-
Notifications
You must be signed in to change notification settings - Fork 447
/
probaln.c
468 lines (428 loc) · 16.9 KB
/
probaln.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
/* The MIT License
Copyright (C) 2003-2006, 2008-2010 by Heng Li <[email protected]>
Copyright (C) 2016-2017, 2020, 2023 Genome Research Ltd.
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#define HTS_BUILDING_LIBRARY // Enables HTSLIB_EXPORT, see htslib/hts_defs.h
#include <config.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <stdint.h>
#include <limits.h>
#include <math.h>
#include <errno.h>
#include "htslib/hts.h"
/*****************************************
* Probabilistic banded glocal alignment *
*****************************************/
#define EI .25
#define EM .33333333333
static float g_qual2prob[256];
#define set_u(u, b, i, k) { int x=(i)-(b); x=x>0?x:0; (u)=((k)-x+1)*3; }
/*
The topology of the profile HMM:
/\ /\ /\ /\
I[1] I[k-1] I[k] I[L]
^ \ \ ^ \ ^ \ \ ^
| \ \ | \ | \ \ |
M[0] M[1] -> ... -> M[k-1] -> M[k] -> ... -> M[L] M[L+1]
\ \/ \/ \/ /
\ /\ /\ /\ /
-> D[k-1] -> D[k] ->
M[0] points to every {M,I}[k] and every {M,I}[k] points to M[L+1].
On input, ref is the reference sequence and query is the query
sequence. Both are sequences of 0/1/2/3/4 where 4 stands for an
ambiguous residue. iqual is the base quality. c sets the gap open
probability, gap extension probability and band width.
On output, state and q are arrays of length l_query. The higher 30
bits give the reference position the query base is matched to and the
lower two bits can be 0 (an alignment match) or 1 (an
insertion). q[i] gives the phred scaled posterior probability of
state[i] being wrong.
Returns phred-scaled likelihood score, or INT_MIN on failure.
*/
int probaln_glocal(const uint8_t *ref, int l_ref, const uint8_t *query,
int l_query, const uint8_t *iqual, const probaln_par_t *c,
int *state, uint8_t *q)
{
double *f = NULL, *b = NULL, *s = NULL, m[9], sI, sM, bI, bM;
float *qual = NULL;
int bw, bw2, i, k, is_backward = 1, Pr;
if ( l_ref<0 || l_query<0 || l_query >= INT_MAX - 2) {
errno = EINVAL;
return INT_MIN;
}
if (l_ref==0 || l_query==0)
return 0; // Is this actually invalid??
/*** initialization ***/
is_backward = state && q? 1 : 0;
bw = l_ref > l_query? l_ref : l_query;
if (bw > c->bw) bw = c->bw;
if (bw < abs(l_ref - l_query)) bw = abs(l_ref - l_query);
bw2 = bw * 2 + 1;
size_t i_dim = bw2 < l_ref ? (size_t) bw2*3+6 : (size_t) l_ref*3+6;
// allocate the forward and backward matrices f[][] and b[][]
// and the scaling array s[]
// Ideally these callocs would be mallocs + initialisation of
// the few bits needed.
if (SIZE_MAX / (l_query+1) / i_dim < sizeof(double)) {
errno = ENOMEM; // Allocation would fail
return INT_MIN;
}
f = calloc((l_query+1)*i_dim, sizeof(double));
if (!f) goto fail;
if (is_backward) {
b = calloc((l_query+1)*i_dim, sizeof(double));
if (!b) goto fail;
}
// s[] is the scaling factor to avoid underflow
s = malloc((l_query+2) * sizeof(double));
if (!s) goto fail;
// initialize qual
qual = malloc(l_query * sizeof(float));
if (!qual) goto fail;
if (g_qual2prob[0] == 0)
for (i = 0; i < 256; ++i)
g_qual2prob[i] = pow(10, -i/10.);
qual[0] = 0.0; // Should be unused
for (i = 0; i < l_query; ++i)
qual[i] = g_qual2prob[iqual? iqual[i] : 30];
// initialize transition probability
// the value here seems not to affect results; FIXME: need proof
sM = sI = 1. / (2 * l_query + 2);
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;
bM = (1 - c->d) / l_ref; // (bM+bI)*l_ref==1
bI = c->d / l_ref;
// f[] and b[] are 2-d arrays of three scores, with rows along the
// query and columns across the band. The first query base and
// first band position appear at index 1 allowing edge conditions
// to be stored in index 0. Hence the loops below appear to use
// 1-based indexing instead of 0-based as you'd normally expect in C,
// and the sequences are accessed using query[i - 1] and ref[k - 1].
