void RBEIMEvaluation::legacy_read_offline_data_from_files(const std::string & directory_name,
bool read_error_bound_data,
const bool read_binary_data)
{
LOG_SCOPE("legacy_read_offline_data_from_files()", "RBEIMEvaluation");
Parent::legacy_read_offline_data_from_files(directory_name, read_error_bound_data);
// First, find out how many basis functions we had when Greedy terminated
// This was set in RBSystem::read_offline_data_from_files
unsigned int n_bfs = this->get_n_basis_functions();
// The writing mode: DECODE for binary, READ for ASCII
XdrMODE mode = read_binary_data ? DECODE : READ;
// The suffix to use for all the files that are written out
const std::string suffix = read_binary_data ? ".xdr" : ".dat";
// Stream for creating file names
std::ostringstream file_name;
// Read in the interpolation matrix
file_name.str("");
file_name << directory_name << "/interpolation_matrix" << suffix;
assert_file_exists(file_name.str());
Xdr interpolation_matrix_in(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
for(unsigned int j=0; j<=i; j++)
{
Number value;
interpolation_matrix_in >> value;
interpolation_matrix(i,j) = value;
}
}
interpolation_matrix_in.close();
// Next read in interpolation_points
file_name.str("");
file_name << directory_name << "/interpolation_points" << suffix;
assert_file_exists(file_name.str());
Xdr interpolation_points_in(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
Real x_val, y_val, z_val = 0.;
interpolation_points_in >> x_val;
if(LIBMESH_DIM >= 2)
interpolation_points_in >> y_val;
if(LIBMESH_DIM >= 3)
interpolation_points_in >> z_val;
Point p(x_val, y_val, z_val);
interpolation_points.push_back(p);
}
interpolation_points_in.close();
// Next read in interpolation_points_var
file_name.str("");
file_name << directory_name << "/interpolation_points_var" << suffix;
assert_file_exists(file_name.str());
Xdr interpolation_points_var_in(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
unsigned int var;
interpolation_points_var_in >> var;
interpolation_points_var.push_back(var);
}
interpolation_points_var_in.close();
// Read in the elements corresponding to the interpolation points
legacy_read_in_interpolation_points_elem(directory_name);
}
void RBEIMEvaluation::legacy_write_offline_data_to_files(const std::string & directory_name,
const bool read_binary_data)
{
LOG_SCOPE("legacy_write_offline_data_to_files()", "RBEIMEvaluation");
Parent::legacy_write_offline_data_to_files(directory_name);
// Get the number of basis functions
unsigned int n_bfs = get_n_basis_functions();
// The writing mode: ENCODE for binary, WRITE for ASCII
XdrMODE mode = read_binary_data ? ENCODE : WRITE;
// The suffix to use for all the files that are written out
const std::string suffix = read_binary_data ? ".xdr" : ".dat";
if(this->processor_id() == 0)
{
std::ostringstream file_name;
// Next write out the interpolation_matrix
file_name.str("");
file_name << directory_name << "/interpolation_matrix" << suffix;
Xdr interpolation_matrix_out(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
for(unsigned int j=0; j<=i; j++)
{
interpolation_matrix_out << interpolation_matrix(i,j);
}
}
// Next write out interpolation_points
file_name.str("");
file_name << directory_name << "/interpolation_points" << suffix;
Xdr interpolation_points_out(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
interpolation_points_out << interpolation_points[i](0);
if(LIBMESH_DIM >= 2)
interpolation_points_out << interpolation_points[i](1);
if(LIBMESH_DIM >= 3)
interpolation_points_out << interpolation_points[i](2);
}
interpolation_points_out.close();
// Next write out interpolation_points_var
file_name.str("");
file_name << directory_name << "/interpolation_points_var" << suffix;
Xdr interpolation_points_var_out(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
interpolation_points_var_out << interpolation_points_var[i];
}
interpolation_points_var_out.close();
}
// Write out the elements associated with the interpolation points.
// This uses mesh I/O, hence we have to do it on all processors.
