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;
}