double 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_lower_bound(i))
ub1 = Math.min(ub1,G[i]);
else if(is_upper_bound(i))
lb1 = Math.max(lb1,G[i]);
else
{
++nr_free1;
sum_free1 += G[i];
}
}
else
{
if(is_lower_bound(i))
ub2 = Math.min(ub2,G[i]);
else if(is_upper_bound(i))
lb2 = Math.max(lb2,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;
}
void Solve(int l, Kernel Q, double[] b_, byte[] y_,
double[] alpha_, double Cp, double Cn, double eps, SolutionInfo si, int shrinking)
{
this.l = l;
this.Q = Q;
b = (double[])b_.clone();
y = (byte[])y_.clone();
alpha = (double[])alpha_.clone();
this.Cp = Cp;
this.Cn = Cn;
this.eps = eps;
this.unshrinked = false;
// initialize alpha_status
{
alpha_status = new byte[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] = b[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 counter = Math.min(l,1000)+1;
int[] working_set = new int[2];
while(true)
{
// show progress and do shrinking
if(--counter == 0)
{
counter = Math.min(l,1000);
if(shrinking!=0) do_shrinking();
System.err.print(".");
}
if(select_working_set(working_set)!=0)
{
// reconstruct the whole gradient
reconstruct_gradient();
// reset active set size and check
active_size = l;
System.err.print("*");
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 delta = (-G[i]-G[j])/(Q_i[i]+Q_j[j]+2*Q_i[j]);
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 delta = (G[i]-G[j])/(Q_i[i]+Q_j[j]-2*Q_i[j]);
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
{
boolean ui = is_upper_bound(i);
boolean 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];
}
}
}
// 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] + b[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;
System.out.print("\noptimization finished, #iter = "+iter+"\n");
}