hom,X,Inhom)
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%
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% Solves the inequality X > 0 where X has linear equation Hom + Inhom
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ineq_one_old_s_n_0([],_,Ix) :- Ix > 0. % X = I: Ix > 0
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ineq_one_old_s_n_0([l(Y*Ky,_)|Tail], X, Ix) :-
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( Tail = [] % X = K*Y + I
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-> Coeff is -Ky,
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Bound is Ix rdiv Coeff,
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update_indep(strict,Y,Coeff,Bound)
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; Tail = [_|_]
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-> get_attr(X,itf,Att),
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arg(2,Att,type(Type)),
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arg(3,Att,strictness(Old)),
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arg(4,Att,lin(Lin)),
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udls(Type,X,Lin,0,Old) % update strict lowerbound
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).
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% ineq_one_old_s_p_i(Hom,C,X,Inhom)
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%
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% Solves the inequality X + C < 0 where X has linear equation Hom + Inhom
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ineq_one_old_s_p_i([],I,_,Ix) :- I + Ix < 0. % X = I
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ineq_one_old_s_p_i([l(Y*Ky,_)|Tail],I,X,Ix) :-
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( Tail = [] % X = K*Y + I
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-> Bound is -(Ix + I) rdiv Ky,
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update_indep(strict,Y,Ky,Bound)
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; Tail = [_|_]
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-> Bound is -I,
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get_attr(X,itf,Att),
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arg(2,Att,type(Type)),
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arg(3,Att,strictness(Old)),
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arg(4,Att,lin(Lin)),
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udus(Type,X,Lin,Bound,Old) % update strict upperbound
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).
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% ineq_one_old_s_n_i(Hom,C,X,Inhom)
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%
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% Solves the inequality X - C > 0 where X has linear equation Hom + Inhom
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ineq_one_old_s_n_i([],I,_,Ix) :- I - Ix < 0. % X = I
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ineq_one_old_s_n_i([l(Y*Ky,_)|Tail],I,X,Ix) :-
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( Tail = [] % X = K*Y + I
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-> Coeff is -Ky,
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Bound is (Ix - I) rdiv Coeff,
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update_indep(strict,Y,Coeff,Bound)
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; Tail = [_|_]
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-> get_attr(X,itf,Att),
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arg(2,Att,type(Type)),
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arg(3,Att,strictness(Old)),
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arg(4,Att,lin(Lin)),
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udls(Type,X,Lin,I,Old) % update strict lowerbound
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).
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% -------------------------- nonstrict --------------------------
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% ineq_one_n_p_0(X)
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%
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% Solves the inequality X =< 0
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ineq_one_n_p_0(X) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!, % old variable, this is deref
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_n_p_0(OrdX,X,Ix)
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).
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ineq_one_n_p_0(X) :- % new variable, nothing depends on it
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var_intern(t_u(0),X,0). % nonstrict upperbound
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% ineq_one_n_n_0(X)
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%
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% Solves the inequality X >= 0
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ineq_one_n_n_0(X) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!,
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_n_n_0(OrdX,X,Ix)
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).
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ineq_one_n_n_0(X) :-
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var_intern(t_l(0),X,0). % nonstrict lowerbound
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% ineq_one_n_p_i(X,I)
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%
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% Solves the inequality X =< -I
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ineq_one_n_p_i(X,I) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!,
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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; ineq_one_old_n_p_i(OrdX,I,X,Ix)
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).
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ineq_one_n_p_i(X,I) :-
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Bound is -I,
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var_intern(t_u(Bound),X,0). % nonstrict upperbound
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% ineq_one_n_n_i(X,I)
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%
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% Solves the inequality X >= I
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ineq_one_n_n_i(X,I) :-
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get_attr(X,itf,Att),
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arg(4,Att,lin([Ix,_|OrdX])),
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!,
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( \+ arg(1,Att,clpq)
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-> throw(error(permission_error('mix CLP(Q) variables with',
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'CLP(R) variables:',X),context(_)))
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|
; ineq_one_old_n_n_i(OrdX,I,X,Ix)
|
||
|
|
).
