PS_Method_CCS_test/Ipopt_lScalableProblems_lib/MittelmannDistCntrlNeumA.cpp

// Copyright (C) 2005, 2006 International Business Machines and others.
// All Rights Reserved.
// This code is published under the Eclipse Public License.
//
// $Id: MittelmannDistCntrlNeumA.cpp 2005 2011-06-06 12:55:16Z stefan $
//
// Authors:  Carl Laird, Andreas Waechter     IBM    2004-11-05

#include "MittelmannDistCntrlNeumA.hpp"

#ifdef HAVE_CASSERT
# include <cassert>
#else
# ifdef HAVE_ASSERT_H
#  include <assert.h>
# else
#  error "don't have header file for assert"
# endif
#endif

using namespace Ipopt;

/* Constructor. */
MittelmannDistCntrlNeumABase::MittelmannDistCntrlNeumABase()
    :
    y_d_(NULL)
{}

MittelmannDistCntrlNeumABase::~MittelmannDistCntrlNeumABase()
{
  delete [] y_d_;
}

void
MittelmannDistCntrlNeumABase::SetBaseParameters(Index N, Number lb_y, Number ub_y,
    Number lb_u, Number ub_u,
    Number b_0j, Number b_1j,
    Number b_i0, Number b_i1,
    Number u_init)
{
  N_ = N;
  h_ = 1./(N+1);
  hh_ = h_*h_;
  lb_y_ = lb_y;
  ub_y_ = ub_y;
  lb_u_ = lb_u;
  ub_u_ = ub_u;
  b_0j_ = b_0j;
  b_1j_ = b_1j;
  b_i0_ = b_i0;
  b_i1_ = b_i1;
  u_init_ = u_init;

  // Initialize the target profile variables
  delete [] y_d_;
  y_d_ = new Number[(N_+2)*(N_+2)];
  for (Index j=0; j<= N_+1; j++) {
    for (Index i=0; i<= N_+1; i++) {
      y_d_[y_index(i,j)] = y_d_cont(x1_grid(i),x2_grid(j));
    }
  }
}

bool MittelmannDistCntrlNeumABase::get_nlp_info(
  Index& n, Index& m, Index& nnz_jac_g,
  Index& nnz_h_lag, IndexStyleEnum& index_style)
{
  // We for each of the N_+2 times N_+2 mesh points we have the value
  // of the functions y, and for each N_ times N_ interior mesh points
  // we have values for u
  n = (N_+2)*(N_+2) + N_*N_;

  // For each of the N_ times N_ interior mesh points we have the
  // discretized PDE, and we have one constriant for each boundary
  // point (except for the corners)
  m = N_*N_ + 4*N_;

  // y(i,j), y(i-1,j), y(i+1,j), y(i,j-1), y(i,j+1), u(i,j) for each
  // of the N_*N_ discretized PDEs, and for the Neumann boundary
  // conditions
  nnz_jac_g = 6*N_*N_ + 8*N_;

  // diagonal entry for each dydy, dudu, dydu in the interior
  nnz_h_lag = 0;
  if (!fint_cont_dydy_alwayszero() || !d_cont_dydy_alwayszero()) {
    nnz_h_lag += N_*N_;
  }
  if (!fint_cont_dudu_alwayszero() || !d_cont_dudu_alwayszero()) {
    nnz_h_lag += N_*N_;
  }
  if (!fint_cont_dydu_alwayszero() || !d_cont_dydu_alwayszero()) {
    nnz_h_lag += N_*N_;
  }

  // We use the C indexing style for row/col entries (corresponding to
  // the C notation, starting at 0)
  index_style = C_STYLE;

  return true;
}

bool
MittelmannDistCntrlNeumABase::get_bounds_info(Index n, Number* x_l, Number* x_u,
    Index m, Number* g_l, Number* g_u)
{
  // Set overall bounds on the variables
  for (Index i=0; i<=N_+1; i++) {
    for (Index j=0; j<=N_+1; j++) {
      Index iy = y_index(i,j);
      x_l[iy] = lb_y_;
      x_u[iy] = ub_y_;
    }
  }
  for (Index i=1; i<=N_; i++) {
    for (Index j=1; j<=N_; j++) {
      Index iu = u_index(i,j);
      x_l[iu] = lb_u_;
      x_u[iu] = ub_u_;
    }
  }

