svm.cpp

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/*
 * Copyright (c) 2000-2014 Chih-Chung Chang and Chih-Jen Lin
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 * notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions and the following disclaimer in the
 * documentation and/or other materials provided with the distribution.
 *
 * 3. Neither name of copyright holders nor the names of its contributors
 * may be used to endorse or promote products derived from this software
 * without specific prior written permission.
 *
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
 
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <float.h>
#include <string.h>
#include <stdarg.h>
#include <limits.h>
#include <locale.h>
#include <assert.h>
#include "svm.h"
int libsvm_version = LIBSVM_VERSION;
typedef float Qfloat;
typedef signed char schar;
#ifndef min
template <class T> static inline T min(T x,T y) { return (x<y)?x:y; }
#endif
#ifndef max
template <class T> static inline T max(T x,T y) { return (x>y)?x:y; }
#endif
template <class T> static inline void swap(T& x, T& y) { T t=x; x=y; y=t; }
template <class S, class T> static inline void clone(T*& dst, S* src, int n)
{
  dst = new T[n];
  memcpy((void *)dst,(void *)src,sizeof(T)*n);
}
static inline double powi(double base, int times)
{
  double tmp = base, ret = 1.0;
 
  for(int t=times; t>0; t/=2)
  {
    if(t%2==1) ret*=tmp;
    tmp = tmp * tmp;
  }
  return ret;
}
#define INF HUGE_VAL
#define TAU 1e-12
#define Malloc(type,n) (type *)malloc((n)*sizeof(type))
 
static void print_string_stdout(const char *s)
{
  fputs(s,stdout);
  fflush(stdout);
}
static void (*svm_print_string) (const char *) = &print_string_stdout;
#if 0
static void info(const char *fmt,...)
{
  char buf[BUFSIZ];
  va_list ap;
  va_start(ap,fmt);
  vsprintf(buf,fmt,ap);
  va_end(ap);
  (*svm_print_string)(buf);
}
#else
static void info(const char *fmt,...) {}
#endif
 
//
// Kernel Cache
//
// l is the number of total data items
// size is the cache size limit in bytes
//
class Cache
{
public:
  Cache(int l,long int size);
  ~Cache();
 
  // request data [0,len)
  // return some position p where [p,len) need to be filled
  // (p >= len if nothing needs to be filled)
  int get_data(const int index, Qfloat **data, int len);
  void swap_index(int i, int j);        
private:
  int l;
  long int size;
  struct head_t
  {
    head_t *prev, *next;        // a circular list
    Qfloat *data;
    int len;            // data[0,len) is cached in this entry
  };
 
  head_t *head;
  head_t lru_head;
  void lru_delete(head_t *h);
  void lru_insert(head_t *h);
};
 
Cache::Cache(int l_,long int size_):l(l_),size(size_)
{
  head = (head_t *)calloc(l,sizeof(head_t));    // initialized to 0
  size /= sizeof(Qfloat);
  size -= l * sizeof(head_t) / sizeof(Qfloat);
  size = max(size, 2 * (long int) l);   // cache must be large enough for two columns
  lru_head.next = lru_head.prev = &lru_head;
}
 
Cache::~Cache()
{
  for(head_t *h = lru_head.next; h != &lru_head; h=h->next)
    free(h->data);
  free(head);
}
 
void Cache::lru_delete(head_t *h)
{
  // delete from current location
  h->prev->next = h->next;
  h->next->prev = h->prev;
}
 
void Cache::lru_insert(head_t *h)
{
  // insert to last position
  h->next = &lru_head;
  h->prev = lru_head.prev;
  h->prev->next = h;
  h->next->prev = h;
}
 
int Cache::get_data(const int index, Qfloat **data, int len)
{
  head_t *h = &head[index];
  if(h->len) lru_delete(h);
  int more = len - h->len;
 
  if(more > 0)
  {
    // free old space
    while(size < more)
    {
      head_t *old = lru_head.next;
      lru_delete(old);
      free(old->data);
      size += old->len;
      old->data = 0;
      old->len = 0;
    }
 
    // allocate new space
    h->data = (Qfloat *)realloc(h->data,sizeof(Qfloat)*len);
    size -= more;
    swap(h->len,len);
  }
 
  lru_insert(h);
  *data = h->data;
  return len;
}
 
void Cache::swap_index(int i, int j)
{
  if(i==j) return;
 
  if(head[i].len) lru_delete(&head[i]);
  if(head[j].len) lru_delete(&head[j]);
  swap(head[i].data,head[j].data);
  swap(head[i].len,head[j].len);
  if(head[i].len) lru_insert(&head[i]);
  if(head[j].len) lru_insert(&head[j]);
 
  if(i>j) swap(i,j);
  for(head_t *h = lru_head.next; h!=&lru_head; h=h->next)
  {
    if(h->len > i)
    {
      if(h->len > j)
        swap(h->data[i],h->data[j]);
      else
      {
        // give up
        lru_delete(h);
        free(h->data);
        size += h->len;
        h->data = 0;
        h->len = 0;
      }
    }
  }
}
 
//
// Kernel evaluation
//
// the static method k_function is for doing single kernel evaluation
// the constructor of Kernel prepares to calculate the l*l kernel matrix
// the member function get_Q is for getting one column from the Q Matrix
//
class QMatrix {
public:
  virtual Qfloat *get_Q(int column, int len) const = 0;
  virtual double *get_QD() const = 0;
  virtual void swap_index(int i, int j) const = 0;
  virtual ~QMatrix() {}
};
 
class Kernel: public QMatrix {
public:
  Kernel(int l, svm_node * const * x, const svm_parameter& param);
  virtual ~Kernel();
 
  static double k_function(const svm_node *x, const svm_node *y,
                           const svm_parameter& param);
 
  virtual Qfloat *get_Q(int column, int len) const = 0;
  virtual double *get_QD() const = 0;
  virtual void swap_index(int i, int j) const   // no so const...
  {
    swap(x[i],x[j]);
    if(x_square) swap(x_square[i],x_square[j]);
  }
protected:
 
  double (Kernel::*kernel_function)(int i, int j) const;
 
private:
  const svm_node **x;
  double *x_square;
 
  // svm_parameter
  const int kernel_type;
  const int degree;
  const double gamma;
  const double coef0;
 
  static double dot(const svm_node *px, const svm_node *py);
  double kernel_linear(int i, int j) const
  {
    return dot(x[i],x[j]);
  }
  double kernel_poly(int i, int j) const
  {
    return powi(gamma*dot(x[i],x[j])+coef0,degree);
  }
  double kernel_rbf(int i, int j) const
  {
    return exp(-gamma*(x_square[i]+x_square[j]-2*dot(x[i],x[j])));
  }
  double kernel_sigmoid(int i, int j) const
  {
    return tanh(gamma*dot(x[i],x[j])+coef0);
  }
  double kernel_precomputed(int i, int j) const
  {
    return x[i][(int)(x[j][0].value)].value;
  }
};
 
 
double k_function(const svm_node* x, const svm_node* y, const svm_parameter& param)
{
  return Kernel::k_function(x, y, param);
}
 
Kernel::Kernel(int l, svm_node * const * x_, const svm_parameter& param)
 :kernel_type(param.kernel_type), degree(param.degree),
  gamma(param.gamma), coef0(param.coef0)
{
  switch(kernel_type)
  {
  case LINEAR:
    kernel_function = &Kernel::kernel_linear;
    break;
  case POLY:
    kernel_function = &Kernel::kernel_poly;
    break;
  case RBF:
    kernel_function = &Kernel::kernel_rbf;
    break;
  case SIGMOID:
    kernel_function = &Kernel::kernel_sigmoid;
    break;
  case PRECOMPUTED:
    kernel_function = &Kernel::kernel_precomputed;
    break;
  }
 
  clone(x,x_,l);
 
  if(kernel_type == RBF)
  {
    x_square = new double[l];
    for(int i=0;i<l;i++)
      x_square[i] = dot(x[i],x[i]);
  }
  else
    x_square = 0;
}
 
