source: branches/ParameterBinding/HeuristicLab.ExtLibs/HeuristicLab.LibSVM/1.6.3/LibSVM-1.6.3/Solver.cs @ 8123

/*
 * SVM.NET Library
 * Copyright (C) 2008 Matthew Johnson
 * 
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */


using System;
using System.IO;

namespace SVM {

  // An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918
  // Solves:
  //
  //  Min 0.5(\alpha^T Q \alpha) + p^T \alpha
  //
  //    y^T \alpha = \delta
  //    y_i = +1 or -1
  //    0 <= alpha_i <= Cp for y_i = 1
  //    0 <= alpha_i <= Cn for y_i = -1
  //
  // Given:
  //
  //  Q, p, y, Cp, Cn, and an initial feasible point \alpha
  //  l is the size of vectors and matrices
  //  eps is the stopping tolerance
  //
  // solution will be put in \alpha, objective value will be put in obj
  //
  internal class Solver {
    protected int active_size;
    protected sbyte[] y;
    protected double[] G;   // gradient of objective function
    private const byte LOWER_BOUND = 0;
    private const byte UPPER_BOUND = 1;
    private const byte FREE = 2;
    private byte[] alpha_status;  // LOWER_BOUND, UPPER_BOUND, FREE
    private double[] alpha;
    protected IQMatrix Q;
    protected float[] QD;
    protected double EPS;
    private double Cp, Cn;
    private double[] p;
    private int[] active_set;
    private double[] G_bar;   // gradient, if we treat free variables as 0
    protected int l;
    protected bool unshrink;  // XXX

    protected const double INF = double.PositiveInfinity;

    private double get_C(int i) {
      return (y[i] > 0) ? Cp : Cn;
    }

    private void update_alpha_status(int i) {
      if (alpha[i] >= get_C(i))
        alpha_status[i] = UPPER_BOUND;
      else if (alpha[i] <= 0)
        alpha_status[i] = LOWER_BOUND;
      else alpha_status[i] = FREE;
    }

    protected bool is_upper_bound(int i) { return alpha_status[i] == UPPER_BOUND; }
    protected bool is_lower_bound(int i) { return alpha_status[i] == LOWER_BOUND; }

    private bool is_free(int i) { return alpha_status[i] == FREE; }

    public class SolutionInfo {
      public double obj;
      public double rho;
      public double upper_bound_p;
      public double upper_bound_n;
      public double r;  // for Solver_NU
    }

    protected void swap_index(int i, int j) {
      Q.SwapIndex(i, j);
      y.SwapIndex(i, j);
      G.SwapIndex(i, j);
      alpha_status.SwapIndex(i, j);
      alpha.SwapIndex(i, j);
      p.SwapIndex(i, j);
      active_set.SwapIndex(i, j);
      G_bar.SwapIndex(i, j);
    }

    protected void reconstruct_gradient() {
      // reconstruct inactive elements of G from G_bar and free variables

      if (active_size == l) return;

      int i, j;
      int nr_free = 0;

      for (j = active_size; j < l; j++)
        G[j] = G_bar[j] + p[j];

      for (j = 0; j < active_size; j++)
        if (is_free(j))
          nr_free++;

      if (2 * nr_free < active_size)
        Procedures.info("\nWarning: using -h 0 may be faster\n");

      if (nr_free * l > 2 * active_size * (l - active_size)) {
        for (i = active_size; i < l; i++) {
          float[] Q_i = Q.GetQ(i, active_size);
          for (j = 0; j < active_size; j++)
            if (is_free(j))
              G[i] += alpha[j] * Q_i[j];
        }
      } else {
        for (i = 0; i < active_size; i++)
          if (is_free(i)) {
            float[] Q_i = Q.GetQ(i, l);
            double alpha_i = alpha[i];
            for (j = active_size; j < l; j++)
              G[j] += alpha_i * Q_i[j];
          }
      }
    }

    public virtual void Solve(int l, IQMatrix Q, double[] p_, sbyte[] y_, double[] alpha_, double Cp, double Cn, double eps, SolutionInfo si, bool shrinking) {
      this.l = l;
      this.Q = Q;
      QD = Q.GetQD();
      p = (double[])p_.Clone();
      y = (sbyte[])y_.Clone();
      alpha = (double[])alpha_.Clone();
      this.Cp = Cp;
      this.Cn = Cn;
      this.EPS = eps;
      this.unshrink = false;

      // initialize alpha_status
      {
        alpha_status = new byte[l];
        for (int i = 0; i < l; i++)
          update_alpha_status(i);
      }

      // initialize active set (for shrinking)
      {
        active_set = new int[l];
        for (int i = 0; i < l; i++)
          active_set[i] = i;
        active_size = l;
      }

      // initialize gradient
      {
        G = new double[l];
        G_bar = new double[l];
        int i;
        for (i = 0; i < l; i++) {
          G[i] = p[i];
          G_bar[i] = 0;
        }
        for (i = 0; i < l; i++)
          if (!is_lower_bound(i)) {
            float[] Q_i = Q.GetQ(i, l);
            double alpha_i = alpha[i];
            int j;
            for (j = 0; j < l; j++)
              G[j] += alpha_i * Q_i[j];
            if (is_upper_bound(i))
              for (j = 0; j < l; j++)
                G_bar[j] += get_C(i) * Q_i[j];
          }
      }

      // optimization step

      int iter = 0;
      int counter = Math.Min(l, 1000) + 1;
      int[] working_set = new int[2];

      while (true) {
        // show progress and do shrinking

        if (--counter == 0) {
          counter = Math.Min(l, 1000);
          if (shrinking) do_shrinking();
          Procedures.info(".");
        }

        if (select_working_set(working_set) != 0) {
          // reconstruct the whole gradient
          reconstruct_gradient();
          // reset active set size and check
          active_size = l;
          Procedures.info("*");
          if (select_working_set(working_set) != 0)
            break;
          else
            counter = 1;  // do shrinking next iteration
        }

        int i = working_set[0];
        int j = working_set[1];

        ++iter;

        // update alpha[i] and alpha[j], handle bounds carefully

        float[] Q_i = Q.GetQ(i, active_size);
        float[] Q_j = Q.GetQ(j, active_size);

        double C_i = get_C(i);
        double C_j = get_C(j);

        double old_alpha_i = alpha[i];
        double old_alpha_j = alpha[j];

        if (y[i] != y[j]) {
          double quad_coef = Q_i[i] + Q_j[j] + 2 * Q_i[j];
          if (quad_coef <= 0)
            quad_coef = 1e-12;
          double delta = (-G[i] - G[j]) / quad_coef;
          double diff = alpha[i] - alpha[j];
          alpha[i] += delta;
          alpha[j] += delta;

          if (diff > 0) {
            if (alpha[j] < 0) {
              alpha[j] = 0;
              alpha[i] = diff;
            }
          } else {
            if (alpha[i] < 0) {
              alpha[i] = 0;
              alpha[j] = -diff;
            }
          }
          if (diff > C_i - C_j) {
            if (alpha[i] > C_i) {
              alpha[i] = C_i;
              alpha[j] = C_i - diff;
            }
          } else {
            if (alpha[j] > C_j) {
              alpha[j] = C_j;
              alpha[i] = C_j + diff;
            }
          }
        } else {
          double quad_coef = Q_i[i] + Q_j[j] - 2 * Q_i[j];
          if (quad_coef <= 0)
            quad_coef = 1e-12;
          double delta = (G[i] - G[j]) / quad_coef;
          double sum = alpha[i] + alpha[j];
          alpha[i] -= delta;
          alpha[j] += delta;

          if (sum > C_i) {
            if (alpha[i] > C_i) {
              alpha[i] = C_i;
              alpha[j] = sum - C_i;
            }
          } else {
            if (alpha[j] < 0) {
              alpha[j] = 0;
              alpha[i] = sum;
            }
          }
          if (sum > C_j) {
            if (alpha[j] > C_j) {
              alpha[j] = C_j;
              alpha[i] = sum - C_j;
            }
          } else {
            if (alpha[i] < 0) {
              alpha[i] = 0;
              alpha[j] = sum;
            }
          }
        }

