Number PDFullSpaceSolver::ComputeResidualRatio(const IteratesVector& rhs,
const IteratesVector& res,
const IteratesVector& resid)
{
DBG_START_METH("PDFullSpaceSolver::ComputeResidualRatio", dbg_verbosity);
Number nrm_rhs = rhs.Amax();
Number nrm_res = res.Amax();
Number nrm_resid = resid.Amax();
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"nrm_rhs = %8.2e nrm_sol = %8.2e nrm_resid = %8.2e\n",
nrm_rhs, nrm_res, nrm_resid);
if (nrm_rhs+nrm_res == 0.) {
return nrm_resid; // this should be zero
}
else {
// ToDo: determine how to include norm of matrix, and what
// safeguard to use against incredibly large solution vectors
Number max_cond = 1e6;
return nrm_resid/(Min(nrm_res, max_cond*nrm_rhs)+nrm_rhs);
}
}
void PDFullSpaceSolver::ComputeResiduals(
const SymMatrix& W,
const Matrix& J_c,
const Matrix& J_d,
const Matrix& Px_L,
const Matrix& Px_U,
const Matrix& Pd_L,
const Matrix& Pd_U,
const Vector& z_L,
const Vector& z_U,
const Vector& v_L,
const Vector& v_U,
const Vector& slack_x_L,
const Vector& slack_x_U,
const Vector& slack_s_L,
const Vector& slack_s_U,
const Vector& sigma_x,
const Vector& sigma_s,
Number alpha,
Number beta,
const IteratesVector& rhs,
const IteratesVector& res,
IteratesVector& resid)
{
DBG_START_METH("PDFullSpaceSolver::ComputeResiduals", dbg_verbosity);
DBG_PRINT_VECTOR(2, "res", res);
IpData().TimingStats().ComputeResiduals().Start();
// Get the current sizes of the perturbation factors
Number delta_x;
Number delta_s;
Number delta_c;
Number delta_d;
perturbHandler_->CurrentPerturbation(delta_x, delta_s, delta_c, delta_d);
SmartPtr<Vector> tmp;
// x
W.MultVector(1., *res.x(), 0., *resid.x_NonConst());
J_c.TransMultVector(1., *res.y_c(), 1., *resid.x_NonConst());
J_d.TransMultVector(1., *res.y_d(), 1., *resid.x_NonConst());
Px_L.MultVector(-1., *res.z_L(), 1., *resid.x_NonConst());
Px_U.MultVector(1., *res.z_U(), 1., *resid.x_NonConst());
resid.x_NonConst()->AddTwoVectors(delta_x, *res.x(), -1., *rhs.x(), 1.);
// s
Pd_U.MultVector(1., *res.v_U(), 0., *resid.s_NonConst());
Pd_L.MultVector(-1., *res.v_L(), 1., *resid.s_NonConst());
resid.s_NonConst()->AddTwoVectors(-1., *res.y_d(), -1., *rhs.s(), 1.);
if (delta_s!=0.) {
resid.s_NonConst()->Axpy(delta_s, *res.s());
}
// c
J_c.MultVector(1., *res.x(), 0., *resid.y_c_NonConst());
resid.y_c_NonConst()->AddTwoVectors(-delta_c, *res.y_c(), -1., *rhs.y_c(), 1.);
// d
J_d.MultVector(1., *res.x(), 0., *resid.y_d_NonConst());
resid.y_d_NonConst()->AddTwoVectors(-1., *res.s(), -1., *rhs.y_d(), 1.);
if (delta_d!=0.) {
resid.y_d_NonConst()->Axpy(-delta_d, *res.y_d());
}
// zL
resid.z_L_NonConst()->Copy(*res.z_L());
resid.z_L_NonConst()->ElementWiseMultiply(slack_x_L);
tmp = z_L.MakeNew();
Px_L.TransMultVector(1., *res.x(), 0., *tmp);
tmp->ElementWiseMultiply(z_L);
resid.z_L_NonConst()->AddTwoVectors(1., *tmp, -1., *rhs.z_L(), 1.);
// zU
resid.z_U_NonConst()->Copy(*res.z_U());
resid.z_U_NonConst()->ElementWiseMultiply(slack_x_U);
tmp = z_U.MakeNew();
Px_U.TransMultVector(1., *res.x(), 0., *tmp);
tmp->ElementWiseMultiply(z_U);
resid.z_U_NonConst()->AddTwoVectors(-1., *tmp, -1., *rhs.z_U(), 1.);
// vL
resid.v_L_NonConst()->Copy(*res.v_L());
resid.v_L_NonConst()->ElementWiseMultiply(slack_s_L);
tmp = v_L.MakeNew();
Pd_L.TransMultVector(1., *res.s(), 0., *tmp);
tmp->ElementWiseMultiply(v_L);
resid.v_L_NonConst()->AddTwoVectors(1., *tmp, -1., *rhs.v_L(), 1.);
// vU
resid.v_U_NonConst()->Copy(*res.v_U());
resid.v_U_NonConst()->ElementWiseMultiply(slack_s_U);
tmp = v_U.MakeNew();
Pd_U.TransMultVector(1., *res.s(), 0., *tmp);
tmp->ElementWiseMultiply(v_U);
resid.v_U_NonConst()->AddTwoVectors(-1., *tmp, -1., *rhs.v_U(), 1.);
DBG_PRINT_VECTOR(2, "resid", resid);
if (Jnlst().ProduceOutput(J_MOREVECTOR, J_LINEAR_ALGEBRA)) {
resid.Print(Jnlst(), J_MOREVECTOR, J_LINEAR_ALGEBRA, "resid");
}
if (Jnlst().ProduceOutput(J_MOREDETAILED, J_LINEAR_ALGEBRA)) {
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_x %e\n", resid.x()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_s %e\n", resid.s()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_c %e\n", resid.y_c()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_d %e\n", resid.y_d()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_zL %e\n", resid.z_L()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_zU %e\n", resid.z_U()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_vL %e\n", resid.v_L()->Amax());