  // There is no information for the y's at the corner points, so just
  // take those variables out
  x_l[y_index(0,0)] = x_u[y_index(0,0)] = 0.;
  x_l[y_index(0,N_+1)] = x_u[y_index(0,N_+1)] = 0.;
  x_l[y_index(N_+1,0)] = x_u[y_index(N_+1,0)] = 0.;
  x_l[y_index(N_+1,N_+1)] = x_u[y_index(N_+1,N_+1)] = 0.;

  // all discretized PDE constraints have right hand side zero
  for (Index i=0; i<m; i++) {
    g_l[i] = 0.;
    g_u[i] = 0.;
  }

  return true;
}

bool
MittelmannDistCntrlNeumABase::get_starting_point(Index n, bool init_x, Number* x,
    bool init_z, Number* z_L, Number* z_U,
    Index m, bool init_lambda,
    Number* lambda)
{
  // Here, we assume we only have starting values for x, if you code
  // your own NLP, you can provide starting values for the others if
  // you wish.
  assert(init_x == true);
  assert(init_z == false);
  assert(init_lambda == false);

  // set all y's to the perfect match with y_d
  for (Index i=0; i<= N_+1; i++) {
    for (Index j=0; j<= N_+1; j++) {
      x[y_index(i,j)] = y_d_[y_index(i,j)];
      //x[y_index(i,j)] += h_*x1_grid(i) + 2*h_*x2_grid(j);
    }
  }

  // Set the initial (constant) value for the u's
  for (Index i=1; i<= N_; i++) {
    for (Index j=1; j<= N_; j++) {
      x[u_index(i,j)] = u_init_;
      //x[u_index(i,j)] -= h_*x1_grid(i) + 2*h_*x2_grid(j);
    }
  }

  return true;
}

bool
MittelmannDistCntrlNeumABase::get_scaling_parameters(Number& obj_scaling,
    bool& use_x_scaling,
    Index n, Number* x_scaling,
    bool& use_g_scaling,
    Index m, Number* g_scaling)
{
  obj_scaling = 1./hh_;
  use_x_scaling = false;
  use_g_scaling = false;
  return true;
}

bool
MittelmannDistCntrlNeumABase::eval_f(Index n, const Number* x,
                                     bool new_x, Number& obj_value)
{
  // return the value of the objective function
  obj_value = 0.;
  for (Index i=1; i<=N_; i++) {
    for (Index j=1; j<= N_; j++) {
      Index iy = y_index(i,j);
      Index iu = u_index(i,j);
      obj_value += fint_cont(x1_grid(i), x2_grid(j), x[iy], x[iu]);
    }
  }
  obj_value *= hh_;

  return true;
}

bool
MittelmannDistCntrlNeumABase::eval_grad_f(Index n, const Number* x, bool new_x, Number* grad_f)
{
  // return the gradient of the objective function grad_{x} f(x)

  // The values are zero for variables on the boundary
  for (Index i=0; i<= N_+1; i++) {
    grad_f[y_index(i,0)] = 0.;
  }
  for (Index i=0; i<= N_+1; i++) {
    grad_f[y_index(i,N_+1)] = 0.;
  }
  for (Index j=1; j<= N_; j++) {
    grad_f[y_index(0,j)] = 0.;
  }
  for (Index j=1; j<= N_; j++) {
    grad_f[y_index(N_+1,j)] = 0.;
  }

