void NeighbourJoining::calcNewD(MatrixXf& currentD, MatrixXi& rowsID, const Pair& p) {
//calculates distances to new node
int j = 0;
for (int i = 0; i < numCurrentNodes - 1; ++i) {
if (i == p.i)
j++;
currentD(numCurrentNodes, i) = (currentD(p.i, i + j) + currentD(p.j, i + j) - currentD(p.i, p.j)) / 2;
currentD(i, numCurrentNodes) = currentD(numCurrentNodes, i);
}
//cout << "distances to new node: " << currentD.row(numCurrentNodes).head(numCurrentNodes-1) <<endl;
//swaps rows and columns so that the closest pair nodes go right and at the bottom of the matrix
currentD.row(p.i).head(numCurrentNodes - 1).swap(
currentD.row(numCurrentNodes - 1).head(numCurrentNodes - 1));
currentD.col(p.i).head(numCurrentNodes - 1).swap(
currentD.col(numCurrentNodes - 1).head(numCurrentNodes - 1));
currentD.row(p.j).head(numCurrentNodes - 1).swap(
currentD.row(numCurrentNodes).head(numCurrentNodes - 1));
currentD.col(p.j).head(numCurrentNodes - 1).swap(
currentD.col(numCurrentNodes).head(numCurrentNodes - 1));
currentD.diagonal().setZero();
//cout << "new Matrix:" << endl; printMatrix(currentD);
//adjusts node IDs to new matrix indices
int newNode = 2 * numObservableNodes - numCurrentNodes;
rowsID.row(p.i).swap(rowsID.row(numCurrentNodes - 1));
rowsID.row(p.j).swap(rowsID.row(newNode));
//cout << "rowsID: " << rowsID.transpose(); cout << endl;
}
VectorXf param_sensitivity_widget::computeSensitivity(
MatrixXf ¶meterMatrix, VectorXf &responseVector)
{
MatrixXf Ctemp = parameterMatrix.transpose()*parameterMatrix;
MatrixXf C;
C = Ctemp.inverse();
VectorXf b = C*parameterMatrix.transpose()*responseVector;
VectorXf Y_hat = parameterMatrix*b;
int p = b.rows();
VectorXf sigma2Vec = responseVector-Y_hat;
float sigma2 = sigma2Vec.squaredNorm();
sigma2= sigma2/(parameterMatrix.rows() - p);
Ctemp = C*sigma2;
MatrixXf denominator = Ctemp.diagonal();
// Do element-wise division
VectorXf t = b;
for (int i = 0; i < b.rows(); i++)
{
t(i) = abs(b(i)/sqrt(denominator(i)));
}
return t;
}
void NeighbourJoining::calcQ(const MatrixXf& currentD, MatrixXf& Q) {
//calculates sum of the rows of the distance matrix
Matrix<float, latentNodes, 1> sumRows;
//MatrixXf sumRows (numObservableNodes+1,1) ;
sumRows.head(numCurrentNodes) = currentD.topLeftCorner(numCurrentNodes,
numCurrentNodes).colwise().sum();
//cout << sumRows.head(numCurrentNodes); cout << endl;
//Q = (n-2) * currentD
Q.topLeftCorner(numCurrentNodes, numCurrentNodes) = (numCurrentNodes - 2)
* currentD.topLeftCorner(numCurrentNodes, numCurrentNodes);
//each row in Q - sumRows and each column in Q - sumRows
Q.topLeftCorner(numCurrentNodes, numCurrentNodes).colwise() -= sumRows.head(
numCurrentNodes);
Q.topLeftCorner(numCurrentNodes, numCurrentNodes).rowwise() -= sumRows.head(
numCurrentNodes).transpose();
Q.diagonal().setZero();
//cout << "Q Matrix:" << endl; printMatrix(Q);
}
void sparsify_soft_relative_to_row_col_max (
const MatrixXf & dense,
MatrixSf & sparse,
float relthresh,
bool ignore_diagonal)
{
ASSERT_LT(0, relthresh);
LOG("sparsifying " << dense.rows() << " x " << dense.cols()
<< " positive matrix to relative threshold " << relthresh);
VectorXf row_max;
VectorXf col_max;
if (ignore_diagonal) {
VectorXf diag = dense.diagonal();
const_cast<MatrixXf &>(dense).diagonal().setZero();
row_max = dense.rowwise().maxCoeff();
col_max = dense.colwise().maxCoeff();
const_cast<MatrixXf &>(dense).diagonal() = diag;
} else {
row_max = dense.rowwise().maxCoeff();
col_max = dense.colwise().maxCoeff();
}
const int I = dense.rows();
const int J = dense.cols();
sparse.resize(I,J);
double sum_dense = 0;
double sum_sparse = 0;
for (int j = 0; j < J; ++j) {
for (int i = 0; i < I; ++i) {
const float dense_ij = dense(i,j);
sum_dense += dense_ij;
const float thresh = relthresh * min(row_max(i), col_max(j));
if (dense_ij > thresh) {
sparse.insert(i,j) = dense_ij;
sum_sparse += dense_ij;
}
}
}
sparse.finalize();
float density = sparse.nonZeros() / float(I * J);
float loss = (sum_dense - sum_sparse) / sum_dense;
LOG("sparsifying to density " << density
<< " loses " << (100 * loss) << "% of mass");
}