|
||
|
|
ineq_one_n_n_i(X,I) :-
|
||
|
|
var_intern(t_l(I),X,0). % nonstrict lowerbound
|
||
|
|
|
||
|
|
% ineq_one_old_n_p_0(Hom,X,Inhom)
|
||
|
|
%
|
||
|
|
% Solves the inequality X =< 0 where X has linear equation Hom + Inhom
|
||
|
|
|
||
|
|
ineq_one_old_n_p_0([],_,Ix) :- Ix =< 0. % X =I
|
||
|
|
ineq_one_old_n_p_0([l(Y*Ky,_)|Tail],X,Ix) :-
|
||
|
|
( Tail = [] % X = K*Y + I
|
||
|
|
-> Bound is -Ix rdiv Ky,
|
||
|
|
update_indep(nonstrict,Y,Ky,Bound)
|
||
|
|
; Tail = [_|_]
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
arg(2,Att,type(Type)),
|
||
|
|
arg(3,Att,strictness(Old)),
|
||
|
|
arg(4,Att,lin(Lin)),
|
||
|
|
udu(Type,X,Lin,0,Old) % update nonstrict upperbound
|
||
|
|
).
|
||
|
|
|
||
|
|
% ineq_one_old_n_n_0(Hom,X,Inhom)
|
||
|
|
%
|
||
|
|
% Solves the inequality X >= 0 where X has linear equation Hom + Inhom
|
||
|
|
|
||
|
|
ineq_one_old_n_n_0([],_,Ix) :- Ix >= 0. % X = I
|
||
|
|
ineq_one_old_n_n_0([l(Y*Ky,_)|Tail], X, Ix) :-
|
||
|
|
( Tail = [] % X = K*Y + I
|
||
|
|
-> Coeff is -Ky,
|
||
|
|
Bound is Ix rdiv Coeff,
|
||
|
|
update_indep(nonstrict,Y,Coeff,Bound)
|
||
|
|
; Tail = [_|_]
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
arg(2,Att,type(Type)),
|
||
|
|
arg(3,Att,strictness(Old)),
|
||
|
|
arg(4,Att,lin(Lin)),
|
||
|
|
udl(Type,X,Lin,0,Old) % update nonstrict lowerbound
|
||
|
|
).
|
||
|
|
|
||
|
|
% ineq_one_old_n_p_i(Hom,C,X,Inhom)
|
||
|
|
%
|
||
|
|
% Solves the inequality X + C =< 0 where X has linear equation Hom + Inhom
|
||
|
|
|
||
|
|
ineq_one_old_n_p_i([],I,_,Ix) :- I + Ix =< 0. % X = I
|
||
|
|
ineq_one_old_n_p_i([l(Y*Ky,_)|Tail],I,X,Ix) :-
|
||
|
|
( Tail = [] % X = K*Y + I
|
||
|
|
-> Bound is -(Ix + I) rdiv Ky,
|
||
|
|
update_indep(nonstrict,Y,Ky,Bound)
|
||
|
|
; Tail = [_|_]
|
||
|
|
-> Bound is -I,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
arg(2,Att,type(Type)),
|
||
|
|
arg(3,Att,strictness(Old)),
|
||
|
|
arg(4,Att,lin(Lin)),
|
||
|
|
udu(Type,X,Lin,Bound,Old) % update nonstrict upperbound
|
||
|
|
).
|
||
|
|
|
||
|
|
% ineq_one_old_n_n_i(Hom,C,X,Inhom)
|
||
|
|
%
|
||
|
|
% Solves the inequality X - C >= 0 where X has linear equation Hom + Inhom
|
||
|
|
|
||
|
|
ineq_one_old_n_n_i([],I,_,Ix) :- I - Ix =< 0. % X = I
|
||
|
|
ineq_one_old_n_n_i([l(Y*Ky,_)|Tail],I,X,Ix) :-
|
||
|
|
( Tail = []
|
||
|
|
-> Coeff is -Ky,
|
||
|
|
Bound is (Ix - I) rdiv Coeff,
|
||
|
|
update_indep(nonstrict,Y,Coeff,Bound)
|
||
|
|
; Tail = [_|_]
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
arg(2,Att,type(Type)),
|
||
|
|
arg(3,Att,strictness(Old)),
|
||
|
|
arg(4,Att,lin(Lin)),
|
||
|
|
udl(Type,X,Lin,I,Old)
|
||
|
|
).
