TEST(EigenEmbedding, ArpackSparseSmallestEigenvector)
{
const int N = 3;
tapkee::tapkee_internal::SparseTriplets sparse_triplets;
for (int i=0; i<N; i++)
sparse_triplets.push_back(tapkee::tapkee_internal::SparseTriplet(i,i,tapkee::ScalarType(i+1)));
#ifdef EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
Eigen::DynamicSparseMatrix<tapkee::ScalarType> dynamic_weight_matrix(N,N);
dynamic_weight_matrix.reserve(sparse_triplets.size());
for (tapkee::tapkee_internal::SparseTriplets::const_iterator it=sparse_triplets.begin(); it!=sparse_triplets.end(); ++it)
dynamic_weight_matrix.coeffRef(it->col(),it->row()) += it->value();
tapkee::SparseWeightMatrix mat(dynamic_weight_matrix);
#else
tapkee::SparseWeightMatrix mat(N,N);
mat.setFromTriplets(sparse_triplets.begin(),sparse_triplets.end());
#endif
tapkee::tapkee_internal::EmbeddingResult result =
tapkee::tapkee_internal::eigen_embedding<tapkee::SparseWeightMatrix,tapkee::tapkee_internal::SparseInverseMatrixOperation>
(tapkee::Arpack, mat, 1, 0);
ASSERT_EQ(1,result.second.size());
// smallest eigenvalue is 1
ASSERT_NEAR(1,result.second[0],PRECISION);
ASSERT_EQ(1,result.first.cols());
ASSERT_EQ(3,result.first.rows());
// check if it is an eigenvector
ASSERT_NEAR(0.0,(mat*result.first - result.second[0]*result.first).norm(),PRECISION);
}
SparseMatrix sparse_matrix_from_triplets(const SparseTriplets& sparse_triplets, IndexType m, IndexType n)
{
#ifdef EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
Eigen::DynamicSparseMatrix<ScalarType> dynamic_weight_matrix(m, n);
dynamic_weight_matrix.reserve(sparse_triplets.size());
for (SparseTriplets::const_iterator it=sparse_triplets.begin(); it!=sparse_triplets.end(); ++it)
dynamic_weight_matrix.coeffRef(it->col(),it->row()) += it->value();
SparseMatrix matrix(dynamic_weight_matrix);
#else
SparseMatrix matrix(m, n);
matrix.setFromTriplets(sparse_triplets.begin(),sparse_triplets.end());
#endif
return matrix;
}
Laplacian compute_laplacian(RandomAccessIterator begin,
RandomAccessIterator end,const Neighbors& neighbors,
DistanceCallback callback, ScalarType width)
{
SparseTriplets sparse_triplets;
timed_context context("Laplacian computation");
const IndexType k = neighbors[0].size();
sparse_triplets.reserve((k+1)*(end-begin));
DenseVector D = DenseVector::Zero(end-begin);
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
const LocalNeighbors& current_neighbors = neighbors[iter-begin];
for (IndexType i=0; i<k; ++i)
{
ScalarType distance = callback(*iter,begin[current_neighbors[i]]);
ScalarType heat = exp(-distance*distance/width);
D(iter-begin) += heat;
D(current_neighbors[i]) += heat;
sparse_triplets.push_back(SparseTriplet(current_neighbors[i],(iter-begin),-heat));
sparse_triplets.push_back(SparseTriplet((iter-begin),current_neighbors[i],-heat));
}
}
for (IndexType i=0; i<(end-begin); ++i)
sparse_triplets.push_back(SparseTriplet(i,i,D(i)));
#ifdef EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
Eigen::DynamicSparseMatrix<ScalarType> dynamic_weight_matrix(end-begin,end-begin);
dynamic_weight_matrix.reserve(sparse_triplets.size());
for (SparseTriplets::const_iterator it=sparse_triplets.begin(); it!=sparse_triplets.end(); ++it)
dynamic_weight_matrix.coeffRef(it->col(),it->row()) += it->value();
SparseWeightMatrix weight_matrix(dynamic_weight_matrix);
#else
SparseWeightMatrix weight_matrix(end-begin,end-begin);
weight_matrix.setFromTriplets(sparse_triplets.begin(),sparse_triplets.end());
#endif
return Laplacian(weight_matrix,DenseDiagonalMatrix(D));
}