twoD_diffusion_ME::
twoD_diffusion_ME(
const Teuchos::RCP<const Epetra_Comm>& comm, int n, int d,
double s, double mu,
const Teuchos::RCP<const Stokhos::OrthogPolyBasis<int,double> >& basis_,
bool log_normal_,
bool eliminate_bcs_,
const Teuchos::RCP<Teuchos::ParameterList>& precParams_) :
mesh(n*n),
basis(basis_),
log_normal(log_normal_),
eliminate_bcs(eliminate_bcs_),
precParams(precParams_)
{
//////////////////////////////////////////////////////////////////////////////
// Construct the mesh.
// The mesh is uniform and the nodes are numbered
// LEFT to RIGHT, DOWN to UP.
//
// 5-6-7-8-9
// | | | | |
// 0-1-2-3-4
/////////////////////////////////////////////////////////////////////////////
double xyLeft = -.5;
double xyRight = .5;
h = (xyRight - xyLeft)/((double)(n-1));
Teuchos::Array<int> global_dof_indices;
for (int j=0; j<n; j++) {
double y = xyLeft + j*h;
for (int i=0; i<n; i++) {
double x = xyLeft + i*h;
int idx = j*n+i;
mesh[idx].x = x;
mesh[idx].y = y;
if (i == 0 || i == n-1 || j == 0 || j == n-1)
mesh[idx].boundary = true;
if (i != 0)
mesh[idx].left = idx-1;
if (i != n-1)
mesh[idx].right = idx+1;
if (j != 0)
mesh[idx].down = idx-n;
if (j != n-1)
mesh[idx].up = idx+n;
if (!(eliminate_bcs && mesh[idx].boundary))
global_dof_indices.push_back(idx);
}
}
// Solution vector map
int n_global_dof = global_dof_indices.size();
int n_proc = comm->NumProc();
int proc_id = comm->MyPID();
int n_my_dof = n_global_dof / n_proc;
if (proc_id == n_proc-1)
n_my_dof += n_global_dof % n_proc;
int *my_dof = global_dof_indices.getRawPtr() + proc_id*(n_global_dof / n_proc);
x_map =
Teuchos::rcp(new Epetra_Map(n_global_dof, n_my_dof, my_dof, 0, *comm));
// Initial guess, initialized to 0.0
x_init = Teuchos::rcp(new Epetra_Vector(*x_map));
x_init->PutScalar(0.0);
// Parameter vector map
p_map = Teuchos::rcp(new Epetra_LocalMap(d, 0, *comm));
// Response vector map
g_map = Teuchos::rcp(new Epetra_LocalMap(1, 0, *comm));
// Initial parameters
p_init = Teuchos::rcp(new Epetra_Vector(*p_map));
p_init->PutScalar(0.0);
// Parameter names
p_names = Teuchos::rcp(new Teuchos::Array<std::string>(d));
for (int i=0;i<d;i++) {
std::stringstream ss;
ss << "KL Random Variable " << i+1;
(*p_names)[i] = ss.str();
}
// Build Jacobian graph
int NumMyElements = x_map->NumMyElements();
int *MyGlobalElements = x_map->MyGlobalElements();
graph = Teuchos::rcp(new Epetra_CrsGraph(Copy, *x_map, 5));
for (int i=0; i<NumMyElements; ++i ) {
// Center
int global_idx = MyGlobalElements[i];
graph->InsertGlobalIndices(global_idx, 1, &global_idx);
if (!mesh[global_idx].boundary) {
// Down
if (!(eliminate_bcs && mesh[mesh[global_idx].down].boundary))
graph->InsertGlobalIndices(global_idx, 1, &mesh[global_idx].down);
// Left
if (!(eliminate_bcs && mesh[mesh[global_idx].left].boundary))
graph->InsertGlobalIndices(global_idx, 1, &mesh[global_idx].left);
// Right
if (!(eliminate_bcs && mesh[mesh[global_idx].right].boundary))
graph->InsertGlobalIndices(global_idx, 1, &mesh[global_idx].right);
// Up