|
||
|
|
|
||
|
|
% ---------------------------------------------------------------
|
||
|
|
|
||
|
|
% ineq_more(Hom,Inhom,Lin,Strictness)
|
||
|
|
%
|
||
|
|
% Solves the inequality Lin < 0 or Lin =< 0 with Lin = Hom + Inhom
|
||
|
|
|
||
|
|
ineq_more([],I,_,Strictness) :- ineq_ground(Strictness,I). % I < 0 or I =< 0
|
||
|
|
ineq_more([l(X*K,_)|Tail],Id,Lind,Strictness) :-
|
||
|
|
( Tail = []
|
||
|
|
-> % X*K < Id or X*K =< Id
|
||
|
|
% one var: update bound instead of slack introduction
|
||
|
|
get_or_add_class(X,_), % makes sure X belongs to a class
|
||
|
|
Bound is -Id rdiv K,
|
||
|
|
update_indep(Strictness,X,K,Bound) % new bound
|
||
|
|
; Tail = [_|_]
|
||
|
|
-> ineq_more(Strictness,Lind)
|
||
|
|
).
|
||
|
|
|
||
|
|
% ineq_more(Strictness,Lin)
|
||
|
|
%
|
||
|
|
% Solves the inequality Lin < 0 or Lin =< 0
|
||
|
|
|
||
|
|
ineq_more(strict,Lind) :-
|
||
|
|
( unconstrained(Lind,U,K,Rest)
|
||
|
|
-> % never fails, no implied value
|
||
|
|
% Lind < 0 => Rest < -K*U where U has no bounds
|
||
|
|
var_intern(t_l(0),S,2), % create slack variable S
|
||
|
|
get_attr(S,itf,AttS),
|
||
|
|
arg(5,AttS,order(OrdS)),
|
||
|
|
Ki is -1 rdiv K,
|
||
|
|
add_linear_ff(Rest,Ki,[0,0,l(S*1,OrdS)],Ki,LinU), % U = (-1/K)*Rest + (-1/K)*S
|
||
|
|
LinU = [_,_|Hu],
|
||
|
|
get_or_add_class(U,Class),
|
||
|
|
same_class(Hu,Class), % put all variables of new lin. eq. of U in the same class
|
||
|
|
get_attr(U,itf,AttU),
|
||
|
|
arg(5,AttU,order(OrdU)),
|
||
|
|
arg(6,AttU,class(ClassU)),
|
||
|
|
backsubst(ClassU,OrdU,LinU) % substitute U by new lin. eq. everywhere in the class
|
||
|
|
; var_with_def_intern(t_u(0),S,Lind,1), % Lind < 0 => Lind = S with S < 0
|
||
|
|
basis_add(S,_), % adds S to the basis
|
||
|
|
determine_active_dec(Lind), % activate bounds
|
||
|
|
reconsider(S) % reconsider basis
|
||
|
|
).
|
||
|
|
ineq_more(nonstrict,Lind) :-
|
||
|
|
( unconstrained(Lind,U,K,Rest)
|
||
|
|
-> % never fails, no implied value
|
||
|
|
% Lind =< 0 => Rest =< -K*U where U has no bounds
|
||
|
|
var_intern(t_l(0),S,0), % create slack variable S
|
||
|
|
Ki is -1 rdiv K,
|
||
|
|
get_attr(S,itf,AttS),
|
||
|
|
arg(5,AttS,order(OrdS)),
|
||
|
|
add_linear_ff(Rest,Ki,[0,0,l(S*1,OrdS)],Ki,LinU), % U = (-1K)*Rest + (-1/K)*S
|
||
|
|
LinU = [_,_|Hu],
|
||
|
|
get_or_add_class(U,Class),
|
||
|
|
same_class(Hu,Class), % put all variables of new lin. eq of U in the same class
|
||
|
|
get_attr(U,itf,AttU),
|
||
|
|
arg(5,AttU,order(OrdU)),
|
||
|
|
arg(6,AttU,class(ClassU)),
|
||
|
|
backsubst(ClassU,OrdU,LinU) % substitute U by new lin. eq. everywhere in the class
|
||
|
|
; % all variables are constrained
|
||
|
|
var_with_def_intern(t_u(0),S,Lind,0), % Lind =< 0 => Lind = S with S =< 0
|
||
|
|
basis_add(S,_), % adds S to the basis
|
||
|
|
determine_active_dec(Lind),
|
||
|
|
reconsider(S)
|
||
|
|
).
|
||
|
|
|
||
|
|
|
||
|
|
% update_indep(Strictness,X,K,Bound)
|
||
|
|
%
|
||
|
|
% Updates the bound of independent variable X where X < Bound or X =< Bound
|
||
|
|
% or X > Bound or X >= Bound, depending on Strictness and K.
