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yap-6.3/CLPQR/clpr/ineq.pl
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% clp(q,r) version 1.3.2 %
% %
% (c) Copyright 1992,1993,1994,1995 %
% Austrian Research Institute for Artificial Intelligence (OFAI) %
% Schottengasse 3 %
% A-1010 Vienna, Austria %
% %
% File: ineq.pl %
% Author: Christian Holzbaur christian@ai.univie.ac.at %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Lin (=)< 0
%
ineq( [], I, _, Strictness) :- ineq_ground( Strictness, I).
ineq( [v(K,[X^1])|Tail], I, Lin, Strictness) :-
ineq_cases( Tail, I, Lin, Strictness, X, K).
ineq_cases( [], I, _, Strictness, X, K) :-
ineq_one( Strictness, X, K, I).
ineq_cases( [_|_], _, Lin, Strictness, _, _) :-
deref( Lin, Lind), % Id+Hd =< 0
decompose( Lind, Hom, _, Inhom),
ineq_more( Hom, Inhom, Lind, Strictness).
ineq_ground( strict, I) :- arith_eval( I < 0).
ineq_ground( nonstrict, I) :- arith_eval( I =< 0).
%
% Special cases: k={+-}1,i=0
%
ineq_one( strict, X, K, I) :-
( arith_eval(K>0) ->
( arith_eval(I=:=0) ->
ineq_one_s_p_0( X)
;
arith_eval( I/K, Inhom),
ineq_one_s_p_i( X, Inhom)
)
;
( arith_eval(I=:=0) ->
ineq_one_s_n_0( X)
;
arith_eval( -I/K, Inhom),
ineq_one_s_n_i( X, Inhom)
)
).
ineq_one( nonstrict, X, K, I) :-
( arith_eval(K>0) ->
( arith_eval(I=:=0) ->
ineq_one_n_p_0( X)
;
arith_eval( I/K, Inhom),
ineq_one_n_p_i( X, Inhom)
)
;
( arith_eval(I=:=0) ->
ineq_one_n_n_0( X)
;
arith_eval( -I/K, Inhom),
ineq_one_n_n_i( X, Inhom)
)
).
/*
ineq_one( Strictness, X, K, I) :-
get_atts( X, lin(LinX)),
!, % old variable, this is deref
decompose( LinX, OrdX, _, Ix),
ineq_one_old( OrdX, K, I, Strictness, X, Ix).
ineq_one( Strictness, X, K, I) :- % new variable, nothing depends on it
arith_eval( -I/K, Bound),
ineq_one_new( Strictness, X, K, Bound).
ineq_one_new( strict, X, K, Bound) :-
arith_eval( 1, One),
( arith_eval( K < 0) ->
var_intern( t_l(Bound), X, 2'10)
;
var_intern( t_u(Bound), X, 2'01)
).
ineq_one_new( nonstrict, X, K, Bound) :-
arith_eval( 1, One),
( arith_eval( K < 0) ->
var_intern( t_l(Bound), X, 2'00)
;
var_intern( t_u(Bound), X, 2'00)
).
ineq_one_old( [], K, I, Strictness, _X, Ix) :-
arith_eval( K*Ix+I, Inhom),
ineq_ground( Strictness, Inhom).
%
% here we would have the choice to bound X or Y
%
ineq_one_old( [Y*Ky|Tail], K, I, Strictness, X, Ix) :-
( Tail = [],
arith_eval( K*Ky, Coeff),
arith_eval( -(K*Ix+I)/Coeff, Bound),
update_indep( Strictness, Y, Coeff, Bound)
; Tail = [_|_],
arith_eval( -I/K, Bound),
update_dep( Strictness, X, K, Bound)
).
update_dep( strict, X, K, Bound) :-
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
( arith_eval( K < 0) ->
udls( Type, X, Lin, Bound, Old)
;
udus( Type, X, Lin, Bound, Old)
).
update_dep( nonstrict, X, K, Bound) :-
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
( arith_eval( K < 0) ->
udl( Type, X, Lin, Bound, Old)
;
udu( Type, X, Lin, Bound, Old)
).