if (!(eliminate_bcs && mesh[mesh[global_idx].up].boundary))
graph->InsertGlobalIndices(global_idx, 1, &mesh[global_idx].up);
}
}
graph->FillComplete();
graph->OptimizeStorage();
KL_Diffusion_Func klFunc(xyLeft, xyRight, mu, s, 1.0, d);
if (!log_normal) {
// Fill coefficients of KL expansion of operator
if (basis == Teuchos::null) {
fillMatrices(klFunc, d+1);
}
else {
Normalized_KL_Diffusion_Func<KL_Diffusion_Func> nklFunc(klFunc, *basis);
fillMatrices(nklFunc, d+1);
}
}
else {
// Fill coefficients of PC expansion of operator
int sz = basis->size();
Teuchos::RCP<const Stokhos::ProductBasis<int, double> > prodbasis =
Teuchos::rcp_dynamic_cast<const Stokhos::ProductBasis<int, double> >(
basis, true);
LogNormal_Diffusion_Func<KL_Diffusion_Func> lnFunc(mu, klFunc, prodbasis);
fillMatrices(lnFunc, sz);
}
// Construct deterministic operator
A = Teuchos::rcp(new Epetra_CrsMatrix(Copy, *graph));
// Construct the RHS vector.
b = Teuchos::rcp(new Epetra_Vector(*x_map));
for( int i=0 ; i<NumMyElements; ++i ) {
int global_idx = MyGlobalElements[i];
if (mesh[global_idx].boundary)
(*b)[i] = 0;
else
(*b)[i] = 1;
}
if (basis != Teuchos::null) {
point.resize(d);
basis_vals.resize(basis->size());
}
if (precParams != Teuchos::null) {
std::string name = precParams->get("Preconditioner Type", "Ifpack");
Teuchos::RCP<Teuchos::ParameterList> p =
Teuchos::rcp(&(precParams->sublist("Preconditioner Parameters")), false);
precFactory =
Teuchos::rcp(new Stokhos::PreconditionerFactory(name, p));
}
}
void ExRandomTrees::buildTree(){
unsigned int treeId;
m_chooseIdLock->lock();
treeId = m_choiceId++;
m_chooseIdLock->unlock();
ExTree& tree = m_trees[treeId];
tree.m_nodes.reserve(m_evaluation->getNumTrainingInstances()*2);
tree.m_nodes.push_back(ExTreeNode(0,m_evaluation->getNumTrainingInstances()));
for(unsigned int i=0; i<m_evaluation->getNumTrainingInstances(); ++i){
++tree.m_nodes[0].classProbs[m_classSetTrain[i]];
}
unsigned int depth = 0;
unsigned int unprocessedNodes = 1, newNodes = 0;
unsigned int numInstances;
boost::random::uniform_int_distribution<> attRand(0,m_document->getNumAttributes()-1);
double split;
std::vector<std::vector<unsigned int>> dist,bestDist;
int k;
bool sensibleSplit = false, priorDone;
double prior, posterior;
double bestVal = -1000;
unsigned int attribute;
double splitPoint;
while(unprocessedNodes != 0){
// Iterate through unprocessed nodes
while(unprocessedNodes != 0){
ExTreeNode& currentNode = tree.m_nodes[tree.m_nodes.size()-(unprocessedNodes+newNodes)];
// Check if node is a leaf
numInstances = currentNode.instIndEnd - currentNode.instIndStart;
if((numInstances > 0 && numInstances < max(2, m_minNumInst)) // small
|| (abs((currentNode.classProbs[0] > currentNode.classProbs[1] ? currentNode.classProbs[0] : currentNode.classProbs[1]) - (currentNode.classProbs[0]+currentNode.classProbs[1])) < 1e-6) // pure
|| ((m_maxDepth > 0) && (depth >= m_maxDepth)) // deep
){
}
else{
boost::random::uniform_int_distribution<> instRand(0,numInstances-1);
priorDone = false;
k = m_numFeatures;