|
||
|
|
|
||
|
|
update_indep(strict,X,K,Bound) :-
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
arg(2,Att,type(Type)),
|
||
|
|
arg(3,Att,strictness(Old)),
|
||
|
|
arg(4,Att,lin(Lin)),
|
||
|
|
( K < 0
|
||
|
|
-> uils(Type,X,Lin,Bound,Old) % update independent lowerbound strict
|
||
|
|
; uius(Type,X,Lin,Bound,Old) % update independent upperbound strict
|
||
|
|
).
|
||
|
|
update_indep(nonstrict,X,K,Bound) :-
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
arg(2,Att,type(Type)),
|
||
|
|
arg(3,Att,strictness(Old)),
|
||
|
|
arg(4,Att,lin(Lin)),
|
||
|
|
( K < 0
|
||
|
|
-> uil(Type,X,Lin,Bound,Old) % update independent lowerbound nonstrict
|
||
|
|
; uiu(Type,X,Lin,Bound,Old) % update independent upperbound nonstrict
|
||
|
|
).
|
||
|
|
|
||
|
|
|
||
|
|
% ---------------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
%
|
||
|
|
% Update a bound on a var xi
|
||
|
|
%
|
||
|
|
% a) independent variable
|
||
|
|
%
|
||
|
|
% a1) update inactive bound: done
|
||
|
|
%
|
||
|
|
% a2) update active bound:
|
||
|
|
% Determine [lu]b including most constraining row R
|
||
|
|
% If we are within: done
|
||
|
|
% else pivot(R,xi) and introduce bound via (b)
|
||
|
|
%
|
||
|
|
% a3) introduce a bound on an unconstrained var:
|
||
|
|
% All vars that depend on xi are unconstrained (invariant) ->
|
||
|
|
% the bound cannot invalidate any Lhs
|
||
|
|
%
|
||
|
|
% b) dependent variable
|
||
|
|
%
|
||
|
|
% repair upper or lower (maybe just swap with an unconstrained var from Rhs)
|
||
|
|
%
|
||
|
|
|
||
|
|
%
|
||
|
|
% Sign = 1,0,-1 means inside,at,outside
|
||
|
|
%
|
||
|
|
|
||
|
|
% Read following predicates as update (dependent/independent) (lowerbound/upperbound) (strict)
|
||
|
|
|
||
|
|
% udl(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates lower bound of dependent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new non-strict
|
||
|
|
% bound Bound.
|
||
|
|
|
||
|
|
udl(t_none,X,Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,AttX),
|
||
|
|
arg(5,AttX,order(Ord)),
|
||
|
|
setarg(2,AttX,type(t_l(Bound))),
|
||
|
|
setarg(3,AttX,strictness(0)),
|
||
|
|
( unconstrained(Lin,Uc,Kuc,Rest)
|
||
|
|
-> Ki is -1 rdiv Kuc,
|
||
|
|
add_linear_ff(Rest,Ki,[0,0,l(X* -1,Ord)],Ki,LinU),
|
||
|
|
get_attr(Uc,itf,AttU),
|
||
|
|
arg(5,AttU,order(OrdU)),
|
||
|
|
arg(6,AttU,class(Class)),
|
||
|
|
backsubst(Class,OrdU,LinU)
|
||
|
|
; basis_add(X,_),
|
||
|
|
determine_active_inc(Lin),
|
||
|
|
reconsider(X)
|
||
|
|
).
|
||
|
|
udl(t_l(L),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_l(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_lower(X,Lin,Bound)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
|
||
|
|
udl(t_u(U),X,Lin,Bound,_Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
reconsider_lower(X,Lin,Bound) % makes sure that Lin still satisfies lowerbound Bound
|
||
|
|
; Bound =:= U,
|
||
|
|
solve_bound(Lin,Bound) % new bound is equal to upperbound: solve
|
||
|
|
).
|
||
|
|
udl(t_lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> ( Bound < U
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_lower(X,Lin,Bound)
|
||
|
|
; Bound =:= U,
|
||
|
|
Sold /\ 1 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
|
||
|
|
% udls(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates lower bound of dependent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new strict
|
||
|
|
% bound Bound.