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"max-norm resid_vU %e\n", resid.v_U()->Amax());
}
IpData().TimingStats().ComputeResiduals().End();
}
bool PDFullSpaceSolver::SolveOnce(bool resolve_with_better_quality,
bool pretend_singular,
const SymMatrix& W,
const Matrix& J_c,
const Matrix& J_d,
const Matrix& Px_L,
const Matrix& Px_U,
const Matrix& Pd_L,
const Matrix& Pd_U,
const Vector& z_L,
const Vector& z_U,
const Vector& v_L,
const Vector& v_U,
const Vector& slack_x_L,
const Vector& slack_x_U,
const Vector& slack_s_L,
const Vector& slack_s_U,
const Vector& sigma_x,
const Vector& sigma_s,
Number alpha,
Number beta,
const IteratesVector& rhs,
IteratesVector& res)
{
// TO DO LIST:
//
// 1. decide for reasonable return codes (e.g. fatal error, too
// ill-conditioned...)
// 2. Make constants parameters that can be set from the outside
// 3. Get Information out of Ipopt structures
// 4. add heuristic for structurally singular problems
// 5. see if it makes sense to distinguish delta_x and delta_s,
// or delta_c and delta_d
// 6. increase pivot tolerance if number of get evals so too small
DBG_START_METH("PDFullSpaceSolver::SolveOnce",dbg_verbosity);
IpData().TimingStats().PDSystemSolverSolveOnce().Start();
// Compute the right hand side for the augmented system formulation
SmartPtr<Vector> augRhs_x = rhs.x()->MakeNewCopy();
Px_L.AddMSinvZ(1.0, slack_x_L, *rhs.z_L(), *augRhs_x);
Px_U.AddMSinvZ(-1.0, slack_x_U, *rhs.z_U(), *augRhs_x);
SmartPtr<Vector> augRhs_s = rhs.s()->MakeNewCopy();
Pd_L.AddMSinvZ(1.0, slack_s_L, *rhs.v_L(), *augRhs_s);
Pd_U.AddMSinvZ(-1.0, slack_s_U, *rhs.v_U(), *augRhs_s);
// Get space into which we can put the solution of the augmented system
SmartPtr<IteratesVector> sol = res.MakeNewIteratesVector(true);
// Now check whether any data has changed
std::vector<const TaggedObject*> deps(13);
deps[0] = &W;
deps[1] = &J_c;
deps[2] = &J_d;
deps[3] = &z_L;
deps[4] = &z_U;
deps[5] = &v_L;
deps[6] = &v_U;
deps[7] = &slack_x_L;
deps[8] = &slack_x_U;
deps[9] = &slack_s_L;
deps[10] = &slack_s_U;
deps[11] = &sigma_x;
deps[12] = &sigma_s;
void* dummy;
bool uptodate = dummy_cache_.GetCachedResult(dummy, deps);
if (!uptodate) {
dummy_cache_.AddCachedResult(dummy, deps);
augsys_improved_ = false;
}
// improve_current_solution can only be true, if that system has
// been solved before
DBG_ASSERT((!resolve_with_better_quality && !pretend_singular) || uptodate);
ESymSolverStatus retval;
if (uptodate && !pretend_singular) {
// Get the perturbation values
Number delta_x;
Number delta_s;
Number delta_c;
Number delta_d;
perturbHandler_->CurrentPerturbation(delta_x, delta_s, delta_c, delta_d);
// No need to go through the pain of finding the appropriate
// values for the deltas, because the matrix hasn't changed since
// the last call. So, just call the Solve Method
//
// Note: resolve_with_better_quality is true, then the Solve
// method has already asked the augSysSolver to increase the
// quality at the end solve, and we are now getting the solution
// with that better quality
retval = augSysSolver_->Solve(&W, 1.0, &sigma_x, delta_x,
&sigma_s, delta_s, &J_c, NULL,
delta_c, &J_d, NULL, delta_d,
*augRhs_x, *augRhs_s, *rhs.y_c(), *rhs.y_d(),
*sol->x_NonConst(), *sol->s_NonConst(),
*sol->y_c_NonConst(), *sol->y_d_NonConst(),
false, 0);
if (retval!=SYMSOLVER_SUCCESS) {
IpData().TimingStats().PDSystemSolverSolveOnce().End();
return false;
}
}
else {
const Index numberOfEVals=rhs.y_c()->Dim()+rhs.y_d()->Dim();
// counter for the number of trial evaluations
// (ToDo is not at the correct place)
Index count = 0;
// Get the very first perturbation values from the perturbation
// Handler
Number delta_x;
Number delta_s;
Number delta_c;
Number delta_d;
perturbHandler_->ConsiderNewSystem(delta_x, delta_s, delta_c, delta_d);
retval = SYMSOLVER_SINGULAR;
bool fail = false;
while (retval!= SYMSOLVER_SUCCESS && !fail) {
if (pretend_singular) {
retval = SYMSOLVER_SINGULAR;
pretend_singular = false;
}
else {
count++;
Jnlst().Printf(J_MOREDETAILED, J_LINEAR_ALGEBRA,
"Solving system with delta_x=%e delta_s=%e\n delta_c=%e delta_d=%e\n",
delta_x, delta_s, delta_c, delta_d);
bool check_inertia = true;