  // now let's take care of the nonzero values
  for (Index i=1; i<=N_; i++) {
    for (Index j=1; j<= N_; j++) {
      Index iy = y_index(i,j);
      Index iu = u_index(i,j);
      grad_f[iy] = hh_*fint_cont_dy(x1_grid(i), x2_grid(j), x[iy], x[iu]);
      grad_f[iu] = hh_*fint_cont_du(x1_grid(i), x2_grid(j), x[iy], x[iu]);
    }
  }

  return true;
}

bool MittelmannDistCntrlNeumABase::eval_g(Index n, const Number* x, bool new_x,
    Index m, Number* g)
{
  // return the value of the constraints: g(x)

  // compute the discretized PDE for each interior grid point
  for (Index i=1; i<=N_; i++) {
    for (Index j=1; j<=N_; j++) {
      Number val;

      // Start with the discretized Laplacian operator
      val = 4.* x[y_index(i,j)]
            - x[y_index(i-1,j)] - x[y_index(i+1,j)]
            - x[y_index(i,j-1)] - x[y_index(i,j+1)];

      // Add the forcing term (including the step size here)
      val += hh_*d_cont(x1_grid(i), x2_grid(j),
                        x[y_index(i,j)], x[u_index(i,j)]);
      g[pde_index(i,j)] = val;
    }
  }

  Index ig = N_*N_;
  // set up the Neumann boundary conditions
  for (Index i=1; i<= N_; i++) {
    g[ig] = (1.+h_*b_i0_)*x[y_index(i,0)] - x[y_index(i,1)];
    ig++;
  }
  for (Index i=1; i<= N_; i++) {
    g[ig] = (1.+h_*b_i1_)*x[y_index(i,N_+1)] - x[y_index(i,N_)];
    ig++;
  }
  for (Index j=1; j<= N_; j++) {
    g[ig] = (1.+h_*b_0j_)*x[y_index(0,j)] - x[y_index(1,j)];
    ig++;
  }
  for (Index j=1; j<= N_; j++) {
    g[ig] = (1.+h_*b_1j_)*x[y_index(N_+1,j)] - x[y_index(N_,j)];
    ig++;
  }

  DBG_ASSERT(ig==m);

  return true;
}

bool MittelmannDistCntrlNeumABase::eval_jac_g(Index n, const Number* x, bool new_x,
    Index m, Index nele_jac, Index* iRow, Index *jCol,
    Number* values)
{
  if (values == NULL) {
    // return the structure of the jacobian of the constraints

    // distretized PDEs
    Index ijac = 0;
    for (Index i=1; i<= N_; i++) {
      for (Index j=1; j<= N_; j++) {
        Index ig = pde_index(i,j);

        // y(i,j)
        iRow[ijac] = ig;
        jCol[ijac] = y_index(i,j);
        ijac++;

        // y(i-1,j)
        iRow[ijac] = ig;
        jCol[ijac] = y_index(i-1,j);
        ijac++;

        // y(i+1,j)
        iRow[ijac] = ig;
        jCol[ijac] = y_index(i+1,j);
        ijac++;

        // y(i,j-1)
        iRow[ijac] = ig;
        jCol[ijac] = y_index(i,j-1);
        ijac++;

        // y(i,j+1)
        iRow[ijac] = ig;
        jCol[ijac] = y_index(i,j+1);
        ijac++;

        // u(i,j)
        iRow[ijac] = ig;
        jCol[ijac] = u_index(i,j);
        ijac++;
      }
    }