legacy_write_out_interpolation_points_elem(directory_name);
}
Real RBEIMEvaluation::rb_solve(unsigned int N)
{
// Short-circuit if we are using the same parameters and value of N
if( (_previous_parameters == get_parameters()) &&
(_previous_N == N) )
{
return _previous_error_bound;
}
// Otherwise, update _previous parameters, _previous_N
_previous_parameters = get_parameters();
_previous_N = N;
LOG_SCOPE("rb_solve()", "RBEIMEvaluation");
if(N > get_n_basis_functions())
libmesh_error_msg("ERROR: N cannot be larger than the number of basis functions in rb_solve");
if(N==0)
libmesh_error_msg("ERROR: N must be greater than 0 in rb_solve");
// Get the rhs by sampling parametrized_function
// at the first N interpolation_points
DenseVector<Number> EIM_rhs(N);
for(unsigned int i=0; i<N; i++)
{
EIM_rhs(i) = evaluate_parametrized_function(interpolation_points_var[i],
interpolation_points[i],
*interpolation_points_elem[i]);
}
DenseMatrix<Number> interpolation_matrix_N;
interpolation_matrix.get_principal_submatrix(N, interpolation_matrix_N);
interpolation_matrix_N.lu_solve(EIM_rhs, RB_solution);
// Optionally evaluate an a posteriori error bound. The EIM error estimate
// recommended in the literature is based on using "next" EIM point, so
// we skip this if N == get_n_basis_functions()
if(evaluate_RB_error_bound && (N != get_n_basis_functions()))
{
// Compute the a posteriori error bound
// First, sample the parametrized function at x_{N+1}
Number g_at_next_x = evaluate_parametrized_function(interpolation_points_var[N],
interpolation_points[N],
*interpolation_points_elem[N]);
// Next, evaluate the EIM approximation at x_{N+1}
Number EIM_approx_at_next_x = 0.;
for(unsigned int j=0; j<N; j++)
{
EIM_approx_at_next_x += RB_solution(j) * interpolation_matrix(N,j);
}
Real error_estimate = std::abs(g_at_next_x - EIM_approx_at_next_x);
_previous_error_bound = error_estimate;
return error_estimate;
}
else // Don't evaluate an error bound
{
_previous_error_bound = -1.;
return -1.;
}
}
void RBEIMEvaluation::read_offline_data_from_files(const std::string& directory_name,
bool read_error_bound_data,
const bool read_binary_data)
{
START_LOG("read_offline_data_from_files()", "RBEIMEvaluation");
Parent::read_offline_data_from_files(directory_name, read_error_bound_data);
// First, find out how many basis functions we had when Greedy terminated
// This was set in RBSystem::read_offline_data_from_files
unsigned int n_bfs = this->get_n_basis_functions();
// The writing mode: DECODE for binary, READ for ASCII
XdrMODE mode = read_binary_data ? DECODE : READ;
// The suffix to use for all the files that are written out
const std::string suffix = read_binary_data ? ".xdr" : ".dat";
// Stream for creating file names
OStringStream file_name;
// Read in the interpolation matrix
file_name.str("");
file_name << directory_name << "/interpolation_matrix" << suffix;
Xdr interpolation_matrix_in(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
for(unsigned int j=0; j<=i; j++)
{
Number value;
interpolation_matrix_in >> value;
interpolation_matrix(i,j) = value;
}
}
interpolation_matrix_in.close();
// Also, read in the "extra" row
file_name.str("");
file_name << directory_name << "/extra_interpolation_matrix_row" << suffix;
Xdr extra_interpolation_matrix_row_in(file_name.str(), mode);
for(unsigned int j=0; j<n_bfs; j++)
{
Number value;
extra_interpolation_matrix_row_in >> value;
extra_interpolation_matrix_row(j) = value;
}
extra_interpolation_matrix_row_in.close();
// Next read in interpolation_points
file_name.str("");
file_name << directory_name << "/interpolation_points" << suffix;
Xdr interpolation_points_in(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
Real x_val, y_val, z_val = 0.;
interpolation_points_in >> x_val;
if(LIBMESH_DIM >= 2)
interpolation_points_in >> y_val;
if(LIBMESH_DIM >= 3)
interpolation_points_in >> z_val;
Point p(x_val, y_val, z_val);
interpolation_points.push_back(p);
}
interpolation_points_in.close();
// Also, read in the extra interpolation point
file_name.str("");
file_name << directory_name << "/extra_interpolation_point" << suffix;
Xdr extra_interpolation_point_in(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
Real x_val, y_val, z_val = 0.;
extra_interpolation_point_in >> x_val;
if(LIBMESH_DIM >= 2)
extra_interpolation_point_in >> y_val;
if(LIBMESH_DIM >= 3)
extra_interpolation_point_in >> z_val;
Point p(x_val, y_val, z_val);
extra_interpolation_point = p;
}
extra_interpolation_point_in.close();
// Next read in interpolation_points_var
file_name.str("");
file_name << directory_name << "/interpolation_points_var" << suffix;
Xdr interpolation_points_var_in(file_name.str(), mode);
for(unsigned int i=0; i<=n_bfs; i++)
{
unsigned int var;
interpolation_points_var_in >> var;
interpolation_points_var.push_back(var);
}
interpolation_points_var_in.close();
// Also, read in extra_interpolation_point_var
file_name.str("");
file_name << directory_name << "/extra_interpolation_point_var" << suffix;
Xdr extra_interpolation_point_var_in(file_name.str(), mode);
for(unsigned int i=0; i<=n_bfs; i++)
{
unsigned int var;
extra_interpolation_point_var_in >> var;
