public void TrainOne(double[] w)
{
// Parameters for updating the iterates.
double eta0 = 1e-4, eta1 = 0.25, eta2 = 0.75;
// Parameters for updating the trust region size delta.
double sigma1 = 0.25, sigma2 = 0.5, sigma3 = 4;
int n = fun_obj.get_nr_variable();
int i, cg_iter;
double delta = 0, sMnorm, one = 1.0;
double alpha, f, fnew, prered, actred, gs;
bool search;
int iter = 1, inc = 1;
double[] s = new double[n];
double[] r = new double[n];
double[] g = new double[n];
const double alpha_pcg = 0.01;
double[] M = new double[n];
// calculate gradient norm at w=0 for stopping condition.
double[] w0 = new double[n];
Array.Clear(w0, 0, n);
fun_obj.fun(w0);
fun_obj.grad(w0, g);
double gnorm0 = Blas.dnrm2_(n, g, inc);
f = fun_obj.fun(w);
fun_obj.grad(w, g);
double gnorm = Blas.dnrm2_(n, g, inc);
search = !(gnorm <= eps * gnorm0);
fun_obj.get_diag_preconditioner(M);
for (i = 0; i < n; i++)
{
M[i] = (1 - alpha_pcg) + alpha_pcg * M[i];
}
delta = Math.Sqrt(uTMv(n, g, M, g));
double[] w_new = new double[n];
Boolean reach_boundary = true;
bool delta_adjusted = false;
while (iter <= max_iter && search)
{
cg_iter = trpcg(delta, ref g, ref M, ref s, ref r, reach_boundary);
for (int ti = 0; ti < n; ti++)
{
w_new[ti] = w[ti];
}
Blas.daxpy_(n, one, s, inc, ref w_new, inc);
gs = Blas.ddot_(n, g, inc, s, inc);
prered = -0.5 * (gs - Blas.ddot_(n, s, inc, r, inc));
fnew = fun_obj.fun(w_new);
// Compute the actual reduction.
actred = f - fnew;
// On the first iteration, adjust the initial step bound.
sMnorm = Math.Sqrt(uTMv(n, s, M, s));
if (iter == 1 && !delta_adjusted)
{
delta = Math.Min(delta, sMnorm);
delta_adjusted = true;
}
// Compute prediction alpha*sMnorm of the step.
if (fnew - f - gs <= 0)
{
alpha = sigma3;
}
else
{
alpha = Math.Max(sigma1, -0.5 * (gs / (fnew - f - gs)));
}
// Update the trust region bound according to the ratio of actual to predicted reduction.
if (actred < eta0 * prered)
{
delta = Math.Min(alpha * sMnorm, sigma2 * delta);
}
else if (actred < eta1 * prered)
{
delta = Math.Max(sigma1 * delta, Math.Min(alpha * sMnorm, sigma2 * delta));
}
else if (actred < eta2 * prered)
{
delta = Math.Max(sigma1 * delta, Math.Min(alpha * sMnorm, sigma3 * delta));
}
else
{
if (reach_boundary)
{
delta = sigma3 * delta;
}
else
{
delta = Math.Max(delta, Math.Min(alpha * sMnorm, sigma3 * delta));
}
}
_logger.LogTrace("iter {0} act {1} pre {2} delta {3} f {4} |g| {5} CG {6}", iter, actred, prered, delta, f, gnorm, cg_iter);
if (actred > eta0 * prered)
{
iter++;
for (int ti = 0; ti < n; ti++)
{
w[ti] = w_new[ti];
}
f = fnew;
fun_obj.grad(w, g);
fun_obj.get_diag_preconditioner(M);
for (i = 0; i < n; i++)
{
M[i] = (1 - alpha_pcg) + alpha_pcg * M[i];
}
gnorm = Blas.dnrm2_(n, g, inc);
if (gnorm <= eps * gnorm0)
{
break;
}
}
if (f < MIN_VALUE)
{
_logger.LogTrace("WARNING: f < {0.00e+00}", MIN_VALUE);
break;
}
if (prered <= 0)
{
_logger.LogTrace("WARNING: prered <= 0");
break;
}
if (Math.Abs(actred) <= SML_VALUE * Math.Abs(f) &&
Math.Abs(prered) <= SML_VALUE * Math.Abs(f))
{
_logger.LogTrace("WARNING: actred and prered too small");
break;
}
}
}
private int trpcg(double delta, ref double[] g, ref double [] M, ref double[] s, ref double[] r, Boolean reach_boundary)
{
int i, inc = 1;
int n = fun_obj.get_nr_variable();
double one = 1;
double[] d = new double[n];
double[] Hd = new double[n];
double zTr, znewTrnew, alpha, beta, cgtol;
double[] z = new double[n];
reach_boundary = false;
for (i = 0; i < n; i++)
{
s[i] = 0;
r[i] = -g[i];
z[i] = r[i] / M[i];
d[i] = z[i];
}
zTr = Blas.ddot_(n, z, inc, r, inc);
cgtol = eps_cg * Math.Sqrt(zTr);
int cg_iter = 0;
while (true)
{
if (Math.Sqrt(zTr) <= cgtol)
{
break;
}
cg_iter++;
fun_obj.Hv(d, Hd);
alpha = zTr / Blas.ddot_(n, d, inc, Hd, inc);
Blas.daxpy_(n, alpha, d, inc, ref s, inc);
double sMnorm = Math.Sqrt(uTMv(n, s, M, s));
if (sMnorm > delta)
{
_logger.LogTrace("cg reaches trust region boundary");
reach_boundary = true;
alpha = -alpha;
Blas.daxpy_(n, alpha, d, inc, ref s, inc);
double sTMd = uTMv(n, s, M, d);
double sTMs = uTMv(n, s, M, s);
double dTMd = uTMv(n, d, M, d);
double dsq = delta * delta;
double rad = Math.Sqrt(sTMd * sTMd + dTMd * (dsq - sTMs));
if (sTMd >= 0)
{
alpha = (dsq - sTMs) / (sTMd + rad);
}
else
{
alpha = (rad - sTMd) / dTMd;
}
Blas.daxpy_(n, alpha, d, inc, ref s, inc);
alpha = -alpha;
Blas.daxpy_(n, alpha, Hd, inc, ref r, inc);
break;
}
alpha = -alpha;
Blas.daxpy_(n, alpha, Hd, inc, ref r, inc);
for (i = 0; i < n; i++)
{
z[i] = r[i] / M[i];
}
znewTrnew = Blas.ddot_(n, z, inc, r, inc);
beta = znewTrnew / zTr;
Blas.dscal_(n, beta, ref d, inc);
Blas.daxpy_(n, one, z, inc, ref d, inc);
zTr = znewTrnew;
}
return(cg_iter);
}