void TestSolver::circle2() {
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
SystemFactory f;
f.add_var(x);
f.add_var(y);
f.add_ctr(sqr(x)+sqr(y)=1);
f.add_ctr(sqr(x-2)+sqr(y)=1);
double _sol1[]={1,0};
Vector sol1(2,_sol1);
System sys(f);
RoundRobin rr(1e-3);
CellStack stack;
CtcHC4 hc4(sys);
Vector prec(2,1e-3);
Solver solver(sys,hc4,rr,stack,prec,prec);
solver.start(IntervalVector(2,Interval(-10,10)));
CovSolverData::BoxStatus status;
bool res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::UNKNOWN);
CPPUNIT_ASSERT(solver.get_data().nb_unknown()==1);
CPPUNIT_ASSERT(solver.get_data().unknown(0).is_superset(sol1));
res=solver.next(status);
CPPUNIT_ASSERT(!res);
}
void TestSolver::circle4() {
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
const ExprSymbol& r2=ExprSymbol::new_("r2");
SystemFactory f;
f.add_var(x);
f.add_var(y);
f.add_var(r2);
f.add_ctr(sqr(x)+sqr(y)=r2);
f.add_ctr(sqr(x-1)+sqr(y)=r2);
double cospi6=0.5;
double sinpi6=::sqrt(3)/2;
double _sol1[]={cospi6,sinpi6,1};
double _sol2[]={cospi6,-sinpi6,1};
Vector sol1(3,_sol1);
Vector sol2(3,_sol2);
System sys(f);
RoundRobin rr(1e-3);
CellStack stack;
CtcHC4 hc4(sys);
VarSet params(sys.f_ctrs,sys.args[2],false);
Vector prec(3,1e-3);
Solver solver(sys,hc4,rr,stack,prec,prec);
solver.set_params(params);
IntervalVector box(3);
box[0]=Interval(-10,10);
box[1]=Interval(-10,10);
box[2]=Interval(1,1);
solver.start(box);
CovSolverData::BoxStatus status;
bool res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::SOLUTION);
CPPUNIT_ASSERT(solver.get_data().nb_solution()==1);
CPPUNIT_ASSERT(solver.get_data().solution(0).is_superset(sol1));
res=solver.next(status);
CPPUNIT_ASSERT(status==CovSolverData::SOLUTION);
CPPUNIT_ASSERT(solver.get_data().nb_solution()==2);
CPPUNIT_ASSERT(solver.get_data().solution(1).is_superset(sol2));
res=solver.next(status);
CPPUNIT_ASSERT(!res);
}
void TestSolver::circle3() {
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
SystemFactory f;
f.add_var(x);
f.add_var(y);
f.add_ctr(sqr(x)+sqr(y)=1);
f.add_ctr(sqr(x-1)+sqr(y)=1);
double cospi6=0.5;
double sinpi6=(sqrt(Interval(3))/2).lb();
f.add_ctr(4*y*abs(y)<=3); // a rigorous way to impose y<=sin(pi/6).