        // update G

        double delta_alpha_i = alpha[i] - old_alpha_i;
        double delta_alpha_j = alpha[j] - old_alpha_j;

        for (int k = 0; k < active_size; k++) {
          G[k] += Q_i[k] * delta_alpha_i + Q_j[k] * delta_alpha_j;
        }

        // update alpha_status and G_bar

        {
          bool ui = is_upper_bound(i);
          bool uj = is_upper_bound(j);
          update_alpha_status(i);
          update_alpha_status(j);
          int k;
          if (ui != is_upper_bound(i)) {
            Q_i = Q.GetQ(i, l);
            if (ui)
              for (k = 0; k < l; k++)
                G_bar[k] -= C_i * Q_i[k];
            else
              for (k = 0; k < l; k++)
                G_bar[k] += C_i * Q_i[k];
          }

          if (uj != is_upper_bound(j)) {
            Q_j = Q.GetQ(j, l);
            if (uj)
              for (k = 0; k < l; k++)
                G_bar[k] -= C_j * Q_j[k];
            else
              for (k = 0; k < l; k++)
                G_bar[k] += C_j * Q_j[k];
          }
        }

      }

      // calculate rho

      si.rho = calculate_rho();

      // calculate objective value
      {
        double v = 0;
        int i;
        for (i = 0; i < l; i++)
          v += alpha[i] * (G[i] + p[i]);

        si.obj = v / 2;
      }

      // put back the solution
      {
        for (int i = 0; i < l; i++)
          alpha_[active_set[i]] = alpha[i];
      }

      si.upper_bound_p = Cp;
      si.upper_bound_n = Cn;

      Procedures.info("\noptimization finished, #iter = " + iter + "\n");
    }

    // return 1 if already optimal, return 0 otherwise
    protected virtual int select_working_set(int[] working_set) {
      // return i,j such that
      // i: Maximizes -y_i * grad(f)_i, i in I_up(\alpha)
      // j: mimimizes the decrease of obj value
      //    (if quadratic coefficeint <= 0, replace it with tau)
      //    -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)

      double GMax = -INF;
      double GMax2 = -INF;
      int GMax_idx = -1;
      int GMin_idx = -1;
      double obj_diff_Min = INF;

      for (int t = 0; t < active_size; t++)
        if (y[t] == +1) {
          if (!is_upper_bound(t))
            if (-G[t] >= GMax) {
              GMax = -G[t];
              GMax_idx = t;
            }
        } else {
          if (!is_lower_bound(t))
            if (G[t] >= GMax) {
              GMax = G[t];
              GMax_idx = t;
            }
        }

      int i = GMax_idx;
      float[] Q_i = null;
      if (i != -1) // null Q_i not accessed: GMax=-INF if i=-1
        Q_i = Q.GetQ(i, active_size);

      for (int j = 0; j < active_size; j++) {
        if (y[j] == +1) {
          if (!is_lower_bound(j)) {
            double grad_diff = GMax + G[j];
            if (G[j] >= GMax2)
              GMax2 = G[j];
            if (grad_diff > 0) {
              double obj_diff;
              double quad_coef = Q_i[i] + QD[j] - 2.0 * y[i] * Q_i[j];
              if (quad_coef > 0)
                obj_diff = -(grad_diff * grad_diff) / quad_coef;
              else
                obj_diff = -(grad_diff * grad_diff) / 1e-12;

              if (obj_diff <= obj_diff_Min) {
                GMin_idx = j;
                obj_diff_Min = obj_diff;
              }
            }
          }
        } else {
          if (!is_upper_bound(j)) {
            double grad_diff = GMax - G[j];
            if (-G[j] >= GMax2)
              GMax2 = -G[j];
            if (grad_diff > 0) {
              double obj_diff;
              double quad_coef = Q_i[i] + QD[j] + 2.0 * y[i] * Q_i[j];
              if (quad_coef > 0)
                obj_diff = -(grad_diff * grad_diff) / quad_coef;
              else
                obj_diff = -(grad_diff * grad_diff) / 1e-12;

              if (obj_diff <= obj_diff_Min) {
                GMin_idx = j;
                obj_diff_Min = obj_diff;
              }
            }
          }
        }
      }

      if (GMax + GMax2 < EPS)
        return 1;

      working_set[0] = GMax_idx;
      working_set[1] = GMin_idx;
      return 0;
    }

    private bool be_shrunk(int i, double GMax1, double GMax2) {
      if (is_upper_bound(i)) {
        if (y[i] == +1)
          return (-G[i] > GMax1);
        else
          return (-G[i] > GMax2);
      } else if (is_lower_bound(i)) {
        if (y[i] == +1)
          return (G[i] > GMax2);
        else
          return (G[i] > GMax1);
      } else
        return (false);
    }

    protected virtual void do_shrinking() {
      int i;
      double GMax1 = -INF;    // Max { -y_i * grad(f)_i | i in I_up(\alpha) }
      double GMax2 = -INF;    // Max { y_i * grad(f)_i | i in I_low(\alpha) }

      // find Maximal violating pair first
      for (i = 0; i < active_size; i++) {
        if (y[i] == +1) {
          if (!is_upper_bound(i)) {
            if (-G[i] >= GMax1)
              GMax1 = -G[i];
          }
          if (!is_lower_bound(i)) {
            if (G[i] >= GMax2)
              GMax2 = G[i];
          }
        } else {
          if (!is_upper_bound(i)) {
            if (-G[i] >= GMax2)
              GMax2 = -G[i];
          }
          if (!is_lower_bound(i)) {
            if (G[i] >= GMax1)
              GMax1 = G[i];
          }
        }
      }

      if (unshrink == false && GMax1 + GMax2 <= EPS * 10) {
        unshrink = true;
        reconstruct_gradient();
        active_size = l;
      }

      for (i = 0; i < active_size; i++)
        if (be_shrunk(i, GMax1, GMax2)) {
          active_size--;
          while (active_size > i) {
            if (!be_shrunk(active_size, GMax1, GMax2)) {
              swap_index(i, active_size);
              break;
            }
            active_size--;
          }
        }
    }

    protected virtual double calculate_rho() {
      double r;
      int nr_free = 0;
      double ub = INF, lb = -INF, sum_free = 0;
      for (int i = 0; i < active_size; i++) {
        double yG = y[i] * G[i];

        if (is_lower_bound(i)) {
          if (y[i] > 0)
            ub = Math.Min(ub, yG);
          else
            lb = Math.Max(lb, yG);
        } else if (is_upper_bound(i)) {
          if (y[i] < 0)
            ub = Math.Min(ub, yG);
          else
            lb = Math.Max(lb, yG);
        } else {
          ++nr_free;
          sum_free += yG;
        }
      }

      if (nr_free > 0)
        r = sum_free / nr_free;
      else
        r = (ub + lb) / 2;

      return r;
    }

  }

  //
  // Solver for nu-svm classification and regression
  //
  // additional constraint: e^T \alpha = constant
  //
  class Solver_NU : Solver {
    private SolutionInfo si;

    public sealed override void Solve(int l, IQMatrix Q, double[] p, sbyte[] y,
           double[] alpha, double Cp, double Cn, double eps,
           SolutionInfo si, bool shrinking) {
      this.si = si;
      base.Solve(l, Q, p, y, alpha, Cp, Cn, eps, si, shrinking);
    }