extra_interpolation_point_var = var;
}
extra_interpolation_point_var_in.close();
STOP_LOG("read_offline_data_from_files()", "RBEIMEvaluation");
}
void RBEIMEvaluation::write_offline_data_to_files(const std::string& directory_name,
const bool read_binary_data)
{
START_LOG("write_offline_data_to_files()", "RBEIMEvaluation");
Parent::write_offline_data_to_files(directory_name);
// Get the number of basis functions
unsigned int n_bfs = get_n_basis_functions();
// The writing mode: ENCODE for binary, WRITE for ASCII
XdrMODE mode = read_binary_data ? ENCODE : WRITE;
// The suffix to use for all the files that are written out
const std::string suffix = read_binary_data ? ".xdr" : ".dat";
if(libMesh::processor_id() == 0)
{
OStringStream file_name;
// Next write out the interpolation_matrix
file_name.str("");
file_name << directory_name << "/interpolation_matrix" << suffix;
Xdr interpolation_matrix_out(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
for(unsigned int j=0; j<=i; j++)
{
interpolation_matrix_out << interpolation_matrix(i,j);
}
}
// Also, write out the "extra" row
file_name.str("");
file_name << directory_name << "/extra_interpolation_matrix_row" << suffix;
Xdr extra_interpolation_matrix_row_out(file_name.str(), mode);
for(unsigned int j=0; j<n_bfs; j++)
{
extra_interpolation_matrix_row_out << extra_interpolation_matrix_row(j);
}
extra_interpolation_matrix_row_out.close();
// Next write out interpolation_points
file_name.str("");
file_name << directory_name << "/interpolation_points" << suffix;
Xdr interpolation_points_out(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
interpolation_points_out << interpolation_points[i](0);
if(LIBMESH_DIM >= 2)
interpolation_points_out << interpolation_points[i](1);
if(LIBMESH_DIM >= 3)
interpolation_points_out << interpolation_points[i](2);
}
interpolation_points_out.close();
// Also, write out the "extra" interpolation point
file_name.str("");
file_name << directory_name << "/extra_interpolation_point" << suffix;
Xdr extra_interpolation_point_out(file_name.str(), mode);
extra_interpolation_point_out << extra_interpolation_point(0);
if(LIBMESH_DIM >= 2)
extra_interpolation_point_out << extra_interpolation_point(1);
if(LIBMESH_DIM >= 3)
extra_interpolation_point_out << extra_interpolation_point(2);
extra_interpolation_point_out.close();
// Next write out interpolation_points_var
file_name.str("");
file_name << directory_name << "/interpolation_points_var" << suffix;
Xdr interpolation_points_var_out(file_name.str(), mode);
for(unsigned int i=0; i<n_bfs; i++)
{
interpolation_points_var_out << interpolation_points_var[i];
}
interpolation_points_var_out.close();
// Also, write out the "extra" interpolation variable
file_name.str("");
file_name << directory_name << "/extra_interpolation_point_var" << suffix;
Xdr extra_interpolation_point_var_out(file_name.str(), mode);
extra_interpolation_point_var_out << extra_interpolation_point_var;
extra_interpolation_point_var_out.close();
}
STOP_LOG("write_offline_data_to_files()", "RBEIMEvaluation");
}
Real RBEIMEvaluation::rb_solve(unsigned int N)
{
// Short-circuit if we are using the same parameters and value of N
if( (_previous_parameters == get_parameters()) &&
(_previous_N == N) )
{
return _previous_error_bound;
}
// Otherwise, update _previous parameters, _previous_N
_previous_parameters = get_parameters();
_previous_N = N;
START_LOG("rb_solve()", "RBEIMEvaluation");
if(N > get_n_basis_functions())
{
libMesh::err << "ERROR: N cannot be larger than the number "
<< "of basis functions in rb_solve" << std::endl;
libmesh_error();
}
if(N==0)
{
libMesh::err << "ERROR: N must be greater than 0 in rb_solve" << std::endl;
libmesh_error();
}
// Get the rhs by sampling parametrized_function
// at the first N interpolation_points
DenseVector<Number> EIM_rhs(N);
for(unsigned int i=0; i<N; i++)
{
EIM_rhs(i) = evaluate_parametrized_function(interpolation_points_var[i], interpolation_points[i]);
}
DenseMatrix<Number> interpolation_matrix_N;
interpolation_matrix.get_principal_submatrix(N, interpolation_matrix_N);
interpolation_matrix_N.lu_solve(EIM_rhs, RB_solution);
// Evaluate an a posteriori error bound
if(evaluate_RB_error_bound)
{
// Compute the a posteriori error bound
// First, sample the parametrized function at x_{N+1}
Number g_at_next_x;
if(N == get_n_basis_functions())
g_at_next_x = evaluate_parametrized_function(extra_interpolation_point_var, extra_interpolation_point);
else
g_at_next_x = evaluate_parametrized_function(interpolation_points_var[N], interpolation_points[N]);
// Next, evaluate the EIM approximation at x_{N+1}
Number EIM_approx_at_next_x = 0.;
for(unsigned int j=0; j<N; j++)
{
if(N == get_n_basis_functions())
{
EIM_approx_at_next_x += RB_solution(j) * extra_interpolation_matrix_row(j);
}
else
{
EIM_approx_at_next_x += RB_solution(j) * interpolation_matrix(N,j);
}
}
Real error_estimate = std::abs(g_at_next_x - EIM_approx_at_next_x);
STOP_LOG("rb_solve()", "RBEIMEvaluation");
_previous_error_bound = error_estimate;
return error_estimate;
}
else // Don't evaluate an error bound
{
STOP_LOG("rb_solve()", "RBEIMEvaluation");
_previous_error_bound = -1.;
return -1.;
}
}