/*** forward ***/
// f[0]
set_u(k, bw, 0, 0);
f[0*i_dim+k] = s[0] = 1.;
{ // f[1]
double *fi = &f[1*i_dim], sum;
int beg = 1, end = l_ref < bw + 1? l_ref : bw + 1;
for (k = beg, sum = 0.; k <= end; ++k) {
int u;
double e = (ref[k - 1] > 3 || query[0] > 3)? 1. : ref[k - 1] == query[0]? 1. - qual[0] : qual[0] * EM;
set_u(u, bw, 1, k);
fi[u+0] = e * bM; fi[u+1] = EI * bI;
sum += fi[u] + fi[u+1];
}
s[1] = sum;
}
// f[2..l_query]
for (i = 2; i <= l_query; ++i) {
double *fi = &f[i*i_dim], *fi1 = &f[(i-1)*i_dim], sum, qli = qual[i-1];
int beg = 1, end = l_ref, x;
uint8_t qyi = query[i - 1];
x = i - bw; beg = beg > x? beg : x; // band start
x = i + bw; end = end < x? end : x; // band end
// NB end-beg is almost always 14 (99.9% of the time)
// Hence not a large volume to parallelise.
//
// Maybe stripe in diagonal doing 14 lines together?
//
// Consider rotation? 150x14 vs 14x150 so inner loop
// takes longer.
double E[] = {
qli * EM, // 00
1. - qli, // 01
1., // 10
1., // 11
};
double M = 1./s[i-1];
// Note this code has the original version listed here (albeit
// with improved formatting), but we do not compile using
// -DPROBALN_ORIG. The purpose of this code is to act as an
// easier(?) to understand version of the heavily optimised
// version following it and as an easy validation path in case
// of any differences in results.
#ifdef PROBALN_ORIG
for (k = beg, sum = 0.; k <= end; ++k) {
int u, v11, v01, v10;
double e;
e = E[(ref[k - 1] > 3 || qyi > 3)*2 + (ref[k - 1] == qyi)];
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] * M*fi1[v11+0] + m[3] * M*fi1[v11+1] + m[6] * M*fi1[v11+2]);
fi[u+1] = EI * (m[1] * M*fi1[v10+0] + m[4] * M*fi1[v10+1]);
fi[u+2] = m[2] * fi[v01+0] + m[8] * fi[v01+2];
sum += fi[u] + fi[u+1] + fi[u+2];
}
#else
// We use EI*(M*m[1]*? + M*m[4]*?) a lot. So factor it out here.
double xm[5];
xm[0] = M*m[0];
xm[1] = M*m[3];
xm[2] = M*m[6];
xm[3] = EI*M*m[1];
xm[4] = EI*M*m[4];
{
int u, v11;
set_u(u, bw, i, beg);
set_u(v11, bw, i-1, beg-1);
// Rather than recompute k->{u,v01,v10,v11} each loop
// we just increment the pointers.
double *xi = &fi[u];
double *yi = &fi1[v11];
// Derived from xi[0,2] in previous loop iter.
double l_x0 = m[2]*xi[0];
double l_x2 = m[8]*xi[2];
for (k = beg, sum = 0.; k <= end; ++k, xi+=3, yi+=3) {
int cond = (ref[k-1] > 3 || qyi > 3)*2 + (ref[k-1] == qyi);
double z0 = xm[0]*yi[0];
double z1 = xm[1]*yi[1];
double z2 = xm[2]*yi[2];
double z3 = xm[3]*yi[3];
double z4 = xm[4]*yi[4];
xi[0] = E[cond] * (z0+z1+z2);
xi[1] = z3 + z4;
xi[2] = l_x0 + l_x2;
sum += xi[0] + xi[1] + xi[2];
l_x0 = m[2]*xi[0];
l_x2 = m[8]*xi[2];
}
}
#endif
s[i] = sum;
}
{ // f[l_query+1]
double sum;
double M = 1./s[l_query];
// Note that this goes from 1 to l_ref inclusive, but as the
// alignment is banded not all of the values will have been
// calculated (the rest are taken as 0), so the summation
// actually goes over the values set in the last iteration of
// the previous loop (when i = l_query). For some reason lost to
// time this is done by looking for valid values of 'u' instead of
// working out 'beg' and 'end'.