double _sol1[]={cospi6,sinpi6};
double _sol2[]={cospi6,-sinpi6};
Vector sol1(2,_sol1);
Vector sol2(2,_sol2);
System sys(f);
RoundRobin rr(1e-3);
CellStack stack;
CtcHC4 hc4(sys);
Vector prec(2,1e-3);
Solver solver(sys,hc4,rr,stack,prec,prec);
solver.start(IntervalVector(2,Interval(-10,10)));
CovSolverData::BoxStatus status;
bool res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::UNKNOWN);
CPPUNIT_ASSERT(solver.get_data().nb_unknown()==1);
CPPUNIT_ASSERT(solver.get_data().unknown(0).is_superset(sol1));
res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::SOLUTION);
CPPUNIT_ASSERT(solver.get_data().nb_solution()==1);
CPPUNIT_ASSERT(solver.get_data().solution(0).is_superset(sol2));
res=solver.next(status);
CPPUNIT_ASSERT(!res);
}
int main() {
ofstream output;
output.open ("doc-modeling.txt");
output << "================= this file is generated ==============" << endl;
{
output << "! [func-eval-O]" << endl;
//! [func-eval-C]
const int nb_rows=2;
const int nb_cols=2;
Variable a(nb_rows,nb_cols),b(nb_rows,nb_cols),c(nb_rows,nb_cols);
Function pA(a,b,c,a);
Function pB(a,b,c,b);
Function pC(a,b,c,c);
Function f(a,b,c, (a+b-c));
double _A[nb_rows*nb_cols][2]={{2,2},{-1,-1},{-1,-1},{2,2}};
IntervalMatrix MA(2,2,_A);
double _B[nb_rows*nb_cols][2]={{1,1},{-1,-1},{1,1},{1,1}};
IntervalMatrix MB(2,2,_B);
double _C[nb_rows*nb_cols][2]={{1,1},{0,0},{0,0},{1,1}};
IntervalMatrix MC(2,2,_C);
IntervalVector box(3*nb_rows*nb_cols);
// the backward call on pA will force the sub-vector of
// "box" that represents the domain of "a" to contain the
// interval matrix "MA".
pA.backward(MA,box);
// idem
pB.backward(MB,box);
pC.backward(MC,box);
IntervalMatrix M = f.eval_matrix(box);
output << "A+B-C=" << M << endl;
//! [func-eval-C]
output << "! [func-eval-O]" << endl;
}
{
output << "! [func-hansen-O]" << endl;
//! [func-hansen-C]
Variable x,y;
Function f(x,y,Return(sqr(x)*y,sqr(y)*x));
IntervalMatrix H(2,2);
IntervalVector box(2,Interval(1,2));
f.hansen_matrix(box,H);
output << "Hansen matrix:\n" << H << endl;
//! [func-hansen-C]
output << "! [func-hansen-O]" << endl;
}
{
output << "! [func-cpp1-O]" << endl;
//! [func-cpp1-C]
Variable x("x");
Variable y("y");
Function f(x,y,sin(x+y)); // create the function (x,y)->sin(x+y)
output << f << endl;
//! [func-cpp1-C]
output << "! [func-cpp1-O]" << endl;
}
{
//! [func-cpp2-C]
Variable a,b,c,d,e,f;
Function _f(a,b,c,d,e,f,a+b+c+d+e+f);
//! [func-cpp2-C]
}
{
output << "! [func-cpp3-O]" << endl;
//! [func-cpp3-C]
Variable x[7]; // not to be confused with x(7)
Array<const ExprSymbol> vars(7);
for (int i=0; i<7; i++)
vars.set_ref(i,x[i]);
Function f(vars, x[0]+x[1]+x[2]+x[3]+x[4]+x[5]+x[6]);
output << f << endl;
//! [func-cpp3-C]
output << "! [func-cpp3-O]" << endl;
}
{
output << "! [func-cpp4-O]" << endl;
//! [func-cpp4-C]
Variable x,y;
Function f(x,y,ibex::min(x,y));
output << f << endl;
//! [func-cpp4-C]
output << "! [func-cpp4-O]" << endl;
}
{
//! [func-cpp-symbols-C]
Variable xa,xb,ya,yb;
Function dist(xa,xb,ya,yb, sqrt(sqr(xa-xb)+sqr(ya-yb)));
//! [func-cpp-symbols-C]
}
{
//! [func-cpp-vec-args-C]
Variable a(2);
Variable b(2);
Function dist(a,b,sqrt(sqr(a[0]-b[0])+sqr(a[1]-b[1])),"dist");
//! [func-cpp-vec-args-C]
}
{
//! [func-cpp-compo-C]
//! [func-cpp-compo-C]
}
{
// ![func-dag-C]
Variable x;
const ExprNode& e=cos(x)+1;
Function f(x,Return(pow(e,2),pow(e,3)));
// ![func-dag-C]
}
{
output << "![func-iterated-sum-O]" << endl;