    // return 1 if already optimal, return 0 otherwise
    protected override sealed int select_working_set(int[] working_set) {
      // return i,j such that y_i = y_j and
      // i: Maximizes -y_i * grad(f)_i, i in I_up(\alpha)
      // j: Minimizes the decrease of obj value
      //    (if quadratic coefficeint <= 0, replace it with tau)
      //    -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)

      double GMaxp = -INF;
      double GMaxp2 = -INF;
      int GMaxp_idx = -1;

      double GMaxn = -INF;
      double GMaxn2 = -INF;
      int GMaxn_idx = -1;

      int GMin_idx = -1;
      double obj_diff_Min = INF;

      for (int t = 0; t < active_size; t++)
        if (y[t] == +1) {
          if (!is_upper_bound(t))
            if (-G[t] >= GMaxp) {
              GMaxp = -G[t];
              GMaxp_idx = t;
            }
        } else {
          if (!is_lower_bound(t))
            if (G[t] >= GMaxn) {
              GMaxn = G[t];
              GMaxn_idx = t;
            }
        }

      int ip = GMaxp_idx;
      int iN = GMaxn_idx;
      float[] Q_ip = null;
      float[] Q_in = null;
      if (ip != -1) // null Q_ip not accessed: GMaxp=-INF if ip=-1
        Q_ip = Q.GetQ(ip, active_size);
      if (iN != -1)
        Q_in = Q.GetQ(iN, active_size);

      for (int j = 0; j < active_size; j++) {
        if (y[j] == +1) {
          if (!is_lower_bound(j)) {
            double grad_diff = GMaxp + G[j];
            if (G[j] >= GMaxp2)
              GMaxp2 = G[j];
            if (grad_diff > 0) {
              double obj_diff;
              double quad_coef = Q_ip[ip] + QD[j] - 2 * Q_ip[j];
              if (quad_coef > 0)
                obj_diff = -(grad_diff * grad_diff) / quad_coef;
              else
                obj_diff = -(grad_diff * grad_diff) / 1e-12;

              if (obj_diff <= obj_diff_Min) {
                GMin_idx = j;
                obj_diff_Min = obj_diff;
              }
            }
          }
        } else {
          if (!is_upper_bound(j)) {
            double grad_diff = GMaxn - G[j];
            if (-G[j] >= GMaxn2)
              GMaxn2 = -G[j];
            if (grad_diff > 0) {
              double obj_diff;
              double quad_coef = Q_in[iN] + QD[j] - 2 * Q_in[j];
              if (quad_coef > 0)
                obj_diff = -(grad_diff * grad_diff) / quad_coef;
              else
                obj_diff = -(grad_diff * grad_diff) / 1e-12;

              if (obj_diff <= obj_diff_Min) {
                GMin_idx = j;
                obj_diff_Min = obj_diff;
              }
            }
          }
        }
      }

      if (Math.Max(GMaxp + GMaxp2, GMaxn + GMaxn2) < EPS)
        return 1;

      if (y[GMin_idx] == +1)
        working_set[0] = GMaxp_idx;
      else
        working_set[0] = GMaxn_idx;
      working_set[1] = GMin_idx;

      return 0;
    }

    private bool be_shrunk(int i, double GMax1, double GMax2, double GMax3, double GMax4) {
      if (is_upper_bound(i)) {
        if (y[i] == +1)
          return (-G[i] > GMax1);
        else
          return (-G[i] > GMax4);
      } else if (is_lower_bound(i)) {
        if (y[i] == +1)
          return (G[i] > GMax2);
        else
          return (G[i] > GMax3);
      } else
        return (false);
    }

    protected override sealed void do_shrinking() {
      double GMax1 = -INF;  // Max { -y_i * grad(f)_i | y_i = +1, i in I_up(\alpha) }
      double GMax2 = -INF;  // Max { y_i * grad(f)_i | y_i = +1, i in I_low(\alpha) }
      double GMax3 = -INF;  // Max { -y_i * grad(f)_i | y_i = -1, i in I_up(\alpha) }
      double GMax4 = -INF;  // Max { y_i * grad(f)_i | y_i = -1, i in I_low(\alpha) }

      // find Maximal violating pair first
      int i;
      for (i = 0; i < active_size; i++) {
        if (!is_upper_bound(i)) {
          if (y[i] == +1) {
            if (-G[i] > GMax1) GMax1 = -G[i];
          } else if (-G[i] > GMax4) GMax4 = -G[i];
        }
        if (!is_lower_bound(i)) {
          if (y[i] == +1) {
            if (G[i] > GMax2) GMax2 = G[i];
          } else if (G[i] > GMax3) GMax3 = G[i];
        }
      }

      if (unshrink == false && Math.Max(GMax1 + GMax2, GMax3 + GMax4) <= EPS * 10) {
        unshrink = true;
        reconstruct_gradient();
        active_size = l;
      }

      for (i = 0; i < active_size; i++)
        if (be_shrunk(i, GMax1, GMax2, GMax3, GMax4)) {
          active_size--;
          while (active_size > i) {
            if (!be_shrunk(active_size, GMax1, GMax2, GMax3, GMax4)) {
              swap_index(i, active_size);
              break;
            }
            active_size--;
          }
        }
    }

    protected override sealed double calculate_rho() {
      int nr_free1 = 0, nr_free2 = 0;
      double ub1 = INF, ub2 = INF;
      double lb1 = -INF, lb2 = -INF;
      double sum_free1 = 0, sum_free2 = 0;

      for (int i = 0; i < active_size; i++) {
        if (y[i] == +1) {
          if (is_lower_bound(i))
            ub1 = Math.Min(ub1, G[i]);
          else if (is_upper_bound(i))
            lb1 = Math.Max(lb1, G[i]);
          else {
            ++nr_free1;
            sum_free1 += G[i];
          }
        } else {
          if (is_lower_bound(i))
            ub2 = Math.Min(ub2, G[i]);
          else if (is_upper_bound(i))
            lb2 = Math.Max(lb2, G[i]);
          else {
            ++nr_free2;
            sum_free2 += G[i];
          }
        }
      }

      double r1, r2;
      if (nr_free1 > 0)
        r1 = sum_free1 / nr_free1;
      else
        r1 = (ub1 + lb1) / 2;

      if (nr_free2 > 0)
        r2 = sum_free2 / nr_free2;
      else
        r2 = (ub2 + lb2) / 2;

      si.r = (r1 + r2) / 2;
      return (r1 - r2) / 2;
    }
  }

  //
  // Q matrices for various formulations
  //
  class SVC_Q : Kernel {
    private sbyte[] y;
    private Cache cache;
    private float[] QD;

    public SVC_Q(Problem prob, Parameter param, sbyte[] y_)
      : base(prob.Count, prob.X, param) {
      y = (sbyte[])y_.Clone();
      cache = new Cache(prob.Count, (long)(param.CacheSize * (1 << 20)));
      QD = new float[prob.Count];
      for (int i = 0; i < prob.Count; i++)
        QD[i] = (float)KernelFunction(i, i);
    }

    public override sealed float[] GetQ(int i, int len) {
      float[] data = null;
      int start, j;
      if ((start = cache.GetData(i, ref data, len)) < len) {
        for (j = start; j < len; j++)
          data[j] = (float)(y[i] * y[j] * KernelFunction(i, j));
      }
      return data;
    }

    public override sealed float[] GetQD() {
      return QD;
    }

    public override sealed void SwapIndex(int i, int j) {
      cache.SwapIndex(i, j);
      base.SwapIndex(i, j);
      y.SwapIndex(i, j);
      QD.SwapIndex(i, j);
    }
  }

  class ONE_CLASS_Q : Kernel {
    private Cache cache;
    private float[] QD;

    public ONE_CLASS_Q(Problem prob, Parameter param)
      : base(prob.Count, prob.X, param) {
      cache = new Cache(prob.Count, (long)(param.CacheSize * (1 << 20)));
      QD = new float[prob.Count];
      for (int i = 0; i < prob.Count; i++)
        QD[i] = (float)KernelFunction(i, i);
    }

    public override sealed float[] GetQ(int i, int len) {
      float[] data = null;
      int start, j;
      if ((start = cache.GetData(i, ref data, len)) < len) {
        for (j = start; j < len; j++)
          data[j] = (float)KernelFunction(i, j);
      }
      return data;
    }

    public override sealed float[] GetQD() {
      return QD;
    }

    public override sealed void SwapIndex(int i, int j) {
      cache.SwapIndex(i, j);
      base.SwapIndex(i, j);
      QD.SwapIndex(i, j);
    }
  }

  class SVR_Q : Kernel {
    private int l;
    private Cache cache;
    private sbyte[] sign;
    private int[] index;
    private int next_buffer;
    private float[][] buffer;
    private float[] QD;

    public SVR_Q(Problem prob, Parameter param)
      : base(prob.Count, prob.X, param) {
      l = prob.Count;
      cache = new Cache(l, (long)(param.CacheSize * (1 << 20)));
      QD = new float[2 * l];
      sign = new sbyte[2 * l];
      index = new int[2 * l];
      for (int k = 0; k < l; k++) {
        sign[k] = 1;
        sign[k + l] = -1;
        index[k] = k;
        index[k + l] = k;
        QD[k] = (float)KernelFunction(k, k);
        QD[k + l] = QD[k];
      }
      buffer = new float[2][];
      buffer[0] = new float[2 * l];
      buffer[1] = new float[2 * l];
      next_buffer = 0;
    }

    public override sealed void SwapIndex(int i, int j) {
      sign.SwapIndex(i, j);
      index.SwapIndex(i, j);
      QD.SwapIndex(i, j);
    }

    public override sealed float[] GetQ(int i, int len) {
      float[] data = null;
      int j, real_i = index[i];
      if (cache.GetData(real_i, ref data, l) < l) {
        for (j = 0; j < l; j++)
          data[j] = (float)KernelFunction(real_i, j);
      }

