void Gradient::jacobian(const Array<Domain>& d, IntervalMatrix& J) {
if (!f.expr().dim.is_vector()) {
ibex_error("Cannot called \"jacobian\" on a real-valued function");
}
int m=f.expr().dim.vec_size();
// calculate the gradient of each component of f
for (int i=0; i<m; i++) {
const Function* fi=dynamic_cast<const Function*>(&f[i]);
if (fi!=NULL) {
// if this is a Function object we can
// directly calculate the gradient with d
fi->deriv_calculator().gradient(d,J[i]);
} else {
// otherwise we must give a box in argument
// TODO add gradient with Array<Domain> in argument
// in Function interface?
// But, for the moment, cannot happen, because
// this function is called by apply_bwd.
IntervalVector box(f.nb_var());
load(box,d);
f[i].gradient(box,J[i]);
if (J[i].is_empty()) { J.set_empty(); return; }
}
}
}
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;
}
bool proj_mul(const IntervalMatrix& y, Interval& x1, IntervalMatrix& x2) {
int n=(y.nb_rows());
assert((x2.nb_rows())==n && (x2.nb_cols())==(y.nb_cols()));
for (int i=0; i<n; i++) {
if (!proj_mul(y[i],x1,x2[i])) {
x2.set_empty();
return false;
}
}
return true;
}
bool proj_mul(const IntervalVector& y, IntervalMatrix& x1, IntervalVector& x2, double ratio) {
assert(x1.nb_rows()==y.size());
assert(x1.nb_cols()==x2.size());
int last_row=0;
int i=0;
int n=y.size();
do {
IntervalVector x2old=x2;
if (!proj_mul(y[i],x1[i],x2)) {
x1.set_empty();
return false;
}
if (x2old.rel_distance(x2)>ratio) last_row=i;
i=(i+1)%n;
} while(i!=last_row);
return true;
}
