void AssembleOptimization::hessian (const NumericVector<Number> & /*soln*/,
SparseMatrix<Number> & H_f,
OptimizationSystem & sys)
{
H_f.zero();
H_f.add(1., *A_matrix);
// We also need to add the Hessian of the inequality and equality constraints,
// \sum_i^n_eq lambda_eq_i H_eq_i + \sum_i^n_ineq lambda_ineq_i H_ineq_i
// where lambda_eq and lambda_ineq denote Lagrange multipliers associated
// with the equality and inequality constraints, respectively.
// In this example, our equality constraints are linear, hence H_eq_i = 0.
// However, our inequality constraint is nonlinear, so it will contribute
// to the Hessian matrix.
sys.optimization_solver->get_dual_variables();
dof_id_type ineq_index = 0;
Number lambda_ineq_0 = 0.;
unsigned int lambda_rank = 0;
if ((sys.lambda_ineq->first_local_index() <= ineq_index) &&
(ineq_index < sys.lambda_ineq->last_local_index()))
{
lambda_ineq_0 = (*sys.lambda_ineq)(0);
lambda_rank = sys.comm().rank();
}
// Sync lambda_rank across all processors.
sys.comm().sum(lambda_rank);
sys.comm().broadcast(lambda_rank, lambda_rank);
if ((sys.get_dof_map().first_dof() <= 200) && (200 < sys.get_dof_map().end_dof()))
H_f.add(200, 200, 2. * lambda_ineq_0);
}
void CSFSolver::compute_system_matrices(const Vector<double> &last_relax_step,
const Vector<double> &previous_time_step,
SparseMatrix<double> &mass_output,
SparseMatrix<double> &stiffness_output) {
mass_output = 0;
stiffness_output = 0;
const QGauss<2> quadrature_formula(3);
FEValues<2> fe_values(fe, quadrature_formula,
update_values | update_gradients | update_JxW_values | update_quadrature_points);
const unsigned int dofs_per_cell = fe.dofs_per_cell;
const unsigned int n_q_points = quadrature_formula.size();
FullMatrix<double> local_mass_matrix(dofs_per_cell, dofs_per_cell);
FullMatrix<double> local_stiffness_matrix(dofs_per_cell, dofs_per_cell);
std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
std::vector<Tensor<1, 2, double>> last_relax_grads(n_q_points);
std::vector<Tensor<1, 2, double>> previous_step_grads(n_q_points);
for(auto cell : dof_handler.active_cell_iterators()) {
local_mass_matrix = 0;
local_stiffness_matrix = 0;
fe_values.reinit(cell);
fe_values.get_function_gradients(last_relax_step, last_relax_grads);
fe_values.get_function_gradients(previous_time_step, previous_step_grads);
for(unsigned int q_pt_idx = 0; q_pt_idx < n_q_points; q_pt_idx++) {
for(unsigned int i = 0; i < dofs_per_cell; i++) {
for(unsigned int j = 0; j < dofs_per_cell; j++) {
// Compute the shared denominator - normalizing to avoid infinities
double grad_sum = last_relax_grads[q_pt_idx].norm() + previous_step_grads[q_pt_idx].norm();
double grad_sum_inv = 1.0 / MAX(grad_sum, grad_epsilon);
// If there is a weight function, compute its value at the quad point
double weight_fn_value = weight_function(fe_values.quadrature_point(q_pt_idx));
// Compute the mass component
local_mass_matrix(i, j) += (fe_values.shape_value(i, q_pt_idx) * fe_values.shape_value(j, q_pt_idx) * weight_fn_value * grad_sum_inv * fe_values.JxW(q_pt_idx));
// Compute the stiffness component
local_stiffness_matrix(i, j) += (fe_values.shape_grad(i, q_pt_idx) * fe_values.shape_grad(j, q_pt_idx) * weight_fn_value * grad_sum_inv * fe_values.JxW(q_pt_idx));
}
}
}
// Copy the local matrices into the global output
cell->get_dof_indices(local_dof_indices);
for(unsigned int i = 0; i < dofs_per_cell; i++) {
for(unsigned int j = 0; j < dofs_per_cell; j++) {
mass_output.add(local_dof_indices[i], local_dof_indices[j], local_mass_matrix(i, j));
stiffness_output.add(local_dof_indices[i], local_dof_indices[j], local_stiffness_matrix(i, j));
}
}
}
}
void
NodalConstraint::computeJacobian(SparseMatrix<Number> & jacobian)
{
_qp = 0;
dof_id_type & dof_idx = _var.nodalDofIndex();
dof_id_type & dof_idx_neighbor = _var.nodalDofIndexNeighbor();
Real scaling_factor = _var.scalingFactor();
jacobian.add(dof_idx, dof_idx, scaling_factor * computeQpJacobian(Moose::MasterMaster));
jacobian.add(dof_idx, dof_idx_neighbor, scaling_factor * computeQpJacobian(Moose::MasterSlave));
jacobian.add(dof_idx_neighbor, dof_idx_neighbor, scaling_factor * computeQpJacobian(Moose::SlaveSlave));
jacobian.add(dof_idx_neighbor, dof_idx, scaling_factor * computeQpJacobian(Moose::SlaveMaster));
}
void AssembleOptimization::hessian (const NumericVector<Number> & /*soln*/,
SparseMatrix<Number> & H_f,
OptimizationSystem & /*sys*/)
{
H_f.zero();
H_f.add(1., *A_matrix);
}
void
Assembly::addCachedJacobian(SparseMatrix<Number> & jacobian)
{
mooseAssert(_cached_jacobian_rows.size() == _cached_jacobian_cols.size(),
"Error: Cached data sizes MUST be the same!");
for(unsigned int i=0; i<_cached_jacobian_rows.size(); i++)
jacobian.add(_cached_jacobian_rows[i], _cached_jacobian_cols[i], _cached_jacobian_values[i]);
if (_max_cached_jacobians < _cached_jacobian_values.size())
_max_cached_jacobians = _cached_jacobian_values.size();
// Try to be more efficient from now on
// The 2 is just a fudge factor to keep us from having to grow the vector during assembly
_cached_jacobian_values.clear();
_cached_jacobian_values.reserve(_max_cached_jacobians*2);
_cached_jacobian_rows.clear();
_cached_jacobian_rows.reserve(_max_cached_jacobians*2);
_cached_jacobian_cols.clear();
_cached_jacobian_cols.reserve(_max_cached_jacobians*2);
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
// We load the mesh on a (-1, 1)^2 domain.