      // reorder and copy
      float[] buf = buffer[next_buffer];
      next_buffer = 1 - next_buffer;
      sbyte si = sign[i];
      for (j = 0; j < len; j++)
        buf[j] = (float)si * sign[j] * data[index[j]];
      return buf;
    }

    public override sealed float[] GetQD() {
      return QD;
    }
  }

  internal class Procedures {
    private static bool _verbose;
    public static bool IsVerbose {
      get {
        return _verbose;
      }
      set {
        _verbose = value;
      }
    }
    //
    // construct and solve various formulations
    //
    public const int LIBSVM_VERSION = 289;

    public static TextWriter svm_print_string = Console.Out;

    public static void info(string s) {
      if (_verbose)
        svm_print_string.Write(s);
    }

    private static void solve_c_svc(Problem prob, Parameter param,
                    double[] alpha, Solver.SolutionInfo si,
                    double Cp, double Cn) {
      int l = prob.Count;
      double[] Minus_ones = new double[l];
      sbyte[] y = new sbyte[l];

      int i;

      for (i = 0; i < l; i++) {
        alpha[i] = 0;
        Minus_ones[i] = -1;
        if (prob.Y[i] > 0) y[i] = +1; else y[i] = -1;
      }

      Solver s = new Solver();
      s.Solve(l, new SVC_Q(prob, param, y), Minus_ones, y,
          alpha, Cp, Cn, param.EPS, si, param.Shrinking);

      double sum_alpha = 0;
      for (i = 0; i < l; i++)
        sum_alpha += alpha[i];

      if (Cp == Cn)
        Procedures.info("nu = " + sum_alpha / (Cp * prob.Count) + "\n");

      for (i = 0; i < l; i++)
        alpha[i] *= y[i];
    }

    private static void solve_nu_svc(Problem prob, Parameter param,
                    double[] alpha, Solver.SolutionInfo si) {
      int i;
      int l = prob.Count;
      double nu = param.Nu;

      sbyte[] y = new sbyte[l];

      for (i = 0; i < l; i++)
        if (prob.Y[i] > 0)
          y[i] = +1;
        else
          y[i] = -1;

      double sum_pos = nu * l / 2;
      double sum_neg = nu * l / 2;

      for (i = 0; i < l; i++)
        if (y[i] == +1) {
          alpha[i] = Math.Min(1.0, sum_pos);
          sum_pos -= alpha[i];
        } else {
          alpha[i] = Math.Min(1.0, sum_neg);
          sum_neg -= alpha[i];
        }

      double[] zeros = new double[l];

      for (i = 0; i < l; i++)
        zeros[i] = 0;

      Solver_NU s = new Solver_NU();
      s.Solve(l, new SVC_Q(prob, param, y), zeros, y, alpha, 1.0, 1.0, param.EPS, si, param.Shrinking);
      double r = si.r;

      Procedures.info("C = " + 1 / r + "\n");

      for (i = 0; i < l; i++)
        alpha[i] *= y[i] / r;

      si.rho /= r;
      si.obj /= (r * r);
      si.upper_bound_p = 1 / r;
      si.upper_bound_n = 1 / r;
    }

    private static void solve_one_class(Problem prob, Parameter param,
                    double[] alpha, Solver.SolutionInfo si) {
      int l = prob.Count;
      double[] zeros = new double[l];
      sbyte[] ones = new sbyte[l];
      int i;

      int n = (int)(param.Nu * prob.Count); // # of alpha's at upper bound

      for (i = 0; i < n; i++)
        alpha[i] = 1;
      if (n < prob.Count)
        alpha[n] = param.Nu * prob.Count - n;
      for (i = n + 1; i < l; i++)
        alpha[i] = 0;

      for (i = 0; i < l; i++) {
        zeros[i] = 0;
        ones[i] = 1;
      }

      Solver s = new Solver();
      s.Solve(l, new ONE_CLASS_Q(prob, param), zeros, ones, alpha, 1.0, 1.0, param.EPS, si, param.Shrinking);
    }

    private static void solve_epsilon_svr(Problem prob, Parameter param, double[] alpha, Solver.SolutionInfo si) {
      int l = prob.Count;
      double[] alpha2 = new double[2 * l];
      double[] linear_term = new double[2 * l];
      sbyte[] y = new sbyte[2 * l];
      int i;

      for (i = 0; i < l; i++) {
        alpha2[i] = 0;
        linear_term[i] = param.P - prob.Y[i];
        y[i] = 1;

        alpha2[i + l] = 0;
        linear_term[i + l] = param.P + prob.Y[i];
        y[i + l] = -1;
      }

      Solver s = new Solver();
      s.Solve(2 * l, new SVR_Q(prob, param), linear_term, y, alpha2, param.C, param.C, param.EPS, si, param.Shrinking);

      double sum_alpha = 0;
      for (i = 0; i < l; i++) {
        alpha[i] = alpha2[i] - alpha2[i + l];
        sum_alpha += Math.Abs(alpha[i]);
      }
      Procedures.info("nu = " + sum_alpha / (param.C * l) + "\n");
    }

    private static void solve_nu_svr(Problem prob, Parameter param,
                    double[] alpha, Solver.SolutionInfo si) {
      int l = prob.Count;
      double C = param.C;
      double[] alpha2 = new double[2 * l];
      double[] linear_term = new double[2 * l];
      sbyte[] y = new sbyte[2 * l];
      int i;

      double sum = C * param.Nu * l / 2;
      for (i = 0; i < l; i++) {
        alpha2[i] = alpha2[i + l] = Math.Min(sum, C);
        sum -= alpha2[i];

        linear_term[i] = -prob.Y[i];
        y[i] = 1;

        linear_term[i + l] = prob.Y[i];
        y[i + l] = -1;
      }

      Solver_NU s = new Solver_NU();
      s.Solve(2 * l, new SVR_Q(prob, param), linear_term, y, alpha2, C, C, param.EPS, si, param.Shrinking);

      Procedures.info("epsilon = " + (-si.r) + "\n");

      for (i = 0; i < l; i++)
        alpha[i] = alpha2[i] - alpha2[i + l];
    }

    //
    // decision_function
    //
    internal class decision_function {
      public double[] alpha;
      public double rho;
    };

    static decision_function svm_train_one(Problem prob, Parameter param, double Cp, double Cn) {
      double[] alpha = new double[prob.Count];
      Solver.SolutionInfo si = new Solver.SolutionInfo();
      switch (param.SvmType) {
        case SvmType.C_SVC:
          solve_c_svc(prob, param, alpha, si, Cp, Cn);
          break;
        case SvmType.NU_SVC:
          solve_nu_svc(prob, param, alpha, si);
          break;
        case SvmType.ONE_CLASS:
          solve_one_class(prob, param, alpha, si);
          break;
        case SvmType.EPSILON_SVR:
          solve_epsilon_svr(prob, param, alpha, si);
          break;
        case SvmType.NU_SVR:
          solve_nu_svr(prob, param, alpha, si);
          break;
      }

      Procedures.info("obj = " + si.obj + ", rho = " + si.rho + "\n");