// ![func-iterated-sum-C]
int N=10;
Variable x(N,"x");
const ExprNode* e=&(sqr(x[0]));
for (int i=1; i<N; i++)
e = & (*e + sqr(x[i]));
Function f(x,*e,"f");
output << f << endl;
// ![func-iterated-sum-C]
output << "![func-iterated-sum-O]" << endl;
}
{
output << "![func-apply-array-O]" << endl;
// ![func-apply-array-C]
Variable x,y;
// formal arguments
Array<const ExprSymbol> vars(2);
vars.set_ref(0,x);
vars.set_ref(1,y);
Function f(vars, x+y,"f");
// actual arguments
const ExprSymbol& z=ExprSymbol::new_("z"); // <=> "Variable z" (but more "safe")
const ExprConstant& c=ExprConstant::new_scalar(1.0);
// =============================================
// before release 2.1.6:
// const ExprNode* args[2];
// args[0]=&z;
// args[1]=&c;
// before release 2.1.6:
// from release 2.1.6 and subsequents:
Array<const ExprNode> args(2);
args.set_ref(0,z);
args.set_ref(1,c);
// =============================================
Function g(z,f(args),"g");
output << g << endl;
// ![func-apply-array-C]
output << "![func-apply-array-O]" << endl;
}
{
output << "![func-diff-O]" << endl;
// ![func-diff-C]
Function f("x","y","z","x*y*z");
Function df(f,Function::DIFF);
output << "df=" << df << endl;
// ![func-diff-C]
output << "![func-diff-O]" << endl;
}
{
Variable x("x"),y("y");
SystemFactory fac;
fac.add_var(x);
fac.add_var(y);
fac.add_ctr(sqr(x)+sqr(y)<=1);
fac.add_ctr(y>=sqr(x));
fac.add_ctr(y+x=1);
System sys(fac);
output << "![sys-copy-O]" << endl;
// ![sys-copy-C]
output << "original system:" << endl;
output << "-------------------------"<< endl;
output << sys;
output << "-------------------------"<< endl << endl;
System sys2(sys,System::INEQ_ONLY);
output << "system with only inequalities" << endl;
output << "-------------------------"<< endl;
output << sys2;
output << "-------------------------"<< endl << endl;
// ![sys-copy-C]
output << "![sys-copy-O]" << endl;
output << "![sys-normalize-O]" << endl;
// ![sys-normalize-C]
output << "original system:" << endl;
output << "-------------------------"<< endl;
output << sys;
output << "-------------------------"<< endl << endl;
// normalize the system with a "thickness"
// set to 0.1
NormalizedSystem norm_sys(sys,0.1);
output << "normalized system:" << endl;
output << "-------------------------"<< endl;
output << norm_sys;
output << "-------------------------"<< endl;
// ![sys-normalize-C]
output << "![sys-normalize-O]" << endl;
}
{
Variable x("x"),y("y");
SystemFactory fac;
fac.add_var(x);
fac.add_var(y);
fac.add_goal(x+y);
fac.add_ctr(sqr(x)+sqr(y)<=1);
fac.add_ctr(y<=sqr(x));
System sys(fac);
output << "![sys-extended-O]" << endl;
// ![sys-extended-C]
output << "original system:" << endl;
output << "-------------------------"<< endl;
output << sys;
output << "-------------------------"<< endl;
output << " number of variables:" << sys.nb_var << endl;
output << " number of constraints:" << sys.nb_ctr << endl << endl;
ExtendedSystem ext_sys(sys);
output << "extended system:" << endl;
output << "-------------------------"<< endl;
output << ext_sys;
output << "-------------------------"<< endl;
output << " number of variables:" << ext_sys.nb_var << endl;
output << " number of constraints:" << ext_sys.nb_ctr << endl;
output << " goal name:" << ext_sys.goal_name() << endl;
output << " goal variable:" << ext_sys.goal_var() << endl;
output << " goal constraint:" << ext_sys.goal_ctr() << endl;
// ![sys-extended-C]
output << "![sys-extended-O]" << endl;