    Index ig = N_*N_;
    // set up the Neumann boundary conditions
    for (Index i=1; i<=N_; i++) {
      iRow[ijac] = ig;
      jCol[ijac] = y_index(i,0);
      ijac++;
      iRow[ijac] = ig;
      jCol[ijac] = y_index(i,1);
      ijac++;
      ig++;
    }
    for (Index i=1; i<=N_; i++) {
      iRow[ijac] = ig;
      jCol[ijac] = y_index(i,N_);
      ijac++;
      iRow[ijac] = ig;
      jCol[ijac] = y_index(i,N_+1);
      ijac++;
      ig++;
    }
    for (Index j=1; j<=N_; j++) {
      iRow[ijac] = ig;
      jCol[ijac] = y_index(0,j);
      ijac++;
      iRow[ijac] = ig;
      jCol[ijac] = y_index(1,j);
      ijac++;
      ig++;
    }
    for (Index j=1; j<=N_; j++) {
      iRow[ijac] = ig;
      jCol[ijac] = y_index(N_,j);
      ijac++;
      iRow[ijac] = ig;
      jCol[ijac] = y_index(N_+1,j);
      ijac++;
      ig++;
    }

    DBG_ASSERT(ijac==nele_jac);
  }
  else {
    // return the values of the jacobian of the constraints
    Index ijac = 0;
    for (Index i=1; i<= N_; i++) {
      for (Index j=1; j<= N_; j++) {
        // y(i,j)
        values[ijac] = 4. + hh_*d_cont_dy(x1_grid(i), x2_grid(j),
                                          x[y_index(i,j)], x[u_index(i,j)]);
        ijac++;

        // y(i-1,j)
        values[ijac] = -1.;
        ijac++;

        // y(i+1,j)
        values[ijac] = -1.;
        ijac++;

        // y(1,j-1)
        values[ijac] = -1.;
        ijac++;

        // y(1,j+1)
        values[ijac] = -1.;
        ijac++;

        // y(i,j)
        values[ijac] = hh_*d_cont_du(x1_grid(i), x2_grid(j),
                                     x[y_index(i,j)], x[u_index(i,j)]);
        ijac++;
      }
    }

    for (Index i=1; i<=N_; i++) {
      values[ijac] = 1.+h_*b_i0_;
      ijac++;
      values[ijac] = -1.;
      ijac++;
    }
    for (Index i=1; i<=N_; i++) {
      values[ijac] = -1.;
      ijac++;
      values[ijac] = 1.+h_*b_i1_;
      ijac++;
    }
    for (Index j=1; j<=N_; j++) {
      values[ijac] = 1.+h_*b_0j_;
      ijac++;
      values[ijac] = -1.;
      ijac++;
    }
    for (Index j=1; j<=N_; j++) {
      values[ijac] = -1.;
      ijac++;
      values[ijac] = 1.+h_*b_1j_;
      ijac++;
    }

    DBG_ASSERT(ijac==nele_jac);
  }

  return true;
}

bool
MittelmannDistCntrlNeumABase::eval_h(Index n, const Number* x, bool new_x,
                                     Number obj_factor, Index m,
                                     const Number* lambda,
                                     bool new_lambda, Index nele_hess, Index* iRow,
                                     Index* jCol, Number* values)
{
  if (values == NULL) {
    // return the structure. This is a symmetric matrix, fill the lower left
    // triangle only.

    Index ihes=0;
    if (!fint_cont_dydy_alwayszero() || !d_cont_dydy_alwayszero()) {
      // First the diagonal entries for dydy
      for (Index i=1; i<= N_; i++) {
        for (Index j=1; j<= N_; j++) {
          iRow[ihes] = y_index(i,j);
          jCol[ihes] = y_index(i,j);
          ihes++;
        }
      }
    }

    if (!fint_cont_dudu_alwayszero() || !d_cont_dudu_alwayszero()) {
      // Now the diagonal entries for dudu
      for (Index i=1; i<= N_; i++) {
        for (Index j=1; j<= N_; j++) {
          iRow[ihes] = u_index(i,j);
          jCol[ihes] = u_index(i,j);
          ihes++;
        }
      }
    }

    if (!fint_cont_dydu_alwayszero() || !d_cont_dydu_alwayszero()) {
      // Now the diagonal entries for dydu
      for (Index i=1; i<= N_; i++) {
        for (Index j=1; j<= N_; j++) {
          iRow[ihes] = y_index(i,j);
          jCol[ihes] = u_index(i,j);
          ihes++;
        }
      }
    }

