void testEigen()
{
JACOBI_ARRAY ja(3), value;
JACOBI_MATRIX jm, vector;
for (int i = 0; i < 100; ++i)
{
jm.clear();
ja[0] = 1;
ja[1] = -1;
ja[2] = 0;
jm.push_back(ja);
ja[0] = -1;
ja[1] = 1;
ja[2] = 2;
jm.push_back(ja);
ja[0] = 0;
ja[1] = 2;
ja[0] = 1;
jm.push_back(ja);
Jacobi j;
j.setMatrix(jm);
value = j.getEigenvalues();
vector = j.getEigenvectors();
j.printEigen();
}
}
BoundaryInt::BoundaryInt( string _name, Mesh* _mesh, Field* _field, Field* _fPrev ) : RHSOp( _name, _mesh, 0.0, _field ) {
int endLoop;
double xCurr, xPrev, x0;
bool* done;
double* temp;
double minVal;
int minInd;
Jacobi* P = mesh->el->polys[mesh->el->N+1];
fPrev = _fPrev;
/* calculate the gaussian quadrature weights and abcissa */
weight = new double[mesh->el->N+1];
abcissa = new double[mesh->el->N+1];
endLoop = (mesh->el->N+1)%2 == 1 ? mesh->el->N/2 : (mesh->el->N+1)/2;
for( int pt_i = 0; pt_i < endLoop; pt_i++ ) {
x0 = (pt_i == 0) ? -1.0 : abcissa[pt_i-1];
do {
x0 += STEP;
xCurr = x0;
do {
xPrev = xCurr;
xCurr = xPrev - P->Eval( xPrev )/P->EvalDeriv( xPrev );
} while( fabs( xCurr - xPrev ) > TOL );
} while( Found( pt_i, abcissa, xCurr ) || xCurr > 0.0 - STEP );
abcissa[pt_i] = xCurr;
abcissa[mesh->el->N-pt_i] = -abcissa[pt_i];
}
if( (mesh->el->N+1)%2 == 1 ) {
abcissa[(mesh->el->N+1)/2] = 0.0;
}
done = new bool[mesh->el->N+1];
temp = new double[mesh->el->N+1];
minInd = 999999999;
for( int pt_i = 0; pt_i < mesh->el->N+1; pt_i++ ) {
done[pt_i] = false;
}
for( int pt_i = 0; pt_i < mesh->el->N+1; pt_i++ ) {
minVal = 1.0e+99;
for( int pt_j = 0; pt_j < mesh->el->N+1; pt_j++ ) {
if( !done[pt_j] && abcissa[pt_j] < minVal ) {
minVal = abcissa[pt_j];
minInd = pt_j;
}
}
temp[pt_i] = minVal;
done[minInd] = true;
}
for( int pt_i = 0; pt_i < mesh->el->N+1; pt_i++ ) {
abcissa[pt_i] = temp[pt_i];
}
delete[] temp;
delete[] done;
for( int pt_i = 0; pt_i < mesh->el->N+1; pt_i++ ) {
weight[pt_i] = 2.0/((1.0 - abcissa[pt_i]*abcissa[pt_i])*P->EvalDeriv(abcissa[pt_i])*P->EvalDeriv(abcissa[pt_i]));
}
}
Jacobi DefKNuton::createJacobian( const System & system )
{
Jacobi det;
auto undefinedVar = system.getUnknownVariables();
const auto& initialData = NS_CORE Singletons::getInstance()->getInitialData();
if ( initialData._numberOfGears * initialData._numberOfPlanetaryGears == undefinedVar.size() )
{
det.setSize( initialData._numberOfGears * initialData._numberOfPlanetaryGears );
for ( size_t i = 0; i < initialData._numberOfGears; i++ )
{
for ( size_t j = 0; j < initialData._numberOfPlanetaryGears; j++ )
{
for ( size_t k = 0; k < undefinedVar.size(); k++ )
{
auto undefVarListeners = undefinedVar[k].getAllListeners();
auto gearSetVariables = system.getVariablesSet( NS_CORE GearNumber( i ), j );
for ( const auto & variable : undefVarListeners )
{
if ( ( !gearSetVariables[variable->getElement().getElemN()].getDefined() ) && variable->getElement().getGearSetN().getValue() == j + 1 && variable->getGear() == NS_CORE GearNumber( i + 1 ) )
{
auto eq = Equations::getEquation( variable->getElement().getElemN() );