// From HTSlib 1.8 to 1.17, the endpoint was incorrectly set
// to i_dim - 3. When l_query <= bandwidth, this caused the last
// column to be missed, and if l_ref == l_query then a match at the end
// could incorrectly be reported as an insertion. See #1605.
for (k = 1, sum = 0.; k <= l_ref; ++k) {
int u;
set_u(u, bw, l_query, k);
if (u < 3 || u >= i_dim) continue;
sum += M*f[l_query*i_dim + u+0] * sM + M*f[l_query*i_dim + u+1] * sI;
}
s[l_query+1] = sum; // the last scaling factor
}
{ // compute likelihood
double p = 1., Pr1 = 0.;
for (i = 0; i <= l_query + 1; ++i) {
p *= s[i];
if (p < 1e-100) Pr1 += -4.343 * log(p), p = 1.;
}
Pr1 += -4.343 * log(p * l_ref * l_query);
Pr = (int)(Pr1 + .499);
if (!is_backward) { // skip backward and MAP
free(f); free(s); free(qual);
return Pr;
}
}
/*** backward ***/
// b[l_query] (b[l_query+1][0]=1 and thus \tilde{b}[][]=1/s[l_query+1]; this is where s[l_query+1] comes from)
for (k = 1; k <= l_ref; ++k) {
int u;
double *bi = &b[l_query*i_dim];
set_u(u, bw, l_query, k);
if (u < 3 || u >= i_dim) continue;
bi[u+0] = sM / s[l_query] / s[l_query+1]; bi[u+1] = sI / s[l_query] / s[l_query+1];
}
// b[l_query-1..1]
for (i = l_query - 1; i >= 1; --i) {
int beg = 1, end = l_ref, x;
double *bi = &b[i*i_dim], *bi1 = &b[(i+1)*i_dim], y = (i > 1), qli1 = qual[i];
uint8_t qyi1 = query[i];
x = i - bw; beg = beg > x? beg : x;
x = i + bw; end = end < x? end : x;
double E[] = {
qli1 * EM, //000
1. - qli1, //001
1., //010
1., //011
//0,0,0,0 //1xx
};
#ifdef PROBALN_ORIG
for (k = end; k >= beg; --k) {
int u, v11, v01, v10;
double e;
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);
e = (k>=l_ref)?0 :E[(ref[k] > 3 || qyi1 > 3)*2 + (ref[k] == qyi1)] * bi1[v11];
bi[u+0] = e * m[0] + EI * m[1] * bi1[v10+1] + m[2] * bi[v01+2]; // bi1[v11] has been foled into e.
bi[u+1] = e * m[3] + EI * m[4] * bi1[v10+1];
bi[u+2] = (e * m[6] + m[8] * bi[v01+2]) * y;
// fprintf(stderr, "B (%d,%d;%d): %lg,%lg,%lg\n", i, k, u, bi[u], bi[u+1], bi[u+2]); // DEBUG
}
// rescale
int _beg, _end;
set_u(_beg, bw, i, beg); set_u(_end, bw, i, end); _end += 2;
for (k = _beg, y = 1./s[i]; k <= _end; ++k) bi[k] *= y;
#else
{
int u, v10;
set_u(u, bw, i, end);
set_u(v10, bw, i+1, end);
// Rather than recompute k->{u,v01,v10,v11} each loop
// we just increment the pointers.
double *xi = &bi[u];
double *yi = &bi1[v10];
// NB xi[5] is equiv to v01+2.
double xi_5 = xi[5];
// Manual loop invariant removal
double e1 = EI*m[1];
double e4 = EI*m[4];
// Do renorm too in the same pass.