|
||
|
|
|
||
|
|
udls(t_none,X,Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,AttX),
|
||
|
|
arg(5,AttX,order(Ord)),
|
||
|
|
setarg(2,AttX,type(t_l(Bound))),
|
||
|
|
setarg(3,AttX,strictness(2)),
|
||
|
|
( unconstrained(Lin,Uc,Kuc,Rest)
|
||
|
|
-> % X = Lin => U = -1/K*Rest + 1/K*X with U an unconstrained variable
|
||
|
|
Ki is -1 rdiv Kuc,
|
||
|
|
add_linear_ff(Rest,Ki,[0,0,l(X* -1,Ord)],Ki,LinU),
|
||
|
|
get_attr(Uc,itf,AttU),
|
||
|
|
arg(5,AttU,order(OrdU)),
|
||
|
|
arg(6,AttU,class(Class)),
|
||
|
|
backsubst(Class,OrdU,LinU)
|
||
|
|
; % no unconstrained variables: add X to basis and reconsider basis
|
||
|
|
basis_add(X,_),
|
||
|
|
determine_active_inc(Lin),
|
||
|
|
reconsider(X)
|
||
|
|
).
|
||
|
|
udls(t_l(L),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true
|
||
|
|
; Bound > L
|
||
|
|
-> Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_l(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_lower(X,Lin,Bound)
|
||
|
|
; % equal to lowerbound: check strictness
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
udls(t_u(U),X,Lin,Bound,Sold) :-
|
||
|
|
Bound < U, % smaller than upperbound: set new bound
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_lower(X,Lin,Bound).
|
||
|
|
udls(t_lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true % smaller than lowerbound: keep
|
||
|
|
; Bound > L
|
||
|
|
-> % larger than lowerbound: check upperbound and possibly use new and reconsider basis
|
||
|
|
Bound < U,
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_lower(X,Lin,Bound)
|
||
|
|
; % equal to lowerbound: put new strictness
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
|
||
|
|
% udu(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates upper bound of dependent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new non-strict
|
||
|
|
% bound Bound.
|
||
|
|
|
||
|
|
udu(t_none,X,Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,AttX),
|
||
|
|
arg(5,AttX,order(Ord)),
|
||
|
|
setarg(2,AttX,type(t_u(Bound))),
|
||
|
|
setarg(3,AttX,strictness(0)),
|
||
|
|
( unconstrained(Lin,Uc,Kuc,Rest)
|
||
|
|
-> % X = Lin => U = -1/K*Rest + 1/K*X with U an unconstrained variable
|
||
|
|
Ki is -1 rdiv Kuc,
|
||
|
|
add_linear_ff(Rest,Ki,[0,0,l(X* -1,Ord)],Ki,LinU),
|
||
|
|
get_attr(Uc,itf,AttU),
|
||
|
|
arg(5,AttU,order(OrdU)),
|
||
|
|
arg(6,AttU,class(Class)),
|
||
|
|
backsubst(Class,OrdU,LinU)
|
||
|
|
; % no unconstrained variables: add X to basis and reconsider basis
|
||
|
|
basis_add(X,_),
|
||
|
|
determine_active_dec(Lin), % try to lower R
|
||
|
|
reconsider(X)
|
||
|
|
).
|
||
|
|
udu(t_u(U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> Strict is Sold /\ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_u(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_upper(X,Lin,Bound)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
udu(t_l(L),X,Lin,Bound,_Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
reconsider_upper(X,Lin,Bound)
|
||
|
|
; Bound =:= L,
|
||
|
|
solve_bound(Lin,Bound) % equal to lowerbound: solve
|
||
|
|
).
|
||
|
|
udu(t_lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> ( Bound > L
|
||
|
|
-> Strict is Sold /\ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_upper(X,Lin,Bound)
|
||
|
|
; Bound =:= L,
|
||
|
|
Sold /\ 2 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
|
||
|
|
% udus(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates upper bound of dependent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new strict
|
||
|
|
% bound Bound.
|
||
|
|
|
||
|
|
udus(t_none,X,Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,AttX),
|
||
|
|
arg(5,AttX,order(Ord)),
|
||
|
|
setarg(2,AttX,type(t_u(Bound))),
|
||
|
|
setarg(3,AttX,strictness(1)),
|
||
|
|
( unconstrained(Lin,Uc,Kuc,Rest)
|
||
|
|
-> % X = Lin => U = -1/K*Rest + 1/K*X with U an unconstrained variable
|
||
|
|
Ki is -1 rdiv Kuc,
|
||
|
|
add_linear_ff(Rest,Ki,[0,0,l(X* -1,Ord)],Ki,LinU),
|
||
|
|
get_attr(Uc,itf,AttU),
|
||
|
|
arg(5,AttU,order(OrdU)),
|
||
|
|
arg(6,AttU,class(Class)),
|
||
|
|
backsubst(Class,OrdU,LinU)
|
||
|
|
; % no unconstrained variables: add X to basis and reconsider basis
|
||
|
|
basis_add(X,_),
|
||
|
|
determine_active_dec(Lin),
|
||
|
|
reconsider(X)
|
||
|
|
).