det.setEquation( i*initialData._numberOfPlanetaryGears + j, k, eq );
}
}
}
}
}
}
else
{
//exception
int a = 5;
}
return det;
}
Matrix DefKNuton::createMatrix( const Jacobi& jacobian, const System & system )
{
auto size = jacobian.size();
Matrix ret( size );
auto undefinedVar = system.getUnknownVariables();
const auto& initialData = NS_CORE Singletons::getInstance()->getInitialData();
for ( size_t i = 0; i < initialData._numberOfGears; i++ )
{
for ( size_t j = 0; j < initialData._numberOfPlanetaryGears; j++ )
{
for ( size_t k = 0; k < undefinedVar.size(); k++ )
{
ret.at( i*initialData._numberOfPlanetaryGears + j, k ) = jacobian[i*initialData._numberOfPlanetaryGears + j][k]( system.getVariablesSet( NS_CORE GearNumber( i ), j ) );
}
}
}
return ret;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Coordinate is a struct of x,y,z
// component is the model to calculate the PCA for
// eVectors are the eigen vectors and values for the three axes
// the longest axis is in eVectors[0]
void PCA(vector<Coordinate> &component, vector<Coordinate> &eVectors, vector<float> &eValues){
int i,j,k;
/*
//find the boundary voxels
vector<Coordinate>voxels;
for (i=0; i<component.size(); i++){
int cntr=0;
for (j=0; j<component.size(); j++){
if (getDistance(component[i], component[j])<1.05)
cntr++;
}
if (cntr<7 && cntr>3)
voxels.push_back(component[i]);
}
*/
vector<Coordinate>voxels (component);
//cout<<endl<<"Number of boundary voxels: "<<voxels.size()<<endl;
//calculate the centroid
Coordinate centroid = getCentroid(voxels);
vector<Coordinate> newVoxels (voxels.size());
float covXX=0.0, covYY=0.0, covZZ=0.0, covXY=0.0, covXZ=0.0, covYZ=0.0;
for (i=0; i<voxels.size(); i++){
newVoxels[i].x = voxels[i].x-centroid.x;
newVoxels[i].y = voxels[i].y-centroid.y;
newVoxels[i].z = voxels[i].z-centroid.z;
covXX += newVoxels[i].x*newVoxels[i].x;
covYY += newVoxels[i].y*newVoxels[i].y;
covZZ += newVoxels[i].z*newVoxels[i].z;
covXY += newVoxels[i].x*newVoxels[i].y;
covXZ += newVoxels[i].x*newVoxels[i].z;
covYZ += newVoxels[i].y*newVoxels[i].z;
}
covXX /= voxels.size()-1;
covYY /= voxels.size()-1;
covZZ /= voxels.size()-1;
covXY /= voxels.size()-1;
covXZ /= voxels.size()-1;
covYZ /= voxels.size()-1;
vector<vector<float> > covMatrix(3, vector<float> (3));
covMatrix[0][0] = covXX;
covMatrix[0][1] = covXY;
covMatrix[0][2] = covXZ;
covMatrix[1][0] = covXY;
covMatrix[1][1] = covYY;
covMatrix[1][2] = covYZ;
covMatrix[2][0] = covXZ;
covMatrix[2][1] = covYZ;
covMatrix[2][2] = covZZ;
/*
//print covMatrix
cout<<"covMatrix: "<<endl;
for (i=0; i<3; i++){
for (j=0; j<3; j++)
cout<<covMatrix[i][j]<<" ";
cout<<endl;
}
*/
Jacobi J;
J.matrix.resize(3);
for (i=0; i<3; i++)
J.matrix[i].resize(3);
J.matrix = covMatrix;
J.dimen = 3;
J.eigenvalues.resize(J.dimen);
J.eigenvectors.resize(J.dimen);
J.e = 1e-8;
J.jacobi();
eValues.clear();
eValues.resize(3);
eVectors.clear();
eVectors.resize(3);
vector<vector<float> > Evector(3, vector<float> (3));
eValues = J.getEigenvalues();