*/
% --------------------------- strict ----------------------------
ineq_one_s_p_0( X) :-
get_atts( X, lin(LinX)),
!, % old variable, this is deref
decompose( LinX, OrdX, _, Ix),
ineq_one_old_s_p_0( OrdX, X, Ix).
ineq_one_s_p_0( X) :- % new variable, nothing depends on it
arith_eval( 0, Zero),
var_intern( t_u(Zero), X, 2'01).
ineq_one_s_n_0( X) :-
get_atts( X, lin(LinX)),
!,
decompose( LinX, OrdX, _, Ix),
ineq_one_old_s_n_0( OrdX, X, Ix).
ineq_one_s_n_0( X) :-
arith_eval( 0, Zero),
var_intern( t_l(Zero), X, 2'10).
ineq_one_s_p_i( X, I) :-
get_atts( X, lin(LinX)),
!,
decompose( LinX, OrdX, _, Ix),
ineq_one_old_s_p_i( OrdX, I, X, Ix).
ineq_one_s_p_i( X, I) :-
arith_eval( -I, Bound),
var_intern( t_u(Bound), X, 2'01).
ineq_one_s_n_i( X, I) :-
get_atts( X, lin(LinX)),
!,
decompose( LinX, OrdX, _, Ix),
ineq_one_old_s_n_i( OrdX, I, X, Ix).
ineq_one_s_n_i( X, I) :-
var_intern( t_l(I), X, 2'10).
ineq_one_old_s_p_0( [], _, Ix) :-
arith_eval( Ix < 0).
ineq_one_old_s_p_0( [Y*Ky|Tail], X, Ix) :-
( Tail = [],
arith_eval( -Ix/Ky, Bound),
update_indep( strict, Y, Ky, Bound)
; Tail = [_|_],
arith_eval( 0, Zero),
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udus( Type, X, Lin, Zero, Old)
).
ineq_one_old_s_n_0( [], _, Ix) :-
arith_eval( Ix > 0).
ineq_one_old_s_n_0( [Y*Ky|Tail], X, Ix) :-
( Tail = [],
arith_eval( -Ky, Coeff),
arith_eval( Ix/Coeff, Bound),
update_indep( strict, Y, Coeff, Bound)
; Tail = [_|_],
arith_eval( 0, Zero),
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udls( Type, X, Lin, Zero, Old)
).
ineq_one_old_s_p_i( [], I, _, Ix) :-
arith_eval( Ix+I < 0).
ineq_one_old_s_p_i( [Y*Ky|Tail], I, X, Ix) :-
( Tail = [],
arith_eval( -(Ix+I)/Ky, Bound),
update_indep( strict, Y, Ky, Bound)
; Tail = [_|_],
arith_eval( -I, Bound),
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udus( Type, X, Lin, Bound, Old)
).
ineq_one_old_s_n_i( [], I, _, Ix) :-
arith_eval( -Ix+I < 0).
ineq_one_old_s_n_i( [Y*Ky|Tail], I, X, Ix) :-
( Tail = [],
arith_eval( -Ky, Coeff),
arith_eval( (Ix-I)/Coeff, Bound),
update_indep( strict, Y, Coeff, Bound)
; Tail = [_|_],
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udls( Type, X, Lin, I, Old)
).