|
||
|
|
udus(t_u(U),X,Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true % larger than upperbound: keep
|
||
|
|
; Bound < U
|
||
|
|
-> % smaller than upperbound: update bound and reconsider basis
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_u(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_upper(X,Lin,Bound)
|
||
|
|
; % equal to upperbound: set new strictness
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
udus(t_l(L),X,Lin,Bound,Sold) :-
|
||
|
|
L < Bound, % larger than lowerbound: update and reconsider basis
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_upper(X,Lin,Bound).
|
||
|
|
udus(t_lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true % larger than upperbound: keep
|
||
|
|
; Bound < U
|
||
|
|
-> % smaller than upperbound: check lowerbound, possibly update and reconsider basis
|
||
|
|
L < Bound,
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
reconsider_upper(X,Lin,Bound)
|
||
|
|
; % equal to upperbound: update strictness
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
|
||
|
|
% uiu(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates upper bound of independent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new non-strict
|
||
|
|
% bound Bound.
|
||
|
|
|
||
|
|
uiu(t_none,X,_Lin,Bound,_) :- % X had no bounds
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_u(Bound))),
|
||
|
|
setarg(3,Att,strictness(0)).
|
||
|
|
uiu(t_u(U),X,_Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true % larger than upperbound: keep
|
||
|
|
; Bound < U
|
||
|
|
-> % smaller than upperbound: update.
|
||
|
|
Strict is Sold /\ 2, % update strictness: strictness of lowerbound is kept,
|
||
|
|
% strictness of upperbound is set to non-strict
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_u(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; true % equal to upperbound and nonstrict: keep
|
||
|
|
).
|
||
|
|
uiu(t_l(L),X,Lin,Bound,_Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> % Upperbound is larger than lowerbound: store new bound
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound)))
|
||
|
|
; Bound =:= L,
|
||
|
|
solve_bound(Lin,Bound) % Lowerbound was equal to new upperbound: solve
|
||
|
|
).
|
||
|
|
uiu(t_L(L),X,Lin,Bound,_Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_Lu(L,Bound)))
|
||
|
|
; Bound =:= L,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
).
|
||
|
|
uiu(t_lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> ( Bound > L
|
||
|
|
-> Strict is Sold /\ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Bound =:= L,
|
||
|
|
Sold /\ 2 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uiu(t_Lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> ( L < Bound
|
||
|
|
-> Strict is Sold /\ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_Lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; L =:= Bound,
|
||
|
|
Sold /\ 2 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uiu(t_U(U),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> Strict is Sold /\ 2,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
lb(ClassX,OrdX,Vlb-Vb-Lb),
|
||
|
|
Bound =< Lb + U
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_U(Bound))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vlb,X,Vb,t_u(Bound)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_U(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - U,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uiu(t_lU(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> ( L < Bound
|
||
|
|
-> Strict is Sold /\ 2,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
lb(ClassX,OrdX,Vlb-Vb-Lb),
|
||
|
|
Bound =< Lb + U
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_lU(L,Bound))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vlb,X,Vb,t_lu(L,Bound)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_lU(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - U,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; L =:= Bound,
|
||
|
|
Sold /\ 2 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
|
||
|
|
% uius(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates upper bound of independent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new strict
|
||
|
|
% bound Bound. (see also uiu/5)
|
||
|
|
|
||
|
|
uius(t_none,X,_Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_u(Bound))),
|
||
|
|
setarg(3,Att,strictness(1)).
|
||
|
|
uius(t_u(U),X,_Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true
|
||
|
|
; Bound < U
|
||
|
|
-> Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_u(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uius(t_l(L),X,_Lin,Bound,Sold) :-
|
||
|
|
L < Bound,
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)).
|
||
|
|
uius(t_L(L),X,_Lin,Bound,Sold) :-
|
||
|
|
L < Bound,
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_Lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)).