if (neg_curv_test_tol_ > 0.) {
check_inertia = false;
}
retval = augSysSolver_->Solve(&W, 1.0, &sigma_x, delta_x,
&sigma_s, delta_s, &J_c, NULL,
delta_c, &J_d, NULL, delta_d,
*augRhs_x, *augRhs_s, *rhs.y_c(), *rhs.y_d(),
*sol->x_NonConst(), *sol->s_NonConst(),
*sol->y_c_NonConst(), *sol->y_d_NonConst(), check_inertia, numberOfEVals);
}
if (retval==SYMSOLVER_FATAL_ERROR) return false;
if (retval==SYMSOLVER_SINGULAR &&
(rhs.y_c()->Dim()+rhs.y_d()->Dim() > 0) ) {
// Get new perturbation factors from the perturbation
// handlers for the singular case
bool pert_return = perturbHandler_->PerturbForSingularity(delta_x, delta_s,
delta_c, delta_d);
if (!pert_return) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"PerturbForSingularity can't be done\n");
IpData().TimingStats().PDSystemSolverSolveOnce().End();
return false;
}
}
else if (retval==SYMSOLVER_WRONG_INERTIA &&
augSysSolver_->NumberOfNegEVals() < numberOfEVals) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Number of negative eigenvalues too small!\n");
// If the number of negative eigenvalues is too small, then
// we first try to remedy this by asking for better quality
// solution (e.g. increasing pivot tolerance), and if that
// doesn't help, we assume that the system is singular
bool assume_singular = true;
if (!augsys_improved_) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Asking augmented system solver to improve quality of its solutions.\n");
augsys_improved_ = augSysSolver_->IncreaseQuality();
if (augsys_improved_) {
IpData().Append_info_string("q");
assume_singular = false;
}
else {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Quality could not be improved\n");
}
}
if (assume_singular) {
bool pert_return =
perturbHandler_->PerturbForSingularity(delta_x, delta_s,
delta_c, delta_d);
if (!pert_return) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"PerturbForSingularity can't be done for assume singular.\n");
IpData().TimingStats().PDSystemSolverSolveOnce().End();
return false;
}
IpData().Append_info_string("a");
}
}
else if (retval==SYMSOLVER_WRONG_INERTIA ||
retval==SYMSOLVER_SINGULAR) {
// Get new perturbation factors from the perturbation
// handlers for the case of wrong inertia
bool pert_return = perturbHandler_->PerturbForWrongInertia(delta_x, delta_s,
delta_c, delta_d);
if (!pert_return) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"PerturbForWrongInertia can't be done for wrong interia or singular.\n");
IpData().TimingStats().PDSystemSolverSolveOnce().End();
return false;
}
}
else if (neg_curv_test_tol_ > 0.) {
DBG_ASSERT(augSysSolver_->ProvidesInertia());
// we now check if the inertia is possible wrong
Index neg_values = augSysSolver_->NumberOfNegEVals();
if (neg_values != numberOfEVals) {
// check if we have a direction of sufficient positive curvature
SmartPtr<Vector> x_tmp = sol->x()->MakeNew();
W.MultVector(1., *sol->x(), 0., *x_tmp);
Number xWx = x_tmp->Dot(*sol->x());
x_tmp->Copy(*sol->x());
x_tmp->ElementWiseMultiply(sigma_x);
xWx += x_tmp->Dot(*sol->x());
SmartPtr<Vector> s_tmp = sol->s()->MakeNewCopy();
s_tmp->ElementWiseMultiply(sigma_s);
xWx += s_tmp->Dot(*sol->s());
if (neg_curv_test_reg_) {
x_tmp->Copy(*sol->x());
x_tmp->Scal(delta_x);
xWx += x_tmp->Dot(*sol->x());
s_tmp->Copy(*sol->s());
s_tmp->Scal(delta_s);
xWx += s_tmp->Dot(*sol->s());
}
Number xs_nrmsq = pow(sol->x()->Nrm2(),2) + pow(sol->s()->Nrm2(),2);
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"In inertia heuristic: xWx = %e xx = %e\n",
xWx, xs_nrmsq);
if (xWx < neg_curv_test_tol_*xs_nrmsq) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
" -> Redo with modified matrix.\n");
bool pert_return = perturbHandler_->PerturbForWrongInertia(delta_x, delta_s,
delta_c, delta_d);
if (!pert_return) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"PerturbForWrongInertia can't be done for inertia heuristic.\n");
IpData().TimingStats().PDSystemSolverSolveOnce().End();
return false;
}
retval = SYMSOLVER_WRONG_INERTIA;
}
}
}
} // while (retval!=SYMSOLVER_SUCCESS && !fail) {
// Some output
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Number of trial factorizations performed: %d\n",
count);
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Perturbation parameters: delta_x=%e delta_s=%e\n delta_c=%e delta_d=%e\n",
