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/* =============================================================================
Copyright (c) 2014 - 2016
F. Georget <fabieng@princeton.edu> Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from this
software without specific prior written permission.
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. *
============================================================================= */
#ifndef SPECMICP_DFPMSOLVER_PARABOLICDRIVER_HPP
#include "parabolic_driver.hpp" // for syntaxic coloration only
#endif
#include "specmicp_common/log.hpp"
#include "specmicp_common/eigen/incl_eigen_sparse_core.hpp"
#ifdef EIGEN3_UNSUPPORTED_FOUND
#include "unsupported/Eigen/SparseExtra"
#endif
namespace specmicp {
namespace dfpmsolver {
template <class Program>
void ParabolicDriver<Program>::compute_jacobian(Vector& displacement,
Vector& velocity,
Eigen::SparseMatrix<scalar_t>& jacobian
)
{
program().compute_jacobian(displacement, velocity, jacobian, get_options().alpha*m_current_dt);
jacobian = jacobian*scaling().asDiagonal();
jacobian.makeCompressed();
get_perfs().nb_call_jacobian += 1;
}
template <class Program>
ParabolicDriverReturnCode ParabolicDriver<Program>::solve_timestep(scalar_t dt, Eigen::VectorXd& displacement)
{
initialize_timestep(dt, displacement);
return restart_timestep(displacement);
}
template <class Program>
void ParabolicDriver<Program>::initialize_timestep(scalar_t dt, Eigen::VectorXd& displacement)
{
// 1) scaling
initialize_scaling();
// 2) predictor, velocity
m_residuals = Eigen::VectorXd::Zero(get_neq());
m_current_dt = dt;
set_predictor(displacement);
reset_velocity();
program().apply_bc(dt, displacement, m_velocity);
// 3) initial residuals
compute_residuals_0(displacement, m_velocity, m_residuals);
m_norm_0 = norm_residuals();
// - If the norm is too low, we set it to 1
// This is important in reactive transport when
// an equation can be driven out of equilibrium
// during a timestep
if (m_norm_0 < get_options().absolute_tolerance) m_norm_0 = 1.0;
// 4) other initialisations
get_perfs().nb_iterations = 0;
}
template <class Program>
void ParabolicDriver<Program>::set_predictor(Vector& displacement)
{
if (get_options().alpha < 1)
m_predictor = displacement + (1.0-get_options().alpha)*m_current_dt*m_velocity;
else
m_predictor = displacement;
}
template <class Program>
scalar_t ParabolicDriver<Program>::update_norm(const Vector& update)
{
// l-∞ scaled norm
scalar_t norm = 0.0;
for (index_t dof=0; dof<program().get_tot_ndf(); ++dof)
{
const index_t id_eq = program().id_equation(dof);
if (id_eq == no_species or update(id_eq) == 0.0) continue;
norm = std::max(norm, std::abs(update(id_eq))/(std::max(std::abs(m_velocity(dof)), 1.0/scaling(id_eq))));
}
return norm;
}
template <class Program>
ParabolicDriverReturnCode ParabolicDriver<Program>::restart_timestep(Vector& displacement)
{
ParabolicDriverReturnCode return_code = ParabolicDriverReturnCode::NotConvergedYet;
//m_solver.reset(nullptr);
Eigen::VectorXd update(get_neq());
update.setZero();
get_perfs().current_update = 0;
bool force_recompute_jacobian = true;
while (return_code == ParabolicDriverReturnCode::NotConvergedYet)
{
compute_residuals(displacement, m_velocity, m_residuals);
get_perfs().absolute_residual = m_residuals.norm();
get_perfs().current_residual = m_residuals.norm()/m_norm_0;
get_perfs().current_update = update_norm(update);
DEBUG << " NB iterations : " << get_perfs().nb_iterations
<< " - res : " << get_perfs().current_residual
<< " - update : " << get_perfs().current_update;
return_code = check_convergence();
if (return_code != ParabolicDriverReturnCode::NotConvergedYet) break;
if (m_solver == nullptr)
{
m_solver = sparse_solvers::get_sparse_solver<
Eigen::SparseMatrix<scalar_t>, Vector, Vector>(
get_options().sparse_solver,