|
||
|
|
uius(t_lu(L,U),X,_Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true
|
||
|
|
; Bound < U
|
||
|
|
-> L < Bound,
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uius(t_Lu(L,U),X,_Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true
|
||
|
|
; Bound < U
|
||
|
|
-> L < Bound,
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_Lu(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uius(t_U(U),X,_Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true
|
||
|
|
; Bound < U
|
||
|
|
-> Strict is Sold \/ 1,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
lb(ClassX,OrdX,Vlb-Vb-Lb),
|
||
|
|
Bound =< Lb + U
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_U(Bound))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vlb,X,Vb,t_u(Bound)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_U(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - U,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uius(t_lU(L,U),X,_Lin,Bound,Sold) :-
|
||
|
|
( U < Bound
|
||
|
|
-> true
|
||
|
|
; Bound < U
|
||
|
|
-> L < Bound,
|
||
|
|
Strict is Sold \/ 1,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
lb(ClassX,OrdX,Vlb-Vb-Lb),
|
||
|
|
Bound =< Lb + U
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_lU(L,Bound))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vlb,X,Vb,t_lu(L,Bound)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_lU(L,Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - U,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; Strict is Sold \/ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
|
||
|
|
% uil(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates lower bound of independent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new non-strict
|
||
|
|
% bound Bound. (see also uiu/5)
|
||
|
|
|
||
|
|
|
||
|
|
uil(t_none,X,_Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_l(Bound))),
|
||
|
|
setarg(3,Att,strictness(0)).
|
||
|
|
uil(t_l(L),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_l(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uil(t_u(U),X,Lin,Bound,_Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U)))
|
||
|
|
; Bound =:= U,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
).
|
||
|
|
uil(t_U(U),X,Lin,Bound,_Sold) :-
|
||
|
|
( Bound < U
|
||
|
|
-> get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lU(Bound,U)))
|
||
|
|
; Bound =:= U,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
).
|
||
|
|
uil(t_lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> ( Bound < U
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Bound =:= U,
|
||
|
|
Sold /\ 1 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uil(t_lU(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> ( Bound < U
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lU(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Bound =:= U,
|
||
|
|
Sold /\ 1 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uil(t_L(L),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
ub(ClassX,OrdX,Vub-Vb-Ub),
|
||
|
|
Bound >= Ub + L
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_L(Bound))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vub,X,Vb,t_l(Bound)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_L(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - L,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
uil(t_Lu(L,U),X,Lin,Bound,Sold) :-
|
||
|
|
( Bound > L
|
||
|
|
-> ( Bound < U
|
||
|
|
-> Strict is Sold /\ 1,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
ub(ClassX,OrdX,Vub-Vb-Ub),
|
||
|
|
Bound >= Ub + L
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,t_Lu(Bound,U)),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vub,X,Vb,t_lu(Bound,U)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_Lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - L,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; Bound =:= U,
|
||
|
|
Sold /\ 1 =:= 0,
|
||
|
|
solve_bound(Lin,Bound)
|
||
|
|
)
|
||
|
|
; true
|
||
|
|
).
|
||
|
|
|
||
|
|
% uils(Type,X,Lin,Bound,Strict)
|
||
|
|
%
|
||
|
|
% Updates lower bound of independent variable X with linear equation
|
||
|
|
% Lin that had type Type and strictness Strict, to the new strict
|
||
|
|
% bound Bound. (see also uiu/5)
|
||
|
|
|
||
|
|
uils(t_none,X,_Lin,Bound,_Sold) :-
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_l(Bound))),
|
||
|
|
setarg(3,Att,strictness(2)).
|
||
|
|
uils(t_l(L),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true
|
||
|
|
; Bound > L
|
||
|
|
-> Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_l(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uils(t_u(U),X,_Lin,Bound,Sold) :-
|
||
|
|
Bound < U,
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)).
|
||
|
|
uils(t_U(U),X,_Lin,Bound,Sold) :-
|
||
|
|
Bound < U,
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lU(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)).
|
||
|
|
uils(t_lu(L,U),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true
|
||
|
|
; Bound > L
|
||
|
|
-> Bound < U,
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uils(t_lU(L,U),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true
|
||
|
|
; Bound > L
|
||
|
|
-> Bound < U,
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(2,Att,type(t_lU(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
; Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uils(t_L(L),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true
|
||
|
|
; Bound > L
|
||
|
|
-> Strict is Sold \/ 2,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
ub(ClassX,OrdX,Vub-Vb-Ub),
|
||
|
|
Bound >= Ub + L
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_L(Bound))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vub,X,Vb,t_l(Bound)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_L(Bound))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - L,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
uils(t_Lu(L,U),X,_Lin,Bound,Sold) :-
|
||
|
|
( Bound < L
|
||
|
|
-> true
|
||
|
|
; Bound > L
|
||
|
|
-> Bound < U,
|
||
|
|
Strict is Sold \/ 2,
|
||
|
|
( get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
ub(ClassX,OrdX,Vub-Vb-Ub),
|
||
|
|
Bound >= Ub + L
|
||
|
|
-> get_attr(X,itf,Att2), % changed?