mloader.load("ref_square.mesh", &mesh);
// Enter boundary markers
// (If no markers are entered, default is a natural BC).
BCTypes bc_types;
// Create an H1 space with default shapeset,
// natural BC, and linear elements.
H1Space space(&mesh, &bc_types, P_INIT);
// The type of element, mesh_mode = 4 means a rectangle element.
int mesh_mode = 4;
int ndof = Space::get_num_dofs(&space);
printf("ndof = %d\n", ndof);
if(ndof > FNS_NUM) error("Max number of shape functions exceeded.");
int *fn_idx = new int [FNS_NUM];
int m = 0;
int order = P_INIT;
// Get the vertex fns index.
info("Get the vertex fns index.");
for (int i = 0; i < mesh_mode; i++, m++)
{
fn_idx[m] = space.get_shapeset()->get_vertex_index(i);
printf("m = %d, get_vertex_index(m) = %d\n",
m, space.get_shapeset()->get_vertex_index(m));
}
// Get the edge fns index.
info("Get the edge fns index.");
for (int edge_order = 2; edge_order <= order; edge_order++)
{
for (int j = 0; j < mesh_mode; j++, m++)
{
fn_idx[m] = space.get_shapeset()->get_edge_index(j, 0, edge_order);
printf("m = %d, get_edge_index(m) = %d\n", m, fn_idx[m]);
}
}
// Get the bubble fns index.
info("Get the bubble fns index.");
int number_bubble = space.get_shapeset()->get_num_bubbles(H2D_MAKE_QUAD_ORDER(order, order));
int *bubble_idx = space.get_shapeset()->get_bubble_indices(H2D_MAKE_QUAD_ORDER(order, order));
for (int i = 0; i < number_bubble; i++, m++ )
{
fn_idx[m] = bubble_idx[i];
printf("m = %d, get_bubble_index(m) = %d\n", m, fn_idx[m]);
}
// Initialize the matrix solver.
SparseMatrix* mat = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, mat, rhs);
// precalc structure
mat->prealloc(ndof);
for (int i = 0; i < ndof; i++)
for (int j = 0; j < ndof; j++)
mat->pre_add_ij(i, j);
mat->alloc();
rhs->alloc(ndof);
info("Assembling matrix ...");
for (int i = 0; i < ndof; i++)
{
for (int j = 0; j < order; j++)
{
double x1 = -1 + (2.0/order)*j;
double y1 = -1;
double value = space.get_shapeset()->get_fn_value(fn_idx[i], x1, y1, 0);
mat->add(i, j, value);
printf("get fn[%d] value = %f ", i, value);
printf("x1 = %f, y1 = %f\n", x1, y1);
}
for (int j = 0; j < order; j++)
{
double y2 = -1 + (2.0/order)*j;;
double x2 = 1;
double value = space.get_shapeset()->get_fn_value(fn_idx[i], x2, y2, 0);
mat->add(i, j+order, value);
printf("get fn[%d] value = %f ", i, value);
printf("x2 = %f, y2 = %f\n", x2, y2);
}
for (int j = 0; j < order; j++)
{
double x3 = 1 + (-1.0)*(2.0/order)*j;
double y3 = 1;
double value = space.get_shapeset()->get_fn_value(fn_idx[i], x3, y3, 0);
mat->add(i, j+2*order, value);
printf("get fn[%d] value = %f ", i, value);
printf("x3 = %f, y3 = %f\n", x3, y3);
}
for (int j = 0; j < order; j++)
{
double x4 = -1;
double y4 = 1 + (-1.0)*(2.0/order)*j;
double value = space.get_shapeset()->get_fn_value(fn_idx[i], x4, y4, 0);
mat->add(i, j+3*order, value);
printf("get fn[%d] value = %f ", i, value);
printf("x4 = %f, y4 = %f\n", x4, y4);
}
}
int bubble = 0;
for (int i = order*4; i < ndof; i++)
{
double x = 0.0 + (1.0/number_bubble)*bubble;
double y = 0.0 + (1.0/number_bubble)*bubble;
double value = space.get_shapeset()->get_fn_value(fn_idx[i], x, y, 0);
mat->add(i, i, value);
printf("get fn[%d] value = %f ", i, value);
printf("x = %f, y = %f\n", x, y);
bubble++;
}
printf("Adding the rhs\n");
for (int i = 0; i < ndof; i++)
{
rhs->add(i, 0.0);
}
// Initialize the solution.
Solution sln;
info("Solution ...");
if(solver->solve())
Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else
error ("Matrix solver failed.\n");
for (int i = 0; i < ndof; i++)
{
// Get the value of the matrix solution by calling Vector::get().
if (rhs->get(i) >= EPS)
{
printf("Shape functions are not linearly independent\n");
return ERR_FAILURE;
}
}
printf("Success!\n");
// Clean up.
delete solver;
delete mat;
delete rhs;
delete [] fn_idx;
return ERR_SUCCESS;
}