    DBG_ASSERT(ihes==nele_hess);
  }
  else {
    // return the values

    Index ihes=0;
    Index ihes_store;
    // First the diagonal entries for dydy
    if (!fint_cont_dydy_alwayszero() || !d_cont_dydy_alwayszero()) {
      ihes_store = ihes;
      if (!fint_cont_dydy_alwayszero()) {
        // Contribution from the objective function
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] =
              obj_factor*hh_*fint_cont_dydy(x1_grid(i), x2_grid(j),
                                            x[y_index(i,j)], x[u_index(i,j)]);
            ihes++;
          }
        }
      }
      else {
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] = 0.;
            ihes++;
          }
        }
      }
      if (!d_cont_dydy_alwayszero()) {
        ihes = ihes_store;
        // Contribution from the constraints
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] +=
              lambda[pde_index(i,j)]*hh_*d_cont_dydy(x1_grid(i), x2_grid(j),
                                                     x[y_index(i,j)], x[u_index(i,j)]);
            ihes++;
          }
        }
      }
    }

    // Finally the entries for dudu
    if (!fint_cont_dudu_alwayszero() || !d_cont_dudu_alwayszero()) {
      ihes_store = ihes;
      if (!fint_cont_dudu_alwayszero()) {
        // Contribution from the objective function
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] =
              obj_factor*hh_*fint_cont_dudu(x1_grid(i), x2_grid(j),
                                            x[y_index(i,j)], x[u_index(i,j)]);
            ihes++;
          }
        }
      }
      else {
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] = 0.;
            ihes++;
          }
        }
      }
      if (!d_cont_dudu_alwayszero()) {
        ihes = ihes_store;
        // Contribution from the constraints
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] +=
              lambda[pde_index(i,j)]*hh_*d_cont_dudu(x1_grid(i), x2_grid(j),
                                                     x[y_index(i,j)], x[u_index(i,j)]);
            ihes++;
          }
        }
      }
    }

    // Now the entries for dydu
    if (!fint_cont_dydu_alwayszero() || !d_cont_dydu_alwayszero()) {
      ihes_store = ihes;
      if (!fint_cont_dydu_alwayszero()) {
        // Contribution from the objective function
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] =
              obj_factor*hh_*fint_cont_dydu(x1_grid(i), x2_grid(j),
                                            x[y_index(i,j)], x[u_index(i,j)]);
            ihes++;
          }
        }
      }
      else {
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] = 0.;
            ihes++;
          }
        }
      }
      if (!d_cont_dydu_alwayszero()) {
        ihes = ihes_store;
        // Contribution from the constraints
        for (Index i=1; i<= N_; i++) {
          for (Index j=1; j<= N_; j++) {
            values[ihes] +=
              lambda[pde_index(i,j)]*hh_*d_cont_dydu(x1_grid(i), x2_grid(j),
                                                     x[y_index(i,j)], x[u_index(i,j)]);
            ihes++;
          }
        }
      }
    }
  }

  return true;
}

void
MittelmannDistCntrlNeumABase::finalize_solution(SolverReturn status,
    Index n, const Number* x, const Number* z_L, const Number* z_U,
    Index m, const Number* g, const Number* lambda, Number obj_value,
    const IpoptData* ip_data,
    IpoptCalculatedQuantities* ip_cq)
{
  /*
  FILE* fp = fopen("solution.txt", "w+");

  for (Index i=0; i<=N_+1; i++) {
    for (Index j=0; j<=N_+1; j++) {
      fprintf(fp, "y[%6d,%6d] = %15.8e\n", i, j, x[y_index(i,j)]);
    }
  }
  for (Index i=1; i<=N_; i++) {
    for (Index j=1; j<=N_; j++) {
      fprintf(fp, "u[%6d,%6d] = %15.8e\n", i, j ,x[u_index(i,j)]);
    }
  }

  fclose(fp);
  */
}