}
{
Variable x("x"),y("y");
SystemFactory fac;
fac.add_var(x);
fac.add_var(y);
fac.add_goal(x+y);
fac.add_ctr(sqr(x)+sqr(y)<=1);
System sys(fac);
output << "![sys-fritz-john-O]" << endl;
// ![sys-fritz-john-C]
output << "original system:" << endl;
output << "-------------------------"<< endl;
output << sys;
output << "-------------------------"<< endl;
FritzJohnCond fj(sys);
output << "Fritz-John system:" << endl;
output << "-------------------------"<< endl;
output << fj << endl;
output << "-------------------------"<< endl;
output << " number of variables:" << fj.nb_var << endl;
// ![sys-fritz-john-C]
output << "![sys-fritz-john-O]" << endl;
}
output.close();
return 0;
}
int main() {
ofstream output;
output.open ("doc-contractor.txt");
output << "================= this file is generated ==============" << endl;
{
vibes::beginDrawing ();
vibes::newFigure("ctc-compo");
//! [ctc-compo-1-C]
// Create the function corresponding to an
// hyperplane of angle alpha
Variable x,y,alpha;
Function f(x,y,alpha,cos(alpha)*x+sin(alpha)*y);
// Size of the polygon
int n=7;
// Array to store constraints (for cleanup)
Array<NumConstraint> ctrs(2*n);
// Arrays to store contractors
Array<Ctc> ctc_out(n), ctc_in(n);
for (int i=0; i<n; i++) {
// create the constraints of the two half-spaces
// delimited by f(x,y,i*2pi/n)=0
// and store them in the array
ctrs.set_ref(2*i, *new NumConstraint(x,y,f(x,y,i*2*Interval::pi()/n)<=1));
ctrs.set_ref(2*i+1,*new NumConstraint(x,y,f(x,y,i*2*Interval::pi()/n)>1));
// create the contractors for these constraints
// and place them in the arrays
ctc_out.set_ref(i,*new CtcFwdBwd(ctrs[2*i]));
ctc_in.set_ref(i, *new CtcFwdBwd(ctrs[2*i+1]));
}
// Composition of the "outer" contractors
CtcCompo ctc_polygon_out(ctc_out);
// Union of the "inner" contractors
CtcUnion ctc_polygon_in(ctc_in);
//! [ctc-compo-1-C]
SepCtcPair sep(ctc_polygon_in,ctc_polygon_out);
Set set(2);
sep.contract(set,0.01);
ToVibes to_vibes(2);
set.visit(to_vibes);
vibes::endDrawing();
//! [ctc-compo-2-C]
// ************ cleanup ***************
for (int i=0; i<n; i++) {
delete &ctc_in[i];
delete &ctc_out[i];
}
for (int i=0; i<2*n; i++) {
delete &ctrs[i];
}
//! [ctc-compo-2-C]
}
{
output << "! [ctc-propag-O]" << endl;
//! [ctc-propag-2-C]
// Load a system of constraints
System sys(IBEX_BENCHS_DIR "/polynom/DiscreteBoundary-0100.bch");
// The array of contractors we will use
Array<Ctc> ctc(sys.nb_ctr);
for (int i=0; i<sys.nb_ctr; i++)
// Create contractors from constraints and store them in "ctc"
ctc.set_ref(i,*new Count(sys.ctrs[i]));
//! [ctc-propag-2-C]
//! [ctc-propag-3-C]
double prec=1e-03; // Precision upto which we calculate the fixpoint
//! [ctc-propag-3-C]
//! [ctc-propag-4-C]
// =============================== with simple fixpoint ==============================
Count::count=0; // initialize the counter
CtcCompo compo(ctc); // make the composition of all contractors
CtcFixPoint fix(compo,prec); // make the fixpoint
IntervalVector box=sys.box; // tested box (load domains written in the file)
fix.contract(box);
output << " Number of contractions with simple fixpoint=" << Count::count << endl;
//! [ctc-propag-4-C]
//! [ctc-propag-5-C]
// ================================= with propagation =================================
Count::count=0; // initialize the counter
CtcPropag propag(ctc, prec); // Propagation of all contractors
IntervalVector box2=sys.box; // tested box (load domains written in the file)