double n = 1./s[i];
for (k = end; k >= beg; --k, xi -= 3, yi -= 3) {
double e = (k>=l_ref)
? 0
: E[(ref[k]>3 || qyi1>3)*2 + (ref[k] == qyi1)] * yi[3];
xi[1] = e * m[3] + e4 * yi[1];
xi[0] = e * m[0] + e1 * yi[1] + m[2] * xi_5;
xi[2] = (e * m[6] + m[8] * xi_5) * y;
// bi[u+2] from this iter becomes bi[v01+2] in next iter
xi_5 = xi[2];
// rescale
xi[1] *= n;
xi[0] *= n;
xi[2] *= n;
}
}
#endif
}
{ // b[0]
int beg = 1, end = l_ref < bw + 1? l_ref : bw + 1;
double sum = 0.;
for (k = end; k >= beg; --k) {
int u;
double e = (ref[k - 1] > 3 || query[0] > 3)? 1. : ref[k - 1] == query[0]? 1. - qual[0] : qual[0] * EM;
set_u(u, bw, 1, k);
if (u < 3 || u >= i_dim) continue;
sum += e * b[1*i_dim + u+0] * bM + EI * b[1*i_dim + u+1] * bI;
}
set_u(k, bw, 0, 0);
b[0*i_dim + k] = sum / s[0]; // if everything works as is expected, b[0][k] == 1.0
}
/*** MAP ***/
for (i = 1; i <= l_query; ++i) {
double sum = 0., *fi = &f[i*i_dim], *bi = &b[i*i_dim], max = 0.;
int beg = 1, end = l_ref, x, max_k = -1;
x = i - bw; beg = beg > x? beg : x;
x = i + bw; end = end < x? end : x;
double M = 1./s[i];
#ifdef PROBALN_ORIG
for (k = beg; k <= end; ++k) {
int u;
double z;
set_u(u, bw, i, k);
z = M*fi[u+0] * bi[u+0];
if (z > max) max = z, max_k = (k-1)<<2 | 0;
sum += z;
z = M*fi[u+1] * bi[u+1];
if (z > max) max = z, max_k = (k-1)<<2 | 1;
sum += z;
}
#else
{
int u;
set_u(u, bw, i, beg);
for (k = beg; k <= end; ++k, u+=3) {
double z1, z2;
z1 = M*fi[u+0] * bi[u+0];
z2 = M*fi[u+1] * bi[u+1];
int which = z2 > z1; // strictly z2 >= z1 matches old code
double zm = which ? z2 : z1;
if (zm > max) {
max = zm;
max_k = (k-1)<<2 | which;
}
sum += z1 + z2;
}
}
#endif
max /= sum; sum *= s[i]; // if everything works as is expected, sum == 1.0
if (state) state[i-1] = max_k;
if (q) k = (int)(-4.343 * log(1. - max) + .499), q[i-1] = k > 100? 99 : k;
#ifdef PROBALN_MAIN
k = 0;
set_u(k, bw, 0, 0);
fprintf(stderr, "(%.10lg,%.10lg) (%d,%d:%c,%c:%d) %lg\n", b[0][k], sum, i-1, max_k>>2,
"ACGT"[query[i - 1]], "ACGT"[ref[(max_k>>2)]], max_k&3, max); // DEBUG
#endif
}
/*** free ***/
free(f); free(b); free(s); free(qual);
return Pr;
fail:
free(f); free(b); free(s); free(qual);
return INT_MIN;
}
#ifdef PROBALN_MAIN
#include <unistd.h>
int main(int argc, char *argv[])
{
uint8_t conv[256], *iqual, *ref, *query;
probaln_par_t par = { 0.001, 0.1, 10 };
int c, l_ref, l_query, i, q = 30, b = 10, P;
while ((c = getopt(argc, argv, "b:q:")) >= 0) {
switch (c) {
case 'b': b = atoi(optarg); break;
case 'q': q = atoi(optarg); break;
}
}
if (optind + 2 > argc) {
fprintf(stderr, "Usage: %s [-q %d] [-b %d] <ref> <query>\n", argv[0], q, b); // example: acttc attc
return 1;
}
memset(conv, 4, 256);
conv['a'] = conv['A'] = 0; conv['c'] = conv['C'] = 1;
conv['g'] = conv['G'] = 2; conv['t'] = conv['T'] = 3;
ref = (uint8_t*)argv[optind]; query = (uint8_t*)argv[optind+1];
l_ref = strlen((char*)ref); l_query = strlen((char*)query);
for (i = 0; i < l_ref; ++i) ref[i] = conv[ref[i]];
for (i = 0; i < l_query; ++i) query[i] = conv[query[i]];
iqual = malloc(l_query);
memset(iqual, q, l_query);
par.bw = b;
P = probaln_glocal(ref, l_ref, query, l_query, iqual, &par, 0, 0);
fprintf(stderr, "%d\n", P);
free(iqual);
return 0;
}
#endif