delta_x, delta_s, delta_c, delta_d);
// Set the perturbation values in the Data object
IpData().setPDPert(delta_x, delta_s, delta_c, delta_d);
}
// Compute the remaining sol Vectors
Px_L.SinvBlrmZMTdBr(-1., slack_x_L, *rhs.z_L(), z_L, *sol->x(), *sol->z_L_NonConst());
Px_U.SinvBlrmZMTdBr(1., slack_x_U, *rhs.z_U(), z_U, *sol->x(), *sol->z_U_NonConst());
Pd_L.SinvBlrmZMTdBr(-1., slack_s_L, *rhs.v_L(), v_L, *sol->s(), *sol->v_L_NonConst());
Pd_U.SinvBlrmZMTdBr(1., slack_s_U, *rhs.v_U(), v_U, *sol->s(), *sol->v_U_NonConst());
// Finally let's assemble the res result vectors
res.AddOneVector(alpha, *sol, beta);
IpData().TimingStats().PDSystemSolverSolveOnce().End();
return true;
}
bool PDFullSpaceSolver::Solve(Number alpha,
Number beta,
const IteratesVector& rhs,
IteratesVector& res,
bool allow_inexact,
bool improve_solution /* = false */)
{
DBG_START_METH("PDFullSpaceSolver::Solve",dbg_verbosity);
DBG_ASSERT(!allow_inexact || !improve_solution);
DBG_ASSERT(!improve_solution || beta==0.);
// Timing of PDSystem solver starts here
IpData().TimingStats().PDSystemSolverTotal().Start();
DBG_PRINT_VECTOR(2, "rhs_x", *rhs.x());
DBG_PRINT_VECTOR(2, "rhs_s", *rhs.s());
DBG_PRINT_VECTOR(2, "rhs_c", *rhs.y_c());
DBG_PRINT_VECTOR(2, "rhs_d", *rhs.y_d());
DBG_PRINT_VECTOR(2, "rhs_zL", *rhs.z_L());
DBG_PRINT_VECTOR(2, "rhs_zU", *rhs.z_U());
DBG_PRINT_VECTOR(2, "rhs_vL", *rhs.v_L());
DBG_PRINT_VECTOR(2, "rhs_vU", *rhs.v_U());
DBG_PRINT_VECTOR(2, "res_x in", *res.x());
DBG_PRINT_VECTOR(2, "res_s in", *res.s());
DBG_PRINT_VECTOR(2, "res_c in", *res.y_c());
DBG_PRINT_VECTOR(2, "res_d in", *res.y_d());
DBG_PRINT_VECTOR(2, "res_zL in", *res.z_L());
DBG_PRINT_VECTOR(2, "res_zU in", *res.z_U());
DBG_PRINT_VECTOR(2, "res_vL in", *res.v_L());
DBG_PRINT_VECTOR(2, "res_vU in", *res.v_U());
// if beta is nonzero, keep a copy of the incoming values in res_ */
SmartPtr<IteratesVector> copy_res;
if (beta != 0.) {
copy_res = res.MakeNewIteratesVectorCopy();
}
// Receive data about matrix
SmartPtr<const Vector> x = IpData().curr()->x();
SmartPtr<const Vector> s = IpData().curr()->s();
SmartPtr<const SymMatrix> W = IpData().W();
SmartPtr<const Matrix> J_c = IpCq().curr_jac_c();
SmartPtr<const Matrix> J_d = IpCq().curr_jac_d();
SmartPtr<const Matrix> Px_L = IpNLP().Px_L();
SmartPtr<const Matrix> Px_U = IpNLP().Px_U();
SmartPtr<const Matrix> Pd_L = IpNLP().Pd_L();
SmartPtr<const Matrix> Pd_U = IpNLP().Pd_U();
SmartPtr<const Vector> z_L = IpData().curr()->z_L();
SmartPtr<const Vector> z_U = IpData().curr()->z_U();
SmartPtr<const Vector> v_L = IpData().curr()->v_L();
SmartPtr<const Vector> v_U = IpData().curr()->v_U();
SmartPtr<const Vector> slack_x_L = IpCq().curr_slack_x_L();
SmartPtr<const Vector> slack_x_U = IpCq().curr_slack_x_U();
SmartPtr<const Vector> slack_s_L = IpCq().curr_slack_s_L();
SmartPtr<const Vector> slack_s_U = IpCq().curr_slack_s_U();
SmartPtr<const Vector> sigma_x = IpCq().curr_sigma_x();
SmartPtr<const Vector> sigma_s = IpCq().curr_sigma_s();
DBG_PRINT_VECTOR(2, "Sigma_x", *sigma_x);
DBG_PRINT_VECTOR(2, "Sigma_s", *sigma_s);
bool done = false;
// The following flag is set to true, if we asked the linear
// solver to improve the quality of the solution in
// the next solve
bool resolve_with_better_quality = false;
// the following flag is set to true, if iterative refinement
// failed and we want to try if a modified system is able to
// remedy that problem by pretending the matrix is singular
bool pretend_singular = false;
bool pretend_singular_last_time = false;
// Beginning of loop for solving the system (including all
// modifications for the linear system to ensure good solution
// quality)
while (!done) {
// if improve_solution is true, we are given already a solution
// from the calling function, so we can skip the first solve
bool solve_retval = true;
if (!improve_solution) {
solve_retval =
SolveOnce(resolve_with_better_quality, pretend_singular,
*W, *J_c, *J_d, *Px_L, *Px_U, *Pd_L, *Pd_U, *z_L, *z_U,
*v_L, *v_U, *slack_x_L, *slack_x_U, *slack_s_L, *slack_s_U,
*sigma_x, *sigma_s, 1., 0., rhs, res);
resolve_with_better_quality = false;
pretend_singular = false;
}
improve_solution = false;
if (!solve_retval) {
// If system seems not to be solvable, we return with false
// and let the calling routine deal with it.
