public virtual void reconstruct_gradient()
{
// reconstruct inactive elements of G from G_bar and free variables
if (active_size == l)
{
return;
}
int i, j;
int nr_free = 0;
for (j = active_size; j < l; j++)
{
G[j] = G_bar[j] + p[j];
}
for (j = 0; j < active_size; j++)
{
if (is_free(j))
{
nr_free++;
}
}
if (2 * nr_free < active_size)
{
SupportVectorMachine.info("\nWARNING: using -h 0 may be faster\n");
}
if (nr_free * l > 2 * active_size * (l - active_size))
{
for (i = active_size; i < l; i++)
{
float[] Q_i = Q.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))
{
float[] 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];
}
}
}
}
}
public virtual void Solve(int l, QMatrix Q, double[] p_, sbyte[] y_,
double[] alpha_, double Cp, double Cn, double eps, SolutionInfo si, int shrinking)
{
this.l = l;
this.Q = Q;
QD = Q.get_QD();
p = (double[])p_.Clone();
y = (sbyte[])y_.Clone();
alpha = (double[])alpha_.Clone();
this.Cp = Cp;
this.Cn = Cn;
this.eps = eps;
this.unshrink = false;
// initialize alpha_status
{
alpha_status = new sbyte[l];
for (int i = 0; i < l; i++)
{
update_alpha_status(i);
}
}
// initialize active set (for shrinking)
{
active_set = new int[l];
for (int i = 0; i < l; i++)
{
active_set[i] = i;
}
active_size = l;
}
// initialize gradient
{
G = new double[l];
G_bar = new double[l];
int i;
for (i = 0; i < l; i++)
{
G[i] = p[i];
G_bar[i] = 0;
}
for (i = 0; i < l; i++)
{
if (!is_lower_bound(i))
{
float[] Q_i = Q.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 = System.Math.Max(10000000, l > int.MaxValue / 100 ? int.MaxValue : 100 * l);
int counter = System.Math.Min(l, 1000) + 1;
int[] working_set = new int[2];
while (iter < max_iter)
{
// show progress and do shrinking
if (--counter == 0)
{
counter = System.Math.Min(l, 1000);
if (shrinking != 0)
{
do_shrinking();
}
SupportVectorMachine.info(".");
}
if (select_working_set(working_set) != 0)
{
// reconstruct the whole gradient
reconstruct_gradient();
// reset active set size and check
active_size = l;
SupportVectorMachine.info("*");
if (select_working_set(working_set) != 0)
{
break;
}
else
{
counter = 1; // do shrinking next iteration
}
}
int i = working_set[0];
int j = working_set[1];
++iter;
// update alpha[i] and alpha[j], handle bounds carefully
float[] Q_i = Q.get_Q(i, active_size);
float[] 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 = 1e-12;
}
double delta = (-G[i] - G[j]) / quad_coef;
double diff = alpha[i] - alpha[j];
alpha[i] += delta;
alpha[j] += delta;
if (diff > 0)
{
if (alpha[j] < 0)
{
alpha[j] = 0;
alpha[i] = diff;
}
}
else
{
if (alpha[i] < 0)
{
alpha[i] = 0;
alpha[j] = -diff;
}
}
if (diff > C_i - C_j)
{
if (alpha[i] > C_i)
{
alpha[i] = C_i;
alpha[j] = C_i - diff;
}
}
else
{
if (alpha[j] > C_j)
{
alpha[j] = C_j;
alpha[i] = C_j + diff;
}
}
}
else
{
double quad_coef = QD[i] + QD[j] - 2 * Q_i[j];
if (quad_coef <= 0)
{
quad_coef = 1e-12;
}
double delta = (G[i] - G[j]) / quad_coef;
double sum = alpha[i] + alpha[j];
alpha[i] -= delta;
alpha[j] += delta;
if (sum > C_i)
{
if (alpha[i] > C_i)
{
alpha[i] = C_i;
alpha[j] = sum - C_i;
}
}
else
{
if (alpha[j] < 0)
{
alpha[j] = 0;
alpha[i] = sum;
}
}
if (sum > C_j)
{
if (alpha[j] > C_j)
{
alpha[j] = C_j;
alpha[i] = sum - C_j;
}
}
else
{
if (alpha[i] < 0)
{
alpha[i] = 0;
alpha[j] = sum;
}
}
}
// update G
double delta_alpha_i = alpha[i] - old_alpha_i;
double delta_alpha_j = alpha[j] - old_alpha_j;
for (int k = 0; k < active_size; k++)
{
G[k] += Q_i[k] * delta_alpha_i + Q_j[k] * delta_alpha_j;
}
// update alpha_status and G_bar
{
bool ui = is_upper_bound(i);
bool uj = is_upper_bound(j);
update_alpha_status(i);
update_alpha_status(j);
int k;
if (ui != is_upper_bound(i))
{
Q_i = Q.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;
SupportVectorMachine.info("*");
}
SupportVectorMachine.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];
}
}
si.upper_bound_p = Cp;
si.upper_bound_n = Cn;
SupportVectorMachine.info("\noptimization finished, #iter = " + iter + "\n");
}