A little code cleanup. Now the forward and backback algorithms give

nearly identical P(x), which means both are close to the correct
forms. However, I have only tested on toy examples. Minor errors in
the implementation may not be obvious.

diff --git a/kaln.c b/kaln.c
index 63e2182ce5885d0be0cdc6a084597398eeabcc1a..f5c9d89c2bb7f2c549ec0114f4eb8670e1cc7ccb 100644 (file)
--- a/kaln.c
+++ b/kaln.c
@@ -27,6 +27,7 @@
 #include <stdio.h>
 #include <string.h>
 #include <stdint.h>
+#include <math.h>
 #include "kaln.h"
 
 #define FROM_M 0
@@ -396,14 +397,9 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float
        }
        // initialize m
        sM = sI = 1. / (2 * l_query + 1);
-       m[0*3+0] = (1 - c->d - c->d) * (1 - sM);
-       m[0*3+1] = m[0*3+2] = c->d * (1 - sM);
-       m[1*3+0] = (1 - c->e) * (1 - sI);
-       m[1*3+1] = c->e * (1 - sI);
-       m[1*3+2] = 0.;
-       m[2*3+0] = 1 - c->e;
-       m[2*3+1] = 0.;
-       m[2*3+2] = c->e;
+       m[0*3+0] = (1 - c->d - c->d) * (1 - sM); m[0*3+1] = m[0*3+2] = c->d * (1 - sM);
+       m[1*3+0] = (1 - c->e) * (1 - sI); m[1*3+1] = c->e * (1 - sI); m[1*3+2] = 0.;
+       m[2*3+0] = 1 - c->e; m[2*3+1] = 0.; m[2*3+2] = c->e;
        /*** forward ***/
        // f[0]
        set_u(k, bw, 0, 0);
@@ -418,14 +414,10 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float
                        int u, v11, v01, v10;
                        double e;
                        e = (ref[k] == 4 || query[i] == 4)? 1. : ref[k] == query[i]? 1. - qual[i] : qual[i]; // FIXME: can be better
-                       set_u(u, bw, i, k);
-                       set_u(v11, bw, i-1, k-1);
-                       set_u(v10, bw, i-1, k);
-                       set_u(v01, bw, i, k-1);
+                       set_u(u, bw, i, k); set_u(v11, bw, i-1, k-1); set_u(v10, bw, i-1, k); set_u(v01, bw, i, k-1);
                        fi[u+0] = e * (m[0] * fi1[v11+0] + m[3] * fi1[v11+1] + m[6] * fi1[v11+2]);
                        fi[u+1] = .25 * (m[1] * fi1[v10+0] + m[4] * fi1[v10+1]);
                        fi[u+2] = m[2] * fi[v01+0] + m[8] * fi[v01+2];
-                       fprintf(stderr, "{%d,%d}@%d %.10lg,%.10lg,%.10lg\n", i, k, u, fi[u], fi[u+1], fi[u+2]);
                }
        }
        // sink
@@ -444,9 +436,8 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float
                set_u(u, bw, l_query, k);
                if (u < 3 || u >= bw2*3+3) continue;
                bi[u+0] = sM; bi[u+1] = sI;
-               fprintf(stderr, "[%d,%d]@%d %.10lg,%.10lg,%.10lg\n", l_query, k, u, bi[u], bi[u+1], bi[u+2]);
        }
-       // b[l_query..1]; core loop
+       // b[l_query-1..1]; core loop
        for (i = l_query - 1; i > 0; --i) {
                int beg = 0, end = l_ref, x;
                double *bi = b[i], *bi1 = b[i+1];
@@ -456,36 +447,25 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float
                        int u, v11, v01, v10;
                        double e;
                        e = k >= l_ref? 0 : (ref[k+1] == 4 || query[i+1] == 4)? 1. : ref[k+1] == query[i+1]? 1. - qual[i+1] : qual[i+1];
-                       set_u(u, bw, i, k);
-                       set_u(v11, bw, i+1, k+1);
-                       set_u(v10, bw, i+1, k);
-                       set_u(v01, bw, i, k+1);
+                       set_u(u, bw, i, k); set_u(v11, bw, i+1, k+1); set_u(v10, bw, i+1, k); set_u(v01, bw, i, k+1);
                        bi[u+0] = e * m[0] * bi1[v11+0] + .25 * m[1] * bi1[v10+1] + m[2] * bi[v01+2];
                        bi[u+1] = e * m[3] * bi1[v11+0] + .25 * m[4] * bi1[v10+1];
                        bi[u+2] = e * m[6] * bi1[v11+0] + m[8] * bi[v01+2];
-                       fprintf(stderr, "[%d,%d]@%d %.10lg,%.10lg,%.10lg\n", i, k, u, bi[u], bi[u+1], bi[u+2]);
                }
        }
-       {
-               int beg = 0, end = l_ref, x;
+       { // the "zero" coordinate (i==k==0)
                double *bi = b[0], *bi1 = b[1];
-               x = i - bw; beg = beg > x? beg : x;
-               x = i + bw; end = end < x? end : x;
-               for (k = end; k >= beg; --k) {
-                       int u, v11, v01, v10;
-                       double e;
-                       e = k >= l_ref? 0 : (ref[k+1] == 4 || query[1] == 4)? 1. : ref[k+1] == query[1]? 1. - qual[1] : qual[1];
-                       set_u(u, bw, 0, k);
-                       set_u(v11, bw, 1, k+1);
-                       set_u(v10, bw, 1, k);
-                       set_u(v01, bw, 0, k+1);
-                       bi[u+0] = e * m[0] * bi1[v11+0] + .25 * m[1] * bi1[v10+1] + m[2] * bi[v01+2];
-                       fprintf(stderr, "[%d,%d]@%d %.10lg,%.10lg,%.10lg\n", i, k, u, bi[u], bi[u+1], bi[u+2]);
-               }
+               int u, v11, v01, v10;
+               double e = (ref[1] == 4 || query[1] == 4)? 1. : ref[1] == query[1]? 1. - qual[1] : qual[1];
+               set_u(u, bw, 0, 0); set_u(v11, bw, 1, 1); set_u(v10, bw, 1, 0); set_u(v01, bw, 0, 1);
+               bi[u+0] = e * m[0] * bi1[v11+0] + .25 * m[1] * bi1[v10+1] + m[2] * bi[v01+2];
        }
        set_u(k, bw, 0, 0);
        pb = b[0][k];
-       fprintf(stderr, "(%.10lg,%.10lg):(%.10lg,%.10lg)\n", pf, pb, pb-pf, pb/pf-1);
+       { // pf should equal pb as they are both the likelihood of data but calculated in different ways
+               double z = fabs(pb/pf - 1.);
+               if (z > 1e-7) fprintf(stderr, "[%s] %lg!=%lg\n", __func__, pf, pb);
+       }
        /*** MAP ***/
        return 0;
 }