/** 2D assignment by belief propagation.
*/
void HardMatching::solve (size_t num_iters)
{
m_message_12.resize(size_arc());
m_message_21.resize(size_arc());
m_post_ass.resize(size_arc());
m_optima.resize(max(size_1(), size_2()));
m_1_non.resize(size_1());
m_2_non.resize(size_2());
m_1_ass.resize(size_arc());
m_2_ass.resize(size_arc());
LOG1("initialize");
for (size_t ij = 0; ij < size_arc(); ++ij) {
m_message_12[ij] = 0;
m_message_21[ij] = 0;
}
m_post_ass = m_prior_ass;
LOG1("propagate belief");
for (size_t iter = 0; iter < num_iters; ++iter) {
LOG1(" propagation step " << iter);
propagate_12();
propagate_21();
}
LOG1("finalize to ensure normalization");
normalize();
}
void SoftMatching::validate_solution ()
{
LOG1("validating solution");
m_total.resize(max(size_1(), size_2()));
LOG1("checking normalization over arcs (i,-)");
for (size_t i = 0; i < size_1(); ++i) {
ASSERT_LE(0, m_post_1_non[i]);
ASSERT_LE(m_post_1_non[i], 1);
m_total[i] = m_post_1_non[i];
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_total[arc.i] += m_post_1_ass[ij];
}
for (size_t i = 0; i < size_1(); ++i) {
ASSERT_LE(fabs(m_total[i] - 1), TOL);
}
LOG1("checking normalization over arcs (-,j)");
for (size_t j = 0; j < size_2(); ++j) {
ASSERT_LE(0, m_post_2_non[j]);
ASSERT_LE(m_post_2_non[j], 1);
m_total[j] = m_post_2_non[j];
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_total[arc.j] += m_post_1_ass[ij];
}
for (size_t j = 0; j < size_2(); ++j) {
ASSERT_LE(fabs(m_total[j] - 1), TOL);
}
}
void HardMatching::validate_solution ()
{
LOG1("validating solution");
std::vector<size_t> total(max(size_1(), size_2()));
LOG1("checking normalization over arcs (i,-)");
for (size_t i = 0; i < size_1(); ++i) {
total[i] = post_1_non(i) ? 1 : 0;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
total[arc.i] += post_ass(ij) ? 1 : 0;
}
for (size_t i = 0; i < size_1(); ++i) {
ASSERT_EQ(total[i], 1);
}
LOG1("checking normalization over arcs (-,j)");
for (size_t j = 0; j < size_2(); ++j) {
total[j] = post_2_non(j) ? 1 : 0;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
total[arc.j] += post_ass(ij) ? 1 : 0;
}
for (size_t j = 0; j < size_2(); ++j) {
ASSERT_EQ(total[j], 1);
}
}
/** 2D assignment by belief propagation.
naming conventions in this note:
p = prior
P = post
m = message
types:
p2,P1 : 1
p2,P2 : 2
p12,m12,m21 : 12
^1 : 12 -> 1
^2 : 12 -> 2
_12 : 1 -> 12
_12 : 2 -> 12
algorithm:
initialize:
P1(0) = p1 p12^1
P2(0) = p2 p12^2
m21(0) = 1
iteratively propagate belief:
for t in [0,...,T-1]:
m12(t+1) = P1(t)_12 / (p12 m21(t))
P2(t+1) = P2(t) m12(t+1)^2
m21(t+1) = P2(t)_12 / (p12 m12(t))
P1(t+1) = P1(t) m21(t+1)^1
finalize:
P[i,j] = min(P1(T)[i,j], P2(T)[i,j])
P[i,-] = 1 - sum j. P1(T)[i,j]
P[-,j] = 1 - sum i. P2(T)[i,j]
representation:
P1[i,-] = post_1_non[i] / total
P1[i,j] = post_1_ass[ij] / total
P2[-,j] = post_2_non[j] / total
P2[i,j] = post_2_ass[ij] / total
operations:
projection:
P1_12[ij] = post_1_ass[ij] / (total - post_1_ass[ij])
lifting:
m^1[ij] = m[ij] * (size_1[i] - 1), whence size_1[i] - 1 =: scale1[i]
fusion:
(pointwise multiplication)
*/
void SoftMatching::solve (size_t num_iters)
{
m_post_1_non.resize(size_1());
m_post_2_non.resize(size_2());
m_post_1_ass.resize(size_arc());
m_post_2_ass.resize(size_arc());
m_scale_1.resize(size_1());
m_scale_2.resize(size_2());
m_total.resize(max(size_1(), size_2()));
m_message.resize(size_arc());
LOG1("initialize");
for (size_t i = 0; i < size_1(); ++i) {
m_scale_1[i] = 0;
}
for (size_t j = 0; j < size_2(); ++j) {
m_scale_2[j] = 0;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_scale_1[arc.i] += 1;
m_scale_2[arc.j] += 1;
}
for (size_t i = 0; i < size_1(); ++i) {
m_post_1_non[i] = m_prior_1_non[i] * m_scale_1[i];
}
for (size_t j = 0; j < size_2(); ++j) {
m_post_2_non[j] = m_prior_2_non[j] * m_scale_2[j];
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_post_1_ass[ij] = m_prior_1_ass[ij] * m_scale_1[arc.i];