Kernel::~Kernel()
{
  delete[] x;
  delete[] x_square;
}
 
double Kernel::dot(const svm_node *px, const svm_node *py)
{
  double sum = 0;
  while(px->index != -1 && py->index != -1)
  {
    if(px->index == py->index)
    {
      sum += px->value * py->value;
      ++px;
      ++py;
    }
    else
    {
      if(px->index > py->index)
        ++py;
      else
        ++px;
    }                   
  }
  return sum;
}
 
double Kernel::k_function(const svm_node *x, const svm_node *y,
                          const svm_parameter& param)
{
  switch(param.kernel_type)
  {
  case LINEAR:
    return dot(x,y);
  case POLY:
    return powi(param.gamma*dot(x,y)+param.coef0,param.degree);
  case RBF:
    {
      double sum = 0;
      while(x->index != -1 && y->index !=-1)
      {
        if(x->index == y->index)
        {
          double d = x->value - y->value;
          sum += d*d;
          ++x;
          ++y;
        }
        else
        {
          if(x->index > y->index)
          {     
            sum += y->value * y->value;
            ++y;
          }
          else
          {
            sum += x->value * x->value;
            ++x;
          }
        }
      }
 
      while(x->index != -1)
      {
        sum += x->value * x->value;
        ++x;
      }
 
      while(y->index != -1)
      {
        sum += y->value * y->value;
        ++y;
      }
                        
      return exp(-param.gamma*sum);
    }
  case SIGMOID:
    return tanh(param.gamma*dot(x,y)+param.coef0);
  case PRECOMPUTED:  //x: test (validation), y: SV
    return x[(int)(y->value)].value;
  default:
    return 0;  // Unreachable 
  }
}
 
// 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
//
class Solver {
public:
  Solver() {};
  virtual ~Solver() {};
 
  struct SolutionInfo {
    double obj;
    double rho;
    double *upper_bound;
    double r;   // for Solver_NU
  };
 
  void Solve(int l, const QMatrix& Q, const double *p_, const schar *y_,
             double *alpha_, const double* C_, double eps,
             SolutionInfo* si, int shrinking);
protected:
  int active_size;
  schar *y;
  double *G;            // gradient of objective function
  enum { LOWER_BOUND, UPPER_BOUND, FREE };
  char *alpha_status;   // LOWER_BOUND, UPPER_BOUND, FREE
  double *alpha;
  const QMatrix *Q;
  const double *QD;
  double eps;
  double Cp,Cn;
  double *C;
  double *p;
  int *active_set;
  double *G_bar;                // gradient, if we treat free variables as 0
  int l;
  bool unshrink;        // XXX
 
  double get_C(int i)
  {
    return C[i];
  }
  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;
  }
  bool is_upper_bound(int i) { return alpha_status[i] == UPPER_BOUND; }
  bool is_lower_bound(int i) { return alpha_status[i] == LOWER_BOUND; }
  bool is_free(int i) { return alpha_status[i] == FREE; }
  void swap_index(int i, int j);
  void reconstruct_gradient();
  virtual int select_working_set(int &i, int &j);
  virtual double calculate_rho();
  virtual void do_shrinking();
private:
  bool be_shrunk(int i, double Gmax1, double Gmax2);    
};
 
void Solver::swap_index(int i, int j)
{
  Q->swap_index(i,j);
  swap(y[i],y[j]);
  swap(G[i],G[j]);
  swap(alpha_status[i],alpha_status[j]);
  swap(alpha[i],alpha[j]);
  swap(p[i],p[j]);
  swap(active_set[i],active_set[j]);
  swap(G_bar[i],G_bar[j]);
  swap(C[i],C[j]);
}
 
void Solver::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)
    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++)
    {
      const Qfloat *Q_i = Q->get_Q(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))
      {
        const Qfloat *Q_i = Q->get_Q(i,l);
        double alpha_i = alpha[i];
        for(j=active_size;j<l;j++)
          G[j] += alpha_i * Q_i[j];
      }
  }
}
 
void Solver::Solve(int l, const QMatrix& Q, const double *p_, const schar *y_,
                   double *alpha_, const double* C_, double eps,
                   SolutionInfo* si, int shrinking)
{
  this->l = l;
  this->Q = &Q;
  QD=Q.get_QD();
  clone(p, p_,l);
  clone(y, y_,l);
  clone(alpha,alpha_,l);
  clone(C,C_,l);
  this->eps = eps;
  unshrink = false;
 
  // initialize alpha_status
  {
    alpha_status = new char[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))
      {
        const Qfloat *Q_i = Q.get_Q(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 max_iter = max(10000000, l>INT_MAX/100 ? INT_MAX : 100*l);
  int counter = min(l,1000)+1;
        
  while(iter < max_iter)
  {
    // show progress and do shrinking
 
    if(--counter == 0)
    {
      counter = min(l,1000);
      if(shrinking) do_shrinking();
      info(".");
    }
 
    int i,j;
    if(select_working_set(i,j)!=0)
    {
      // reconstruct the whole gradient
      reconstruct_gradient();
      // reset active set size and check
      active_size = l;
      info("*");
      if(select_working_set(i,j)!=0)
        break;
      else
        counter = 1;    // do shrinking next iteration
    }
                
    ++iter;
 
    // update alpha[i] and alpha[j], handle bounds carefully
                
    const Qfloat *Q_i = Q.get_Q(i,active_size);
    const Qfloat *Q_j = Q.get_Q(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 = QD[i]+QD[j]+2*Q_i[j];
      if (quad_coef <= 0)
        quad_coef = TAU;
      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 = QD[i]+QD[j]-2*Q_i[j];
      if (quad_coef <= 0)
        quad_coef = TAU;
      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.get_Q(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.get_Q(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];
      }
    }
  }
 
  if(iter >= max_iter)
  {
    if(active_size < l)
    {
      // reconstruct the whole gradient to calculate objective value
      reconstruct_gradient();
      active_size = l;
      info("*");
    }
    fprintf(stderr,"\nWARNING: reaching max number of iterations\n");
  }
 
  // 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];
  }
 
  // juggle everything back
  /*{
    for(int i=0;i<l;i++)
    while(active_set[i] != i)
    swap_index(i,active_set[i]);
    // or Q.swap_index(i,active_set[i]);
        }*/
 
  for(int i=0;i<l;i++)
    si->upper_bound[i] = C[i];
 
  info("\noptimization finished, #iter = %d\n",iter);
 
  delete[] p;
  delete[] y;
  delete[] C;
  delete[] alpha;
  delete[] alpha_status;
  delete[] active_set;
  delete[] G;
  delete[] G_bar;
}
 
// return 1 if already optimal, return 0 otherwise
int Solver::select_working_set(int &out_i, int &out_j)
{
  // return i,j such that
  // 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 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;
  const Qfloat *Q_i = NULL;
  if(i != -1) // NULL Q_i not accessed: Gmax=-INF if i=-1
    Q_i = Q->get_Q(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 = QD[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)/TAU;
 
          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 = QD[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)/TAU;
 
          if (obj_diff <= obj_diff_min)
          {
            Gmin_idx=j;
            obj_diff_min = obj_diff;
          }
        }
      }
    }
  }
 
  if(Gmax+Gmax2 < eps)
    return 1;
 
  out_i = Gmax_idx;
  out_j = Gmin_idx;
  return 0;
}
 
bool Solver::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);
}
 
void Solver::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;
    info("*");
  }
 
  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--;
      }
    }
}
 
double Solver::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_upper_bound(i))
    {
      if(y[i]==-1)
        ub = min(ub,yG);
      else
        lb = max(lb,yG);
    }
    else if(is_lower_bound(i))
    {
      if(y[i]==+1)
        ub = min(ub,yG);
      else
        lb = 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 : public Solver
{
public:
  Solver_NU() {}
  void Solve(int l, const QMatrix& Q, const double *p, const schar *y,
             double *alpha, double* C_, double eps,
             SolutionInfo* si, int shrinking)
  {
    this->si = si;
    Solver::Solve(l,Q,p,y,alpha,C_,eps,si,shrinking);
  }
private:
  SolutionInfo *si;
  int select_working_set(int &i, int &j);
  double calculate_rho();
  bool be_shrunk(int i, double Gmax1, double Gmax2, double Gmax3, double Gmax4);
  void do_shrinking();
};
 
