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ibex_LoupFinderXTaylor.cpp
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ibex_LoupFinderXTaylor.cpp
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//============================================================================
// I B E X
// File : ibex_LoupFinderXTaylor.cpp
// Author : Gilles Chabert, Ignacio Araya, Bertrand Neveu
// Copyright : IMT Atlantique (France)
// License : See the LICENSE file
// Created : Jul 12, 2012
// Last Update : Jul 09, 2017
//============================================================================
#include "ibex_LoupFinderXTaylor.h"
#include "ibex_LoupFinderProbing.h"
#include "ibex_BitSet.h"
#include "ibex_Linear.h"
using namespace std;
namespace ibex {
//TODO: remove this recipe for the argument of the max number of iterations of the LP solver
LoupFinderXTaylor::LoupFinderXTaylor(const System& sys) : sys(sys), lr(sys,LinearizerXTaylor::RESTRICT,LinearizerXTaylor::RANDOM), lp_solver(sys.nb_var) {
lp_solver.set_max_iter(std::min(sys.nb_var*3, int(LPSolver::default_max_iter)));
// nb_simplex=0;
// diam_simplex=0;
}
void LoupFinderXTaylor::add_property(const IntervalVector& init_box, BoxProperties& prop) {
lr.add_property(init_box,prop);
}
std::pair<IntervalVector, double> LoupFinderXTaylor::postproc(const Vector& x, double current_loup) {
// Will be normalized
Matrix A = lp_solver.rows();
// Will be normalized
IntervalVector b = lp_solver.lhs_rhs();
uint n = sys.nb_var;
uint m = A.nb_rows();
// Vector of normalized pseudo-satisfiability errors a_i*x -b_i.
// Can correspond to either a violation or a false inactivation
// (g(x)<0 but g(x)~0).
// To ease sorting, we set by convention a positive value for violation
// and a negative value for false inactivation (almost active), whatever
// is the actual inequality sign. The lhs_active array allows to
// memorize the sign of the retained inequality.
Vector error(m);
bool* lhs_active = new bool[m]; // do we consider ax>=b_l or ax<=b_u?
uint* indices = new uint[m]; // for sorting
for (uint i=0; i<m; i++) {
indices[i] = i;
// normalize constraints
double inv_norm_a = 1./norm(A.row(i));
A[i] *= inv_norm_a;
b[i] *= inv_norm_a;
// calculate max delta
double delta_lb = POS_INFINITY;
bool lb_violated = false;
if (b[i].lb()>NEG_INFINITY) {
delta_lb = A.row(i)*x-b[i].lb();
if (delta_lb<0) lb_violated = true;
}
double delta_ub = NEG_INFINITY;
bool ub_violated = false;
if (b[i].ub()<POS_INFINITY) {
delta_ub = A.row(i)*x-b[i].ub();
if (delta_ub>0) ub_violated = true;
}
if (lb_violated && ub_violated) {
ibex_warning("linear constraint with both lhs and rhs violated (should not happen)");
throw NotFound();
}
if (lb_violated) {
lhs_active[i] = true;
error[i] = -delta_lb; // = fabs(delta_lb). Violation = positive value
} else if (ub_violated) {
lhs_active[i] = false;
error[i] = delta_ub; // Violation = positive value
} else if (delta_lb < -delta_ub) {
// the bound with delta closest to zero is the most
// potentially active one at the real minimum
lhs_active[i] = true;
error[i] = -delta_lb; // false activation = negative value
} else {
lhs_active[i] = false;
error[i] = delta_ub; // false activation = negative value
}
//cout << "a=" << A[i] << " error=" << error[i] << endl;
}
std::sort(indices,indices+m,[error](uint i1,uint i2)->bool { return error[i1]>error[i2]; });
// the maximal violation (obtained with interval evaluation)
// of the normalized system
double max_error = error[indices[0]];
if (max_error<=0) {
delete[] lhs_active;
delete[] indices;
// This case typically happens with linear constraints.
// The System::is_inner function imposes strict inequality
// satisfaction g(x)<0, but with linear constraints,
// we may actually have g(x)=0.
if (max_error<0)
ibex_warning("Found a point strictly inside the linear restriction of a system, \
but not strictly inside the system itself. Seems like a bug.");
return std::make_pair(x,current_loup);
}
// consider the active constraints as the n first
// with min error.
Matrix Aact(n,n);
Vector db(n);
uint nb_violated=0; // for debug
for (uint i=0; i<n; i++) {
uint c=indices[i];
if (error[c]>0) nb_violated++;
Aact[i]=A[c];
if (lhs_active[c])
db[i] = +1;
else
db[i] = -1;
}
delete[] lhs_active;
delete[] indices;
// build feasible direction from x
Vector dx(n);
try {
// solve the shifted linear system
Matrix LU(n,n);
int* p=new int[n]; // will be ignored
real_LU(Aact,LU,p);
real_LU_solve(LU, p, db, dx);
} catch(SingularMatrixException&) {
//cout << "singularity (#violated=" << nb_violated << ")\n";
throw NotFound();
}
// normalize the direction
dx *= 1./norm(dx);
// try different moves
for (double eps=1; eps>=1e-20; eps/=2) {
Vector new_candidate = x+eps*dx;
for (uint i=0; i<n; i++) {
// simple fix if out of bounds
if (new_candidate[i] < sys.box[i].lb()) new_candidate[i] = sys.box[i].lb();
if (new_candidate[i] > sys.box[i].ub()) new_candidate[i] = sys.box[i].ub();
}
double new_loup = current_loup;
//if ((Aitv*new_candidate).is_subset(b)) { // ---> a faster but stronger condition!
if (check(sys,new_candidate,new_loup,false)) {
return std::make_pair(new_candidate,new_loup);
}
}
// means: we could not find a candidate inside system or
// the cost is above the current loup.
throw NotFound();
}
std::pair<IntervalVector, double> LoupFinderXTaylor::find(const IntervalVector& box, const IntervalVector&, double current_loup, BoxProperties& prop) {
int n=sys.nb_var;
if (box.is_unbounded())
throw NotFound();
lp_solver.clear_constraints();
lp_solver.set_bounds(box);
IntervalVector ig=sys.goal->gradient(box.mid());
if (ig.is_empty()) // unfortunately, at the midpoint the function is not differentiable
throw NotFound(); // not a big deal: wait for another box...
Vector g=ig.mid();
// set the objective coefficient
// TODO: replace with lp_solver.set_cost(g) when implemented
for (int j=0; j<n; j++)
lp_solver.set_cost(j,g[j]);
int count = lr.linearize(box,lp_solver,prop);
if (count==-1) {
lp_solver.clear_constraints();
throw NotFound();
}
LPSolver::Status stat = lp_solver.minimize();
if (stat == LPSolver::Status::Optimal) {
//the linear solution is mapped to intervals and evaluated
Vector loup_point = lp_solver.not_proved_primal_sol();
double new_loup=current_loup;
// we allow finding a loup outside of the current box, but
// not outside of the system box.
if (!sys.box.contains(loup_point)) {
// try simple fix (the loup point is lost anyway)
for (uint i=0; i<n; i++) {
if (loup_point[i] < sys.box[i].lb()) loup_point[i] = sys.box[i].lb();
if (loup_point[i] > sys.box[i].ub()) loup_point[i] = sys.box[i].ub();
}
}
if (check(sys,loup_point,new_loup,false)) {
return std::make_pair(loup_point,new_loup);
} else {
//throw NotFound();
return postproc(loup_point, current_loup); // try to correct the loup-point. May throw NotFound
}
}
throw NotFound();
}
} /* namespace ibex */