% -------------------------- nonstrict --------------------------
ineq_one_n_p_0( X) :-
get_atts( X, lin(LinX)),
!, % old variable, this is deref
decompose( LinX, OrdX, _, Ix),
ineq_one_old_n_p_0( OrdX, X, Ix).
ineq_one_n_p_0( X) :- % new variable, nothing depends on it
arith_eval( 0, Zero),
var_intern( t_u(Zero), X, 2'00).
ineq_one_n_n_0( X) :-
get_atts( X, lin(LinX)),
!,
decompose( LinX, OrdX, _, Ix),
ineq_one_old_n_n_0( OrdX, X, Ix).
ineq_one_n_n_0( X) :-
arith_eval( 0, Zero),
var_intern( t_l(Zero), X, 2'00).
ineq_one_n_p_i( X, I) :-
get_atts( X, lin(LinX)),
!,
decompose( LinX, OrdX, _, Ix),
ineq_one_old_n_p_i( OrdX, I, X, Ix).
ineq_one_n_p_i( X, I) :-
arith_eval( -I, Bound),
var_intern( t_u(Bound), X, 2'00).
ineq_one_n_n_i( X, I) :-
get_atts( X, lin(LinX)),
!,
decompose( LinX, OrdX, _, Ix),
ineq_one_old_n_n_i( OrdX, I, X, Ix).
ineq_one_n_n_i( X, I) :-
var_intern( t_l(I), X, 2'00).
ineq_one_old_n_p_0( [], _, Ix) :-
arith_eval( Ix =< 0).
ineq_one_old_n_p_0( [Y*Ky|Tail], X, Ix) :-
( Tail = [],
arith_eval( -Ix/Ky, Bound),
update_indep( nonstrict, Y, Ky, Bound)
; Tail = [_|_],
arith_eval( 0, Zero),
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udu( Type, X, Lin, Zero, Old)
).
ineq_one_old_n_n_0( [], _, Ix) :-
arith_eval( Ix >= 0).
ineq_one_old_n_n_0( [Y*Ky|Tail], X, Ix) :-
( Tail = [],
arith_eval( -Ky, Coeff),
arith_eval( Ix/Coeff, Bound),
update_indep( nonstrict, Y, Coeff, Bound)
; Tail = [_|_],
arith_eval( 0, Zero),
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udl( Type, X, Lin, Zero, Old)
).
ineq_one_old_n_p_i( [], I, _, Ix) :-
arith_eval( Ix+I =< 0).
ineq_one_old_n_p_i( [Y*Ky|Tail], I, X, Ix) :-
( Tail = [],
arith_eval( -(Ix+I)/Ky, Bound),
update_indep( nonstrict, Y, Ky, Bound)
; Tail = [_|_],
arith_eval( -I, Bound),
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udu( Type, X, Lin, Bound, Old)
).
ineq_one_old_n_n_i( [], I, _, Ix) :-
arith_eval( -Ix+I =< 0).
ineq_one_old_n_n_i( [Y*Ky|Tail], I, X, Ix) :-
( Tail = [],
arith_eval( -Ky, Coeff),
arith_eval( (Ix-I)/Coeff, Bound),
update_indep( nonstrict, Y, Coeff, Bound)
; Tail = [_|_],
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
udl( Type, X, Lin, I, Old)
).
% ---------------------------------------------------------------
ineq_more( [], I, _, Strictness) :- ineq_ground( Strictness, I).
ineq_more( [X*K|Tail], Id, Lind, Strictness) :-
( Tail = [], % one var: update bound instead of slack introduction
get_or_add_class( X, _),
arith_eval( -Id/K, Bound),
update_indep( Strictness, X, K, Bound)
; Tail = [_|_],
ineq_more( Strictness, Lind)
).
ineq_more( strict, Lind) :-
( unconstrained( Lind, U,K, Rest) -> % never fails, no implied value
arith_eval( 0, Z),
arith_eval( 1, One),
var_intern( t_l(Z), S, 2'10),
arith_eval( -1/K, Ki),
add_linear_ff( Rest, Ki, [Z,Z,S*One], Ki, LinU),
decompose( LinU, Hu, _, _),
get_or_add_class( U, Class),
same_class( Hu, Class),
backsubst( U, LinU)
;
arith_eval( 0, Z),
var_with_def_intern( t_u(Z), S, Lind, 2'01),
basis_add( S, _),
determine_active_dec( Lind),
reconsider( S)
).
