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;
  }