IpData().TimingStats().PDSystemSolverTotal().End();
return false;
}
if (allow_inexact) {
// no safety checks required
if (Jnlst().ProduceOutput(J_MOREDETAILED, J_LINEAR_ALGEBRA)) {
SmartPtr<IteratesVector> resid = res.MakeNewIteratesVector(true);
ComputeResiduals(*W, *J_c, *J_d, *Px_L, *Px_U, *Pd_L, *Pd_U,
*z_L, *z_U, *v_L, *v_U, *slack_x_L, *slack_x_U,
*slack_s_L, *slack_s_U, *sigma_x, *sigma_s,
alpha, beta, rhs, res, *resid);
}
break;
}
// Get space for the residual
SmartPtr<IteratesVector> resid = res.MakeNewIteratesVector(true);
// ToDo don't to that after max refinement?
ComputeResiduals(*W, *J_c, *J_d, *Px_L, *Px_U, *Pd_L, *Pd_U,
*z_L, *z_U, *v_L, *v_U, *slack_x_L, *slack_x_U,
*slack_s_L, *slack_s_U, *sigma_x, *sigma_s,
alpha, beta, rhs, res, *resid);
Number residual_ratio =
ComputeResidualRatio(rhs, res, *resid);
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"residual_ratio = %e\n", residual_ratio);
Number residual_ratio_old = residual_ratio;
// Beginning of loop for iterative refinement
Index num_iter_ref = 0;
bool quit_refinement = false;
while (!allow_inexact && !quit_refinement &&
(num_iter_ref < min_refinement_steps_ ||
residual_ratio > residual_ratio_max_) ) {
// To the next back solve
solve_retval =
SolveOnce(resolve_with_better_quality, false,
*W, *J_c, *J_d, *Px_L, *Px_U, *Pd_L, *Pd_U, *z_L, *z_U,
*v_L, *v_U, *slack_x_L, *slack_x_U, *slack_s_L, *slack_s_U,
*sigma_x, *sigma_s, -1., 1., *resid, res);
ASSERT_EXCEPTION(solve_retval, INTERNAL_ABORT,
"SolveOnce returns false during iterative refinement.");
ComputeResiduals(*W, *J_c, *J_d, *Px_L, *Px_U, *Pd_L, *Pd_U,
*z_L, *z_U, *v_L, *v_U, *slack_x_L, *slack_x_U,
*slack_s_L, *slack_s_U, *sigma_x, *sigma_s,
alpha, beta, rhs, res, *resid);
residual_ratio =
ComputeResidualRatio(rhs, res, *resid);
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"residual_ratio = %e\n", residual_ratio);
num_iter_ref++;
// Check if we have to give up on iterative refinement
if (residual_ratio > residual_ratio_max_ &&
num_iter_ref>min_refinement_steps_ &&
(num_iter_ref>max_refinement_steps_ ||
residual_ratio>residual_improvement_factor_*residual_ratio_old)) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Iterative refinement failed with residual_ratio = %e\n", residual_ratio);
quit_refinement = true;
// Pretend singularity only once - if it didn't help, we
// have to live with what we got so far
resolve_with_better_quality = false;
DBG_PRINT((1, "pretend_singular = %d\n", pretend_singular));
if (!pretend_singular_last_time) {
// First try if we can ask the augmented system solver to
// improve the quality of the solution (only if that hasn't
// been done before for this linear system)
if (!augsys_improved_) {
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Asking augmented system solver to improve quality of its solutions.\n");
augsys_improved_ = augSysSolver_->IncreaseQuality();
if (augsys_improved_) {
IpData().Append_info_string("q");
resolve_with_better_quality = true;
}
else {
// solver said it cannot improve quality, so let
// possibly conclude that the current modification is
// singular
pretend_singular = true;
}
}
else {
// we had already asked the solver before to improve the
// quality of the solution, so let's now pretend that the
// modification is possibly singular
pretend_singular = true;
}
pretend_singular_last_time = pretend_singular;
if (pretend_singular) {
// let's only conclude that the current linear system
// including modifications is singular, if the residual is
// quite bad