ineq_more( nonstrict, Lind) :-
( unconstrained( Lind, U,K, Rest) -> % never fails, no implied value
arith_eval( 0, Z),
arith_eval( 1, One),
var_intern( t_l(Z), S, 2'00),
arith_eval( -1/K, Ki),
add_linear_ff( Rest, Ki, [Z,Z,S*One], Ki, LinU),
decompose( LinU, Hu, _, _),
get_or_add_class( U, Class),
same_class( Hu, Class),
backsubst( U, LinU)
;
arith_eval( 0, Z),
var_with_def_intern( t_u(Z), S, Lind, 2'00),
basis_add( S, _),
determine_active_dec( Lind),
reconsider( S)
).
update_indep( strict, X, K, Bound) :-
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
( arith_eval( K < 0) ->
uils( Type, X, Lin, Bound, Old)
;
uius( Type, X, Lin, Bound, Old)
).
update_indep( nonstrict, X, K, Bound) :-
get_atts( X, [lin(Lin),type(Type),strictness(Old)]),
( arith_eval( K < 0) ->
uil( Type, X, Lin, Bound, Old)
;
uiu( Type, X, Lin, Bound, Old)
).
% ---------------------------------------------------------------------------------------
%
% 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
%
udl( t_none, X, Lin, Bound, _Sold) :-
put_atts( X, [type(t_l(Bound)),strictness(2'00)]),
( unconstrained( Lin, Uc,Kuc, Rest) ->
arith_eval( -1/Kuc, Ki),
arith_eval( 0, Z),
arith_eval( -1, Mone),
add_linear_ff( Rest, Ki, [Z,Z,X*Mone], Ki, LinU),
backsubst( Uc, LinU)
;
basis_add( X, _),
determine_active_inc( Lin),
reconsider( X)
).
udl( t_l(L), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
Strict is Sold /\ 2'01,
put_atts( X, [type(t_l(Bound)),strictness(Strict)]),
reconsider_lower( X, Lin, Bound)
)).
udl( t_u(U), X, Lin, Bound, _Sold) :-
case_signum( U-Bound,
fail,
solve_bound( Lin, Bound),
(
put_atts( X, type(t_lu(Bound,U))),
reconsider_lower( X, Lin, Bound)
)).
udl( t_lu(L,U), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
case_signum( U-Bound,
fail,
(
Sold /\ 2'01 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'01,
put_atts( X, [type(t_lu(Bound,U)),strictness(Strict)]),
reconsider_lower( X, Lin, Bound)
))
)).
udls( t_none, X, Lin, Bound, _Sold) :-
put_atts( X, [type(t_l(Bound)),strictness(2'10)]),
( unconstrained( Lin, Uc,Kuc, Rest) ->
arith_eval( -1/Kuc, Ki),
arith_eval( -1, Mone),
arith_eval( 0, Z),
add_linear_ff( Rest, Ki, [Z,Z,X*Mone], Ki, LinU),
backsubst( Uc, LinU)
;
basis_add( X, _),
determine_active_inc( Lin),
reconsider( X)
).
udls( t_l(L), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
Strict is Sold \/ 2'10,
put_atts( X, [type(t_l(Bound)),strictness(Strict)]),
reconsider_lower( X, Lin, Bound)
)).
udls( t_u(U), X, Lin, Bound, Sold) :-
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
put_atts( X, [type(t_lu(Bound,U)),strictness(Strict)]),
reconsider_lower( X, Lin, Bound).
udls( t_lu(L,U), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
put_atts( X, [type(t_lu(Bound,U)),strictness(Strict)]),
reconsider_lower( X, Lin, Bound)
)).
udu( t_none, X, Lin, Bound, _Sold) :-
put_atts( X, [type(t_u(Bound)),strictness(2'00)]),
( unconstrained( Lin, Uc,Kuc, Rest) ->
arith_eval( -1/Kuc, Ki),
arith_eval( -1, Mone),
arith_eval( 0, Z),
add_linear_ff( Rest, Ki, [Z,Z,X*Mone], Ki, LinU),
backsubst( Uc, LinU)
;
basis_add( X, _),
determine_active_dec( Lin),
reconsider( X)
).