      // output SVs

      int nSV = 0;
      int nBSV = 0;
      for (int i = 0; i < prob.Count; i++) {
        if (Math.Abs(alpha[i]) > 0) {
          ++nSV;
          if (prob.Y[i] > 0) {
            if (Math.Abs(alpha[i]) >= si.upper_bound_p)
              ++nBSV;
          } else {
            if (Math.Abs(alpha[i]) >= si.upper_bound_n)
              ++nBSV;
          }
        }
      }

      Procedures.info("nSV = " + nSV + ", nBSV = " + nBSV + "\n");

      decision_function f = new decision_function();
      f.alpha = alpha;
      f.rho = si.rho;
      return f;
    }

    // Platt's binary SVM Probablistic Output: an improvement from Lin et al.
    private static void sigmoid_train(int l, double[] dec_values, double[] labels,
                  double[] probAB) {
      double A, B;
      double prior1 = 0, prior0 = 0;
      int i;

      for (i = 0; i < l; i++)
        if (labels[i] > 0) prior1 += 1;
        else prior0 += 1;

      int Max_iter = 100; // Maximal number of iterations
      double Min_step = 1e-10;  // Minimal step taken in line search
      double sigma = 1e-12; // For numerically strict PD of Hessian
      double eps = 1e-5;
      double hiTarget = (prior1 + 1.0) / (prior1 + 2.0);
      double loTarget = 1 / (prior0 + 2.0);
      double[] t = new double[l];
      double fApB, p, q, h11, h22, h21, g1, g2, det, dA, dB, gd, stepsize;
      double newA, newB, newf, d1, d2;
      int iter;

      // Initial Point and Initial Fun Value
      A = 0.0; B = Math.Log((prior0 + 1.0) / (prior1 + 1.0));
      double fval = 0.0;

      for (i = 0; i < l; i++) {
        if (labels[i] > 0) t[i] = hiTarget;
        else t[i] = loTarget;
        fApB = dec_values[i] * A + B;
        if (fApB >= 0)
          fval += t[i] * fApB + Math.Log(1 + Math.Exp(-fApB));
        else
          fval += (t[i] - 1) * fApB + Math.Log(1 + Math.Exp(fApB));
      }
      for (iter = 0; iter < Max_iter; iter++) {
        // Update Gradient and Hessian (use H' = H + sigma I)
        h11 = sigma; // numerically ensures strict PD
        h22 = sigma;
        h21 = 0.0; g1 = 0.0; g2 = 0.0;
        for (i = 0; i < l; i++) {
          fApB = dec_values[i] * A + B;
          if (fApB >= 0) {
            p = Math.Exp(-fApB) / (1.0 + Math.Exp(-fApB));
            q = 1.0 / (1.0 + Math.Exp(-fApB));
          } else {
            p = 1.0 / (1.0 + Math.Exp(fApB));
            q = Math.Exp(fApB) / (1.0 + Math.Exp(fApB));
          }
          d2 = p * q;
          h11 += dec_values[i] * dec_values[i] * d2;
          h22 += d2;
          h21 += dec_values[i] * d2;
          d1 = t[i] - p;
          g1 += dec_values[i] * d1;
          g2 += d1;
        }

        // Stopping Criteria
        if (Math.Abs(g1) < eps && Math.Abs(g2) < eps)
          break;

        // Finding Newton direction: -inv(H') * g
        det = h11 * h22 - h21 * h21;
        dA = -(h22 * g1 - h21 * g2) / det;
        dB = -(-h21 * g1 + h11 * g2) / det;
        gd = g1 * dA + g2 * dB;


        stepsize = 1;   // Line Search
        while (stepsize >= Min_step) {
          newA = A + stepsize * dA;
          newB = B + stepsize * dB;

          // New function value
          newf = 0.0;
          for (i = 0; i < l; i++) {
            fApB = dec_values[i] * newA + newB;
            if (fApB >= 0)
              newf += t[i] * fApB + Math.Log(1 + Math.Exp(-fApB));
            else
              newf += (t[i] - 1) * fApB + Math.Log(1 + Math.Exp(fApB));
          }
          // Check sufficient decrease
          if (newf < fval + 0.0001 * stepsize * gd) {
            A = newA; B = newB; fval = newf;
            break;
          } else
            stepsize = stepsize / 2.0;
        }

        if (stepsize < Min_step) {
          Procedures.info("Line search fails in two-class probability estimates\n");
          break;
        }
      }

      if (iter >= Max_iter)
        Procedures.info("Reaching Maximal iterations in two-class probability estimates\n");
      probAB[0] = A; probAB[1] = B;
    }

    private static double sigmoid_predict(double decision_value, double A, double B) {
      double fApB = decision_value * A + B;
      if (fApB >= 0)
        return Math.Exp(-fApB) / (1.0 + Math.Exp(-fApB));
      else
        return 1.0 / (1 + Math.Exp(fApB));
    }

    // Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
    private static void multiclass_probability(int k, double[,] r, double[] p) {
      int t, j;
      int iter = 0, Max_iter = Math.Max(100, k);
      double[,] Q = new double[k, k];
      double[] Qp = new double[k];
      double pQp, eps = 0.005 / k;

      for (t = 0; t < k; t++) {
        p[t] = 1.0 / k;  // Valid if k = 1
        Q[t, t] = 0;
        for (j = 0; j < t; j++) {
          Q[t, t] += r[j, t] * r[j, t];
          Q[t, j] = Q[j, t];
        }
        for (j = t + 1; j < k; j++) {
          Q[t, t] += r[j, t] * r[j, t];
          Q[t, j] = -r[j, t] * r[t, j];
        }
      }
      for (iter = 0; iter < Max_iter; iter++) {
        // stopping condition, recalculate QP,pQP for numerical accuracy
        pQp = 0;
        for (t = 0; t < k; t++) {
          Qp[t] = 0;
          for (j = 0; j < k; j++)
            Qp[t] += Q[t, j] * p[j];
          pQp += p[t] * Qp[t];
        }
        double Max_error = 0;
        for (t = 0; t < k; t++) {
          double error = Math.Abs(Qp[t] - pQp);
          if (error > Max_error)
            Max_error = error;
        }
        if (Max_error < eps) break;

        for (t = 0; t < k; t++) {
          double diff = (-Qp[t] + pQp) / Q[t, t];
          p[t] += diff;
          pQp = (pQp + diff * (diff * Q[t, t] + 2 * Qp[t])) / (1 + diff) / (1 + diff);
          for (j = 0; j < k; j++) {
            Qp[j] = (Qp[j] + diff * Q[t, j]) / (1 + diff);
            p[j] /= (1 + diff);
          }
        }
      }
      if (iter >= Max_iter)
        Procedures.info("Exceeds Max_iter in multiclass_prob\n");
    }

    // Cross-validation decision values for probability estimates
    private static void svm_binary_svc_probability(Problem prob, Parameter param, double Cp, double Cn, double[] probAB) {
      int i;
      int nr_fold = 5;
      int[] perm = new int[prob.Count];
      double[] dec_values = new double[prob.Count];