if (residual_ratio < residual_ratio_singular_) {
pretend_singular = false;
IpData().Append_info_string("S");
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Just accept current solution.\n");
}
else {
IpData().Append_info_string("s");
Jnlst().Printf(J_DETAILED, J_LINEAR_ALGEBRA,
"Pretend that the current system (including modifications) is singular.\n");
}
}
}
else {
pretend_singular = false;
DBG_PRINT((1,"Resetting pretend_singular to false.\n"));
}
}
residual_ratio_old = residual_ratio;
} // End of loop for iterative refinement
done = !(resolve_with_better_quality) && !(pretend_singular);
} // End of loop for solving the linear system (incl. modifications)
// Finally let's assemble the res result vectors
if (alpha != 0.) {
res.Scal(alpha);
}
if (beta != 0.) {
res.Axpy(beta, *copy_res);
}
DBG_PRINT_VECTOR(2, "res_x", *res.x());
DBG_PRINT_VECTOR(2, "res_s", *res.s());
DBG_PRINT_VECTOR(2, "res_c", *res.y_c());
DBG_PRINT_VECTOR(2, "res_d", *res.y_d());
DBG_PRINT_VECTOR(2, "res_zL", *res.z_L());
DBG_PRINT_VECTOR(2, "res_zU", *res.z_U());
DBG_PRINT_VECTOR(2, "res_vL", *res.v_L());
DBG_PRINT_VECTOR(2, "res_vU", *res.v_U());
IpData().TimingStats().PDSystemSolverTotal().End();
return true;
}
bool StdStepCalculator::Step(DenseVector& delta_u,
IteratesVector& sol)
{
DBG_START_METH("StdStepCalculator::Step", dbg_verbosity);
bool retval = false;
SmartPtr<IteratesVector> delta_u_long = IpData().trial()->MakeNewIteratesVector();
ift_data_->TransMultiply(delta_u, *delta_u_long);
SmartPtr<IteratesVector> r_s = IpData().trial()->MakeNewIteratesVector();
if (kkt_residuals_) {
/* This should be almost zero... */
r_s->Set_x_NonConst(*IpCq().curr_grad_lag_x()->MakeNewCopy());
r_s->Set_s_NonConst(*IpCq().curr_grad_lag_s()->MakeNewCopy());
r_s->Set_y_c_NonConst(*IpCq().curr_c()->MakeNewCopy());
r_s->Set_y_d_NonConst(*IpCq().curr_d_minus_s()->MakeNewCopy());
r_s->Set_z_L_NonConst(*IpCq().curr_compl_x_L()->MakeNewCopy());
r_s->Set_z_U_NonConst(*IpCq().curr_compl_x_U()->MakeNewCopy());
r_s->Set_v_L_NonConst(*IpCq().curr_compl_s_L()->MakeNewCopy());
r_s->Set_v_U_NonConst(*IpCq().curr_compl_s_U()->MakeNewCopy());
r_s->Print(Jnlst(),J_VECTOR,J_USER1,"r_s init");
delta_u.Print(Jnlst(),J_VECTOR,J_USER1,"delta_u init");
DBG_PRINT((dbg_verbosity,"r_s init Nrm2=%23.16e\n", r_s->Asum()));
delta_u_long->Axpy(-1.0, *r_s);
}
backsolver_->Solve(&sol, ConstPtr(delta_u_long));
SmartPtr<IteratesVector> Kr_s;
if (Do_Boundcheck()) {
Kr_s = sol.MakeNewIteratesVectorCopy();
}
sol.Axpy(1.0, *IpData().trial());
if (Do_Boundcheck()) {
DBG_PRINT((dbg_verbosity, "Entering boundcheck"));
// initialize
Index new_du_size =0;
Number* new_du_values;
std::vector<Index> x_bound_violations_idx;
std::vector<Number> x_bound_violations_du;
std::vector<Index> delta_u_sort;
bool bounds_violated;
SmartPtr<DenseVectorSpace> delta_u_space = new DenseVectorSpace(0);
SmartPtr<DenseVector> old_delta_u = new DenseVector(GetRawPtr(delta_u_space));
SmartPtr<DenseVector> new_delta_u;
bounds_violated = BoundCheck(sol, x_bound_violations_idx, x_bound_violations_du);
while (bounds_violated) {
Driver()->data_A()->Print(Jnlst(),J_VECTOR,J_USER1,"data_A_init");
Driver()->data_B()->Print(Jnlst(),J_VECTOR,J_USER1,"data_B_init");
// write new schurdata A
dynamic_cast<IndexSchurData*>(GetRawPtr(Driver()->data_A_nonconst()))->AddData_List(x_bound_violations_idx, delta_u_sort, new_du_size, 1);
// write new schurdata B
dynamic_cast<IndexSchurData*>(GetRawPtr(Driver()->data_B_nonconst()))->AddData_List(x_bound_violations_idx, delta_u_sort, new_du_size, 1);