// return 1 if already optimal, return 0 otherwise
int Solver_NU::select_working_set(int &out_i, int &out_j)
{
  // 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;
  const Qfloat *Q_ip = NULL;
  const Qfloat *Q_in = NULL;
  if(ip != -1) // NULL Q_ip not accessed: Gmaxp=-INF if ip=-1
    Q_ip = Q->get_Q(ip,active_size);
  if(in != -1)
    Q_in = Q->get_Q(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 = QD[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)/TAU;
 
          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 = QD[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)/TAU;
 
          if (obj_diff <= obj_diff_min)
          {
            Gmin_idx=j;
            obj_diff_min = obj_diff;
          }
        }
      }
    }
  }
 
  if(max(Gmaxp+Gmaxp2,Gmaxn+Gmaxn2) < eps)
    return 1;
 
  if (y[Gmin_idx] == +1)
    out_i = Gmaxp_idx;
  else
    out_i = Gmaxn_idx;
  out_j = Gmin_idx;
 
  return 0;
}
 
bool Solver_NU::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);
}
 
void Solver_NU::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 && 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--;
      }
    }
}
 
double Solver_NU::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_upper_bound(i))
        lb1 = max(lb1,G[i]);
      else if(is_lower_bound(i))
        ub1 = min(ub1,G[i]);
      else
      {
        ++nr_free1;
        sum_free1 += G[i];
      }
    }
    else
    {
      if(is_upper_bound(i))
        lb2 = max(lb2,G[i]);
      else if(is_lower_bound(i))
        ub2 = min(ub2,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: public Kernel
{ 
public:
  SVC_Q(const svm_problem& prob, const svm_parameter& param, const schar *y_)
        :Kernel(prob.l, prob.x, param)
  {
    clone(y,y_,prob.l);
    cache = new Cache(prob.l,(long int)(param.cache_size*(1<<20)));
    QD = new double[prob.l];
    for(int i=0;i<prob.l;i++)
      QD[i] = (this->*kernel_function)(i,i);
  }
        
  Qfloat *get_Q(int i, int len) const
  {
    Qfloat *data;
    int start, j;
    if((start = cache->get_data(i,&data,len)) < len)
    {
      for(j=start;j<len;j++)
        data[j] = (Qfloat)(y[i]*y[j]*(this->*kernel_function)(i,j));
    }
    return data;
  }
 
  double *get_QD() const
  {
    return QD;
  }
 
  void swap_index(int i, int j) const
  {
    cache->swap_index(i,j);
    Kernel::swap_index(i,j);
    swap(y[i],y[j]);
    swap(QD[i],QD[j]);
  }
 
  ~SVC_Q()
  {
    delete[] y;
    delete cache;
    delete[] QD;
  }
private:
  schar *y;
  Cache *cache;
  double *QD;
};
 
class ONE_CLASS_Q: public Kernel
{
public:
  ONE_CLASS_Q(const svm_problem& prob, const svm_parameter& param)
        :Kernel(prob.l, prob.x, param)
  {
    cache = new Cache(prob.l,(long int)(param.cache_size*(1<<20)));
    QD = new double[prob.l];
    for(int i=0;i<prob.l;i++)
      QD[i] = (this->*kernel_function)(i,i);
  }
        
  Qfloat *get_Q(int i, int len) const
  {
    Qfloat *data;
    int start, j;
    if((start = cache->get_data(i,&data,len)) < len)
    {
      for(j=start;j<len;j++)
        data[j] = (Qfloat)(this->*kernel_function)(i,j);
    }
    return data;
  }
 
  double *get_QD() const
  {
    return QD;
  }
 
  void swap_index(int i, int j) const
  {
    cache->swap_index(i,j);
    Kernel::swap_index(i,j);
    swap(QD[i],QD[j]);
  }
 
  ~ONE_CLASS_Q()
  {
    delete cache;
    delete[] QD;
  }
private:
  Cache *cache;
  double *QD;
};
 
class SVR_Q: public Kernel
{ 
public:
  SVR_Q(const svm_problem& prob, const svm_parameter& param)
        :Kernel(prob.l, prob.x, param)
  {
    l = prob.l;
    cache = new Cache(l,(long int)(param.cache_size*(1<<20)));
    QD = new double[2*l];
    sign = new schar[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] = (this->*kernel_function)(k,k);
      QD[k+l] = QD[k];
    }
    buffer[0] = new Qfloat[2*l];
    buffer[1] = new Qfloat[2*l];
    next_buffer = 0;
  }
 
  void swap_index(int i, int j) const
  {
    swap(sign[i],sign[j]);
    swap(index[i],index[j]);
    swap(QD[i],QD[j]);
  }
        
  Qfloat *get_Q(int i, int len) const
  {
    Qfloat *data;
    int j, real_i = index[i];
    if(cache->get_data(real_i,&data,l) < l)
    {
      for(j=0;j<l;j++)
        data[j] = (Qfloat)(this->*kernel_function)(real_i,j);
    }
 
    // reorder and copy
    Qfloat *buf = buffer[next_buffer];
    next_buffer = 1 - next_buffer;
    schar si = sign[i];
    for(j=0;j<len;j++)
      buf[j] = (Qfloat) si * (Qfloat) sign[j] * data[index[j]];
    return buf;
  }
 
  double *get_QD() const
  {
    return QD;
  }
 
  ~SVR_Q()
  {
    delete cache;
    delete[] sign;
    delete[] index;
    delete[] buffer[0];
    delete[] buffer[1];
    delete[] QD;
  }
private:
  int l;
  Cache *cache;
  schar *sign;
  int *index;
  mutable int next_buffer;
  Qfloat *buffer[2];
  double *QD;
};
#include <iostream>
//
// construct and solve various formulations
//
static void solve_c_svc(
                        const svm_problem *prob, const svm_parameter* param,
                        double *alpha, Solver::SolutionInfo* si, double Cp, double Cn)
{
  int l = prob->l;
  double *minus_ones = new double[l];
  schar *y = new schar[l];
  double *C = new double[l];
 
  int i;
 
  for(i=0;i<l;i++)
  {
    alpha[i] = 0;
    minus_ones[i] = -1;
    if(prob->y[i] > 0)
    {
      y[i] = +1;
      C[i] = prob->W[i]*Cp;
    }
    else
    {
      y[i] = -1;
      C[i] = prob->W[i]*Cn;
    }
    //std::cout << C[i] << " ";
  }
  //std::cout << std::endl;
 
  Solver s;
  s.Solve(l, SVC_Q(*prob,*param,y), minus_ones, y,
          alpha, C, param->eps, si, param->shrinking);
 
  /*
        double sum_alpha=0;
        for(i=0;i<l;i++)
    sum_alpha += alpha[i];
        if (Cp==Cn)
    info("nu = %f\n", sum_alpha/(Cp*prob->l));
  */
 
  for(i=0;i<l;i++)
    alpha[i] *= y[i];
 
  delete[] C;
  delete[] minus_ones;
  delete[] y;
}
 
static void solve_nu_svc(
                         const svm_problem *prob, const svm_parameter *param,
                         double *alpha, Solver::SolutionInfo* si)
{
  int i;
  int l = prob->l;
  double nu = param->nu;
 
  schar *y = new schar[l];
  double *C = new double[l];
 
  for(i=0;i<l;i++)
  {
    if(prob->y[i]>0)
      y[i] = +1;
    else
      y[i] = -1;
    C[i] = prob->W[i];
  }
        
  double nu_l = 0;
  for(i=0;i<l;i++) nu_l += nu*C[i];
  double sum_pos = nu_l/2;
  double sum_neg = nu_l/2;
 
  for(i=0;i<l;i++)
    if(y[i] == +1)
    {
      alpha[i] = min(C[i],sum_pos);
      sum_pos -= alpha[i];
    }
    else
    {
      alpha[i] = min(C[i],sum_neg);
      sum_neg -= alpha[i];
    }
 
  double *zeros = new double[l];
 
  for(i=0;i<l;i++)
    zeros[i] = 0;
 
