SparseMatrix NeighborhoodBuilder::build(DenseMatrix mat) const
{
/*
* This matrix contains the k_ best neighbors for every vertex.
* The candidates are sorted in ascending order.
*
* The matrix is updated for entry as correlations are computed.
* This allows us to cut the computation time in half!
*
* We allocate twice the (worst-case) storage needed, as we have
* to symmetrize the matrix afterwards. Alternatively we could
* resize later, which might lead to a full copy.
*/
std::vector<T> entries(2 * k_ * mat.rows());
std::vector<DenseMatrix::value_type> sd(mat.rows());
DenseMatrix::Vector mu = mat.matrix().rowwise().mean();
for(unsigned int i = 0; i < mat.rows(); ++i) {
mat.row(i) = mat.row(i).array() - mu[i];
sd[i] = mat.row(i).norm();
}
for(unsigned int i = 0; i < mat.rows(); ++i) {
for(unsigned int j = i + 1; j < mat.rows(); ++j) {
double cov = mat.row(i).dot(mat.row(j));
cov = fabs(cov) / (sd[i] * sd[j]);
// Insert into the entries vector
insert_(T(i, j, cov), entries.begin() + i * k_);
insert_(T(i, j, cov), entries.begin() + j * k_);
}
}
return buildMatrix_(entries, mat);
}
EmbeddingResult project(const ProjectionResult& projection_result, RandomAccessIterator begin,
RandomAccessIterator end, FeatureVectorCallback callback, unsigned int dimension)
{
timed_context context("Data projection");
DenseVector current_vector(dimension);
const DenseSymmetricMatrix& projection_matrix = projection_result.first;
DenseMatrix embedding = DenseMatrix::Zero((end-begin),projection_matrix.cols());
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
embedding.row(iter-begin) = projection_matrix.transpose()*current_vector;
}
return EmbeddingResult(embedding,DenseVector());
}
DenseMatrix project(const DenseMatrix& projection_matrix, const DenseVector& mean_vector,
RandomAccessIterator begin, RandomAccessIterator end,
FeatureVectorCallback callback, IndexType dimension)
{
timed_context context("Data projection");
DenseVector current_vector(dimension);
DenseVector current_vector_subtracted_mean(dimension);
DenseMatrix embedding = DenseMatrix::Zero((end-begin),projection_matrix.cols());
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
current_vector_subtracted_mean = current_vector - mean_vector;
embedding.row(iter-begin) = projection_matrix.transpose()*current_vector_subtracted_mean;
}
return embedding;
}
template<typename SparseMatrixType> void sparse_block(const SparseMatrixType& ref)
{
const Index rows = ref.rows();
const Index cols = ref.cols();
const Index inner = ref.innerSize();
const Index outer = ref.outerSize();
typedef typename SparseMatrixType::Scalar Scalar;
typedef typename SparseMatrixType::StorageIndex StorageIndex;
double density = (std::max)(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic,SparseMatrixType::IsRowMajor?RowMajor:ColMajor> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
typedef SparseVector<Scalar> SparseVectorType;
Scalar s1 = internal::random<Scalar>();
{
SparseMatrixType m(rows, cols);
DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
initSparse<Scalar>(density, refMat, m);
VERIFY_IS_APPROX(m, refMat);
// test InnerIterators and Block expressions
for (int t=0; t<10; ++t)
{
Index j = internal::random<Index>(0,cols-2);
Index i = internal::random<Index>(0,rows-2);
Index w = internal::random<Index>(1,cols-j);
Index h = internal::random<Index>(1,rows-i);
VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
for(Index r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
}
}
for(Index r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
}
}
VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w));
VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h));
for(Index r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r));
VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r));
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r));
VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c));
VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c));
VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
if(m.middleCols(j,w).coeff(r,c) != Scalar(0))
{
VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c));
}
if(m.middleRows(i,h).coeff(r,c) != Scalar(0))
{
VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
}
}
}
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c));
VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c));
}
}
for(Index c=0; c<cols; c++)
{
VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
}
for(Index r=0; r<rows; r++)
{
VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
}
}
// test innerVector()
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
SparseMatrixType m2(rows, cols);
initSparse<Scalar>(density, refMat2, m2);
Index j0 = internal::random<Index>(0,outer-1);
Index j1 = internal::random<Index>(0,outer-1);
Index r0 = internal::random<Index>(0,rows-1);
Index c0 = internal::random<Index>(0,cols-1);
