svm.cpp

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#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 "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 1
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;
  }
};

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_p;
    double upper_bound_n;
    double r; // for Solver_NU
  };

  void Solve(int l, const QMatrix& Q, const double *p_, const schar *y_,
             double *alpha_, double Cp, double Cn, 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 *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 (y[i] > 0) ? Cp : Cn;
  }
  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]);
}

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_, double Cp, double Cn, 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);
  this->Cp = Cp;
  this->Cn = Cn;
  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]);
  }*/

  si->upper_bound_p = Cp;
  si->upper_bound_n = Cn;

  //info("\noptimization finished, #iter = %d\n",iter);

  delete[] p;
  delete[] y;
  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 Cp, double Cn, double eps,
             SolutionInfo* si, int shrinking)
  {
    this->si = si;
    Solver::Solve(l, Q, p, y, alpha, Cp, Cn, 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;
};

//
// 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];

  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;
  s.Solve(l, 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)
  //info("nu = %f\n", sum_alpha/(Cp*prob->l));

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

  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];

  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] = min(1.0, sum_pos);
      sum_pos -= alpha[i];
    }
    else
    {
      alpha[i] = 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;
  s.Solve(l, SVC_Q(*prob, *param, y), zeros, y,
          alpha, 1.0, 1.0, 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->rho /= r;
  si->obj /= (r * r);
  si->upper_bound_p = 1 / r;
  si->upper_bound_n = 1 / r;

  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];
  int i;

  int n = (int)(param->nu * prob->l); // # of alpha's at upper bound

  for (i = 0; i < n; i++)
    alpha[i] = 1;
  if (n < prob->l)
    alpha[n] = param->nu * prob->l - 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;
  s.Solve(l, ONE_CLASS_Q(*prob, *param), zeros, ones,
          alpha, 1.0, 1.0, param->eps, si, param->shrinking);

  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];
  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;

    alpha2[i + l] = 0;
    linear_term[i + l] = param->p + prob->y[i];
    y[i + l] = -1;
  }

  Solver s;
  s.Solve(2 * l, 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 += fabs(alpha[i]);
  }
  //info("nu = %f\n",sum_alpha/(param->C*l));

  delete[] alpha2;
  delete[] linear_term;
  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 = param->C;
  double *alpha2 = new double[2 * l];
  double *linear_term = new double[2 * l];
  schar *y = new schar[2 * l];
  int i;

  double sum = C * param->nu * l / 2;
  for (i = 0; i < l; i++)
  {
    alpha2[i] = alpha2[i + l] = 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;
  s.Solve(2 * l, SVR_Q(*prob, *param), linear_term, y,
          alpha2, C, 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[] 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:
    solve_c_svc(prob, param, alpha, &si, Cp, Cn);
    break;
  case NU_SVC:
    solve_nu_svc(prob, param, alpha, &si);
    break;
  case ONE_CLASS:
    solve_one_class(prob, param, alpha, &si);
    break;
  case EPSILON_SVR:
    solve_epsilon_svr(prob, param, alpha, &si);
    break;
  case NU_SVR:
    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_p)
          ++nBSV;
      }
      else
      {
        if (fabs(alpha[i]) >= si.upper_bound_n)
          ++nBSV;
      }
    }
  }

  //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);

    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->l; 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
    {
      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);
  }
  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);
}

//
// Interface functions
//
svm_model *svm_train(const svm_problem *prob, const svm_parameter *param)
{
  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);
    int i;
    for (i = 0; i < l; i++)
      x[i] = prob->x[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);
        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)
          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);
        ++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(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);
  }
  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);

    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;
    }
    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(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_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);
    int *count = Malloc(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;
          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;
      }
    }

    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 > 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;
}