EmbeddingResult embed(const MatrixType& wm, IndexType target_dimension, unsigned int skip)
{
timed_context context("Randomized eigendecomposition");
DenseMatrix O(wm.rows(), target_dimension+skip);
for (IndexType i=0; i<O.rows(); ++i)
{
IndexType j=0;
for ( ; j+1 < O.cols(); j+= 2)
{
ScalarType v1 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType v2 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType len = sqrt(-2.f*log(v1));
O(i,j) = len*cos(2.f*M_PI*v2);
O(i,j+1) = len*sin(2.f*M_PI*v2);
}
for ( ; j < O.cols(); j++)
{
ScalarType v1 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType v2 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType len = sqrt(-2.f*log(v1));
O(i,j) = len*cos(2.f*M_PI*v2);
}
}
MatrixTypeOperation operation(wm);
DenseMatrix Y = operation(O);
for (IndexType i=0; i<Y.cols(); i++)
{
for (IndexType j=0; j<i; j++)
{
ScalarType r = Y.col(i).dot(Y.col(j));
Y.col(i) -= r*Y.col(j);
}
ScalarType norm = Y.col(i).norm();
if (norm < 1e-4)
{
for (int k = i; k<Y.cols(); k++)
Y.col(k).setZero();
}
Y.col(i) *= (1.f / norm);
}
DenseMatrix B1 = operation(Y);
DenseMatrix B = Y.householderQr().solve(B1);
DenseSelfAdjointEigenSolver eigenOfB(B);
if (eigenOfB.info() == Eigen::Success)
{
DenseMatrix embedding = (Y*eigenOfB.eigenvectors()).block(0, skip, wm.cols(), target_dimension);
return EmbeddingResult(embedding,eigenOfB.eigenvalues());
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EmbeddingResult();
}
EigendecompositionResult eigendecomposition_impl_randomized(const MatrixType& wm, IndexType target_dimension, unsigned int skip)
{
timed_context context("Randomized eigendecomposition");
DenseMatrix O(wm.rows(), target_dimension+skip);
for (IndexType i=0; i<O.rows(); ++i)
{
for (IndexType j=0; j<O.cols(); j++)
{
O(i,j) = tapkee::gaussian_random();
}
}
MatrixOperationType operation(wm);
DenseMatrix Y = operation(O);
for (IndexType i=0; i<Y.cols(); i++)
{
for (IndexType j=0; j<i; j++)
{
ScalarType r = Y.col(i).dot(Y.col(j));
Y.col(i) -= r*Y.col(j);
}
ScalarType norm = Y.col(i).norm();
if (norm < 1e-4)
{
for (int k = i; k<Y.cols(); k++)
Y.col(k).setZero();
}
Y.col(i) *= (1.f / norm);
}
DenseMatrix B1 = operation(Y);
DenseMatrix B = Y.householderQr().solve(B1);
DenseSelfAdjointEigenSolver eigenOfB(B);
if (eigenOfB.info() == Eigen::Success)
{
if (MatrixOperationType::largest)
{
assert(skip==0);
DenseMatrix selected_eigenvectors = (Y*eigenOfB.eigenvectors()).rightCols(target_dimension);
return EigendecompositionResult(selected_eigenvectors,eigenOfB.eigenvalues());
}
else
{
DenseMatrix selected_eigenvectors = (Y*eigenOfB.eigenvectors()).leftCols(target_dimension+skip).rightCols(target_dimension);
return EigendecompositionResult(selected_eigenvectors,eigenOfB.eigenvalues());
}
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EigendecompositionResult();
}