propag.contract(box2);
output << " Number of contractions with propagation=" << Count::count << endl;
output << " Are the results the same? " << (box.rel_distance(box2)<prec? "YES" : "NO") << endl;
//! [ctc-propag-5-C]
output << "! [ctc-propag-O]" << endl;
}
{
output << "! [ctc-input-output-O]" << endl;
// Load a system of constraints
System sys(IBEX_BENCHS_DIR "/polynom/DiscreteBoundary-0100.bch");
// The array of contractors we will use
Array<Ctc> ctc(sys.nb_ctr);
for (int i=0; i<sys.nb_ctr; i++)
// Create contractors from constraints and store them in "ctc"
ctc.set_ref(i,*new Count2(sys.ctrs[i]));
//! [ctc-propag-2-C]
//! [ctc-propag-3-C]
double prec=1e-03; // Precision upto which we calculate the fixpoint
//! [ctc-propag-3-C]
//! [ctc-propag-4-C]
// =============================== with simple fixpoint ==============================
Count2::count=0; // initialize the counter
CtcPropag propag(ctc, prec); // Propagation of all contractors
IntervalVector box2=sys.box; // tested box (load domains written in the file)
propag.contract(box2);
output << " Number of contractions with propagation=" << Count2::count << endl;
output << "! [ctc-input-output-O]" << endl;
}
{
output << "! [ctc-hc4-O]" << endl;
//! [ctc-hc4-C]
// Load a system of equations
System sys(IBEX_BENCHS_DIR "/others/hayes1.bch");
// Create the HC4 propagation loop with this system
CtcHC4 hc4(sys);
// Test the contraction
IntervalVector box(sys.box);
output << " Box before HC4:" << box << endl;
hc4.contract(box);
output << " Box after HC4:" << box << endl;
//! [ctc-hc4-C]
output << "! [ctc-hc4-O]" << endl;
}
{
output << "! [ctc-inv-O]" << endl;
//! [ctc-inv-C]
// Build a contractor on R² wrt (x>=0 and y>=0).
Function gx("x","y","x"); // build (x,y)->x
Function gy("x","y","y"); // build (x,y)->y
NumConstraint geqx(gx,GEQ); // build x>=0
NumConstraint geqy(gy,GEQ); // build y>=0
CtcFwdBwd cx(geqx);
CtcFwdBwd cy(geqy);
CtcCompo compo(cx,cy); // final contractor wrt (x>=0, y>=0)
// Build a mapping from R to R²
Function f("t","(cos(t),sin(t))");
// Build the inverse contractor
CtcInverse inv(compo,f);
double pi=3.14;
IntervalVector box(1,Interval(0,2*pi));
inv.contract(box);
output << "contracted box (first time):" << box << endl;
inv.contract(box);
output << "contracted box (second time):" << box << endl;
//! [ctc-inv-C]
output << "! [ctc-inv-O]" << endl;
}
{
output << "! [ctc-polytope-1-O]" << endl;
//! [ctc-polytope-1-C]
// build the matrix
double _A[4]= {1,1,1,-1};
Matrix A(2,2,_A);
// build the vector
Vector b=Vector::zeros(2);
// create the linear system (with fixed matrix/vector)
LinearizerFixed lin(A,b);
// create the contractor w.r.t the linear system
CtcPolytopeHull ctc(lin);
// create a box
IntervalVector box(2,Interval(-1,1));
// contract it
output << "box before contraction=" << box << endl;
ctc.contract(box);
output << "box after contraction=" << box << endl;
//! [ctc-polytope-1-C]
output << "! [ctc-polytope-1-O]" << endl;
}
{
output << "! [ctc-exist-1-O]" << endl;
//! [ctc-exist-1-C]
// create a constraint on (x,y)
Variable x,y;
NumConstraint c(x,y,sqr(x)+sqr(y)<=1);
// create domains for x and y
IntervalVector box_x(1, Interval(-10,10));
IntervalVector box_y(1, Interval(-1,1));
// set the precision that controls how much y will be bisected
double epsilon=1.0;
// create a contractor on x by transforming y into an
// existentially-quantified parameter.
