#include "svm.h"
#include <ctype.h>
#include <float.h>
#include <limits.h>
#include <locale.h>
#include <math.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#pragma warning(disable : 4996)

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 || Gmin_idx == -1)
        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 || Gmin_idx == -1)
        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;
        }
    }

    //
    // Labels are ordered by their first occurrence in the training set.
    // However, for two-class sets with -1/+1 labels and -1 appears first,
    // we swap labels to ensure that internally the binary SVM has positive data corresponding to
    // the +1 instances.
    //
    if (nr_class == 2 && label[0] == -1 && label[1] == 1)
    {
        swap (label[0], label[1]);
        swap (count[0], count[1]);
        for (i = 0; i < l; i++)
        {
            if (data_label[i] == 0)
                data_label[i] = 1;
            else
                data_label[i] = 0;
        }
    }

    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;
    int l = prob->l;
    int *perm = Malloc (int, l);
    int nr_class;
    if (nr_fold > l)
    {
        nr_fold = l;
        fprintf (stderr,
            "WARNING: # folds > # data. Will use # folds = # data instead (i.e., leave-one-out "
            "cross validation)\n");
    }
    fold_start = Malloc (int, nr_fold + 1);
    // 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++;
            }
        if (nr_class == 2)
        {
            prob_estimates[0] = pairwise_prob[0][1];
            prob_estimates[1] = pairwise_prob[1][0];
        }
        else
            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 = setlocale (LC_ALL, NULL);
    if (old_locale)
    {
        old_locale = strdup (old_locale);
    }
    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 %.17g\n", param.gamma);

    if (param.kernel_type == POLY || param.kernel_type == SIGMOID)
        fprintf (fp, "coef0 %.17g\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, " %.17g", 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, " %.17g", 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, " %.17g", 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, "%.17g ", 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;
}

//
// FSCANF helps to handle fscanf failures.
// Its do-while block avoids the ambiguity when
// if (...)
//    FSCANF();
// is used
//
#define FSCANF(_stream, _format, _var)                                                             \
    do                                                                                             \
    {                                                                                              \
        if (fscanf (_stream, _format, _var) != 1)                                                  \
            return false;                                                                          \
    } while (0)
bool read_model_header (FILE *fp, svm_model *model)
{
    svm_parameter &param = model->param;
    // parameters for training only won't be assigned, but arrays are assigned as NULL for safety
    param.nr_weight = 0;
    param.weight_label = NULL;
    param.weight = 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");
                return false;
            }
        }
        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");
                return false;
            }
        }
        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);
            return false;
        }
    }

    return true;
}

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 = setlocale (LC_ALL, NULL);
    if (old_locale)
    {
        old_locale = strdup (old_locale);
    }
    setlocale (LC_ALL, "C");

    // read parameters

    svm_model *model = Malloc (svm_model, 1);
    model->rho = NULL;
    model->probA = NULL;
    model->probB = NULL;
    model->sv_indices = NULL;
    model->label = NULL;
    model->nSV = NULL;

    // read header
    if (!read_model_header (fp, model))
    {
        fprintf (stderr, "ERROR: fscanf failed to read model\n");
        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->sv_indices);
    model_ptr->sv_indices = 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 ((kernel_type == POLY || kernel_type == RBF || kernel_type == SIGMOID) && param->gamma < 0)
        return "gamma < 0";

    if (kernel_type == POLY && 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;
}
