void Function::hansen_matrix(const IntervalVector& box, IntervalMatrix& H) const {
int n=nb_var();
int m=expr().dim.vec_size();
assert(H.nb_cols()==n);
assert(box.size()==n);
assert(expr().dim.is_vector());
assert(H.nb_rows()==m);
IntervalVector x=box.mid();
IntervalMatrix J(m,n);
// test!
// int tab[box.size()];
// box.sort_indices(false,tab);
// int var;
for (int var=0; var<n; var++) {
//var=tab[i];
x[var]=box[var];
jacobian(x,J);
H.set_col(var,J.col(var));
}
}
bool proj_mul(const IntervalMatrix& y, IntervalMatrix& x1, IntervalMatrix& x2, double ratio) {
int m=y.nb_rows();
int n=y.nb_cols();
assert(x1.nb_cols()==x2.nb_rows());
assert(x1.nb_rows()==m);
assert(x2.nb_cols()==n);
// each coefficient (i,j) of y is considered as a binary "dot product" constraint
// between the ith row of x1 and the jth column of x2
// (advantage: we have exact projection for the dot product)
//
// we propagate these constraints using a simple agenda.
Agenda a(m*n);
//init
for (int i=0; i<m; i++)
for (int j=0; j<n; j++)
a.push(i*n+j);
int k;
while (!a.empty()) {
a.pop(k);
int i=k/n;
int j=k%n;
IntervalVector x1old=x1[i];
IntervalVector x2j=x2.col(j);
IntervalVector x2old=x2j;
if (!proj_mul(y[i][j],x1[i],x2j)) {
x1.set_empty();
x2.set_empty();
return false;
} else {
if (x1old.rel_distance(x1[i])>=ratio) {
for (int j2=0; j2<n; j2++)
if (j2!=j) a.push(i*n+j2);
}
if (x2old.rel_distance(x2j)>=ratio) {
for (int i2=0; i2<m; i2++)
if (i2!=i) a.push(i2*n+j);
}
x2.set_col(j,x2j);
}
}
return true;
}
void Function::hansen_matrix(const IntervalVector& box, IntervalMatrix& H, const VarSet& set) const {
int n=set.nb_var;
int m=image_dim();
assert(H.nb_cols()==n);
assert(box.size()==nb_var());
assert(H.nb_rows()==m);
IntervalVector var_box=set.var_box(box);
IntervalVector param_box=set.param_box(box);
IntervalVector x=var_box.mid();
IntervalMatrix J(m,n);
for (int var=0; var<n; var++) {
//var=tab[i];
x[var]=var_box[var];
jacobian(set.full_box(x,param_box),J,set);
H.set_col(var,J.col(var));
}
}
