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#ifndef _DA_H_
#define _DA_H_
#include <cmath>
#include <cassert>
// m = trg len
// n = src len
// i = trg index
// j = src index
struct DiagonalAlignment {
static double UnnormalizedProb(const unsigned i, const unsigned j, const unsigned m, const unsigned n, const double alpha) {
#if 0
assert(i > 0);
assert(n > 0);
assert(m >= i);
assert(n >= j);
#endif
return exp(feat(i, j, m, n) * alpha);
}
static double ComputeZ(const unsigned i, const unsigned m, const unsigned n, const double alpha) {
#if 0
assert(i > 0);
assert(n > 0);
assert(m >= i);
#endif
const double split = double(i) * n / m;
const unsigned floor = split;
unsigned ceil = floor + 1;
const double ratio = exp(-alpha / n);
const unsigned num_top = n - floor;
double ezt = 0;
double ezb = 0;
if (num_top)
ezt = UnnormalizedProb(i, ceil, m, n, alpha) * (1.0 - pow(ratio, num_top)) / (1.0 - ratio);
if (floor)
ezb = UnnormalizedProb(i, floor, m, n, alpha) * (1.0 - pow(ratio, floor)) / (1.0 - ratio);
return ezb + ezt;
}
static double ComputeDLogZ(const unsigned i, const unsigned m, const unsigned n, const double alpha) {
const double z = ComputeZ(i, n, m, alpha);
const double split = double(i) * n / m;
const unsigned floor = split;
const unsigned ceil = floor + 1;
const double ratio = exp(-alpha / n);
const double d = -1.0 / n;
const unsigned num_top = n - floor;
double pct = 0;
double pcb = 0;
if (num_top) {
pct = arithmetico_geometric_series(feat(i, ceil, m, n), UnnormalizedProb(i, ceil, m, n, alpha), ratio, d, num_top);
//cerr << "PCT = " << pct << endl;
}
if (floor) {
pcb = arithmetico_geometric_series(feat(i, floor, m, n), UnnormalizedProb(i, floor, m, n, alpha), ratio, d, floor);
//cerr << "PCB = " << pcb << endl;
}
return (pct + pcb) / z;
}
private:
inline static double feat(const unsigned i, const unsigned j, const unsigned m, const unsigned n) {
return -fabs(double(j) / n - double(i) / m);
}
inline static double arithmetico_geometric_series(const double a_1, const double g_1, const double r, const double d, const unsigned n) {
const double g_np1 = g_1 * pow(r, n);
const double a_n = d * (n - 1) + a_1;
const double x_1 = a_1 * g_1;
const double g_2 = g_1 * r;
const double rm1 = r - 1;
return (a_n * g_np1 - x_1) / rm1 - d*(g_np1 - g_2) / (rm1 * rm1);
}
};
#endif
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