|
||
|
|
setarg(2,Att2,type(t_Lu(Bound,U))),
|
||
|
|
setarg(3,Att2,strictness(Strict)),
|
||
|
|
pivot_a(Vub,X,Vb,t_lu(Bound,U)),
|
||
|
|
reconsider(X)
|
||
|
|
; get_attr(X,itf,Att),
|
||
|
|
arg(5,Att,order(OrdX)),
|
||
|
|
arg(6,Att,class(ClassX)),
|
||
|
|
setarg(2,Att,type(t_Lu(Bound,U))),
|
||
|
|
setarg(3,Att,strictness(Strict)),
|
||
|
|
Delta is Bound - L,
|
||
|
|
backsubst_delta(ClassX,OrdX,X,Delta)
|
||
|
|
)
|
||
|
|
; Strict is Sold \/ 2,
|
||
|
|
get_attr(X,itf,Att),
|
||
|
|
setarg(3,Att,strictness(Strict))
|
||
|
|
).
|
||
|
|
|
||
|
|
% reconsider_upper(X,Lin,U)
|
||
|
|
%
|
||
|
|
% Checks if the upperbound of X which is U, satisfies the bounds
|
||
|
|
% of the variables in Lin: let R be the sum of all the bounds on
|
||
|
|
% the variables in Lin, and I be the inhomogene part of Lin, then
|
||
|
|
% upperbound U should be larger than R + I (R may contain
|
||
|
|
% lowerbounds).
|
||
|
|
% See also rcb/3 in bv.pl
|
||
|
|
|
||
|
|
% The code could probably be further specialized to only
|
||
|
|
% decrement/increment in case a variable takes a value equal to a
|
||
|
|
% _strict_ upper/lower bound. Also note that this is only for the
|
||
|
|
% CLP(Q) version. The CLP(R) fuzzy arithmetic makes it useless to
|
||
|
|
% really distinguish between strict and non-strict inequalities.
|
||
|
|
|
||
|
|
reconsider_upper(X,[I,R|H],U) :-
|
||
|
|
R + I >= U, % violation
|
||
|
|
!,
|
||
|
|
dec_step(H,Status), % we want to decrement R
|
||
|
|
rcbl_status(Status,X,[],Binds,[],u(U)),
|
||
|
|
export_binding(Binds).
|
||
|
|
reconsider_upper( _, _, _).
|
||
|
|
|
||
|
|
% reconsider_lower(X,Lin,L)
|
||
|
|
%
|
||
|
|
% Checks if the lowerbound of X which is L, satisfies the bounds
|
||
|
|
% of the variables in Lin: let R be the sum of all the bounds on
|
||
|
|
% the variables in Lin, and I be the inhomogene part of Lin, then
|
||
|
|
% lowerbound L should be smaller than R + I (R may contain
|
||
|
|
% upperbounds).
|
||
|
|
% See also rcb/3 in bv.pl
|
||
|
|
|
||
|
|
reconsider_lower(X,[I,R|H],L) :-
|
||
|
|
R + I =< L, % violation
|
||
|
|
!,
|
||
|
|
inc_step(H,Status), % we want to increment R
|
||
|
|
rcbl_status(Status,X,[],Binds,[],l(L)),
|
||
|
|
export_binding(Binds).
|
||
|
|
reconsider_lower(_,_,_).
|
||
|
|
|
||
|
|
%
|
||
|
|
% lin is dereferenced
|
||
|
|
%
|
||
|
|
|
||
|
|
% solve_bound(Lin,Bound)
|
||
|
|
%
|
||
|
|
% Solves the linear equation Lin - Bound = 0
|
||
|
|
% Lin is the linear equation of X, a variable whose bounds have narrowed to value Bound
|
||
|
|
|
||
|
|
solve_bound(Lin,Bound) :-
|
||
|
|
Bound =:= 0,
|
||
|
|
!,
|
||
|
|
solve(Lin).
|
||
|
|
solve_bound(Lin,Bound) :-
|
||
|
|
Nb is -Bound,
|
||
|
|
normalize_scalar(Nb,Nbs),
|
||
|
|
add_linear_11(Nbs,Lin,Eq),
|
||
|
|
solve(Eq).
|