  Solver_NU s;
  s.Solve(l, SVC_Q(*prob,*param,y), zeros, y,
          alpha, C, param->eps, si,  param->shrinking);
  double r = si->r;
 
  info("C = %f\n",1/r);
 
  for(i=0;i<l;i++)
  {
    alpha[i] *= y[i]/r;
    si->upper_bound[i] /= r;
  }
 
  si->rho /= r;
  si->obj /= (r*r);
 
  delete[] C;
  delete[] y;
  delete[] zeros;
}
 
static void solve_one_class(
                            const svm_problem *prob, const svm_parameter *param,
                            double *alpha, Solver::SolutionInfo* si)
{
  int l = prob->l;
  double *zeros = new double[l];
  schar *ones = new schar[l];
  double *C = new double[l];
  int i;
 
  double nu_l = 0;
 
  for(i=0;i<l;i++)
  {
    C[i] = prob->W[i];
    nu_l += C[i] * param->nu;
  }
 
  i = 0;
  while(nu_l > 0)
  {
    alpha[i] = min(C[i],nu_l);
    nu_l -= alpha[i];
    ++i;
  }
  for(;i<l;i++)
    alpha[i] = 0;
 
  for(i=0;i<l;i++)
  {
    zeros[i] = 0;
    ones[i] = 1;
  }
 
  Solver s;
  s.Solve(l, ONE_CLASS_Q(*prob,*param), zeros, ones,
          alpha, C, param->eps, si, param->shrinking);
 
  delete[] C;
  delete[] zeros;
  delete[] ones;
}
 
static void solve_epsilon_svr(
                              const svm_problem *prob, const svm_parameter *param,
                              double *alpha, Solver::SolutionInfo* si)
{
  int l = prob->l;
  double *alpha2 = new double[2*l];
  double *linear_term = new double[2*l];
  double *C = new double[2*l];
  schar *y = new schar[2*l];
  int i;
 
  for(i=0;i<l;i++)
  {
    alpha2[i] = 0;
    linear_term[i] = param->p - prob->y[i];
    y[i] = 1;
    C[i] = prob->W[i]*param->C;
 
    alpha2[i+l] = 0;
    linear_term[i+l] = param->p + prob->y[i];
    y[i+l] = -1;
    C[i+l] = prob->W[i]*param->C;
  }
 
  Solver s;
  s.Solve(2*l, SVR_Q(*prob,*param), linear_term, y,
          alpha2, 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 += fabs(alpha[i]);
  }
  //info("nu = %f\n",sum_alpha/(param->C*l));
  delete[] alpha2;
  delete[] linear_term;
  delete[] C;
  delete[] y;
}
 
static void solve_nu_svr(
                         const svm_problem *prob, const svm_parameter *param,
                         double *alpha, Solver::SolutionInfo* si)
{
  int l = prob->l;
  double *C = new double[2*l];
  double *alpha2 = new double[2*l];
  double *linear_term = new double[2*l];
  schar *y = new schar[2*l];
  int i;
 
  double sum = 0;
  for(i=0;i<l;i++)
  {
    C[i] = C[i+l] = prob->W[i]*param->C;
    sum += C[i] * param->nu;
  }
  sum /= 2;
 
  for(i=0;i<l;i++)
  {
    alpha2[i] = alpha2[i+l] = min(sum,C[i]);
    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;
  s.Solve(2*l, SVR_Q(*prob,*param), linear_term, y,
          alpha2, C, param->eps, si, param->shrinking);
 
  info("epsilon = %f\n",-si->r);
 
  for(i=0;i<l;i++)
    alpha[i] = alpha2[i] - alpha2[i+l];
 
  delete[] alpha2;
  delete[] linear_term;
  delete[] C;
  delete[] y;
}
 
//
// decision_function
//
struct decision_function
{
  double *alpha;
  double rho;   
};
 
static decision_function svm_train_one(
                                       const svm_problem *prob, const svm_parameter *param,
                                       double Cp, double Cn)
{
  double *alpha = Malloc(double,prob->l);
  Solver::SolutionInfo si;
  switch(param->svm_type)
  {
  case C_SVC:
    si.upper_bound = Malloc(double,prob->l); 
    solve_c_svc(prob,param,alpha,&si,Cp,Cn);
    break;
  case NU_SVC:
    si.upper_bound = Malloc(double,prob->l); 
    solve_nu_svc(prob,param,alpha,&si);
    break;
  case ONE_CLASS:
    si.upper_bound = Malloc(double,prob->l); 
    solve_one_class(prob,param,alpha,&si);
    break;
  case EPSILON_SVR:
    si.upper_bound = Malloc(double,2*prob->l); 
    solve_epsilon_svr(prob,param,alpha,&si);
    break;
  case NU_SVR:
    si.upper_bound = Malloc(double,2*prob->l); 
    solve_nu_svr(prob,param,alpha,&si);
    break;
  }
 
  info("obj = %f, rho = %f\n",si.obj,si.rho);
 
  // output SVs
 
  int nSV = 0;
  int nBSV = 0;
  for(int i=0;i<prob->l;i++)
  {
    if(fabs(alpha[i]) > 0)
    {
      ++nSV;
      if(prob->y[i] > 0)
      {
        if(fabs(alpha[i]) >= si.upper_bound[i])
          ++nBSV;
      }
      else
      {
        if(fabs(alpha[i]) >= si.upper_bound[i])
          ++nBSV;
      }
    }
  }
 
  free(si.upper_bound);
 
  info("nSV = %d, nBSV = %d\n",nSV,nBSV);
 
  decision_function f;
  f.alpha = alpha;
  f.rho = si.rho;
  return f;
}
 
// Platt's binary SVM Probablistic Output: an improvement from Lin et al.
static void sigmoid_train(
                          int l, const double *dec_values, const double *labels, 
                          double& A, double& 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=Malloc(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=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 + log(1+exp(-fApB));
    else
      fval += (t[i] - 1)*fApB +log(1+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=exp(-fApB)/(1.0+exp(-fApB));
        q=1.0/(1.0+exp(-fApB));
      }
      else
      {
        p=1.0/(1.0+exp(fApB));
        q=exp(fApB)/(1.0+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 (fabs(g1)<eps && fabs(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 + log(1+exp(-fApB));
        else
          newf += (t[i] - 1)*fApB +log(1+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)
    {
      info("Line search fails in two-class probability estimates\n");
      break;
    }
  }
 
  if (iter>=max_iter)
    info("Reaching maximal iterations in two-class probability estimates\n");
  free(t);
}
 
static double sigmoid_predict(double decision_value, double A, double B)
{
  double fApB = decision_value*A+B;
  // 1-p used later; avoid catastrophic cancellation
  if (fApB >= 0)
    return exp(-fApB)/(1.0+exp(-fApB));
  else
    return 1.0/(1+exp(fApB)) ;
}
 
// Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
static void multiclass_probability(int k, double **r, double *p)
{
  int t,j;
  int iter = 0, max_iter=max(100,k);
  double **Q=Malloc(double *,k);
  double *Qp=Malloc(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]=Malloc(double,k);
    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=fabs(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)
    info("Exceeds max_iter in multiclass_prob\n");
  for(t=0;t<k;t++) free(Q[t]);
  free(Q);
  free(Qp);
}
 
// Cross-validation decision values for probability estimates
static void svm_binary_svc_probability(
                                       const svm_problem *prob, const svm_parameter *param,
                                       double Cp, double Cn, double& probA, double& probB)
{
  int i;
  int nr_fold = 5;
  int *perm = Malloc(int,prob->l);
  double *dec_values = Malloc(double,prob->l);
 