      // random shuffle
      Random rand = new Random();
      for (i = 0; i < prob.Count; i++) perm[i] = i;
      for (i = 0; i < prob.Count; i++) {
        int j = i + (int)(rand.NextDouble() * (prob.Count - i));
        do { int _ = perm[i]; perm[i] = perm[j]; perm[j] = _; } while (false);
      }
      for (i = 0; i < nr_fold; i++) {
        int begin = i * prob.Count / nr_fold;
        int end = (i + 1) * prob.Count / nr_fold;
        int j, k;
        Problem subprob = new Problem();

        subprob.Count = prob.Count - (end - begin);
        subprob.X = new Node[subprob.Count][];
        subprob.Y = new double[subprob.Count];

        k = 0;
        for (j = 0; j < begin; j++) {
          subprob.X[k] = prob.X[perm[j]];
          subprob.Y[k] = prob.Y[perm[j]];
          ++k;
        }
        for (j = end; j < prob.Count; j++) {
          subprob.X[k] = prob.X[perm[j]];
          subprob.Y[k] = prob.Y[perm[j]];
          ++k;
        }
        int p_count = 0, n_count = 0;
        for (j = 0; j < k; j++)
          if (subprob.Y[j] > 0)
            p_count++;
          else
            n_count++;

        if (p_count == 0 && n_count == 0)
          for (j = begin; j < end; j++)
            dec_values[perm[j]] = 0;
        else if (p_count > 0 && n_count == 0)
          for (j = begin; j < end; j++)
            dec_values[perm[j]] = 1;
        else if (p_count == 0 && n_count > 0)
          for (j = begin; j < end; j++)
            dec_values[perm[j]] = -1;
        else {
          Parameter subparam = (Parameter)param.Clone();
          subparam.Probability = false;
          subparam.C = 1.0;
          subparam.Weights[1] = Cp;
          subparam.Weights[-1] = Cn;
          Model submodel = svm_train(subprob, subparam);
          for (j = begin; j < end; j++) {
            double[] dec_value = new double[1];
            svm_predict_values(submodel, prob.X[perm[j]], dec_value);
            dec_values[perm[j]] = dec_value[0];
            // ensure +1 -1 order; reason not using CV subroutine
            dec_values[perm[j]] *= submodel.ClassLabels[0];
          }
        }
      }
      sigmoid_train(prob.Count, dec_values, prob.Y, probAB);
    }

    // Return parameter of a Laplace distribution 
    private static double svm_svr_probability(Problem prob, Parameter param) {
      int i;
      int nr_fold = 5;
      double[] ymv = new double[prob.Count];
      double mae = 0;

      Parameter newparam = (Parameter)param.Clone();
      newparam.Probability = false;
      svm_cross_validation(prob, newparam, nr_fold, ymv, true);
      for (i = 0; i < prob.Count; i++) {
        ymv[i] = prob.Y[i] - ymv[i];
        mae += Math.Abs(ymv[i]);
      }
      mae /= prob.Count;
      double std = Math.Sqrt(2 * mae * mae);
      int count = 0;
      mae = 0;
      for (i = 0; i < prob.Count; i++)
        if (Math.Abs(ymv[i]) > 5 * std)
          count = count + 1;
        else
          mae += Math.Abs(ymv[i]);
      mae /= (prob.Count - count);
      Procedures.info("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma=" + mae + "\n");
      return mae;
    }

    // label: label name, start: begin of each class, count: #data of classes, perm: indices to the original data
    // perm, length l, must be allocated before calling this subroutine
    private static void svm_group_classes(Problem prob, int[] nr_class_ret, int[][] label_ret, int[][] start_ret, int[][] count_ret, int[] perm) {
      int l = prob.Count;
      int Max_nr_class = 16;
      int nr_class = 0;
      int[] label = new int[Max_nr_class];
      int[] count = new int[Max_nr_class];
      int[] data_label = new int[l];
      int i;

      for (i = 0; i < l; i++) {
        int this_label = (int)(prob.Y[i]);
        int j;
        for (j = 0; j < nr_class; j++) {
          if (this_label == label[j]) {
            ++count[j];
            break;
          }
        }
        data_label[i] = j;
        if (j == nr_class) {
          if (nr_class == Max_nr_class) {
            Max_nr_class *= 2;
            int[] new_data = new int[Max_nr_class];
            Array.Copy(label, 0, new_data, 0, label.Length);
            label = new_data;
            new_data = new int[Max_nr_class];
            Array.Copy(count, 0, new_data, 0, count.Length);
            count = new_data;
          }
          label[nr_class] = this_label;
          count[nr_class] = 1;
          ++nr_class;
        }
      }

      int[] start = new int[nr_class];
      start[0] = 0;
      for (i = 1; i < nr_class; i++)
        start[i] = start[i - 1] + count[i - 1];
      for (i = 0; i < l; i++) {
        perm[start[data_label[i]]] = i;
        ++start[data_label[i]];
      }
      start[0] = 0;
      for (i = 1; i < nr_class; i++)
        start[i] = start[i - 1] + count[i - 1];

      nr_class_ret[0] = nr_class;
      label_ret[0] = label;
      start_ret[0] = start;
      count_ret[0] = count;
    }

    //
    // Interface functions
    //
    public static Model svm_train(Problem prob, Parameter param) {
      Model model = new Model();
      model.Parameter = param;

      if (param.SvmType == SvmType.ONE_CLASS ||
         param.SvmType == SvmType.EPSILON_SVR ||
         param.SvmType == SvmType.NU_SVR) {
        // regression or one-class-svm
        model.NumberOfClasses = 2;
        model.ClassLabels = null;
        model.NumberOfSVPerClass = null;
        model.PairwiseProbabilityA = null; model.PairwiseProbabilityB = null;
        model.SupportVectorCoefficients = new double[1][];

        if (param.Probability &&
           (param.SvmType == SvmType.EPSILON_SVR ||
            param.SvmType == SvmType.NU_SVR)) {
          model.PairwiseProbabilityA = new double[1];
          model.PairwiseProbabilityA[0] = svm_svr_probability(prob, param);
        }

        decision_function f = svm_train_one(prob, param, 0, 0);
        model.Rho = new double[1];
        model.Rho[0] = f.rho;

        int nSV = 0;
        int i;
        for (i = 0; i < prob.Count; i++)
          if (Math.Abs(f.alpha[i]) > 0) ++nSV;
        model.SupportVectorCount = nSV;
        model.SupportVectorIndizes = new int[nSV];
        model.SupportVectors = new Node[nSV][];
        model.SupportVectorCoefficients[0] = new double[nSV];

        int j = 0;
        for (i = 0; i < prob.Count; i++)
          if (Math.Abs(f.alpha[i]) > 0) {
            model.SupportVectors[j] = prob.X[i];
            model.SupportVectorIndizes[j] = i;
            model.SupportVectorCoefficients[0][j] = f.alpha[i];

            ++j;
          }
      } else {
        // classification
        int l = prob.Count;
        int[] tmp_nr_class = new int[1];
        int[][] tmp_label = new int[1][];
        int[][] tmp_start = new int[1][];
        int[][] tmp_count = new int[1][];
        int[] perm = new int[l];

        // group training data of the same class
        svm_group_classes(prob, tmp_nr_class, tmp_label, tmp_start, tmp_count, perm);
        int nr_class = tmp_nr_class[0];
        int[] label = tmp_label[0];
        int[] start = tmp_start[0];
        int[] count = tmp_count[0];
        Node[][] x = new Node[l][];
        int i;
        for (i = 0; i < l; i++)
          x[i] = prob.X[perm[i]];

        // calculate weighted C

        double[] weighted_C = new double[nr_class];
        for (i = 0; i < nr_class; i++)
          weighted_C[i] = param.C;
        foreach (int weightedLabel in param.Weights.Keys) {
          int index = Array.IndexOf<int>(label, weightedLabel);
          if (index < 0)
            Console.Error.WriteLine("warning: class label " + weightedLabel + " specified in weight is not found");
          else weighted_C[index] *= param.Weights[weightedLabel];
        }

        // train k*(k-1)/2 models

        bool[] nonzero = new bool[l];
        for (i = 0; i < l; i++)
          nonzero[i] = false;
        decision_function[] f = new decision_function[nr_class * (nr_class - 1) / 2];

        double[] probA = null, probB = null;
        if (param.Probability) {
          probA = new double[nr_class * (nr_class - 1) / 2];
          probB = new double[nr_class * (nr_class - 1) / 2];
        }

        int p = 0;
        for (i = 0; i < nr_class; i++)
          for (int j = i + 1; j < nr_class; j++) {
            Problem sub_prob = new Problem();
            int si = start[i], sj = start[j];
            int ci = count[i], cj = count[j];
            sub_prob.Count = ci + cj;
            sub_prob.X = new Node[sub_prob.Count][];
            sub_prob.Y = new double[sub_prob.Count];
            int k;
            for (k = 0; k < ci; k++) {
              sub_prob.X[k] = x[si + k];
              sub_prob.Y[k] = +1;
            }
            for (k = 0; k < cj; k++) {
              sub_prob.X[ci + k] = x[sj + k];
              sub_prob.Y[ci + k] = -1;
            }

            if (param.Probability) {
              double[] probAB = new double[2];
              svm_binary_svc_probability(sub_prob, param, weighted_C[i], weighted_C[j], probAB);
              probA[p] = probAB[0];
              probB[p] = probAB[1];
            }

            f[p] = svm_train_one(sub_prob, param, weighted_C[i], weighted_C[j]);
            for (k = 0; k < ci; k++)
              if (!nonzero[si + k] && Math.Abs(f[p].alpha[k]) > 0)
                nonzero[si + k] = true;
            for (k = 0; k < cj; k++)
              if (!nonzero[sj + k] && Math.Abs(f[p].alpha[ci + k]) > 0)
                nonzero[sj + k] = true;
            ++p;
          }