get_options().sparse_solver_pivots_threshold);
compute_jacobian(displacement, m_velocity, m_jacobian);
m_solver->analyse_pattern(m_jacobian);
sparse_solvers::SparseSolverReturnCode retcode = m_solver->decompose(m_jacobian);
if (retcode != sparse_solvers::SparseSolverReturnCode::Success)
{
ERROR << "Error when factorizing jacobian : " << (int) retcode;
#ifdef EIGEN3_UNSUPPORTED_FOUND
WARNING << "Saved matrix in : dfpm_matrix.mkt";
Eigen::saveMarket(m_jacobian, "dfpm_matrix.mkt");
#endif
return ParabolicDriverReturnCode::ErrorLinearSystem;
}
force_recompute_jacobian =false;
}
else if (force_recompute_jacobian
or get_perfs().nb_iterations % get_options().quasi_newton == 0)
{
compute_jacobian(displacement, m_velocity, m_jacobian);
sparse_solvers::SparseSolverReturnCode retcode = m_solver->decompose(m_jacobian);
if (retcode != sparse_solvers::SparseSolverReturnCode::Success)
{
ERROR << "Error when factorizing jacobian : " << (int) retcode;
#ifdef EIGEN3_UNSUPPORTED_FOUND
WARNING << "Saved matrix in : dfpm_matrix.mkt";
Eigen::saveMarket(m_jacobian, "dfpm_matrix.mkt");
#endif
return ParabolicDriverReturnCode::ErrorLinearSystem;
}
}
get_perfs().nb_iterations += 1;
m_gradient = m_jacobian.transpose()*m_residuals;
sparse_solvers::SparseSolverReturnCode retcode = m_solver->solve_scaling(m_residuals, scaling(), update);
if (retcode != sparse_solvers::SparseSolverReturnCode::Success)
{
ERROR << "Error when solving linear system : " << (int) retcode << std::endl;
return ParabolicDriverReturnCode::ErrorLinearSystem;
}
//if (update.norm() < get_options().step_tolerance) return_code = ParabolicDriverReturnCode::ErrorMinimized;
//else
return_code = linesearch(update, displacement);
}
return return_code;
}
template <class Program>
ParabolicDriverReturnCode ParabolicDriver<Program>::check_convergence()
{
ParabolicDriverReturnCode termcode = ParabolicDriverReturnCode::NotConvergedYet;
const int nb_iterations = get_perfs().nb_iterations;
const scalar_t norm_residuals = get_perfs().current_residual;
const scalar_t norm_update = get_perfs().current_update;
//std::cout << "Residuals : " << nb_iterations << " - " << norm_residuals/m_norm_0 << std::endl;
DEBUG << "Residuals : " << nb_iterations << " - " << norm_residuals/m_norm_0;
if (norm_residuals < get_options().residuals_tolerance)
{
termcode = ParabolicDriverReturnCode::ResidualMinimized;
}
else if (get_perfs().absolute_residual < get_options().absolute_tolerance)
{
termcode = ParabolicDriverReturnCode::ResidualMinimized;
}
else if (nb_iterations > 0 and norm_update > 0.0 and norm_update < 1.01*get_options().step_tolerance)
{
if (norm_residuals > get_options().threshold_stationary_point)
{
ERROR << "Stationary point detected !";
termcode = ParabolicDriverReturnCode::StationaryPoint;
}
WARNING << "Error is minimized - may indicate a stationnary point";
termcode = ParabolicDriverReturnCode::ErrorMinimized;
}
else if (nb_iterations > get_options().maximum_iterations)
{
ERROR << "Maximum number of iterations reached (" << get_options().maximum_iterations << ")";
termcode = ParabolicDriverReturnCode::MaxIterations;
}
else if (get_perfs().maximum_step_taken)
{
get_perfs().nb_consecutive_max_step_taken += 1;
get_perfs().nb_max_step_taken += 1;
if (get_perfs().nb_consecutive_max_step_taken == get_options().max_iterations_at_max_length) {
ERROR << "Divergence detected - Maximum step length taken two many times";
termcode = ParabolicDriverReturnCode::MaxStepTakenTooManyTimes;
}
}
else
{
get_perfs().nb_consecutive_max_step_taken = 0;
}
get_perfs().return_code = termcode;
return termcode;
}
template <class Program>
double ParabolicDriver<Program>::compute_residuals_linesearch(
Vector &update,
scalar_t lambda,
Vector &displacement
)
{
Eigen::VectorXd velocity(m_velocity);
Eigen::VectorXd residual = Eigen::VectorXd::Zero(get_neq());
