void
TensorProductBasis<BASIS0,BASIS1>::reconstruct_1(const Index& lambda,
const int j,
InfiniteVector<double, Index>& c) const {
if (lambda.j() >= j) {
// then we can just copy \psi_\lambda
c.add_coefficient(lambda, 1.0);
} else {
// reconstruct by recursion
typedef typename BASIS0::Index Index0;
typedef typename BASIS1::Index Index1;
InfiniteVector<double,Index0> c1;
InfiniteVector<double,Index1> c2;
basis0().reconstruct_1(lambda.index0(), lambda.j()+1, c1);
basis1().reconstruct_1(lambda.index1(), lambda.j()+1, c2);
for (typename InfiniteVector<double,Index0>::const_iterator it1(c1.begin()), it1end(c1.end());
it1 != it1end; ++it1)
for (typename InfiniteVector<double,Index1>::const_iterator it2(c2.begin()), it2end(c2.end());
it2 != it2end; ++it2) {
InfiniteVector<double,Index> d;
reconstruct_1(Index(it1.index(), it2.index()), j, d);
c.add(*it1 * *it2, d);
}
}
}
void
TensorProductBasis<BASIS0,BASIS1>::decompose_1(const Index& lambda,
const int j0,
InfiniteVector<double, Index>& c) const {
assert(lambda.j() >= j0);
c.clear();
if (lambda.index0().e() != 0 || lambda.index1().e() != 0) {
// the true wavelet coefficients don't have to be modified
c.set_coefficient(lambda, 1.0);
} else {
// a generator on a (possibly) fine level
if (lambda.j() == j0) {
// generators from the coarsest level can be copied
c.set_coefficient(lambda, 1.0);
} else {
// j>j0, perform multiscale decomposition
typedef typename BASIS0::Index Index0;
typedef typename BASIS1::Index Index1;
InfiniteVector<double,Index0> c1;
InfiniteVector<double,Index1> c2;
basis0().decompose_1(lambda.index0(), lambda.j()-1, c1);
basis1().decompose_1(lambda.index1(), lambda.j()-1, c2);
for (typename InfiniteVector<double,Index0>::const_iterator it1(c1.begin()), it1end(c1.end());
it1 != it1end; ++it1)
for (typename InfiniteVector<double,Index1>::const_iterator it2(c2.begin()), it2end(c2.end());
it2 != it2end; ++it2) {
// if (it1.index().e() == 0 && it2.index().e() == 0) { // generators have to be refined further
InfiniteVector<double,Index> d;
decompose_1(Index(it1.index(), it2.index()), j0, d);
c.add(*it1 * *it2, d);
// } else
// c.set_coefficient(Index(this, it1.index(), it2.index()), *it1 * *it2);
}
}
}
}
Matrix<double> BspCurvBasisFuncSet::CreateMatrixIntegral(int lev1, int lev2) const
{
KnotSet kset1 = KnotSet(*kts,ord,num).CreateKnotSetDeriv(lev1);
KnotSet kset2 = KnotSet(*kts,ord,num).CreateKnotSetDeriv(lev2);
Matrix<double> mat(kset1.GetNum()-(ord-lev1),kset2.GetNum()-(ord-lev2));
BspCurvBasisFuncSet basis1(kset1.GetKnots(),ord-lev1,kset1.GetNum());
BspCurvBasisFuncSet basis2(kset2.GetKnots(),ord-lev2,kset2.GetNum());
// find the first basis function for which the last distinct
// knot is greater than x1
Matrix<double> mat1(kset1.GetNum()-ord+lev1,kset2.GetNum()-ord+lev2,0.0);
for (int i=0; i<kset1.GetNum()-ord+lev1; i++)
for (int j=0; j<kset2.GetNum()-ord+lev2; j++) {
// create the two std::sets representing the two knot std::sets
Vector<double> temp1((*(basis1.b))[i].GetKnots());
Vector<double> temp2((*(basis2.b))[j].GetKnots());
std::set<double> s1(temp1.begin(),temp1.end());
std::set<double> s2(temp2.begin(),temp2.end());
if (*(--s2.end()) > *(s1.begin())) {
// form the intersection
std::set<double> s3;
std::set_intersection(s1.begin(),s1.end(),s2.begin(),s2.end(),std::inserter(s3,s3.begin()));
// if there is an intersection
if (s3.size() > 1) {
Vector<double> v(s3.size());
std::set<double>::iterator s = s3.begin();
// copy the elements into a vector
for (unsigned int k=0; k<s3.size(); k++) v[k] = *s++;
// create the compbezcurvs
Vector<BezCurv<double> > vec1(s3.size()-1);
Vector<BezCurv<double> > vec2(s3.size()-1);
BspCurv<double> b1((*(basis1.b))[i].GetBspCurv()), b2((*(basis2.b))[j].GetBspCurv());
// find the segments of intersection
for (unsigned int k=0; k<s3.size()-1; k++) {
int segb1 = b1.GetKnotSet().Find_segment(v[k]);
int segb2 = b2.GetKnotSet().Find_segment(v[k]);
vec1[k] = b1.GetSegment(segb1);
vec2[k] = b2.GetSegment(segb2);
}
CompBezCurv<double> cb1(vec1,s3.size()-1,v);
CompBezCurv<double> cb2(vec2,s3.size()-1,v);
CompBezCurv<double> prod = cb1.Product(cb2);
mat1[i][j] = prod.ConvertBspCurv().Integrate((*kts)[ord-1],(*kts)[num-ord]);
}
}
}
return mat1;
}