udu( t_u(U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
Strict is Sold /\ 2'10,
put_atts( X, [type(t_u(Bound)),strictness(Strict)]),
reconsider_upper( X, Lin, Bound)
)).
udu( t_l(L), X, Lin, Bound, _Sold) :-
case_signum( Bound-L,
fail,
solve_bound( Lin, Bound),
(
put_atts( X, type(t_lu(L,Bound))),
reconsider_upper( X, Lin, Bound)
)).
udu( t_lu(L,U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
case_signum( Bound-L,
fail,
(
Sold /\ 2'10 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'10,
put_atts( X, [type(t_lu(L,Bound)),strictness(Strict)]),
reconsider_upper( X, Lin, Bound)
))
)).
udus( t_none, X, Lin, Bound, _Sold) :-
put_atts( X, [type(t_u(Bound)),strictness(2'01)]),
( unconstrained( Lin, Uc,Kuc, Rest) ->
arith_eval( -1/Kuc, Ki),
arith_eval( -1, Mone),
arith_eval( 0, Z),
add_linear_ff( Rest, Ki, [Z,Z,X*Mone], Ki, LinU),
backsubst( Uc, LinU)
;
basis_add( X, _),
determine_active_dec( Lin),
reconsider( X)
).
udus( t_u(U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
Strict is Sold \/ 2'01,
put_atts( X, [type(t_u(Bound)),strictness(Strict)]),
reconsider_upper( X, Lin, Bound)
)).
udus( t_l(L), X, Lin, Bound, Sold) :-
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
put_atts( X, [type(t_lu(L,Bound)),strictness(Strict)]),
reconsider_upper( X, Lin, Bound).
udus( t_lu(L,U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
put_atts( X, [type(t_lu(L,Bound)),strictness(Strict)]),
reconsider_upper( X, Lin, Bound)
)).
uiu( t_none, X, _Lin, Bound, _) :-
put_atts( X, [type(t_u(Bound)),strictness(2'00)]).
uiu( t_u(U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
Strict is Sold /\ 2'10,
put_atts( X, [type(t_u(Bound)),strictness(Strict)])
)).
uiu( t_l(L), X, Lin, Bound, _Sold) :-
case_signum( Bound-L,
fail,
solve_bound( Lin, Bound),
put_atts( X, type(t_lu(L,Bound)))).
uiu( t_L(L), X, Lin, Bound, _Sold) :-
case_signum( Bound-L,
fail,
solve_bound( Lin, Bound),
put_atts( X, type(t_Lu(L,Bound)))).
uiu( t_lu(L,U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
case_signum( Bound-L,
fail,
(
Sold /\ 2'10 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'10,
put_atts( X, [type(t_lu(L,Bound)),strictness(Strict)])
))
)).
uiu( t_Lu(L,U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
case_signum( Bound-L,
fail,
(
Sold /\ 2'10 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'10,
put_atts( X, [type(t_Lu(L,Bound)),strictness(Strict)])
))
)).
%
% update active:
%
uiu( t_U(U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
Strict is Sold /\ 2'10,
( lb( X, Vlb-Vb-Lb),
arith_eval( Bound =< Lb+U) ->
put_atts( X, [type(t_U(Bound)),strictness(Strict)]),
pivot_a( Vlb, X, Vb, t_u(Bound)),
reconsider( X)
;
put_atts( X, [type(t_U(Bound)),strictness(Strict)]),
arith_eval( Bound-U, Delta),
backsubst_delta( X, Delta)
)
)).
uiu( t_lU(L,U), X, Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
true,
(
case_signum( Bound-L,
fail,
(
Sold /\ 2'10 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'10,
( lb( X, Vlb-Vb-Lb),
arith_eval( Bound =< Lb+U) ->
put_atts( X, [type(t_lU(L,Bound)),strictness(Strict)]),
pivot_a( Vlb, X, Vb, t_lu(L,Bound)),
reconsider( X)
;
put_atts( X, [type(t_lU(L,Bound)),strictness(Strict)]),
arith_eval( Bound-U, Delta),
backsubst_delta( X, Delta)
)
))
)).
