libsvm.cpp

#include "libsvm.h"

namespace LIBSVM {

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 = std::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;
 std::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]);
 std::swap(head[i].data,head[j].data);
 std::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) std::swap(i,j);
 for(head_t *h = lru_head.next; h!=&lru_head; h=h->next)
 {
 if(h->len > i)
 {
 if(h->len > j)
 std::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...
 {
 std::swap(x[i],x[j]);
 if(x_square) std::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);
 std::swap(y[i],y[j]);
 std::swap(G[i],G[j]);
 std::swap(alpha_status[i],alpha_status[j]);
 std::swap(alpha[i],alpha[j]);
 std::swap(p[i],p[j]);
 std::swap(active_set[i],active_set[j]);
 std::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 = std::max(10000000, l>INT_MAX/100 ? INT_MAX : 100*l);
 int counter = std::min(l,1000)+1;
 
 while(iter < max_iter)
 {
 // show progress and do shrinking

 if(--counter == 0)
 {
 counter = std::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("*");
 }
 info("\nWARNING: reaching max number of iterations");
 }

 // 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 = std::min(ub,yG);
 else
 lb = std::max(lb,yG);
 }
 else if(is_lower_bound(i))
 {
 if(y[i]==+1)
 ub = std::min(ub,yG);
 else
 lb = std::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(std::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 && std::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 = std::max(lb1,G[i]);
 else if(is_lower_bound(i))
 ub1 = std::min(ub1,G[i]);
 else
 {
 ++nr_free1;
 sum_free1 += G[i];
 }
 }
 else
 {
 if(is_upper_bound(i))
 lb2 = std::max(lb2,G[i]);
 else if(is_lower_bound(i))
 ub2 = std::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);
 std::swap(y[i],y[j]);
 std::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);
 std::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
 {
 std::swap(sign[i],sign[j]);
 std::swap(index[i],index[j]);
 std::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] = std::min(1.0,sum_pos);
 sum_pos -= alpha[i];
 }
 else
 {
 alpha[i] = std::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] = std::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=std::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);
 std::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);
 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];
 ++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);
 p = 0;
 for(i=0;i<l;i++)
 if(nonzero[i]) model->SV[p++] = x[i];

 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);
 std::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);
 std::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];
}

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]=std::min(std::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];
 for(unsigned int i=0; i<81; i++) cmd[i] = '\0';
 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 > std::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;
}
 
} //End of namespace LIBSVM