/// Solve the linear system Ax = b, with A being the
/// combined derivative matrix of the residual and b
/// being the residual itself.
/// \param[in] residual residual object containing A and b.
/// \return the solution x
NewtonIterationBlackoilSimple::SolutionVector
NewtonIterationBlackoilSimple::computeNewtonIncrement(const LinearisedBlackoilResidual& residual) const
{
typedef LinearisedBlackoilResidual::ADB ADB;
const int np = residual.material_balance_eq.size();
ADB mass_res = residual.material_balance_eq[0];
for (int phase = 1; phase < np; ++phase) {
mass_res = vertcat(mass_res, residual.material_balance_eq[phase]);
}
const ADB well_res = vertcat(residual.well_flux_eq, residual.well_eq);
const ADB total_residual = collapseJacs(vertcat(mass_res, well_res));
Eigen::SparseMatrix<double, Eigen::RowMajor> matr;
total_residual.derivative()[0].toSparse(matr);
SolutionVector dx(SolutionVector::Zero(total_residual.size()));
Opm::LinearSolverInterface::LinearSolverReport rep
= linsolver_->solve(matr.rows(), matr.nonZeros(),
matr.outerIndexPtr(), matr.innerIndexPtr(), matr.valuePtr(),
total_residual.value().data(), dx.data(), parallelInformation_);
// store iterations
iterations_ = rep.iterations;
if (!rep.converged) {
OPM_THROW(LinearSolverProblem,
"FullyImplicitBlackoilSolver::solveJacobianSystem(): "
"Linear solver convergence failure.");
}
return dx;
}
void MacauOnePrior<FType>::sample_latents(
Eigen::MatrixXd &U,
const Eigen::SparseMatrix<double> &Ymat,
double mean_value,
const Eigen::MatrixXd &V,
double alpha,
const int num_latent)
{
const int N = U.cols();
const int D = U.rows();
#pragma omp parallel for schedule(dynamic, 4)
for (int i = 0; i < N; i++) {
const int nnz = Ymat.outerIndexPtr()[i + 1] - Ymat.outerIndexPtr()[i];
VectorXd Yhat(nnz);
// precalculating Yhat and Qi
int idx = 0;
VectorXd Qi = lambda;
for (SparseMatrix<double>::InnerIterator it(Ymat, i); it; ++it, idx++) {
Qi.noalias() += alpha * V.col(it.row()).cwiseAbs2();
Yhat(idx) = mean_value + U.col(i).dot( V.col(it.row()) );
}
VectorXd rnorms(num_latent);
bmrandn_single(rnorms);
for (int d = 0; d < D; d++) {
// computing Lid
const double uid = U(d, i);
double Lid = lambda(d) * (mu(d) + Uhat(d, i));
idx = 0;
for ( SparseMatrix<double>::InnerIterator it(Ymat, i); it; ++it, idx++) {
const double vjd = V(d, it.row());
// L_id += alpha * (Y_ij - k_ijd) * v_jd
Lid += alpha * (it.value() - (Yhat(idx) - uid*vjd)) * vjd;
}
// Now use Lid and Qid to update uid
double uid_old = U(d, i);
double uid_var = 1.0 / Qi(d);
// sampling new u_id ~ Norm(Lid / Qid, 1/Qid)
U(d, i) = Lid * uid_var + sqrt(uid_var) * rnorms(d);
// updating Yhat
double uid_delta = U(d, i) - uid_old;
idx = 0;
for (SparseMatrix<double>::InnerIterator it(Ymat, i); it; ++it, idx++) {
Yhat(idx) += uid_delta * V(d, it.row());
}
}
}
}
void createSearchKey(unsigned int numberRows, unsigned int NBFS, std::vector<int> &search_key, const Eigen::SparseMatrix<int> &EdgeMatrix)
{
//columndegree contains number of nonzeros per column
//for removing searchkey values that are not connected to main graph
std::vector<int> columndegree;
columndegree.reserve(numberRows);
for (unsigned int i = 0; i < numberRows; i++)
{
columndegree.push_back(EdgeMatrix.outerIndexPtr()[i+1]-EdgeMatrix.outerIndexPtr()[i]);
}
//generate search key values based on time seed
std::mt19937 generator(std::chrono::system_clock::now().time_since_epoch()/std::chrono::seconds(1));
std::cout << "creating search key vector" << std::endl;
for (unsigned int i = 0; i < numberRows; i++)
{
search_key.push_back(i);
}
//shuffle search key values
std::shuffle(search_key.begin(),search_key.end(),generator);
//take first 64 or entire search key, whichever is smaller
if (search_key.size() > NBFS)
{
for (unsigned int i = 0; i < NBFS+20; i++)
{
//remove search key values that aren't connected to main graph
if (columndegree.at(search_key.at(i)) == 0)
{
search_key.erase(search_key.begin()+i);
i--;
}
}
search_key.erase(search_key.begin()+NBFS, search_key.end());
}
std::cout << "Removing search keys with no edges" << std::endl;
for (unsigned int i = 0; i < search_key.size(); i++)
{
//remove search key values that aren't connected to main graph
if (columndegree.at(search_key.at(i)) == 0)
{
search_key.erase(search_key.begin()+i);
i--;
}
}