  // random shuffle
  for(i=0;i<prob->l;i++) perm[i]=i;
  for(i=0;i<prob->l;i++)
  {
    int j = i+rand()%(prob->l-i);
    swap(perm[i],perm[j]);
  }
  for(i=0;i<nr_fold;i++)
  {
    int begin = i*prob->l/nr_fold;
    int end = (i+1)*prob->l/nr_fold;
    int j,k;
    struct svm_problem subprob;
 
    subprob.l = prob->l-(end-begin);
    subprob.x = Malloc(struct svm_node*,subprob.l);
    subprob.y = Malloc(double,subprob.l);
    subprob.W = Malloc(double,subprob.l);
                        
    k=0;
    for(j=0;j<begin;j++)
    {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      subprob.W[k] = prob->W[perm[j]];
      ++k;
    }
    for(j=end;j<prob->l;j++)
    {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      subprob.W[k] = prob->W[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
    {
      svm_parameter subparam = *param;
      subparam.probability=0;
      subparam.C=1.0;
      subparam.nr_weight=2;
      subparam.weight_label = Malloc(int,2);
      subparam.weight = Malloc(double,2);
      subparam.weight_label[0]=+1;
      subparam.weight_label[1]=-1;
      subparam.weight[0]=Cp;
      subparam.weight[1]=Cn;
      struct svm_model *submodel = svm_train(&subprob,&subparam);
      for(j=begin;j<end;j++)
      {
        svm_predict_values(submodel,prob->x[perm[j]],&(dec_values[perm[j]])); 
        // ensure +1 -1 order; reason not using CV subroutine
        dec_values[perm[j]] *= submodel->label[0];
      }         
      svm_free_and_destroy_model(&submodel);
      svm_destroy_param(&subparam);
    }
    free(subprob.x);
    free(subprob.y);
    free(subprob.W);
  }             
  sigmoid_train(prob->l,dec_values,prob->y,probA,probB);
  free(dec_values);
  free(perm);
}
 
// Return parameter of a Laplace distribution 
static double svm_svr_probability(
                                  const svm_problem *prob, const svm_parameter *param)
{
  int i;
  int nr_fold = 5;
  double *ymv = Malloc(double,prob->l);
  double mae = 0;
 
  svm_parameter newparam = *param;
  newparam.probability = 0;
  svm_cross_validation(prob,&newparam,nr_fold,ymv);
  for(i=0;i<prob->l;i++)
  {
    ymv[i]=prob->y[i]-ymv[i];
    mae += fabs(ymv[i]);
  }             
  mae /= prob->l;
  double std=sqrt(2*mae*mae);
  int count=0;
  mae=0;
  for(i=0;i<prob->l;i++)
    if (fabs(ymv[i]) > 5*std) 
      count=count+1;
    else 
      mae+=fabs(ymv[i]);
  mae /= (prob->l-count);
  info("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma= %g\n",mae);
  free(ymv);
  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
static void svm_group_classes(const svm_problem *prob, int *nr_class_ret, int **label_ret, int **start_ret, int **count_ret, int *perm)
{
  int l = prob->l;
  int max_nr_class = 16;
  int nr_class = 0;
  int *label = Malloc(int,max_nr_class);
  int *count = Malloc(int,max_nr_class);
  int *data_label = Malloc(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;
        label = (int *)realloc(label,max_nr_class*sizeof(int));
        count = (int *)realloc(count,max_nr_class*sizeof(int));
      }
      label[nr_class] = this_label;
      count[nr_class] = 1;
      ++nr_class;
    }
  }
 
  int *start = Malloc(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 = nr_class;
  *label_ret = label;
  *start_ret = start;
  *count_ret = count;
  free(data_label);
}
 
//
// Remove zero weighed data as libsvm and some liblinear solvers require C > 0.
//
static void remove_zero_weight(svm_problem *newprob, const svm_problem *prob) 
{
  int i;
  int l = 0;
  for(i=0;i<prob->l;i++)
    if(prob->W[i] > 0) l++;
  *newprob = *prob;
  newprob->l = l;
  newprob->x = Malloc(svm_node*,l);
  newprob->y = Malloc(double,l);
  newprob->W = Malloc(double,l);
 
  int j = 0;
  for(i=0;i<prob->l;i++)
    if(prob->W[i] > 0)
    {
      newprob->x[j] = prob->x[i];
      newprob->y[j] = prob->y[i];
      newprob->W[j] = prob->W[i];
      j++;
    }
}
 
//
// Interface functions
//
svm_model *svm_train(const svm_problem *prob, const svm_parameter *param)
{
  svm_problem newprob;
  remove_zero_weight(&newprob, prob);
  prob = &newprob;
        
  svm_model *model = Malloc(svm_model,1);
  model->param = *param;
  model->free_sv = 0;   // XXX
 
  if(param->svm_type == ONE_CLASS ||
     param->svm_type == EPSILON_SVR ||
     param->svm_type == NU_SVR)
  {
    // regression or one-class-svm
    model->nr_class = 2;
    model->label = NULL;
    model->nSV = NULL;
    model->probA = NULL; model->probB = NULL;
    model->sv_coef = Malloc(double *,1);
 
    if(param->probability && 
       (param->svm_type == EPSILON_SVR ||
        param->svm_type == NU_SVR))
    {
      model->probA = Malloc(double,1);
      model->probA[0] = svm_svr_probability(prob,param);
    }
 
    decision_function f = svm_train_one(prob,param,0,0);
    model->rho = Malloc(double,1);
    model->rho[0] = f.rho;
 
    int nSV = 0;
    int i;
    for(i=0;i<prob->l;i++)
      if(fabs(f.alpha[i]) > 0) ++nSV;
    model->l = nSV;
    model->SV = Malloc(svm_node *,nSV);
    model->sv_coef[0] = Malloc(double,nSV);
    model->sv_indices = Malloc(int,nSV);
    int j = 0;
    for(i=0;i<prob->l;i++)
      if(fabs(f.alpha[i]) > 0)
      {
        model->SV[j] = prob->x[i];
        model->sv_coef[0][j] = f.alpha[i];
        model->sv_indices[j] = i+1;
        ++j;
      }         
 
    free(f.alpha);
  }
  else
  {
    // classification
    int l = prob->l;
    int nr_class;
    int *label = NULL;
    int *start = NULL;
    int *count = NULL;
    int *perm = Malloc(int,l);
 
    // group training data of the same class
    svm_group_classes(prob,&nr_class,&label,&start,&count,perm);
    if(nr_class == 1) 
      info("WARNING: training data in only one class. See README for details.\n");
                
    svm_node **x = Malloc(svm_node *,l);
    double *W;
    W = Malloc(double,l);
 
    int i;
    for(i=0;i<l;i++)
    {
      x[i] = prob->x[perm[i]];
      W[i] = prob->W[perm[i]];
    }
 
    // calculate weighted C
 
    double *weighted_C = Malloc(double, nr_class);
    for(i=0;i<nr_class;i++)
      weighted_C[i] = param->C;
    for(i=0;i<param->nr_weight;i++)
    {   
      int j;
      for(j=0;j<nr_class;j++)
        if(param->weight_label[i] == label[j])
          break;
      if(j == nr_class)
        fprintf(stderr,"WARNING: class label %d specified in weight is not found\n", param->weight_label[i]);
      else
        weighted_C[j] *= param->weight[i];
    }
 
    // train k*(k-1)/2 models
                
    bool *nonzero = Malloc(bool,l);
    for(i=0;i<l;i++)
      nonzero[i] = false;
    decision_function *f = Malloc(decision_function,nr_class*(nr_class-1)/2);
 
    double *probA=NULL,*probB=NULL;
    if (param->probability)
    {
      probA=Malloc(double,nr_class*(nr_class-1)/2);
      probB=Malloc(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++)
      {
        svm_problem sub_prob;
        int si = start[i], sj = start[j];
        int ci = count[i], cj = count[j];
        sub_prob.l = ci+cj;
        sub_prob.x = Malloc(svm_node *,sub_prob.l);
        sub_prob.y = Malloc(double,sub_prob.l);
        sub_prob.W = Malloc(double,sub_prob.l);
        int k;
        for(k=0;k<ci;k++)
        {
          sub_prob.x[k] = x[si+k];
          sub_prob.y[k] = +1;
          sub_prob.W[k] = W[si+k];
        }
        for(k=0;k<cj;k++)
        {
          sub_prob.x[ci+k] = x[sj+k];
          sub_prob.y[ci+k] = -1;
          sub_prob.W[ci+k] = W[sj+k];
        }
 
        if(param->probability)
          svm_binary_svc_probability(&sub_prob,param,weighted_C[i],weighted_C[j],probA[p],probB[p]);
 
        f[p] = svm_train_one(&sub_prob,param,weighted_C[i],weighted_C[j]);
        for(k=0;k<ci;k++)
          if(!nonzero[si+k] && fabs(f[p].alpha[k]) > 0)
            nonzero[si+k] = true;
        for(k=0;k<cj;k++)
          if(!nonzero[sj+k] && fabs(f[p].alpha[ci+k]) > 0)
            nonzero[sj+k] = true;
        free(sub_prob.x);
        free(sub_prob.y);
        free(sub_prob.W);
        ++p;
      }
 
