IGL_INLINE void igl::hessian(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedF> & F,
Eigen::SparseMatrix<Scalar>& H)
{
typedef typename DerivedV::Scalar denseScalar;
typedef typename Eigen::Matrix<denseScalar, Eigen::Dynamic, 1> VecXd;
typedef typename Eigen::SparseMatrix<Scalar> SparseMat;
typedef typename Eigen::DiagonalMatrix
<Scalar, Eigen::Dynamic, Eigen::Dynamic> DiagMat;
int dim = V.cols();
assert((dim==2 || dim==3) &&
"The dimension of the vertices should be 2 or 3");
//Construct the combined gradient matric
SparseMat G;
igl::grad(Eigen::PlainObjectBase<DerivedV>(V),
Eigen::PlainObjectBase<DerivedF>(F),
G, false);
SparseMat GG(F.rows(), dim*V.rows());
GG.reserve(G.nonZeros());
for(int i=0; i<dim; ++i)
GG.middleCols(i*G.cols(),G.cols()) = G.middleRows(i*F.rows(),F.rows());
SparseMat D;
igl::repdiag(GG,dim,D);
//Compute area matrix
VecXd areas;
igl::doublearea(V, F, areas);
DiagMat A = (0.5*areas).replicate(dim,1).asDiagonal();
//Compute FEM Hessian
H = D.transpose()*A*G;
}
SparseMat SparseMat::operator*(const SparseMat &right) const {
if(!consolidated() || !right.consolidated())
throw ErrProgrammingError("Attempt to multiply unconsolidated SparseMats!",
__FILE__, __LINE__);
SparseMat result(nrows(), right.ncols());
const SparseMat rightt = right.transpose();
for(unsigned int i=0; i<nrows(); i++) {
for(unsigned int j=0; j<rightt.nrows(); j++) {
const_row_iterator ai = begin(i);
const_row_iterator bj = rightt.begin(j);
while(ai < end(i) && bj < rightt.end(j)) {
if(ai.col() == bj.col()) {
result.insert(i, j, (*ai)*(*bj));
++ai;
++bj;
}
else if(ai.col() < bj.col())
++ai;
else
++bj;
}
}
result.consolidate_row(i);
}
// result.consolidate();
result.consolidated_ = true;
return result;
}