Evector = J.getEigenvectors();
for (i=0; i<3; i++){
eVectors[i].x = Evector[i][0];
eVectors[i].y = Evector[i][1];
eVectors[i].z = Evector[i][2];
}
//cout<<endl<<"PCA..."<<endl;
//J.printEigen();
}
Jacobi::LogCountTable::LogCountTable(const Jacobi &jac,unsigned p_)
: p(p_),
table(p_*p_)
{
jac.addLog(p_, [=] (unsigned a,unsigned b) { add(a,b); } );
}
void MultiColored<OperatorType, VectorType, ValueType>::Decompose_(void) {
LOG_DEBUG(this, "MultiColored::Decompose_()",
" * beging");
if (this->decomp_ == true) {
assert(this->num_blocks_ > 0);
assert(this->block_sizes_ != NULL);
int *offsets = NULL;
allocate_host(this->num_blocks_+1, &offsets);
offsets[0] = 0 ;
for(int i=0; i<this->num_blocks_; ++i)
offsets[i+1] = this->block_sizes_[i];
// sum up
for(int i=0; i<this->num_blocks_; ++i)
offsets[i+1] += offsets[i];
this->diag_solver_ = new Solver<OperatorType, VectorType, ValueType>* [this->num_blocks_];
this->preconditioner_block_ = new OperatorType** [this->num_blocks_];
for (int i=0; i<this->num_blocks_; ++i)
this->preconditioner_block_[i] = new OperatorType* [this->num_blocks_];
this->x_block_ = new VectorType* [this->num_blocks_];
this->diag_block_ = new VectorType* [this->num_blocks_];
for(int i=0; i<this->num_blocks_; ++i)
for(int j=0; j<this->num_blocks_; ++j) {
this->preconditioner_block_[i][j] = new LocalMatrix<ValueType>;
this->preconditioner_block_[i][j]->CloneBackend( *this->op_ );
}
this->preconditioner_->ExtractSubMatrices(this->num_blocks_,
this->num_blocks_,
offsets,
offsets,
this->preconditioner_block_);
free_host(&offsets);
int x_offset = 0;
for (int i=0; i<this->num_blocks_; ++i) {
this->diag_block_[i] = new VectorType;
this->diag_block_[i]->CloneBackend(*this->op_); // clone backend
this->diag_block_[i]->Allocate("Diagonal preconditioners blocks",
this->block_sizes_[i]);
this->preconditioner_block_[i][i]->ExtractDiagonal(this->diag_block_[i]);
this->x_block_[i] = new VectorType; // empty vector
this->x_block_[i]->CloneBackend(*this->op_); // clone backend
this->x_block_[i]->Allocate("MultiColored Preconditioner x_block_",
this->block_sizes_[i]);
x_offset += this->block_sizes_[i];
Jacobi<OperatorType, VectorType, ValueType> *jacobi = new Jacobi<OperatorType, VectorType, ValueType>;
jacobi->SetOperator(*this->preconditioner_block_[i][i]);
jacobi->Build();
this->diag_solver_[i] = jacobi;
this->preconditioner_block_[i][i]->Clear();
}
// Clone the format
// e.g. the preconditioner block matrices will have the same format as this->op_
if (this->op_mat_format_ == true)
for(int i=0; i<this->num_blocks_; ++i)
for(int j=0; j<this->num_blocks_; ++j)
this->preconditioner_block_[i][j]->ConvertTo(this->precond_mat_format_);
} else {
this->diag_.CloneBackend(*this->op_);
this->preconditioner_->ExtractDiagonal(&this->diag_);
}
this->x_.CloneBackend(*this->op_);
this->x_.Allocate("Permuted solution vector",
this->op_->get_nrow());
LOG_DEBUG(this, "MultiColored::Decompose_()",
" * end");
}
int main(int argc, char* argv[]) {
Mat<double> mH;