    // build output
 
    model->nr_class = nr_class;
                
    model->label = Malloc(int,nr_class);
    for(i=0;i<nr_class;i++)
      model->label[i] = label[i];
                
    model->rho = Malloc(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->probA = Malloc(double,nr_class*(nr_class-1)/2);
      model->probB = Malloc(double,nr_class*(nr_class-1)/2);
      for(i=0;i<nr_class*(nr_class-1)/2;i++)
      {
        model->probA[i] = probA[i];
        model->probB[i] = probB[i];
      }
    }
    else
    {
      model->probA=NULL;
      model->probB=NULL;
    }
 
    int total_sv = 0;
    int *nz_count = Malloc(int,nr_class);
    model->nSV = Malloc(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;
          ++total_sv;
        }
      model->nSV[i] = nSV;
      nz_count[i] = nSV;
    }
                
    info("Total nSV = %d\n",total_sv);
 
    model->l = total_sv;
    model->SV = Malloc(svm_node *,total_sv);
    model->sv_indices = Malloc(int,total_sv);
    p = 0;
    for(i=0;i<l;i++)
      if(nonzero[i]) 
      {
        model->SV[p] = x[i];
        model->sv_indices[p++] = perm[i] + 1;
      }
 
    int *nz_start = Malloc(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->sv_coef = Malloc(double *,nr_class-1);
    for(i=0;i<nr_class-1;i++)
      model->sv_coef[i] = Malloc(double,total_sv);
 
    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->sv_coef[j-1][q++] = f[p].alpha[k];
        q = nz_start[j];
        for(k=0;k<cj;k++)
          if(nonzero[sj+k])
            model->sv_coef[i][q++] = f[p].alpha[ci+k];
        ++p;
      }
                
    free(label);
    free(probA);
    free(probB);
    free(count);
    free(perm);
    free(start);
    free(W);
    free(x);
    free(weighted_C);
    free(nonzero);
    for(i=0;i<nr_class*(nr_class-1)/2;i++)
      free(f[i].alpha);
    free(f);
    free(nz_count);
    free(nz_start);
  }
  free(newprob.x);
  free(newprob.y);
  free(newprob.W);
  return model;
}
 
// Stratified cross validation
void svm_cross_validation(const svm_problem *prob, const svm_parameter *param, int nr_fold, double *target)
{
  int i;
  int *fold_start = Malloc(int,nr_fold+1);
  int l = prob->l;
  int *perm = Malloc(int,l);
  int nr_class;
 
  // stratified cv may not give leave-one-out rate
  // Each class to l folds -> some folds may have zero elements
  if((param->svm_type == C_SVC ||
      param->svm_type == NU_SVC) && nr_fold < l)
  {
    int *start = NULL;
    int *label = NULL;
    int *count = NULL;
    svm_group_classes(prob,&nr_class,&label,&start,&count,perm);
 
    // random shuffle and then data grouped by fold using the array perm
    int *fold_count = Malloc(int,nr_fold);
    int c;
    int *index = Malloc(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+rand()%(count[c]-i);
        swap(index[start[c]+j],index[start[c]+i]);
      }
    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];
    free(start);        
    free(label);
    free(count);        
    free(index);
    free(fold_count);
  }
  else
  {
    for(i=0;i<l;i++) perm[i]=i;
    for(i=0;i<l;i++)
    {
      int j = i+rand()%(l-i);
      swap(perm[i],perm[j]);
    }
    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;
    struct svm_problem subprob;
 
    subprob.l = l-(end-begin);
    subprob.x = Malloc(struct svm_node*,subprob.l);
    subprob.y = Malloc(double,subprob.l);
                        
    subprob.W = Malloc(double,subprob.l);
    k=0;
    for(j=0;j<begin;j++)
    {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      subprob.W[k] = prob->W[perm[j]];
      ++k;
    }
    for(j=end;j<l;j++)
    {
      subprob.x[k] = prob->x[perm[j]];
      subprob.y[k] = prob->y[perm[j]];
      subprob.W[k] = prob->W[perm[j]];
      ++k;
    }
    struct svm_model *submodel = svm_train(&subprob,param);
    if(param->probability && 
       (param->svm_type == C_SVC || param->svm_type == NU_SVC))
    {
      double *prob_estimates=Malloc(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);
      free(prob_estimates);                     
    }
    else
      for(j=begin;j<end;j++)
        target[perm[j]] = svm_predict(submodel,prob->x[perm[j]]);
    svm_free_and_destroy_model(&submodel);
    free(subprob.x);
    free(subprob.y);
    free(subprob.W);
  }             
  free(fold_start);
  free(perm);   
}
 
 
int svm_get_svm_type(const svm_model *model)
{
  return model->param.svm_type;
}
 
int svm_get_nr_class(const svm_model *model)
{
  return model->nr_class;
}
 
void svm_get_labels(const svm_model *model, int* label)
{
  if (model->label != NULL)
    for(int i=0;i<model->nr_class;i++)
      label[i] = model->label[i];
}
 
void svm_get_sv_indices(const svm_model *model, int* indices)
{
  if (model->sv_indices != NULL)
    for(int i=0;i<model->l;i++)
      indices[i] = model->sv_indices[i];
}
 
int svm_get_nr_sv(const svm_model *model)
{
  return model->l;
}
 
double svm_get_svr_probability(const svm_model *model)
{
  if ((model->param.svm_type == EPSILON_SVR || model->param.svm_type == NU_SVR) &&
      model->probA!=NULL)
    return model->probA[0];
  else
  {
    fprintf(stderr,"Model doesn't contain information for SVR probability inference\n");
    return 0;
  }
}
 
double svm_hyper_w_normsqr_twoclass(const struct svm_model* model)
{
  assert(model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC);
  int i, j;
  // int nr_class = model->nr_class;
  // assert(nr_class == 2);
  int l = model->l;
 
  double sum = 0;
  double *coef = model->sv_coef[0];
        
  for(i=0;i<l;++i)
    for(j=0;j<l;++j)
    {
      double kv = Kernel::k_function(model->SV[i],model->SV[j],model->param);
      sum += kv * coef[i] * coef[j];
    }
 
  return sum;
}
 
double svm_predict_values_twoclass(const struct svm_model* model, const struct svm_node* x)
{
        
  assert(model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC);
  int i;
  // int nr_class = model->nr_class;
  // assert(nr_class == 2);
  int l = model->l;
 
  double *kvalue = Malloc(double,l);
  for(i=0;i<l;i++)
    kvalue[i] = Kernel::k_function(x,model->SV[i],model->param);
 
 
  double sum = 0;
  double *coef = model->sv_coef[0];
  for(i=0;i<l;++i)
    sum += coef[i] * kvalue[i];
  sum -= model->rho[0];
 
  free(kvalue);
        
  return sum * model->label[0];
}
 
double svm_predict_values(const svm_model *model, const svm_node *x, double* dec_values)
{
  int i;
  if(model->param.svm_type == ONE_CLASS ||
     model->param.svm_type == EPSILON_SVR ||
     model->param.svm_type == NU_SVR)
  {
    double *sv_coef = model->sv_coef[0];
    double sum = 0;
    for(i=0;i<model->l;i++)
      sum += sv_coef[i] * Kernel::k_function(x,model->SV[i],model->param);
    sum -= model->rho[0];
    *dec_values = sum;
 
    if(model->param.svm_type == ONE_CLASS)
      return (sum>0)?1:-1;
    else
      return sum;
  }
  else
  {
    int nr_class = model->nr_class;
    int l = model->l;
                
    double *kvalue = Malloc(double,l);
    for(i=0;i<l;i++)
      kvalue[i] = Kernel::k_function(x,model->SV[i],model->param);
 
    int *start = Malloc(int,nr_class);
    start[0] = 0;
    for(i=1;i<nr_class;i++)
      start[i] = start[i-1]+model->nSV[i-1];
 
    int *vote = Malloc(int,nr_class);
    for(i=0;i<nr_class;i++)
      vote[i] = 0;
 