CtcExist exist_y(c,y,box_y,epsilon);
// contract the domain of x
output << "box before contraction=" << box_x << endl;
exist_y.contract(box_x);
output << "box after contraction=" << box_x << endl;
//! [ctc-exist-1-C]
output << "! [ctc-exist-1-O]" << endl;
}
{
output << "! [ctc-exist-2-O]" << endl;
//! [ctc-exist-2-C]
// create a conjunction of two constraint on (x,y)
Variable x,y;
Function f(x,y,Return(sqr(x)+sqr(2*y-y),y-x));
IntervalVector z(2);
z[0]=Interval(0,1);
z[1]=Interval::zero();
NumConstraint c(x,y,f(x,y)=z);
// create domains for y
IntervalVector box_y(1, Interval(-1,1));
// observe the result of the contraction for
// different precision epsilon=10^{-_log}
for (int _log=0; _log<=8; _log++) {
// create the domain for x
IntervalVector box_x(1, Interval(-10,10));
// create the exist-contractor with the new precision
CtcExist exist_y(c,y,box_y,::pow(10,-_log));
// contract the box
exist_y.contract(box_x);
output << "epsilon=1e-" << _log << " box after contraction=" << box_x << endl;
}
//! [ctc-exist-2-C]
output << "! [ctc-exist-2-O]" << endl;
}
{
output << "! [ctc-exist-3-O]" << endl;
//! [ctc-exist-3-C]
// create a system
Variable x,y;
SystemFactory fac;
fac.add_var(x);
fac.add_var(y);
fac.add_ctr(sqr(x)+sqr(2*y-y)<=1);
fac.add_ctr(x=y);
System sys(fac);
CtcHC4 hc4(sys);
// create domains for y
IntervalVector box_y(1, Interval(-1,1));
// Creates the bitset structure that indicates which
// component are "quantified". The indices vary
// from 0 to 1 (2 variables only). The bitset is
// initially empty which means that, by default,
// all the variables are parameters.
BitSet vars(2);
// Add "x" as variable.
vars.add(0);
// observe the result of the contraction for
// different precision epsilon=10^{-_log}
for (int _log=0; _log<=8; _log++) {
// create the domain for x
IntervalVector box_x(1, Interval(-10,10));
// create the exist-contractor with the new precision
CtcExist exist_y(hc4,vars,box_y,::pow(10,-_log));
// contract the box
exist_y.contract(box_x);
output << "epsilon=1e-" << _log << " box after contraction=" << box_x << endl;
}
//! [ctc-exist-3-C]
output << "! [ctc-exist-3-O]" << endl;
}
}
int main() {
ofstream output;
output.open ("doc-covfiles.txt");
output << "================= this file is generated ==============" << endl;
{
//! [cov-ex1-build-C]
// create a simple inequality x^2+y^2<=1.
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
SystemFactory fac;
fac.add_var(x);
fac.add_var(y);
fac.add_ctr(sqr(x)+sqr(y)<=1);
System sys(fac);
// run the solver with a coarse precision (1.0)
// to have a limited number of boxes
DefaultSolver solver(sys,1);
// we set a very short storage capacity
// to have a partial solving only.