m_post_2_ass[ij] = m_prior_2_ass[ij] * m_scale_2[arc.j];
m_message[ij] = 1 / m_scale_2[arc.j]; // uniform
}
LOG1("propagate belief");
for (size_t iter = 0; iter < num_iters; ++iter) {
LOG1(" propagation step " << iter);
propagate_12();
propagate_21();
}
LOG1("finalize to ensure normalization");
normalize();
}
void HardMatching::normalize ()
{
optimize_1();
for (size_t i = 0; i < size_1(); ++i) {
m_1_non[i] = true;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_1_ass[ij] = (m_post_ass[ij] == m_optima[arc.i]);
}
optimize_2();
for (size_t j = 0; j < size_2(); ++j) {
m_2_non[j] = true;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_2_ass[ij] = (m_post_ass[ij] == m_optima[arc.j]);
if (post_1_ass(ij) and post_2_ass(ij)) {
m_1_ass[ij] = true;
m_1_non[arc.i] = false;
m_2_non[arc.j] = false;
} else {
m_1_ass[ij] = false;
}
}
}
void HardMatching::optimize_2 ()
{
for (size_t j = 0; j < size_2(); ++j) {
m_optima[j].init(m_prior_2_non[j]);
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_optima[arc.j].update(m_post_ass[ij]);
}
}
void HardMatching::validate_problem () const
{
LOG1("validating matching");
for (size_t i = 0; i < size_1(); ++i) ASSERTW_COST(m_prior_1_non[i]);
for (size_t j = 0; j < size_2(); ++j) ASSERTW_COST(m_prior_2_non[j]);
for (size_t ij = 0; ij < size_arc(); ++ij) ASSERTW_COST(m_prior_ass[ij]);
std::set<Arc> unique_arcs;
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
ASSERT_LT(arc.i, size_1());
ASSERT_LT(arc.j, size_2());
ASSERT(unique_arcs.find(arc) == unique_arcs.end(),
"arc " << arc << " appears twice");
unique_arcs.insert(arc);
}
}
void SoftMatching::total_2 ()
{
for (size_t j = 0; j < size_2(); ++j) {
m_total[j] = m_post_2_non[j];
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_total[arc.j] += m_post_2_ass[ij];
}
}
void SoftMatching::print_post () const
{
LOG("matching.post = ");
for (size_t i = 0; i < size_1(); ++i) {
LOG(" (" << i << ",-) \t" << post_1_non(i));
}
for (size_t j = 0; j < size_2(); ++j) {
LOG(" (-," << j << ") \t" << post_2_non(j));
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
LOG(" " << arc(ij) << "\t" << post_ass(ij));
}
}
void HardMatching::print_prior () const
{
LOG("matching.prior = ");
for (size_t i = 0; i < size_1(); ++i) {
LOG(" (" << i << ",-) \t" << prior_1_non(i));
}
for (size_t j = 0; j < size_2(); ++j) {
LOG(" (-," << j << ") \t" << prior_2_non(j));
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
LOG(" " << arc(ij) << "\t" << prior_ass(ij));
}
}
void SoftMatching::normalize ()
{
total_1();
for (size_t i = 0; i < size_1(); ++i) {
m_total[i] = 1 / m_total[i];
m_post_1_non[i] = 1;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_post_1_ass[ij] *= m_total[arc.i];
}
total_2();
for (size_t j = 0; j < size_2(); ++j) {
m_total[j] = 1 / m_total[j];
m_post_2_non[j] = 1;
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
Arc arc = m_arcs[ij];
m_post_2_ass[ij] *= m_total[arc.j];
float prob = min(m_post_1_ass[ij], m_post_2_ass[ij]);
m_post_1_ass[ij] = prob;
m_post_1_non[arc.i] -= prob;
m_post_2_non[arc.j] -= prob;
}
for (size_t i = 0; i < size_1(); ++i) {
clamp_nonneg(m_post_1_non[i]);
}
for (size_t j = 0; j < size_2(); ++j) {
clamp_nonneg(m_post_2_non[j]);
}
}
char *set_born(char *arg, int *beg, int *end)
{
char **tab;
char *ret;
int len;
int tmp;
ret = NULL;
*beg = 0;
len = len_tab(tab = my_str_to_wordtab(arg, ':'));
if (len > 3)
return (NULL);
ret = (len == 1 ? size_1(tab, beg, end) \
: ((len == 2) ? size_2(tab, beg, end) \
: size_3(tab, beg, end)));
return (ret);
}
void HardMatching::print_post () const
{
LOG("matching.post = ");
for (size_t ij = 0; ij < size_arc(); ++ij) {
LOG(" " << arc(ij) << "\t" << m_post_ass[ij]);
}
LOG("matching.solution = ");
for (size_t i = 0; i < size_1(); ++i) {
if (post_1_non(i)) LOG(" (" << i << ",-)");
}
for (size_t j = 0; j < size_2(); ++j) {
if (post_2_non(j)) LOG(" (-," << j << ")");
}
for (size_t ij = 0; ij < size_arc(); ++ij) {
if (post_ass(ij)) LOG(" " << arc(ij));
}
}