Driver()->data_A()->Print(Jnlst(),J_VECTOR,J_USER1,"data_A");
Driver()->data_B()->Print(Jnlst(),J_VECTOR,J_USER1,"data_B");
Driver()->SchurBuild();
Driver()->SchurFactorize();
old_delta_u->Print(Jnlst(),J_VECTOR,J_USER1,"old_delta_u");
delta_u_space = NULL; // delete old delta_u space
delta_u_space = new DenseVectorSpace(new_du_size); // create new delta_u space
new_delta_u = new DenseVector(GetRawPtr(ConstPtr(delta_u_space)));
new_du_values = new_delta_u->Values();
IpBlasDcopy(old_delta_u->Dim(), old_delta_u->Values(), 1, new_du_values, 1);
for (UINT i=0; i<x_bound_violations_idx.size(); ++i) {
// printf("i=%d, delta_u_sort[i]=%d, x_bound_viol_du[i]=%f\n", i, delta_u_sort[i], x_bound_violations_du[i]);
new_du_values[delta_u_sort[i]] = x_bound_violations_du[i];
}
SmartPtr<IteratesVector> new_sol = sol.MakeNewIteratesVector();
new_delta_u->Print(Jnlst(),J_VECTOR,J_USER1,"new_delta_u");
// solve with new data_B and delta_u
retval = Driver()->SchurSolve(&sol, ConstPtr(delta_u_long), dynamic_cast<Vector*>(GetRawPtr(new_delta_u)), Kr_s);
sol.Axpy(1.0, *IpData().trial());
x_bound_violations_idx.clear();
x_bound_violations_du.clear();
delta_u_sort.clear();
bounds_violated = BoundCheck(sol, x_bound_violations_idx, x_bound_violations_du);
// copy new vector in old vector ->has to be done becpause otherwise only pointers will be copied and then it makes no sense
old_delta_u = new_delta_u->MakeNewDenseVector();
old_delta_u->Copy(*new_delta_u);
}
}
return retval;
}
bool StdStepCalculator::BoundCheck(IteratesVector& sol,
std::vector<Index>& x_bound_violations_idx,
std::vector<Number>& x_bound_violations_du)
{
DBG_START_METH("StdStepCalculator::BoundCheck", dbg_verbosity);
DBG_ASSERT(x_bound_violations_idx.empty());
DBG_ASSERT(x_bound_violations_du.empty());
// find bound violations in x vector
const Number* x_val = dynamic_cast<const DenseVector*>(GetRawPtr(IpData().curr()->x()))->Values();
const Number* sol_val = dynamic_cast<const DenseVector*>(GetRawPtr(sol.x()))->Values();
SmartPtr<Vector> x_L_exp = IpData().curr()->x()->MakeNew();
SmartPtr<Vector> x_U_exp = IpData().curr()->x()->MakeNew();
SmartPtr<Vector> x_L_comp = IpNLP().x_L()->MakeNew();
SmartPtr<Vector> x_U_comp = IpNLP().x_U()->MakeNew();
IpNLP().Px_L()->TransMultVector(1.0, *sol.x(), 0.0, *x_L_comp);
IpNLP().Px_U()->TransMultVector(1.0, *sol.x(), 0.0, *x_U_comp);
x_L_comp->Print(Jnlst(),J_VECTOR,J_USER1,"x_L_comp");
x_U_comp->Print(Jnlst(),J_VECTOR,J_USER1,"x_U_comp");
// return false;
Number* x_L_val = dynamic_cast<DenseVector*>(GetRawPtr(x_L_comp))->Values();
Number* x_U_val = dynamic_cast<DenseVector*>(GetRawPtr(x_U_comp))->Values();
const Number* x_L_bound = dynamic_cast<const DenseVector*>(GetRawPtr(IpNLP().x_L()))->Values();
const Number* x_U_bound = dynamic_cast<const DenseVector*>(GetRawPtr(IpNLP().x_U()))->Values();
for (Index i=0; i<x_L_comp->Dim(); ++i) {
x_L_val[i] -= x_L_bound[i];
}
for (Index i=0; i<x_U_comp->Dim(); ++i) {
x_U_val[i] -= x_U_bound[i];
}
// project back
IpNLP().Px_L()->MultVector(1.0, *x_L_comp, 0.0, *x_L_exp);
IpNLP().Px_U()->MultVector(1.0, *x_U_comp, 0.0, *x_U_exp);
const Number* x_L_exp_val = dynamic_cast<DenseVector*>(GetRawPtr(x_L_exp))->Values();
const Number* x_U_exp_val = dynamic_cast<DenseVector*>(GetRawPtr(x_U_exp))->Values();
for (Index i=0; i<x_L_exp->Dim(); ++i) {
if (x_L_exp_val[i]<-bound_eps_) {
x_bound_violations_idx.push_back(i);
x_bound_violations_du.push_back(-x_L_exp_val[i]+sol_val[i]-x_val[i]); // this is just an awkward way to compute x_bound[i] - x_curr_val[i].