        // build output

        model.NumberOfClasses = nr_class;

        model.ClassLabels = new int[nr_class];
        for (i = 0; i < nr_class; i++)
          model.ClassLabels[i] = label[i];

        model.Rho = new double[nr_class * (nr_class - 1) / 2];
        for (i = 0; i < nr_class * (nr_class - 1) / 2; i++)
          model.Rho[i] = f[i].rho;

        if (param.Probability) {
          model.PairwiseProbabilityA = new double[nr_class * (nr_class - 1) / 2];
          model.PairwiseProbabilityB = new double[nr_class * (nr_class - 1) / 2];
          for (i = 0; i < nr_class * (nr_class - 1) / 2; i++) {
            model.PairwiseProbabilityA[i] = probA[i];
            model.PairwiseProbabilityB[i] = probB[i];
          }
        } else {
          model.PairwiseProbabilityA = null;
          model.PairwiseProbabilityB = null;
        }

        int nnz = 0;
        int[] nz_count = new int[nr_class];
        model.NumberOfSVPerClass = new int[nr_class];
        for (i = 0; i < nr_class; i++) {
          int nSV = 0;
          for (int j = 0; j < count[i]; j++)
            if (nonzero[start[i] + j]) {
              ++nSV;
              ++nnz;
            }
          model.NumberOfSVPerClass[i] = nSV;
          nz_count[i] = nSV;
        }

        Procedures.info("Total nSV = " + nnz + "\n");

        model.SupportVectorCount = nnz;
        model.SupportVectors = new Node[nnz][];
        model.SupportVectorIndizes = new int[nnz];
        p = 0;
        for (i = 0; i < l; i++) {
          if (nonzero[i]) {
            model.SupportVectors[p] = x[i];
            model.SupportVectorIndizes[p] = i;
            p++;
          }
        }

        int[] nz_start = new int[nr_class];
        nz_start[0] = 0;
        for (i = 1; i < nr_class; i++)
          nz_start[i] = nz_start[i - 1] + nz_count[i - 1];

        model.SupportVectorCoefficients = new double[nr_class - 1][];
        for (i = 0; i < nr_class - 1; i++)
          model.SupportVectorCoefficients[i] = new double[nnz];

        p = 0;
        for (i = 0; i < nr_class; i++)
          for (int j = i + 1; j < nr_class; j++) {
            // classifier (i,j): coefficients with
            // i are in sv_coef[j-1][nz_start[i]...],
            // j are in sv_coef[i][nz_start[j]...]

            int si = start[i];
            int sj = start[j];
            int ci = count[i];
            int cj = count[j];

            int q = nz_start[i];
            int k;
            for (k = 0; k < ci; k++)
              if (nonzero[si + k])
                model.SupportVectorCoefficients[j - 1][q++] = f[p].alpha[k];
            q = nz_start[j];
            for (k = 0; k < cj; k++)
              if (nonzero[sj + k])
                model.SupportVectorCoefficients[i][q++] = f[p].alpha[ci + k];
            ++p;
          }
      }
      return model;
    }

    // Stratified cross validation
    public static void svm_cross_validation(Problem prob, Parameter param, int nr_fold, double[] target, bool shuffleTraining) {
      Random rand = new Random();
      int i;
      int[] fold_start = new int[nr_fold + 1];
      int l = prob.Count;
      int[] perm = new int[l];

      // stratified cv may not give leave-one-out rate
      // Each class to l folds -> some folds may have zero elements
      if ((param.SvmType == SvmType.C_SVC ||
          param.SvmType == SvmType.NU_SVC) && nr_fold < l) {
        int[] tmp_nr_class = new int[1];
        int[][] tmp_label = new int[1][];
        int[][] tmp_start = new int[1][];
        int[][] tmp_count = new int[1][];

        svm_group_classes(prob, tmp_nr_class, tmp_label, tmp_start, tmp_count, perm);

        int nr_class = tmp_nr_class[0];
        int[] label = tmp_label[0];
        int[] start = tmp_start[0];
        int[] count = tmp_count[0];

        // random shuffle and then data grouped by fold using the array perm
        int[] fold_count = new int[nr_fold];
        int c;
        int[] index = new int[l];
        for (i = 0; i < l; i++)
          index[i] = perm[i];
        for (c = 0; c < nr_class; c++)
          for (i = 0; i < count[c]; i++) {
            int j = i + (int)(rand.NextDouble() * (count[c] - i));
            do { int _ = index[start[c] + j]; index[start[c] + j] = index[start[c] + i]; index[start[c] + i] = _; } while (false);
          }
        for (i = 0; i < nr_fold; i++) {
          fold_count[i] = 0;
          for (c = 0; c < nr_class; c++)
            fold_count[i] += (i + 1) * count[c] / nr_fold - i * count[c] / nr_fold;
        }
        fold_start[0] = 0;
        for (i = 1; i <= nr_fold; i++)
          fold_start[i] = fold_start[i - 1] + fold_count[i - 1];
        for (c = 0; c < nr_class; c++)
          for (i = 0; i < nr_fold; i++) {
            int begin = start[c] + i * count[c] / nr_fold;
            int end = start[c] + (i + 1) * count[c] / nr_fold;
            for (int j = begin; j < end; j++) {
              perm[fold_start[i]] = index[j];
              fold_start[i]++;
            }
          }
        fold_start[0] = 0;
        for (i = 1; i <= nr_fold; i++)
          fold_start[i] = fold_start[i - 1] + fold_count[i - 1];
      } else {
        for (i = 0; i < l; i++) perm[i] = i;
        if (shuffleTraining) {
          for (i = 0; i < l; i++) {
            int j = i + (int)(rand.NextDouble() * (l - i));
            do { int _ = perm[i]; perm[i] = perm[j]; perm[j] = _; } while (false);
          }
        }
        for (i = 0; i <= nr_fold; i++)
          fold_start[i] = i * l / nr_fold;
      }

      for (i = 0; i < nr_fold; i++) {
        int begin = fold_start[i];
        int end = fold_start[i + 1];
        int j, k;
        Problem subprob = new Problem();

        subprob.Count = l - (end - begin);
        subprob.X = new Node[subprob.Count][];
        subprob.Y = new double[subprob.Count];

        k = 0;
        for (j = 0; j < begin; j++) {
          subprob.X[k] = prob.X[perm[j]];
          subprob.Y[k] = prob.Y[perm[j]];
          ++k;
        }
        for (j = end; j < l; j++) {
          subprob.X[k] = prob.X[perm[j]];
          subprob.Y[k] = prob.Y[perm[j]];
          ++k;
        }
        Model submodel = svm_train(subprob, param);
        if (param.Probability &&
           (param.SvmType == SvmType.C_SVC ||
            param.SvmType == SvmType.NU_SVC)) {
          double[] prob_estimates = new double[svm_get_nr_class(submodel)];
          for (j = begin; j < end; j++)
            target[perm[j]] = svm_predict_probability(submodel, prob.X[perm[j]], prob_estimates);
        } else
          for (j = begin; j < end; j++)
            target[perm[j]] = svm_predict(submodel, prob.X[perm[j]]);
      }
    }

    public static SvmType svm_get_svm_type(Model model) {
      return model.Parameter.SvmType;
    }

    public static int svm_get_nr_class(Model model) {
      return model.NumberOfClasses;
    }

    public static void svm_get_labels(Model model, int[] label) {
      if (model.ClassLabels != null)
        for (int i = 0; i < model.NumberOfClasses; i++)
          label[i] = model.ClassLabels[i];
    }