program().update_solution(update, lambda, get_options().alpha*m_current_dt, m_predictor, displacement, velocity);
compute_residuals(displacement, velocity, residual);
return 0.5*residual.squaredNorm();
}
template <class Program>
double ParabolicDriver<Program>::compute_residuals_strang_linesearch(
Vector &update,
scalar_t lambda,
Vector &displacement
)
{
Eigen::VectorXd velocity(m_velocity);
Eigen::VectorXd residual = Eigen::VectorXd::Zero(get_neq());
program().update_solution(update, lambda, get_options().alpha*m_current_dt, m_predictor, displacement, velocity);
compute_residuals(displacement, velocity, residual);
return update.dot(residual);
}
template <class Program>
void ParabolicDriver<Program>::update_variable(
const Vector& update,
scalar_t lambda,
Vector& displacement
)
{
program().update_solution(update, lambda, get_options().alpha*m_current_dt,
m_predictor, displacement, m_velocity);
}
template <class Program>
ParabolicDriverReturnCode ParabolicDriver<Program>::linesearch(
Vector &update,
Vector &displacements
)
{
base::is_step_too_long(update);
get_perfs().maximum_step_taken = false;
scalar_t lambda;
ParabolicLinesearchReturnCode retcode;
switch (get_options().linesearch) {
case ParabolicLinesearch::Backtracking:
retcode = backtracking_linesearch(update, displacements, lambda);
break;
case ParabolicLinesearch::Strang:
retcode = strang_linesearch(update, displacements, lambda);
break;
default:
throw std::runtime_error("Linesearch type for Parabolic driver is not recognized");
break;
}
if (retcode != ParabolicLinesearchReturnCode::Success)
{
return ParabolicDriverReturnCode::LinesearchFailed;
}
update_variable(update, lambda, displacements);
update *= lambda;
return ParabolicDriverReturnCode::NotConvergedYet;
}
namespace internal
{
//! \brief Return true if a and b have the same sign
inline bool have_same_sign(double a, double b)
{
return (std::copysign(1., a) * std::copysign(1., b) > 0);
}
} // end namespace internal
template <class Program>
ParabolicLinesearchReturnCode ParabolicDriver<Program>::strang_linesearch(
Vector& update,
Vector& displacements,
scalar_t& lambda
)
{
DEBUG << "Strang linesearch";
Eigen::VectorXd xp(displacements);
const scalar_t s_tol = 0.5;
const scalar_t s_max = 2.0;
const int lin_max = 10;
scalar_t s_b = 0.0;
scalar_t g_b = 0.5*m_residuals.squaredNorm();
scalar_t s_a = 1.0;
scalar_t g_a = compute_residuals_strang_linesearch(update, 1.0, xp);
scalar_t newtlen = (scaling().asDiagonal()*update).norm();
// const scalar_t s_r = s_a;
const scalar_t g_r = g_a;
if (std::abs(g_a) <= s_tol*std::abs(g_b))
{
DEBUG << "Skip linesearch ";
lambda = 1.0;
if (lambda == 1.0 and (newtlen > 0.99 * get_options().maximum_step_length)) {
get_perfs().maximum_step_taken = true;
}
return ParabolicLinesearchReturnCode::Success;
}
while (internal::have_same_sign(g_a, g_b) and s_a < s_max)
{
s_b = s_a;
s_a = 2*s_a;
g_b = g_a;
g_a = compute_residuals_strang_linesearch(update, s_a, xp);
}
scalar_t g_ = g_a;
scalar_t g_0 = g_a;
scalar_t s = s_a;
int l;
for (l=0; l<lin_max; ++l)
{
if (internal::have_same_sign(g_a, g_b) or
std::abs(g_) < s_tol*std::abs(g_0)
or std::abs(s_a - s_b) < s_tol*(s_a + s_b)/2 )
break;
s = s_a - g_a * ( s_a - s_b)/(g_a - g_b);
g_ = compute_residuals_strang_linesearch(update, s, xp);
if (internal::have_same_sign(g_, g_a))
g_b = g_b/2.;
else
{
s_b = s_a;
g_b = g_a;
}
s_a = s;
g_a = g_;
}
if (l == lin_max) return ParabolicLinesearchReturnCode::MaximumIterations;
if (g_a >= g_r) {
WARNING << "Failed to find better update in Strang linesearch";
//lambda = 0.1*s_r;
return backtracking_linesearch(update, displacements, lambda);
}
lambda = s_a;
if (lambda == 1.0 and (newtlen > 0.99 * get_options().maximum_step_length)) {
get_perfs().maximum_step_taken = true;
}
return ParabolicLinesearchReturnCode::Success;
}
template <class Program>