solver.cell_limit = 12;
solver.solve(sys.box);
//! [cov-ex1-build-C]
{
output << "! [cov-ex1-list-O]" << endl;
//! [cov-ex1-list-C]
const CovList& cov = solver.get_data();
output << "The list contains " << cov.size() << " boxes" << endl;
for (size_t i=0; i<cov.size(); i++) {
output << "box n°" << i << " = " << cov[i] << endl;
}
//! [cov-ex1-list-C]
output << "! [cov-ex1-list-O]" << endl;
}
{
output << "! [cov-ex1-IUlist-O]" << endl;
//! [cov-ex1-IUlist-C]
const CovIUList& cov = solver.get_data();
output << "Inner boxes:" << endl;
for (size_t i=0; i<cov.nb_inner(); i++) {
output << "inner n°" << i << " = " << cov.inner(i) << endl;
}
output << endl << "Unknown boxes:" << endl;
for (size_t i=0; i<cov.nb_unknown(); i++) {
output << "unknown n°" << i << " = " << cov.unknown(i) << endl;
}
//! [cov-ex1-IUlist-C]
output << "! [cov-ex1-IUlist-O]" << endl;
}
{
output << "! [cov-ex1-SolverData-O]" << endl;
//! [cov-ex1-SolverData-C]
const CovSolverData& cov = solver.get_data();
output << "Inner boxes:" << endl;
for (size_t i=0; i<cov.nb_inner(); i++) {
output << "inner n°" << i << " = " << cov.inner(i) << endl;
}
output << endl << "Unknown boxes:" << endl;
for (size_t i=0; i<cov.nb_unknown(); i++) {
output << "unknown n°" << i << " = " << cov.unknown(i) << endl;
}
output << endl << "Pending boxes:" << endl;
for (size_t i=0; i<cov.nb_pending(); i++) {
output << "Pending n°" << i << " = " << cov.pending(i) << endl;
}
//! [cov-ex1-SolverData-C]
output << "! [cov-ex1-SolverData-O]" << endl;
}
}
{
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
SystemFactory fac;
fac.add_var(x);
fac.add_var(y);
fac.add_ctr(sqr(x)+sqr(y)<=1);
System sys(fac);
//! [cov-ex2-solver-C]
// solve the problem with boundary boxes
// of diameter < 0.1
DefaultSolver solver(sys,0.1,0.1);
solver.solve(sys.box);
//! [cov-ex2-solver-C]
//! [cov-ex2-optim-C]
SystemFactory opt_fac;
opt_fac.add_var(x);
opt_fac.add_var(y);
opt_fac.add_goal(x+y);
System opt(opt_fac);
//! [cov-ex2-optim-C]
output << "! [cov-ex2-run-O]" << endl;
//! [cov-ex2-run-C]
DefaultOptimizer optim(opt);
// run the optimizer with solver data as input covering:
optim.optimize(solver.get_data());
output << " best bound=" << optim.get_loup() << endl;
//! [cov-ex2-run-C]
output << "! [cov-ex2-run-O]" << endl;
}
{
//! [cov-ex3-optim-sys-C]
// build the problem "minimize |x^2+y^2-1|"
// -------------------------------------
Function g("x","y","abs(x^2+y^2-[0.9,1.1])");
SystemFactory opt_fac;
opt_fac.add_var(g.args());
opt_fac.add_goal(g);
System opt(opt_fac);
// we need bounded domain for unconstrained optimization:
opt.box[0]=Interval(-100,100);
opt.box[1]=Interval(-100,100);
// -------------------------------------
//! [cov-ex3-optim-sys-C]
//! [cov-ex3-optim-run-C]
// solve it
DefaultOptimizer optim(opt); // 1 is a very coarse precision
optim.timeout = 1;
optim.extended_COV = false;
optim.optimize(opt.box);
//! [cov-ex3-optim-run-C]
//! [cov-ex3-solver-sys-C]
// Build the system "solve x+y=0"
// -------------------------------------
Function f("x","y","x-y");
NumConstraint c(f);
SystemFactory sys_fac;
sys_fac.add_var(g.args());
sys_fac.add_ctr(c);
System sys(sys_fac);
// -------------------------------------
//! [cov-ex3-solver-sys-C]
output << "! [cov-ex3-solver-run-O]" << endl;
//! [cov-ex3-solver-run-C]
// solve the problem
DefaultSolver solver(sys,0.1,0.1);
solver.solve(optim.get_data());
output << solver.get_data() << endl;
//! [cov-ex3-solver-run-C]
output << "! [cov-ex3-solver-run-O]" << endl;
}
}