VERIFY_IS_APPROX(m2.innerVector(j0), innervec(refMat2,j0));
VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), innervec(refMat2,j0)+innervec(refMat2,j1));
m2.innerVector(j0) *= Scalar(2);
innervec(refMat2,j0) *= Scalar(2);
VERIFY_IS_APPROX(m2, refMat2);
m2.row(r0) *= Scalar(3);
refMat2.row(r0) *= Scalar(3);
VERIFY_IS_APPROX(m2, refMat2);
m2.col(c0) *= Scalar(4);
refMat2.col(c0) *= Scalar(4);
VERIFY_IS_APPROX(m2, refMat2);
m2.row(r0) /= Scalar(3);
refMat2.row(r0) /= Scalar(3);
VERIFY_IS_APPROX(m2, refMat2);
m2.col(c0) /= Scalar(4);
refMat2.col(c0) /= Scalar(4);
VERIFY_IS_APPROX(m2, refMat2);
SparseVectorType v1;
VERIFY_IS_APPROX(v1 = m2.col(c0) * 4, refMat2.col(c0)*4);
VERIFY_IS_APPROX(v1 = m2.row(r0) * 4, refMat2.row(r0).transpose()*4);
SparseMatrixType m3(rows,cols);
m3.reserve(VectorXi::Constant(outer,int(inner/2)));
for(Index j=0; j<outer; ++j)
for(Index k=0; k<(std::min)(j,inner); ++k)
m3.insertByOuterInner(j,k) = internal::convert_index<StorageIndex>(k+1);
for(Index j=0; j<(std::min)(outer, inner); ++j)
{
VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
if(j>0)
VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
}
m3.makeCompressed();
for(Index j=0; j<(std::min)(outer, inner); ++j)
{
VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
if(j>0)
VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
}
VERIFY(m3.innerVector(j0).nonZeros() == m3.transpose().innerVector(j0).nonZeros());
// m2.innerVector(j0) = 2*m2.innerVector(j1);
// refMat2.col(j0) = 2*refMat2.col(j1);
// VERIFY_IS_APPROX(m2, refMat2);
}
// test innerVectors()
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
SparseMatrixType m2(rows, cols);
initSparse<Scalar>(density, refMat2, m2);
if(internal::random<float>(0,1)>0.5f) m2.makeCompressed();
Index j0 = internal::random<Index>(0,outer-2);
Index j1 = internal::random<Index>(0,outer-2);
Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols));
else
VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0));
else
VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
VERIFY_IS_APPROX(m2, refMat2);
VERIFY(m2.innerVectors(j0,n0).nonZeros() == m2.transpose().innerVectors(j0,n0).nonZeros());
m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);
if(SparseMatrixType::IsRowMajor)
refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval();
else
refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval();
VERIFY_IS_APPROX(m2, refMat2);
}
// test generic blocks
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
SparseMatrixType m2(rows, cols);
initSparse<Scalar>(density, refMat2, m2);
Index j0 = internal::random<Index>(0,outer-2);
Index j1 = internal::random<Index>(0,outer-2);
Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols));
else
VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols),
refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols));
else
VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0),
refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
Index i = internal::random<Index>(0,m2.outerSize()-1);
if(SparseMatrixType::IsRowMajor) {
m2.innerVector(i) = m2.innerVector(i) * s1;
refMat2.row(i) = refMat2.row(i) * s1;
VERIFY_IS_APPROX(m2,refMat2);
} else {
m2.innerVector(i) = m2.innerVector(i) * s1;
refMat2.col(i) = refMat2.col(i) * s1;
VERIFY_IS_APPROX(m2,refMat2);
}
Index r0 = internal::random<Index>(0,rows-2);
Index c0 = internal::random<Index>(0,cols-2);
Index r1 = internal::random<Index>(1,rows-r0);
Index c1 = internal::random<Index>(1,cols-c0);
VERIFY_IS_APPROX(DenseVector(m2.col(c0)), refMat2.col(c0));
VERIFY_IS_APPROX(m2.col(c0), refMat2.col(c0));
VERIFY_IS_APPROX(RowDenseVector(m2.row(r0)), refMat2.row(r0));
VERIFY_IS_APPROX(m2.row(r0), refMat2.row(r0));
VERIFY_IS_APPROX(m2.block(r0,c0,r1,c1), refMat2.block(r0,c0,r1,c1));
VERIFY_IS_APPROX((2*m2).block(r0,c0,r1,c1), (2*refMat2).block(r0,c0,r1,c1));
if(m2.nonZeros()>0)
{
VERIFY_IS_APPROX(m2, refMat2);
SparseMatrixType m3(rows, cols);
DenseMatrix refMat3(rows, cols); refMat3.setZero();
Index n = internal::random<Index>(1,10);
for(Index k=0; k<n; ++k)
{
Index o1 = internal::random<Index>(0,outer-1);
Index o2 = internal::random<Index>(0,outer-1);
if(SparseMatrixType::IsRowMajor)
{
m3.innerVector(o1) = m2.row(o2);
refMat3.row(o1) = refMat2.row(o2);
}
else
{
m3.innerVector(o1) = m2.col(o2);
refMat3.col(o1) = refMat2.col(o2);
}
if(internal::random<bool>())
m3.makeCompressed();
}
if(m3.nonZeros()>0)
VERIFY_IS_APPROX(m3, refMat3);
}
}
}
static void run(SparseMatrixType& m2, SparseMatrixType& m4, DenseMatrix& refMat2, DenseMatrix& refMat4) {
int r = internal::random(0,m2.rows()-1);
int c1 = internal::random(0,m2.cols()-1);
VERIFY_IS_APPROX(m4=m2.row(r).transpose()*refMat2.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*refMat2.col(c1).transpose());
VERIFY_IS_APPROX(m4=refMat2.col(c1)*m2.row(r), refMat4=refMat2.col(c1)*refMat2.row(r));
}