ParabolicLinesearchReturnCode ParabolicDriver<Program>::backtracking_linesearch(
Vector& update,
Vector& displacements,
scalar_t& lambda_out
)
{
// References
// ----------
// - Algo A6.3.1 : Dennis and Schnabel (1983)
// - Nocedal & Wrigth (2006)
DEBUG << "Linesearch";
Eigen::VectorXd xp(displacements);
double fcp;
int retcode = 2; // 2 not converged, 1 problem, 0 success
const scalar_t alpha = 1e-4;
scalar_t newtlen = (scaling().asDiagonal()*update).norm();
scalar_t init_slope = m_gradient.dot(update);
const scalar_t rellength = update_norm(update);
const scalar_t minlambda = get_options().step_tolerance / rellength;
scalar_t lambda = 1.0;
scalar_t lambda_prev = lambda;
scalar_t merit_value = 0.5*m_residuals.squaredNorm();
// new residual
fcp = compute_residuals_linesearch(update, lambda, xp);
// Skip linesearch if enough progress is done
// ------------------------------------------
if (fcp < get_options().coeff_accept_newton_step *merit_value)
{
DEBUG << "Skip linesearch ";
lambda_out = 1.0;
return ParabolicLinesearchReturnCode::Success;
}
// The linesearch
// --------------
scalar_t fc = merit_value;
scalar_t fcp_prev;
int cnt = 0;
do
{
SPAM << "cnt : " <<cnt << " - lambda : " << lambda << " # " << fc << " # " << fcp << " # " << init_slope;
if (fcp <= fc + alpha*lambda*init_slope) //pg760 Fachinei2003
{
retcode = 0;
if (lambda == 1.0 and (newtlen > 0.99 * get_options().maximum_step_length)) {
get_perfs().maximum_step_taken = true;
}
break;
}
else if (lambda < minlambda)
{
retcode = 0;
lambda = minlambda;
//retcode = 1;
break;
}
else
{
// Select a new step length
// - - - - - - - - - - - -
double lambdatmp;
if (cnt == 0) { // only a quadratic at the first
lambdatmp = - init_slope / (2*(fcp - fc -init_slope));
}
else
{
const scalar_t factor = 1.0 /(lambda - lambda_prev);
const scalar_t x1 = fcp - fc - lambda*init_slope;
const scalar_t x2 = fcp_prev - fc - lambda_prev*init_slope;
const scalar_t a = factor * ( x1/(lambda*lambda) - x2/(lambda_prev*lambda_prev));
const scalar_t b = factor * ( -x1*lambda_prev/(lambda*lambda) + x2*lambda/(lambda_prev*lambda_prev));
if (a == 0)
{ // cubic interpolation is in fact a quadratic interpolation
lambdatmp = - init_slope/(2*b);
}
else
{
const scalar_t disc = b*b-3*a*init_slope;
lambdatmp = (-b+std::sqrt(disc))/(3*a);
}
if (lambdatmp > 0.5*lambda ) lambdatmp = 0.5*lambda;
}
lambda_prev = lambda;
fcp_prev = fcp;
if (lambdatmp < 0.1*lambda) {
lambda = 0.1 * lambda;
} else {
lambda = lambdatmp;
}
}
if (not std::isfinite(lambda))
{
ERROR << "Lambda is non finite - we stop \n"
<< "Proposed update : \n ---- \n" << update << "\n ---- \n"
<< "Current displacements \n ---- \n" << displacements << "\n ---- \n";
return ParabolicLinesearchReturnCode::Divergence;
}
fcp = compute_residuals_linesearch(update, lambda, xp);
++cnt;
} while(retcode == 2 and cnt < 50);
if (cnt == 50)
{
ERROR << "Too much linesearch iterations ! We stop";
return ParabolicLinesearchReturnCode::MaximumIterations;
}
lambda_out = lambda;
switch (retcode) {
case 0:
return ParabolicLinesearchReturnCode::Success;
break;
case 1:
return ParabolicLinesearchReturnCode::LambdaTooSmall;
default:
return ParabolicLinesearchReturnCode::NotSupposedToHappen;
break;
}
}
template <class Program>
void ParabolicDriver<Program>::set_velocity(Vector& velocity_vector)
{
m_velocity.resize(program().get_tot_ndf());
m_velocity.setZero();
for (index_t dof=0; dof<program().get_tot_ndf(); ++dof)
{
if (program().id_equation(dof) == no_equation)
{
m_velocity(dof) = velocity_vector(dof);
}
}
}
template <class Program>
void ParabolicDriver<Program>::reset_velocity()
{
for (index_t dof=0; dof<program().get_tot_ndf(); ++dof)
{
if (program().id_equation(dof) == no_equation) continue;
m_velocity(dof) = 0.0;
}
}
} // end namespace dfpmsolver
} // end namespace specmicp

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