inline
float
compute_quadratic_cubic_approximate_error(fastuidraw::c_array<const fastuidraw::vec2> p)
{
/* This is derivied fromt the article at
* http://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
*
* The derivation for the error comes from the following:
*
* Let p(t) = (1-t)^3 p0 + 3t(1-t)^2 p1 + 3t^2(1-t) p2 + t^3 p3
*
* Set A = 3p1 - p0, B = 3p2 - p1
* q0 = p0, q1 = (A + B) / 4 and q2 = p2
*
* then, after lots of algebra,
*
* p(t) - q(t) = (A - B) (t^3 - 1.5t^2 + 0.5t)
*
* then the maximum error in each coordinate occurs when
* the polynomial Z(t) = t^3 - 1.5t^2 + 0.5t has maixmal
* absolute value the critical points; thus we need to only
* check the critical points which are when Z'(t) = 0 which
* are t1 = 0.5 * (1 - sqrt(3)) and t2 = 0.5 * (1 + sqrt(3)).
* Z(t1) = sqrt(3) / 36 and Z(t2) = -sqrt(3) / 36. Hence,
* the maximal error of max ||p(t) - q(t) || over 0 <= t < 1
* is ||A - B|| * sqrt(3) / 36
*/
const float error_coeff(0.04811252243f);
fastuidraw::vec2 error_vec(p[3] - 3.0f * p[2] + 3.0f * p[1] - p[0]);
float error(error_coeff * error_vec.magnitude());
return error;
}
void line_trainer_path::train_path(int mode, int *node_lst, real alpha, real *_error_vec, real *_error_p, real *_error_q, double (*func_rand_num)(), unsigned long long &rand_index, int model)
{
int target, label, u, v, vector_size, trans_id;
real f, g;
std::string path_type = std::string();
int step_bg = 0, step_ed = 0, pst_bg = 0, pst_ed = 0;
line_node *node_u = phin->node_u, *node_v = phin->node_v;
vector_size = node_u->vector_size;
Eigen::Map<BLPVector> error_vec(_error_vec, vector_size);
Eigen::Map<BLPVector> error_p(_error_p, vector_size);
Eigen::Map<BLPVector> error_q(_error_q, vector_size);
error_vec.setZero();
error_p.setZero();
error_q.setZero();
sample_path(node_lst, func_rand_num);
if (model == 0)
{
step_bg = path_size - 1; step_ed = path_size;
pst_bg = 0; pst_ed = 1;
}
else if (model == 1)
{
step_bg = 1; step_ed = 2;
pst_bg = 0; pst_ed = path_size - 1;
}
else if (model == 2)
{
step_bg = 1; step_ed = path_size;
pst_bg = 0; pst_ed = path_size - 1;
}
for (int step = step_bg; step != step_ed; step++) for (int pst = pst_bg; pst != pst_ed; pst++)
{
if (pst + step >= path_size) continue;
path_type = path.substr(pst * 2, step * 2 + 1);
trans_id = map_trans[path_type];
if (trans_id == 0)
{
printf("ERROR: trans id error!\n");
exit(1);
}
trans_id--;
u = node_lst[pst];
v = node_lst[pst + step];
error_vec.setZero();
error_p.setZero();
error_q.setZero();
for (int d = 0; d < neg_samples + 1; d++)
{
if (d == 0)
{
target = v;
label = 1;
}
else
{
rand_index = rand_index * (unsigned long long)25214903917 + 11;
target = neg_table[pst + step][(rand_index >> 16) % neg_table_size];
if (target == v) continue;
label = 0;
}
f = 0;
f += node_u->vec.row(u) * node_v->vec.row(target).transpose();
if (mode == 1 || mode == 2 || mode == 3)
{
f += (node_u->vec.row(u)) * (vec_trans[trans_id]->P.transpose());
f += (node_v->vec.row(target)) * (vec_trans[trans_id]->Q.transpose());
f += vec_trans[trans_id]->bias;
}
if (f > MAX_EXP) g = (label - 1) * alpha;
else if (f < -MAX_EXP) g = (label - 0) * alpha;
else g = (label - expTable[(int)((f + MAX_EXP) * (EXP_TABLE_SIZE / MAX_EXP / 2))]) * alpha;
if (mode == 2 || mode == 3)
{
error_p += g * (node_u->vec.row(u));
error_q += g * (node_v->vec.row(target));
}
if (mode == 1 || mode == 3)
{
error_vec += g * ((node_v->vec.row(target)));
error_vec += g * (vec_trans[trans_id]->P);