uius( t_none, X, _Lin, Bound, _Sold) :-
put_atts( X, [type(t_u(Bound)),strictness(2'01)]).
uius( t_u(U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
Strict is Sold \/ 2'01,
put_atts( X, [type(t_u(Bound)),strictness(Strict)])
)).
uius( t_l(L), X, _Lin, Bound, Sold) :-
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
put_atts( X, [type(t_lu(L,Bound)),strictness(Strict)]).
uius( t_L(L), X, _Lin, Bound, Sold) :-
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
put_atts( X, [type(t_Lu(L,Bound)),strictness(Strict)]).
uius( t_lu(L,U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
put_atts( X, [type(t_lu(L,Bound)),strictness(Strict)])
)).
uius( t_Lu(L,U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
put_atts( X, [type(t_Lu(L,Bound)),strictness(Strict)])
)).
%
% update active:
%
uius( t_U(U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
Strict is Sold \/ 2'01,
( lb( X, Vlb-Vb-Lb),
arith_eval( Bound =< Lb+U) ->
put_atts( X, [type(t_U(Bound)),strictness(Strict)]),
pivot_a( Vlb, X, Vb, t_u(Bound)),
reconsider( X)
;
put_atts( X, [type(t_U(Bound)),strictness(Strict)]),
arith_eval( Bound-U, Delta),
backsubst_delta( X, Delta)
)
)).
uius( t_lU(L,U), X, _Lin, Bound, Sold) :-
case_signum( U-Bound,
true,
(
Strict is Sold \/ 2'01,
put_atts( X, strictness(Strict))
),
(
arith_eval( Bound>L),
Strict is Sold \/ 2'01,
( lb( X, Vlb-Vb-Lb),
arith_eval( Bound =< Lb+U) ->
put_atts( X, [type(t_lU(L,Bound)),strictness(Strict)]),
pivot_a( Vlb, X, Vb, t_lu(L,Bound)),
reconsider( X)
;
put_atts( X, [type(t_lU(L,Bound)),strictness(Strict)]),
arith_eval( Bound-U, Delta),
backsubst_delta( X, Delta)
)
)).
uil( t_none, X, _Lin, Bound, _Sold) :-
put_atts( X, [type(t_l(Bound)),strictness(2'00)]).
uil( t_l(L), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
Strict is Sold /\ 2'01,
put_atts( X, [type(t_l(Bound)),strictness(Strict)])
)).
uil( t_u(U), X, Lin, Bound, _Sold) :-
case_signum( U-Bound,
fail,
solve_bound( Lin, Bound),
put_atts( X, type(t_lu(Bound,U)))).
uil( t_U(U), X, Lin, Bound, _Sold) :-
case_signum( U-Bound,
fail,
solve_bound( Lin, Bound),
put_atts( X, type(t_lU(Bound,U)))).
uil( t_lu(L,U), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
case_signum( U-Bound,
fail,
(
Sold /\ 2'01 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'01,
put_atts( X, [type(t_lu(Bound,U)),strictness(Strict)])
))
)).
uil( t_lU(L,U), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
case_signum( U-Bound,
fail,
(
Sold /\ 2'01 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'01,
put_atts( X, [type(t_lU(Bound,U)),strictness(Strict)])
))
)).
%
% update active bound: % { a>=100,d=<5000,c>=10,-2*a+d-c=10,a>=2490 }.