sensibleSplit = false;
bestVal = -1000;
unsigned int numIter = 0;
while(numIter < m_document->getNumAttributes() && (k-- > 0 || !sensibleSplit)){
++numIter;
attribute = attRand(tree.m_rng);
split = 0;
for(unsigned int i=0; i<10; ++i){
split += m_evaluation->getTrainingInstance(tree.m_instIndices[tree.m_bufferId][currentNode.instIndStart+instRand(tree.m_rng)])->getValue(attribute);
}
splitPoint = split/10;
// Calculate distribution
dist = std::vector<std::vector<unsigned int>>(2,std::vector<unsigned int>(2,0));
unsigned int instId;
for(unsigned int i=0; i<numInstances; ++i){
instId = tree.m_instIndices[tree.m_bufferId][currentNode.instIndStart+i];
++dist[m_dataSetTrain[attribute][instId] < splitPoint ? 0 : 1][m_classSetTrain[instId]];
}
if(!priorDone){ // needs to be computed only once per branch
// Entropy over collumns
prior = 0;
double sumForColumn, total = 0;
for (size_t j = 0; j < dist[0].size(); j++) {
sumForColumn = 0;
for (size_t i = 0; i < dist.size(); i++) {
sumForColumn += dist[i][j];
}
prior -= lnFunc(sumForColumn);
total += sumForColumn;
}
prior = (prior + lnFunc(total));
priorDone = true;
}
// Entropy over rows
posterior = 0;
double sumForBranch;
for (size_t branchNum = 0; branchNum < dist.size(); branchNum++) {
sumForBranch = 0;
for(size_t classNum = 0; classNum < dist[0].size(); classNum++) {
posterior = posterior + lnFunc(dist[branchNum][classNum]);
sumForBranch += dist[branchNum][classNum];
}
posterior = posterior - lnFunc(sumForBranch);
}
posterior = -posterior;
if(bestVal < prior - posterior){
bestVal = prior - posterior;
currentNode.m_attribute = attribute;
currentNode.m_splitPoint = splitPoint;
bestDist = dist;
}
if(prior - posterior > 1e-2) // we allow some leeway here to compensate
sensibleSplit = true; // for imprecision in entropy computation
}
if(sensibleSplit){
// Split node
unsigned int cpyBuffer = (tree.m_bufferId == 0 ? 1 : 0);
unsigned int instId;
tree.m_nodes.push_back(ExTreeNode(currentNode.instIndStart,currentNode.instIndStart+bestDist[0][0]+bestDist[0][1]));
tree.m_nodes.back().classProbs[0] = bestDist[0][0];
tree.m_nodes.back().classProbs[1] = bestDist[0][1];
currentNode.m_children.push_back(&tree.m_nodes.back());
tree.m_nodes.push_back(ExTreeNode(currentNode.instIndStart+bestDist[0][0]+bestDist[0][1],currentNode.instIndEnd));
tree.m_nodes.back().classProbs[0] = bestDist[1][0];
tree.m_nodes.back().classProbs[1] = bestDist[1][1];
currentNode.m_children.push_back(&tree.m_nodes.back());
unsigned int left = currentNode.instIndStart, right = currentNode.instIndEnd-1;
for(unsigned int i=0; i<numInstances; ++i){
instId = tree.m_instIndices[tree.m_bufferId][currentNode.instIndStart+i];
if(m_dataSetTrain[currentNode.m_attribute][instId] < currentNode.m_splitPoint){
tree.m_instIndices[cpyBuffer][left] = instId;
++left;
}
else{
tree.m_instIndices[cpyBuffer][right] = instId;
--right;
}
}
newNodes += 2;
}
}
unprocessedNodes--;
}
tree.m_bufferId = (tree.m_bufferId == 0 ? 1 : 0);
depth++;
unprocessedNodes = newNodes;
newNodes = 0;
}
}