    public static double svm_get_svr_probability(Model model) {
      if ((model.Parameter.SvmType == SvmType.EPSILON_SVR || model.Parameter.SvmType == SvmType.NU_SVR) &&
          model.PairwiseProbabilityA != null)
        return model.PairwiseProbabilityA[0];
      else {
        Console.Error.WriteLine("Model doesn't contain information for SVR probability inference");
        return 0;
      }
    }

    public static void svm_predict_values(Model model, Node[] x, double[] dec_values) {
      if (model.Parameter.SvmType == SvmType.ONE_CLASS ||
         model.Parameter.SvmType == SvmType.EPSILON_SVR ||
         model.Parameter.SvmType == SvmType.NU_SVR) {
        double[] sv_coef = model.SupportVectorCoefficients[0];
        double sum = 0;
        for (int i = 0; i < model.SupportVectorCount; i++)
          sum += sv_coef[i] * Kernel.KernelFunction(x, model.SupportVectors[i], model.Parameter);
        sum -= model.Rho[0];
        dec_values[0] = sum;
      } else {
        int i;
        int nr_class = model.NumberOfClasses;
        int l = model.SupportVectorCount;

        double[] kvalue = new double[l];
        for (i = 0; i < l; i++)
          kvalue[i] = Kernel.KernelFunction(x, model.SupportVectors[i], model.Parameter);

        int[] start = new int[nr_class];
        start[0] = 0;
        for (i = 1; i < nr_class; i++)
          start[i] = start[i - 1] + model.NumberOfSVPerClass[i - 1];

        int p = 0;
        for (i = 0; i < nr_class; i++)
          for (int j = i + 1; j < nr_class; j++) {
            double sum = 0;
            int si = start[i];
            int sj = start[j];
            int ci = model.NumberOfSVPerClass[i];
            int cj = model.NumberOfSVPerClass[j];

            int k;
            double[] coef1 = model.SupportVectorCoefficients[j - 1];
            double[] coef2 = model.SupportVectorCoefficients[i];
            for (k = 0; k < ci; k++)
              sum += coef1[si + k] * kvalue[si + k];
            for (k = 0; k < cj; k++)
              sum += coef2[sj + k] * kvalue[sj + k];
            sum -= model.Rho[p];
            dec_values[p] = sum;
            p++;
          }
      }
    }

    public static double svm_predict(Model model, Node[] x) {
      if (model.Parameter.SvmType == SvmType.ONE_CLASS ||
         model.Parameter.SvmType == SvmType.EPSILON_SVR ||
         model.Parameter.SvmType == SvmType.NU_SVR) {
        double[] res = new double[1];
        svm_predict_values(model, x, res);

        if (model.Parameter.SvmType == SvmType.ONE_CLASS)
          return (res[0] > 0) ? 1 : -1;
        else
          return res[0];
      } else {
        int i;
        int nr_class = model.NumberOfClasses;
        double[] dec_values = new double[nr_class * (nr_class - 1) / 2];
        svm_predict_values(model, x, dec_values);

        int[] vote = new int[nr_class];
        for (i = 0; i < nr_class; i++)
          vote[i] = 0;
        int pos = 0;
        for (i = 0; i < nr_class; i++)
          for (int j = i + 1; j < nr_class; j++) {
            if (dec_values[pos++] > 0)
              ++vote[i];
            else
              ++vote[j];
          }

        int vote_Max_idx = 0;
        for (i = 1; i < nr_class; i++)
          if (vote[i] > vote[vote_Max_idx])
            vote_Max_idx = i;
        return model.ClassLabels[vote_Max_idx];
      }
    }

    public static double svm_predict_probability(Model model, Node[] x, double[] prob_estimates) {
      if ((model.Parameter.SvmType == SvmType.C_SVC || model.Parameter.SvmType == SvmType.NU_SVC) &&
          model.PairwiseProbabilityA != null && model.PairwiseProbabilityB != null) {
        int i;
        int nr_class = model.NumberOfClasses;
        double[] dec_values = new double[nr_class * (nr_class - 1) / 2];
        svm_predict_values(model, x, dec_values);

        double Min_prob = 1e-7;
        double[,] pairwise_prob = new double[nr_class, nr_class];

        int k = 0;
        for (i = 0; i < nr_class; i++) {
          for (int j = i + 1; j < nr_class; j++) {
            pairwise_prob[i, j] = Math.Min(Math.Max(sigmoid_predict(dec_values[k], model.PairwiseProbabilityA[k], model.PairwiseProbabilityB[k]), Min_prob), 1 - Min_prob);
            pairwise_prob[j, i] = 1 - pairwise_prob[i, j];
            k++;
          }
        }
        multiclass_probability(nr_class, pairwise_prob, prob_estimates);

        int prob_Max_idx = 0;
        for (i = 1; i < nr_class; i++)
          if (prob_estimates[i] > prob_estimates[prob_Max_idx])
            prob_Max_idx = i;
        return model.ClassLabels[prob_Max_idx];
      } else
        return svm_predict(model, x);
    }

    public static string svm_check_parameter(Problem prob, Parameter param) {
      // svm_type

      SvmType svm_type = param.SvmType;

      // kernel_type, degree

      KernelType kernel_type = param.KernelType;

      if (param.Degree < 0)
        return "degree of polynomial kernel < 0";

      // cache_size,eps,C,nu,p,shrinking

      if (param.CacheSize <= 0)
        return "cache_size <= 0";

      if (param.EPS <= 0)
        return "eps <= 0";

      if (param.Gamma == 0)
        param.Gamma = 1.0 / prob.MaxIndex;

      if (svm_type == SvmType.C_SVC ||
         svm_type == SvmType.EPSILON_SVR ||
         svm_type == SvmType.NU_SVR)
        if (param.C <= 0)
          return "C <= 0";

      if (svm_type == SvmType.NU_SVC ||
         svm_type == SvmType.ONE_CLASS ||
         svm_type == SvmType.NU_SVR)
        if (param.Nu <= 0 || param.Nu > 1)
          return "nu <= 0 or nu > 1";

      if (svm_type == SvmType.EPSILON_SVR)
        if (param.P < 0)
          return "p < 0";

      if (param.Probability &&
         svm_type == SvmType.ONE_CLASS)
        return "one-class SVM probability output not supported yet";

      // check whether nu-svc is feasible

      if (svm_type == SvmType.NU_SVC) {
        int l = prob.Count;
        int Max_nr_class = 16;
        int nr_class = 0;
        int[] label = new int[Max_nr_class];
        int[] count = new int[Max_nr_class];

        int i;
        for (i = 0; i < l; i++) {
          int this_label = (int)prob.Y[i];
          int j;
          for (j = 0; j < nr_class; j++)
            if (this_label == label[j]) {
              ++count[j];
              break;
            }

          if (j == nr_class) {
            if (nr_class == Max_nr_class) {
              Max_nr_class *= 2;
              int[] new_data = new int[Max_nr_class];
              Array.Copy(label, 0, new_data, 0, label.Length);
              label = new_data;

              new_data = new int[Max_nr_class];
              Array.Copy(count, 0, new_data, 0, count.Length);
              count = new_data;
            }
            label[nr_class] = this_label;
            count[nr_class] = 1;
            ++nr_class;
          }
        }

        for (i = 0; i < nr_class; i++) {
          int n1 = count[i];
          for (int j = i + 1; j < nr_class; j++) {
            int n2 = count[j];
            if (param.Nu * (n1 + n2) / 2 > Math.Min(n1, n2))
              return "specified nu is infeasible";
          }
        }
      }

      return null;
    }

    public static int svm_check_probability_model(Model model) {
      if (((model.Parameter.SvmType == SvmType.C_SVC || model.Parameter.SvmType == SvmType.NU_SVC) &&
      model.PairwiseProbabilityA != null && model.PairwiseProbabilityB != null) ||
      ((model.Parameter.SvmType == SvmType.EPSILON_SVR || model.Parameter.SvmType == SvmType.NU_SVR) &&
       model.PairwiseProbabilityA != null))
        return 1;
      else
        return 0;
    }
  }
}