%
uil( t_L(L), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
Strict is Sold /\ 2'01,
( ub( X, Vub-Vb-Ub),
arith_eval( Bound >= Ub+L) ->
put_atts( X, [type(t_L(Bound)),strictness(Strict)]),
pivot_a( Vub, X, Vb, t_l(Bound)),
reconsider( X)
; %
% max(X) >= Ub, no implied value missed
%
put_atts( X, [type(t_L(Bound)),strictness(Strict)]),
arith_eval( Bound-L, Delta),
backsubst_delta( X, Delta)
)
)).
uil( t_Lu(L,U), X, Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
true,
(
case_signum( U-Bound,
fail,
(
Sold /\ 2'01 =:= 0,
solve_bound( Lin, Bound)
),
(
Strict is Sold /\ 2'01,
( ub( X, Vub-Vb-Ub),
arith_eval( Bound >= Ub+L) ->
put_atts( X, [type(t_Lu(Bound,U)),strictness(Strict)]),
pivot_a( Vub, X, Vb, t_lu(Bound,U)),
reconsider( X)
;
put_atts( X, [type(t_Lu(Bound,U)),strictness(Strict)]),
arith_eval( Bound-L, Delta),
backsubst_delta( X, Delta)
)
)))).
uils( t_none, X, _Lin, Bound, _Sold) :-
put_atts( X, [type(t_l(Bound)),strictness(2'10)]).
uils( t_l(L), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
Strict is Sold \/ 2'10,
put_atts( X, [type(t_l(Bound)),strictness(Strict)])
)).
uils( t_u(U), X, _Lin, Bound, Sold) :-
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
put_atts( X, [type(t_lu(Bound,U)),strictness(Strict)]).
uils( t_U(U), X, _Lin, Bound, Sold) :-
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
put_atts( X, [type(t_lU(Bound,U)),strictness(Strict)]).
uils( t_lu(L,U), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
put_atts( X, [type(t_lu(Bound,U)),strictness(Strict)])
)).
uils( t_lU(L,U), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
put_atts( X, [type(t_lU(Bound,U)),strictness(Strict)])
)).
%
% update active bound:
%
uils( t_L(L), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
Strict is Sold \/ 2'10,
( ub( X, Vub-Vb-Ub),
arith_eval( Bound >= Ub+L) ->
put_atts( X, [type(t_L(Bound)),strictness(Strict)]),
pivot_a( Vub, X, Vb, t_l(Bound)),
reconsider( X)
; %
% max(X) >= Ub, no implied value missed
%
put_atts( X, [type(t_L(Bound)),strictness(Strict)]),
arith_eval( Bound-L, Delta),
backsubst_delta( X, Delta)
))).
uils( t_Lu(L,U), X, _Lin, Bound, Sold) :-
case_signum( Bound-L,
true,
(
Strict is Sold \/ 2'10,
put_atts( X, strictness(Strict))
),
(
arith_eval( U>Bound),
Strict is Sold \/ 2'10,
( ub( X, Vub-Vb-Ub),
arith_eval( Bound >= Ub+L) ->
put_atts( X, [type(t_Lu(Bound,U)),strictness(Strict)]),
pivot_a( Vub, X, Vb, t_lu(Bound,U)),
reconsider( X)
;
put_atts( X, [type(t_Lu(Bound,U)),strictness(Strict)]),
arith_eval( Bound-L, Delta),
backsubst_delta( X, Delta)
))).
reconsider_upper( X, Lin, U) :-
decompose( Lin, H, R, I),
arith_eval( R+I >= U),
!,
dec_step( H, Status),
rcbl_status( Status, X, [], Binds,[], u(U)),
export_binding( Binds).
reconsider_upper( _, _, _).
reconsider_lower( X, Lin, L) :-
decompose( Lin, H, R, I),
arith_eval( R+I =< L),
!,
inc_step( H, Status),
rcbl_status( Status, X, [], Binds,[], l(L)),
export_binding( Binds).
reconsider_lower( _, _, _).
%
% lin is dereferenced
%
solve_bound( Lin, Bound) :-
arith_eval( Bound =:= 0),
!,
solve( Lin).
solve_bound( Lin, Bound) :-
arith_eval( -Bound, Nb),
normalize_scalar( Nb, Nbs),
add_linear_11( Nbs, Lin, Eq),
solve( Eq).
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