    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->nSV[i];
        int cj = model->nSV[j];
                                
        int k;
        double *coef1 = model->sv_coef[j-1];
        double *coef2 = model->sv_coef[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;
 
        if(dec_values[p] > 0)
          ++vote[i];
        else
          ++vote[j];
        p++;
      }
 
    int vote_max_idx = 0;
    for(i=1;i<nr_class;i++)
      if(vote[i] > vote[vote_max_idx])
        vote_max_idx = i;
 
    free(kvalue);
    free(start);
    free(vote);
    return model->label[vote_max_idx];
  }
}
 
double svm_predict(const svm_model *model, const svm_node *x)
{
  int nr_class = model->nr_class;
  double *dec_values;
  if(model->param.svm_type == ONE_CLASS ||
     model->param.svm_type == EPSILON_SVR ||
     model->param.svm_type == NU_SVR)
    dec_values = Malloc(double, 1);
  else 
    dec_values = Malloc(double, nr_class*(nr_class-1)/2);
  double pred_result = svm_predict_values(model, x, dec_values);
  free(dec_values);
  return pred_result;
}
 
double svm_predict_probability(
                               const svm_model *model, const svm_node *x, double *prob_estimates)
{
  if ((model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC) &&
      model->probA!=NULL && model->probB!=NULL)
  {
    int i;
    int nr_class = model->nr_class;
    double *dec_values = Malloc(double, nr_class*(nr_class-1)/2);
    svm_predict_values(model, x, dec_values);
 
    double min_prob=1e-7;
    double **pairwise_prob=Malloc(double *,nr_class);
    for(i=0;i<nr_class;i++)
      pairwise_prob[i]=Malloc(double,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]=min(max(sigmoid_predict(dec_values[k],model->probA[k],model->probB[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;
    for(i=0;i<nr_class;i++)
      free(pairwise_prob[i]);
    free(dec_values);
    free(pairwise_prob);             
    return model->label[prob_max_idx];
  }
  else 
    return svm_predict(model, x);
}
 
static const char *svm_type_table[] =
  {
        "c_svc","nu_svc","one_class","epsilon_svr","nu_svr",NULL
  };
 
static const char *kernel_type_table[]=
  {
        "linear","polynomial","rbf","sigmoid","precomputed",NULL
  };
 
int svm_save_model(const char *model_file_name, const svm_model *model)
{
  FILE *fp = fopen(model_file_name,"w");
  if(fp==NULL) return -1;
 
  char *old_locale = strdup(setlocale(LC_ALL, NULL));
  setlocale(LC_ALL, "C");
 
  const svm_parameter& param = model->param;
 
  fprintf(fp,"svm_type %s\n", svm_type_table[param.svm_type]);
  fprintf(fp,"kernel_type %s\n", kernel_type_table[param.kernel_type]);
 
  if(param.kernel_type == POLY)
    fprintf(fp,"degree %d\n", param.degree);
 
  if(param.kernel_type == POLY || param.kernel_type == RBF || param.kernel_type == SIGMOID)
    fprintf(fp,"gamma %g\n", param.gamma);
 
  if(param.kernel_type == POLY || param.kernel_type == SIGMOID)
    fprintf(fp,"coef0 %g\n", param.coef0);
 
  int nr_class = model->nr_class;
  int l = model->l;
  fprintf(fp, "nr_class %d\n", nr_class);
  fprintf(fp, "total_sv %d\n",l);
        
  {
    fprintf(fp, "rho");
    for(int i=0;i<nr_class*(nr_class-1)/2;i++)
      fprintf(fp," %g",model->rho[i]);
    fprintf(fp, "\n");
  }
        
  if(model->label)
  {
    fprintf(fp, "label");
    for(int i=0;i<nr_class;i++)
      fprintf(fp," %d",model->label[i]);
    fprintf(fp, "\n");
  }
 
  if(model->probA) // regression has probA only
  {
    fprintf(fp, "probA");
    for(int i=0;i<nr_class*(nr_class-1)/2;i++)
      fprintf(fp," %g",model->probA[i]);
    fprintf(fp, "\n");
  }
  if(model->probB)
  {
    fprintf(fp, "probB");
    for(int i=0;i<nr_class*(nr_class-1)/2;i++)
      fprintf(fp," %g",model->probB[i]);
    fprintf(fp, "\n");
  }
 
  if(model->nSV)
  {
    fprintf(fp, "nr_sv");
    for(int i=0;i<nr_class;i++)
      fprintf(fp," %d",model->nSV[i]);
    fprintf(fp, "\n");
  }
 
  fprintf(fp, "SV\n");
  const double * const *sv_coef = model->sv_coef;
  const svm_node * const *SV = model->SV;
 
  for(int i=0;i<l;i++)
  {
    for(int j=0;j<nr_class-1;j++)
      fprintf(fp, "%.16g ",sv_coef[j][i]);
 
    const svm_node *p = SV[i];
 
    if(param.kernel_type == PRECOMPUTED)
      fprintf(fp,"0:%d ",(int)(p->value));
    else
      while(p->index != -1)
      {
        fprintf(fp,"%d:%.8g ",p->index,p->value);
        p++;
      }
    fprintf(fp, "\n");
  }
 
  setlocale(LC_ALL, old_locale);
  free(old_locale);
 
  if (ferror(fp) != 0 || fclose(fp) != 0) return -1;
  else return 0;
}
 
static char *line = NULL;
static int max_line_len;
 
static char* readline(FILE *input)
{
  int len;
 
  if(fgets(line,max_line_len,input) == NULL)
    return NULL;
 
  while(strrchr(line,'\n') == NULL)
  {
    max_line_len *= 2;
    line = (char *) realloc(line,max_line_len);
    len = (int) strlen(line);
    if(fgets(line+len,max_line_len-len,input) == NULL)
      break;
  }
  return line;
}
 
svm_model *svm_load_model(const char *model_file_name)
{
  FILE *fp = fopen(model_file_name,"rb");
  if(fp==NULL) return NULL;
 
  char *old_locale = strdup(setlocale(LC_ALL, NULL));
  setlocale(LC_ALL, "C");
 
  // read parameters
 
  svm_model *model = Malloc(svm_model,1);
  svm_parameter& param = model->param;
  model->rho = NULL;
  model->probA = NULL;
  model->probB = NULL;
  model->label = NULL;
  model->nSV = NULL;
 
  char cmd[81];
  while(1)
  {
    fscanf(fp,"%80s",cmd);
 
    if(strcmp(cmd,"svm_type")==0)
    {
      fscanf(fp,"%80s",cmd);
      int i;
      for(i=0;svm_type_table[i];i++)
      {
        if(strcmp(svm_type_table[i],cmd)==0)
        {
          param.svm_type=i;
          break;
        }
      }
      if(svm_type_table[i] == NULL)
      {
        fprintf(stderr,"unknown svm type.\n");
                                
        setlocale(LC_ALL, old_locale);
        free(old_locale);
        free(model->rho);
        free(model->label);
        free(model->nSV);
        free(model);
        return NULL;
      }
    }
    else if(strcmp(cmd,"kernel_type")==0)
    {           
      fscanf(fp,"%80s",cmd);
      int i;
      for(i=0;kernel_type_table[i];i++)
      {
        if(strcmp(kernel_type_table[i],cmd)==0)
        {
          param.kernel_type=i;
          break;
        }
      }
      if(kernel_type_table[i] == NULL)
      {
        fprintf(stderr,"unknown kernel function.\n");
                                