} else if (-x_U_exp_val[i]<-bound_eps_) {
x_bound_violations_idx.push_back(i);
x_bound_violations_du.push_back(-x_U_exp_val[i]+sol_val[i]-x_val[i]);
}
}
// z_L and z_U bound violations -> These are much easier since there is no projecting back and forth
SmartPtr<const DenseVector> z_L = dynamic_cast<const DenseVector*>(GetRawPtr(sol.z_L()));
SmartPtr<const DenseVector> z_U = dynamic_cast<const DenseVector*>(GetRawPtr(sol.z_U()));
z_L->Print(Jnlst(),J_VECTOR,J_USER1,"z_L_boundcheck");
z_U->Print(Jnlst(),J_VECTOR,J_USER1,"z_U_boundcheck");
const Number* z_L_val = z_L->Values();
const Number* z_U_val = z_U->Values();
SmartPtr<const DenseVector> z_L_trial = dynamic_cast<const DenseVector*>(GetRawPtr(IpData().trial()->z_L()));
SmartPtr<const DenseVector> z_U_trial = dynamic_cast<const DenseVector*>(GetRawPtr(IpData().trial()->z_U()));
const Number* z_L_trial_val = z_L_trial->Values();
const Number* z_U_trial_val = z_U_trial->Values();
// find absolute index of z_L and z_U in IteratesVector
Index z_L_ItVec_idx = 0;
for (Index i=0; i<4; ++i) {
z_L_ItVec_idx += (sol.GetComp(i))->Dim();
}
Index z_U_ItVec_idx = z_L_ItVec_idx + sol.z_L()->Dim();
for (Index i=0; i<z_L->Dim(); ++i) {
if (z_L_val[i]<-bound_eps_) {
x_bound_violations_idx.push_back(i+z_L_ItVec_idx);
x_bound_violations_du.push_back(-z_L_trial_val[i]);
//printf("Lower Bound Mult. no. i=%d invalid: delta_u=%f\n", i+z_L_ItVec_idx, z_L_val[i]);
}
}
for (Index i=0; i<z_U->Dim(); ++i) {
if (z_U_val[i]<-bound_eps_) {
x_bound_violations_idx.push_back(i+z_U_ItVec_idx);
x_bound_violations_du.push_back(-z_U_trial_val[i]);
//printf("Upper Bound Mult. no. i=%d invalid: delta_u=%f\n", i+z_U_ItVec_idx, z_U_val[i]);
}
}
// if (x_bound_violations_idx.empty() || z_L_bound_violations_idx.empty() || z_U_bound_violations_idx.empty()) {
if (x_bound_violations_idx.empty()) {
return false;
}
else {
return true;
}
}
Number ProbingMuOracle::CalculateAffineMu(
Number alpha_primal,
Number alpha_dual,
const IteratesVector& step
)
{
// Get the current values of the slack variables and bound multipliers
SmartPtr<const Vector> slack_x_L = IpCq().curr_slack_x_L();
SmartPtr<const Vector> slack_x_U = IpCq().curr_slack_x_U();
SmartPtr<const Vector> slack_s_L = IpCq().curr_slack_s_L();
SmartPtr<const Vector> slack_s_U = IpCq().curr_slack_s_U();
SmartPtr<const Vector> z_L = IpData().curr()->z_L();
SmartPtr<const Vector> z_U = IpData().curr()->z_U();
SmartPtr<const Vector> v_L = IpData().curr()->v_L();
SmartPtr<const Vector> v_U = IpData().curr()->v_U();
SmartPtr<Vector> tmp_slack;
SmartPtr<Vector> tmp_mult;
SmartPtr<const Matrix> P;
Index ncomp = 0;
Number sum = 0.;
// For each combination of slack and multiplier, compute the new
// values and their dot products.
// slack_x_L
if( slack_x_L->Dim() > 0 )
{
ncomp += slack_x_L->Dim();
P = IpNLP().Px_L();
tmp_slack = slack_x_L->MakeNew();
tmp_slack->Copy(*slack_x_L);
P->TransMultVector(alpha_primal, *step.x(), 1.0, *tmp_slack);
tmp_mult = z_L->MakeNew();
tmp_mult->Copy(*z_L);
tmp_mult->Axpy(alpha_dual, *step.z_L());
sum += tmp_slack->Dot(*tmp_mult);
}
// slack_x_U
if( slack_x_U->Dim() > 0 )
{
ncomp += slack_x_U->Dim();
P = IpNLP().Px_U();
tmp_slack = slack_x_U->MakeNew();
tmp_slack->Copy(*slack_x_U);
P->TransMultVector(-alpha_primal, *step.x(), 1.0, *tmp_slack);
tmp_mult = z_U->MakeNew();
tmp_mult->Copy(*z_U);
tmp_mult->Axpy(alpha_dual, *step.z_U());
sum += tmp_slack->Dot(*tmp_mult);
}
// slack_s_L
if( slack_s_L->Dim() > 0 )
{
ncomp += slack_s_L->Dim();
P = IpNLP().Pd_L();
tmp_slack = slack_s_L->MakeNew();
tmp_slack->Copy(*slack_s_L);
P->TransMultVector(alpha_primal, *step.s(), 1.0, *tmp_slack);
tmp_mult = v_L->MakeNew();
tmp_mult->Copy(*v_L);
tmp_mult->Axpy(alpha_dual, *step.v_L());
sum += tmp_slack->Dot(*tmp_mult);
}
// slack_s_U
if( slack_s_U->Dim() > 0 )
{
ncomp += slack_s_U->Dim();
P = IpNLP().Pd_U();
tmp_slack = slack_s_U->MakeNew();
tmp_slack->Copy(*slack_s_U);
P->TransMultVector(-alpha_primal, *step.s(), 1.0, *tmp_slack);
tmp_mult = v_U->MakeNew();
tmp_mult->Copy(*v_U);
tmp_mult->Axpy(alpha_dual, *step.v_U());
sum += tmp_slack->Dot(*tmp_mult);
}
DBG_ASSERT(ncomp > 0);
return sum / ((Number) ncomp);
}