search_key.shrink_to_fit();
}
ColCompressedMatrix convert_from_Eigen(const Eigen::SparseMatrix<double> &m)
{
assert(m.rows() == m.cols());
assert(m.isCompressed());
return ColCompressedMatrix(m.rows, m.nonZeros(),
m.valuePtr(), m.outerIndexPtr(), m.innerIndexPtr());
}
void ProbitNoise::evalModel(Eigen::SparseMatrix<double> & Ytest, const int n, Eigen::VectorXd & predictions, Eigen::VectorXd & predictions_var, const Eigen::MatrixXd &cols, const Eigen::MatrixXd &rows, double mean_rating) {
const unsigned N = Ytest.nonZeros();
Eigen::VectorXd pred(N);
Eigen::VectorXd test(N);
// #pragma omp parallel for schedule(dynamic,8) reduction(+:se, se_avg) <- dark magic :)
for (int k = 0; k < Ytest.outerSize(); ++k) {
int idx = Ytest.outerIndexPtr()[k];
for (Eigen::SparseMatrix<double>::InnerIterator it(Ytest,k); it; ++it) {
pred[idx] = nCDF(cols.col(it.col()).dot(rows.col(it.row())));
test[idx] = it.value();
// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Online_algorithm
double pred_avg;
if (n == 0) {
pred_avg = pred[idx];
} else {
double delta = pred[idx] - predictions[idx];
pred_avg = (predictions[idx] + delta / (n + 1));
predictions_var[idx] += delta * (pred[idx] - pred_avg);
}
predictions[idx++] = pred_avg;
}
}
auc_test_onesample = auc(pred,test);
auc_test = auc(predictions, test);
}
CollOfScalar EquelleRuntimeCPU::solveForUpdate(const CollOfScalar& residual) const
{
Eigen::SparseMatrix<double, Eigen::RowMajor> matr = residual.derivative()[0];
CollOfScalar::V du = CollOfScalar::V::Zero(residual.size());
Opm::time::StopWatch clock;
clock.start();
// solve(n, # nonzero values ("val"), ptr to col indices
// ("col_ind"), ptr to row locations in val array ("row_ind")
// (these two may be swapped, not sure about the naming convention
// here...), array of actual values ("val") (I guess... '*sa'...),
// rhs, solution)
Opm::LinearSolverInterface::LinearSolverReport rep
= linsolver_.solve(matr.rows(), matr.nonZeros(),
matr.outerIndexPtr(), matr.innerIndexPtr(), matr.valuePtr(),
residual.value().data(), du.data());
if (verbose_ > 2) {
std::cout << " solveForUpdate: Linear solver took: " << clock.secsSinceLast() << " seconds." << std::endl;
}
if (!rep.converged) {
OPM_THROW(std::runtime_error, "Linear solver convergence failure.");
}
return du;
}
ConvertToMklResult to_mkl(const Eigen::SparseMatrix<double> &Ain,
sparse_status_t &status) {
ConvertToMklResult result;
const int N = static_cast<int>(Ain.rows());
// const-cast to work with C-api.
int *row_starts = const_cast<int *>(Ain.outerIndexPtr());
int *col_index = const_cast<int *>(Ain.innerIndexPtr());
double *values = const_cast<double *>(Ain.valuePtr());
result.descr.type = SPARSE_MATRIX_TYPE_GENERAL; /* Full matrix is stored */
result.status =
mkl_sparse_d_create_csr(&result.matrix, SPARSE_INDEX_BASE_ZERO, N, N,
row_starts, row_starts + 1, col_index, values);
return result;
}
void NewtonIterationBlackoilInterleaved::formInterleavedSystem(const std::vector<ADB>& eqs,
const Eigen::SparseMatrix<double, Eigen::RowMajor>& A,
Mat& istlA) const
{
const int np = eqs.size();
// Find sparsity structure as union of basic block sparsity structures,
// corresponding to the jacobians with respect to pressure.
// Use addition to get to the union structure.
Eigen::SparseMatrix<double> structure = eqs[0].derivative()[0];
for (int phase = 0; phase < np; ++phase) {
structure += eqs[phase].derivative()[0];
}
Eigen::SparseMatrix<double, Eigen::RowMajor> s = structure;
// Create ISTL matrix with interleaved rows and columns (block structured).
assert(np == 3);
istlA.setSize(s.rows(), s.cols(), s.nonZeros());
istlA.setBuildMode(Mat::row_wise);
const int* ia = s.outerIndexPtr();
const int* ja = s.innerIndexPtr();
for (Mat::CreateIterator row = istlA.createbegin(); row != istlA.createend(); ++row) {
int ri = row.index();
for (int i = ia[ri]; i < ia[ri + 1]; ++i) {
row.insert(ja[i]);
}
}
const int size = s.rows();
Span span[3] = { Span(size, 1, 0),
Span(size, 1, size),
Span(size, 1, 2*size) };
for (int row = 0; row < size; ++row) {
for (int col_ix = ia[row]; col_ix < ia[row + 1]; ++col_ix) {
const int col = ja[col_ix];
MatrixBlockType block;
for (int p1 = 0; p1 < np; ++p1) {
for (int p2 = 0; p2 < np; ++p2) {
block[p1][p2] = A.coeff(span[p1][row], span[p2][col]);
}
}
istlA[row][col] = block;
}
}
}