        setlocale(LC_ALL, old_locale);
        free(old_locale);
        free(model->rho);
        free(model->label);
        free(model->nSV);
        free(model);
        return NULL;
      }
    }
    else if(strcmp(cmd,"degree")==0)
      fscanf(fp,"%d",&param.degree);
    else if(strcmp(cmd,"gamma")==0)
      fscanf(fp,"%lf",&param.gamma);
    else if(strcmp(cmd,"coef0")==0)
      fscanf(fp,"%lf",&param.coef0);
    else if(strcmp(cmd,"nr_class")==0)
      fscanf(fp,"%d",&model->nr_class);
    else if(strcmp(cmd,"total_sv")==0)
      fscanf(fp,"%d",&model->l);
    else if(strcmp(cmd,"rho")==0)
    {
      int n = model->nr_class * (model->nr_class-1)/2;
      model->rho = Malloc(double,n);
      for(int i=0;i<n;i++)
        fscanf(fp,"%lf",&model->rho[i]);
    }
    else if(strcmp(cmd,"label")==0)
    {
      int n = model->nr_class;
      model->label = Malloc(int,n);
      for(int i=0;i<n;i++)
        fscanf(fp,"%d",&model->label[i]);
    }
    else if(strcmp(cmd,"probA")==0)
    {
      int n = model->nr_class * (model->nr_class-1)/2;
      model->probA = Malloc(double,n);
      for(int i=0;i<n;i++)
        fscanf(fp,"%lf",&model->probA[i]);
    }
    else if(strcmp(cmd,"probB")==0)
    {
      int n = model->nr_class * (model->nr_class-1)/2;
      model->probB = Malloc(double,n);
      for(int i=0;i<n;i++)
        fscanf(fp,"%lf",&model->probB[i]);
    }
    else if(strcmp(cmd,"nr_sv")==0)
    {
      int n = model->nr_class;
      model->nSV = Malloc(int,n);
      for(int i=0;i<n;i++)
        fscanf(fp,"%d",&model->nSV[i]);
    }
    else if(strcmp(cmd,"SV")==0)
    {
      while(1)
      {
        int c = getc(fp);
        if(c==EOF || c=='\n') break;    
      }
      break;
    }
    else
    {
      fprintf(stderr,"unknown text in model file: [%s]\n",cmd);
                        
      setlocale(LC_ALL, old_locale);
      free(old_locale);
      free(model->rho);
      free(model->label);
      free(model->nSV);
      free(model);
      return NULL;
    }
  }
 
  // read sv_coef and SV
 
  int elements = 0;
  long pos = ftell(fp);
 
  max_line_len = 1024;
  line = Malloc(char,max_line_len);
  char *p,*endptr,*idx,*val;
 
  while(readline(fp)!=NULL)
  {
    p = strtok(line,":");
    while(1)
    {
      p = strtok(NULL,":");
      if(p == NULL)
        break;
      ++elements;
    }
  }
  elements += model->l;
 
  fseek(fp,pos,SEEK_SET);
 
  int m = model->nr_class - 1;
  int l = model->l;
  model->sv_coef = Malloc(double *,m);
  int i;
  for(i=0;i<m;i++)
    model->sv_coef[i] = Malloc(double,l);
  model->SV = Malloc(svm_node*,l);
  svm_node *x_space = NULL;
  if(l>0) x_space = Malloc(svm_node,elements);
 
  int j=0;
  for(i=0;i<l;i++)
  {
    readline(fp);
    model->SV[i] = &x_space[j];
 
    p = strtok(line, " \t");
    model->sv_coef[0][i] = strtod(p,&endptr);
    for(int k=1;k<m;k++)
    {
      p = strtok(NULL, " \t");
      model->sv_coef[k][i] = strtod(p,&endptr);
    }
 
    while(1)
    {
      idx = strtok(NULL, ":");
      val = strtok(NULL, " \t");
 
      if(val == NULL)
        break;
      x_space[j].index = (int) strtol(idx,&endptr,10);
      x_space[j].value = strtod(val,&endptr);
 
      ++j;
    }
    x_space[j++].index = -1;
  }
  free(line);
 
  setlocale(LC_ALL, old_locale);
  free(old_locale);
 
  if (ferror(fp) != 0 || fclose(fp) != 0)
    return NULL;
 
  model->free_sv = 1;   // XXX
  return model;
}
 
void svm_free_model_content(svm_model* model_ptr)
{
  if(model_ptr->free_sv && model_ptr->l > 0 && model_ptr->SV != NULL)
    free((void *)(model_ptr->SV[0]));
  if(model_ptr->sv_coef)
  {
    for(int i=0;i<model_ptr->nr_class-1;i++)
      free(model_ptr->sv_coef[i]);
  }
 
  free(model_ptr->SV);
  model_ptr->SV = NULL;
 
  free(model_ptr->sv_coef);
  model_ptr->sv_coef = NULL;
 
  free(model_ptr->rho);
  model_ptr->rho = NULL;
 
  free(model_ptr->label);
  model_ptr->label= NULL;
 
  free(model_ptr->probA);
  model_ptr->probA = NULL;
 
  free(model_ptr->probB);
  model_ptr->probB= NULL;
 
  free(model_ptr->nSV);
  model_ptr->nSV = NULL;
}
 
void svm_free_and_destroy_model(svm_model** model_ptr_ptr)
{
  if(model_ptr_ptr != NULL && *model_ptr_ptr != NULL)
  {
    svm_free_model_content(*model_ptr_ptr);
    free(*model_ptr_ptr);
    *model_ptr_ptr = NULL;
  }
}
 
void svm_destroy_param(svm_parameter* param)
{
  free(param->weight_label);
  free(param->weight);
}
 
const char *svm_check_parameter(const svm_problem *prob, const svm_parameter *param)
{
  // svm_type
 
  int svm_type = param->svm_type;
  if(svm_type != C_SVC &&
     svm_type != NU_SVC &&
     svm_type != ONE_CLASS &&
     svm_type != EPSILON_SVR &&
     svm_type != NU_SVR)
    return "unknown svm type";
        
  // kernel_type, degree
        
  int kernel_type = param->kernel_type;
  if(kernel_type != LINEAR &&
     kernel_type != POLY &&
     kernel_type != RBF &&
     kernel_type != SIGMOID &&
     kernel_type != PRECOMPUTED)
    return "unknown kernel type";
 
  if(param->gamma < 0)
    return "gamma < 0";
 
  if(param->degree < 0)
    return "degree of polynomial kernel < 0";
 
  // cache_size,eps,C,nu,p,shrinking
 
  if(param->cache_size <= 0)
    return "cache_size <= 0";
 
  if(param->eps <= 0)
    return "eps <= 0";
 
  if(svm_type == C_SVC ||
     svm_type == EPSILON_SVR ||
     svm_type == NU_SVR)
    if(param->C <= 0)
      return "C <= 0";
 
  if(svm_type == NU_SVC ||
     svm_type == ONE_CLASS ||
     svm_type == NU_SVR)
    if(param->nu <= 0 || param->nu > 1)
      return "nu <= 0 or nu > 1";
 
  if(svm_type == EPSILON_SVR)
    if(param->p < 0)
      return "p < 0";
 
  if(param->shrinking != 0 &&
     param->shrinking != 1)
    return "shrinking != 0 and shrinking != 1";
 
  if(param->probability != 0 &&
     param->probability != 1)
    return "probability != 0 and probability != 1";
 
  if(param->probability == 1 &&
     svm_type == ONE_CLASS)
    return "one-class SVM probability output not supported yet";
 
 
  // check whether nu-svc is feasible
        
  if(svm_type == NU_SVC)
  {
    int l = prob->l;
    int max_nr_class = 16;
    int nr_class = 0;
    int *label = Malloc(int,max_nr_class);
    double *count = Malloc(double,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] += prob->W[i];
          break;
        }
      if(j == nr_class)
      {
        if(nr_class == max_nr_class)
        {
          max_nr_class *= 2;
          label = (int *)realloc(label,max_nr_class*sizeof(int));
          count = (double *)realloc(count,max_nr_class*sizeof(double));
        }
        label[nr_class] = this_label;
        count[nr_class] = prob->W[i];
        ++nr_class;
      }
    }
        
    for(i=0;i<nr_class;i++)
    {
      double n1 = count[i];
      for(int j=i+1;j<nr_class;j++)
      {
        double n2 = count[j];
        if(param->nu*(n1+n2)/2 > min(n1,n2))
        {
          free(label);
          free(count);
          return "specified nu is infeasible";
        }
      }
    }
    free(label);
    free(count);
  }
 
  return NULL;
}
 
int svm_check_probability_model(const svm_model *model)
{
  return ((model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC) &&
          model->probA!=NULL && model->probB!=NULL) ||
    ((model->param.svm_type == EPSILON_SVR || model->param.svm_type == NU_SVR) &&
     model->probA!=NULL);
}
 
void svm_set_print_string_function(void (*print_func)(const char *))
{
  if(print_func == NULL)
    svm_print_string = &print_string_stdout;
  else
    svm_print_string = print_func;
}