node_v->vec.row(target) += g * ((node_u->vec.row(u)));
node_v->vec.row(target) += g * (vec_trans[trans_id]->Q);
}
if (mode == 0)
{
error_vec += g * node_v->vec.row(target);
node_v->vec.row(target) += g * node_u->vec.row(u);
}
}
if (mode == 0 || mode == 1 || mode == 3) node_u->vec.row(u) += error_vec;
if (mode == 2 || mode == 3)
{
vec_trans[trans_id]->P += error_p;
vec_trans[trans_id]->Q += error_q;
}
}
new (&error_vec) Eigen::Map<BLPMatrix>(NULL, 0, 0);
new (&error_p) Eigen::Map<BLPMatrix>(NULL, 0, 0);
new (&error_q) Eigen::Map<BLPMatrix>(NULL, 0, 0);
}
void line_trainer_edge::train_sample_randwalk(int mode, real alpha, real restart, real *_error_vec, real *_error_p, real *_error_q, double (*func_rand_num)(), unsigned long long &rand_index)
{
int target, label, u, v, node, index, vector_size, trans_id;
real f, g;
std::string edge_type = std::string();
line_node *node_u = phin->node_u, *node_v = phin->node_v;
std::vector<int> node_lst;
int node_cnt = 0;
vector_size = node_u->vector_size;
Eigen::Map<BLPVector> error_vec(_error_vec, vector_size);
Eigen::Map<BLPVector> error_p(_error_p, vector_size);
Eigen::Map<BLPVector> error_q(_error_q, vector_size);
error_vec.setZero();
error_p.setZero();
error_q.setZero();
edge_type += edge_tp;
trans_id = map_trans[edge_type];
if (trans_id == 0)
{
printf("ERROR: trans id error!\n");
exit(1);
}
trans_id--;
node_lst.clear();
node = (int)(ransampl_draw(smp_u, func_rand_num(), func_rand_num()));
node_lst.push_back(node);
node_cnt = 0;
while(1)
{
if (func_rand_num() < restart) break;
if (u_nb_cnt[node_lst[node_cnt]] == 0) break;
index = (int)(ransampl_draw(smp_u_nb[node_lst[node_cnt]], func_rand_num(), func_rand_num()));
node = u_nb_id[node_lst[node_cnt]][index];
node_lst.push_back(node);
node_cnt++;
}
for (int k = 1; k <= node_cnt; k++)
{
u = node_lst[0];
v = node_lst[k];
error_vec.setZero();
error_p.setZero();
error_q.setZero();
for (int d = 0; d < neg_samples + 1; d++)
{
if (d == 0)
{
target = v;
label = 1;
}
else
{
rand_index = rand_index * (unsigned long long)25214903917 + 11;
target = neg_table[(rand_index >> 16) % neg_table_size];
if (target == v) continue;
label = 0;
}
f = 0;
f += node_u->vec.row(u) * node_v->vec.row(target).transpose();
if (mode == 1 || mode == 2 || mode == 3)
{
f += (node_u->vec.row(u)) * (vec_trans[trans_id]->P.transpose());
f += (node_v->vec.row(target)) * (vec_trans[trans_id]->Q.transpose());
f += vec_trans[trans_id]->bias;
}
if (f > MAX_EXP) g = (label - 1) * alpha;
else if (f < -MAX_EXP) g = (label - 0) * alpha;
else g = (label - expTable[(int)((f + MAX_EXP) * (EXP_TABLE_SIZE / MAX_EXP / 2))]) * alpha;
if (mode == 2 || mode == 3)
{
error_p += g * (node_u->vec.row(u));
error_q += g * (node_v->vec.row(target));
}
if (mode == 1 || mode == 3)
{
error_vec += g * ((node_v->vec.row(target)));
error_vec += g * (vec_trans[trans_id]->P);
node_v->vec.row(target) += g * ((node_u->vec.row(u)));
node_v->vec.row(target) += g * (vec_trans[trans_id]->Q);
}
if (mode == 0)
{
error_vec += g * node_v->vec.row(target);
node_v->vec.row(target) += g * node_u->vec.row(u);
}
}
if (mode == 0 || mode == 1 || mode == 3) node_u->vec.row(u) += error_vec;
if (mode == 2 || mode == 3)
{
vec_trans[trans_id]->P += error_p;
vec_trans[trans_id]->Q += error_q;
}
}
new (&error_vec) Eigen::Map<BLPMatrix>(NULL, 0, 0);
new (&error_p) Eigen::Map<BLPMatrix>(NULL, 0, 0);
new (&error_q) Eigen::Map<BLPMatrix>(NULL, 0, 0);
}