Col<double> mV;
Mat<cx_double> mEigVec;
Col<cx_double> mEigVal;
int iN, iIt, iRot;
int iMethod = 0;
Jacobi *oJacobi = new Jacobi();
time_t tStart, tStop;
stringstream ssFile;
// Default Matrix
if(argc == 4) {
iMethod = atoi(argv[1]);
ssFile << "Data/";
if(atoi(argv[3]) == 0) ssFile << "Std/";
if(atoi(argv[3]) == 1) ssFile << "Eff/";
if(atoi(argv[3]) == 2) ssFile << "EffECut/";
ssFile << "Ham-2P-" << argv[2] << "R.arma";
mH.load(ssFile.str());
} else {
cout << endl;
cout << "Jacobi takes three arguments: " << endl;
cout << " #1 : Method" << endl;
cout << " 0 = Armadillo eig_gen()" << endl;
cout << " 1 = Simple w/Rotate" << endl;
cout << " 2 = Simple" << endl;
cout << " 3 = Cyclic" << endl;
cout << " 4 = Parallel" << endl;
cout << " #2 : Number of shells for the Hamiltonian (2-20)" << endl;
cout << " #3 : Interaction type" << endl;
cout << " 0 = Standard" << endl;
cout << " 1 = Effective" << endl;
cout << " 2 = Effective w/energy cut" << endl;
cout << endl;
return 0;
}
iN = (int)mH.n_cols;
iIt = 0;
iRot = 0;
mV = zeros(iN);
cout << endl;
#ifndef ONLY_LOWEST
cout << "Initial Matrix:" << endl;
cout << mH << endl;
#endif
cout << "Dimension: " << iN << "x" << iN << endl;
cout << "Sparsity: " << oJacobi->Sparsity(&mH) << endl;
cout << endl;
switch(iMethod) {
case 0: // Aramdillo's Eigenvalue Solver
tStart = clock();
eig_gen(mEigVal, mEigVec, mH);
tStop = clock();
mV = sort(real(mEigVal));
cout << "Armadillo's eig_gen():" << endl;
cout << " Time: " << ((double)tStop-tStart)/CLOCKS_PER_SEC << " sec" << endl;
cout << " Iterations: N/A" << endl;
cout << " Rotations: N/A" << endl;
break;
case 1: // Simple Jacobi w/Rotate
tStart = clock();
oJacobi->SimpleRotate(&mH, &mV, &iIt, &iRot);
tStop = clock();
mV = sort(mV);
cout << "Simple Jacobi w/Rotations:" << endl;
cout << " Time: " << ((double)tStop-tStart)/CLOCKS_PER_SEC << " sec" << endl;
cout << " Iterations: " << iIt << endl;
cout << " Rotations: " << iRot << endl;
break;
case 2: // Simple Jacobi
tStart = clock();
oJacobi->Simple(&mH, &mV, &iIt, &iRot);
tStop = clock();
mV = sort(mV);
cout << "Simple Jacobi:" << endl;
cout << " Time: " << ((double)tStop-tStart)/CLOCKS_PER_SEC << " sec" << endl;
cout << " Iterations: " << iIt << endl;
cout << " Rotations: " << iRot << endl;
break;
case 3: // Cyclic Jacobi
tStart = clock();
oJacobi->Cyclic(&mH, &mV, &iIt, &iRot);
tStop = clock();
mV = sort(mV);
cout << "Cyclic Jacobi:" << endl;
cout << " Time: " << ((double)tStop-tStart)/CLOCKS_PER_SEC << " sec" << endl;
cout << " Iterations: " << iIt << endl;
cout << " Rotations: " << iRot << endl;
break;
}
#ifdef ONLY_LOWEST
if(mV.n_elem > 0) cout << " Eigenvalue 1: " << mV(0) << endl;
if(mV.n_elem > 1) cout << " Eigenvalue 2: " << mV(1) << endl;
if(mV.n_elem > 2) cout << " Eigenvalue 3: " << mV(2) << endl;
if(mV.n_elem > 3) cout << " Eigenvalue 4: " << mV(3) << endl;
if(mV.n_elem > 4) cout << " Eigenvalue 5: " << mV(4) << endl;
#else
cout << " Eigenvalues:" << endl << mV << endl;
#endif
cout << endl;
return 0;
}