IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::getGeneralCoeffConstraints(const Eigen::VectorXi &isConstrained,
const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
int k,
const Eigen::VectorXi &rootsIndex,
Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> &Ck)
{
int numConstrained = isConstrained.sum();
Ck.resize(numConstrained,1);
// int n = rootsIndex.cols();
Eigen::MatrixXi allCombs;
{
Eigen::VectorXi V = Eigen::VectorXi::LinSpaced(n,0,n-1);
igl::nchoosek(V,k+1,allCombs);
}
int ind = 0;
for (int fi = 0; fi <numF; ++fi)
{
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b1 = B1.row(fi);
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b2 = B2.row(fi);
if(isConstrained[fi])
{
std::complex<typename DerivedV::Scalar> ck(0);
for (int j = 0; j < allCombs.rows(); ++j)
{
std::complex<typename DerivedV::Scalar> tk(1.);
//collect products
for (int i = 0; i < allCombs.cols(); ++i)
{
int index = allCombs(j,i);
int ri = rootsIndex[index];
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> w;
if (ri>0)
w = cfW.block(fi,3*(ri-1),1,3);
else
w = -cfW.block(fi,3*(-ri-1),1,3);
typename DerivedV::Scalar w0 = w.dot(b1);
typename DerivedV::Scalar w1 = w.dot(b2);
std::complex<typename DerivedV::Scalar> u(w0,w1);
tk*= u;
}
//collect sum
ck += tk;
}
Ck(ind) = ck;
ind ++;
}
}
}
IGL_INLINE bool igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::
solve(const Eigen::VectorXi &isConstrained,
const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
const Eigen::VectorXi &rootsIndex,
Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &output)
{
// polynomial is of the form:
// z^(2n) +
// -c[0]z^(2n-1) +
// c[1]z^(2n-2) +
// -c[2]z^(2n-3) +
// ... +
// (-1)^n c[n-1]
std::vector<Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1>> coeffs(n,Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1>::Zero(numF, 1));
for (int i =0; i<n; ++i)
{
int degree = i+1;
Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> Ck;
getGeneralCoeffConstraints(isConstrained,
cfW,
i,
rootsIndex,
Ck);
Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > DD;
computeCoefficientLaplacian(degree, DD);
Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > f; f.resize(numF,1);
if (isConstrained.sum() == numF)
coeffs[i] = Ck;
else
minQuadWithKnownMini(DD, f, isConstrained, Ck, coeffs[i]);
}
std::vector<Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> > pv;
setFieldFromGeneralCoefficients(coeffs, pv);
output.setZero(numF,3*n);
for (int fi=0; fi<numF; ++fi)
{
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b1 = B1.row(fi);
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b2 = B2.row(fi);
for (int i=0; i<n; ++i)
output.block(fi,3*i, 1, 3) = pv[i](fi,0)*b1 + pv[i](fi,1)*b2;
}
return true;
}
IGL_INLINE void igl::PolyVectorFieldFinder<DerivedV, DerivedF>::getGeneralCoeffConstraints(const Eigen::VectorXi &isConstrained,
const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
int k,
Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> &Ck)
{
int numConstrained = isConstrained.sum();
Ck.resize(numConstrained,1);
int n = cfW.cols()/3;
std::vector<std::vector<int>> allCombs;
igl::nchoosek(0,k+1,n,allCombs);
int ind = 0;
for (int fi = 0; fi <numF; ++fi)
{
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b1 = B1.row(fi);
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b2 = B2.row(fi);
if(isConstrained[fi])
{
std::complex<typename DerivedV::Scalar> ck(0);
for (int j = 0; j < allCombs.size(); ++j)
{
std::complex<typename DerivedV::Scalar> tk(1.);
//collect products
for (int i = 0; i < allCombs[j].size(); ++i)
{
int index = allCombs[j][i];
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &w = cfW.block(fi,3*index,1,3);
typename DerivedV::Scalar w0 = w.dot(b1);
typename DerivedV::Scalar w1 = w.dot(b2);
std::complex<typename DerivedV::Scalar> u(w0,w1);
tk*= u*u;
}
//collect sum
ck += tk;
}
Ck(ind) = ck;
ind ++;
}
}
}