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comparison PsiCLASS-1.0.2/samtools-0.1.19/bcftools/prob1.c @ 0:903fc43d6227 draft default tip

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author lsong10
date Fri, 26 Mar 2021 16:52:45 +0000
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1 #include <math.h>
2 #include <stdlib.h>
3 #include <string.h>
4 #include <stdio.h>
5 #include <errno.h>
6 #include <assert.h>
7 #include <limits.h>
8 #include <zlib.h>
9 #include "prob1.h"
10 #include "kstring.h"
11
12 #include "kseq.h"
13 KSTREAM_INIT(gzFile, gzread, 16384)
14
15 #define MC_MAX_EM_ITER 16
16 #define MC_EM_EPS 1e-5
17 #define MC_DEF_INDEL 0.15
18
19 gzFile bcf_p1_fp_lk;
20
21 unsigned char seq_nt4_table[256] = {
22 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
23 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
24 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 /*'-'*/, 4, 4,
25 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
26 4, 0, 4, 1, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4,
27 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
28 4, 0, 4, 1, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4,
29 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
30 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
31 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
32 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
33 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
34 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
35 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
36 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
37 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
38 };
39
40 struct __bcf_p1aux_t {
41 int n, M, n1, is_indel;
42 uint8_t *ploidy; // haploid or diploid ONLY
43 double *q2p, *pdg; // pdg -> P(D|g)
44 double *phi, *phi_indel;
45 double *z, *zswap; // aux for afs
46 double *z1, *z2, *phi1, *phi2; // only calculated when n1 is set
47 double **hg; // hypergeometric distribution
48 double *lf; // log factorial
49 double t, t1, t2;
50 double *afs, *afs1; // afs: accumulative AFS; afs1: site posterior distribution
51 const uint8_t *PL; // point to PL
52 int PL_len;
53 };
54
55 void bcf_p1_indel_prior(bcf_p1aux_t *ma, double x)
56 {
57 int i;
58 for (i = 0; i < ma->M; ++i)
59 ma->phi_indel[i] = ma->phi[i] * x;
60 ma->phi_indel[ma->M] = 1. - ma->phi[ma->M] * x;
61 }
62
63 static void init_prior(int type, double theta, int M, double *phi)
64 {
65 int i;
66 if (type == MC_PTYPE_COND2) {
67 for (i = 0; i <= M; ++i)
68 phi[i] = 2. * (i + 1) / (M + 1) / (M + 2);
69 } else if (type == MC_PTYPE_FLAT) {
70 for (i = 0; i <= M; ++i)
71 phi[i] = 1. / (M + 1);
72 } else {
73 double sum;
74 for (i = 0, sum = 0.; i < M; ++i)
75 sum += (phi[i] = theta / (M - i));
76 phi[M] = 1. - sum;
77 }
78 }
79
80 void bcf_p1_init_prior(bcf_p1aux_t *ma, int type, double theta)
81 {
82 init_prior(type, theta, ma->M, ma->phi);
83 bcf_p1_indel_prior(ma, MC_DEF_INDEL);
84 }
85
86 void bcf_p1_init_subprior(bcf_p1aux_t *ma, int type, double theta)
87 {
88 if (ma->n1 <= 0 || ma->n1 >= ma->M) return;
89 init_prior(type, theta, 2*ma->n1, ma->phi1);
90 init_prior(type, theta, 2*(ma->n - ma->n1), ma->phi2);
91 }
92
93 int bcf_p1_read_prior(bcf_p1aux_t *ma, const char *fn)
94 {
95 gzFile fp;
96 kstring_t s;
97 kstream_t *ks;
98 long double sum;
99 int dret, k;
100 memset(&s, 0, sizeof(kstring_t));
101 fp = strcmp(fn, "-")? gzopen(fn, "r") : gzdopen(fileno(stdin), "r");
102 ks = ks_init(fp);
103 memset(ma->phi, 0, sizeof(double) * (ma->M + 1));
104 while (ks_getuntil(ks, '\n', &s, &dret) >= 0) {
105 if (strstr(s.s, "[afs] ") == s.s) {
106 char *p = s.s + 6;
107 for (k = 0; k <= ma->M; ++k) {
108 int x;
109 double y;
110 x = strtol(p, &p, 10);
111 if (x != k && (errno == EINVAL || errno == ERANGE)) return -1;
112 ++p;
113 y = strtod(p, &p);
114 if (y == 0. && (errno == EINVAL || errno == ERANGE)) return -1;
115 ma->phi[ma->M - k] += y;
116 }
117 }
118 }
119 ks_destroy(ks);
120 gzclose(fp);
121 free(s.s);
122 for (sum = 0., k = 0; k <= ma->M; ++k) sum += ma->phi[k];
123 fprintf(stderr, "[prior]");
124 for (k = 0; k <= ma->M; ++k) ma->phi[k] /= sum;
125 for (k = 0; k <= ma->M; ++k) fprintf(stderr, " %d:%.3lg", k, ma->phi[ma->M - k]);
126 fputc('\n', stderr);
127 for (sum = 0., k = 1; k < ma->M; ++k) sum += ma->phi[ma->M - k] * (2.* k * (ma->M - k) / ma->M / (ma->M - 1));
128 fprintf(stderr, "[%s] heterozygosity=%lf, ", __func__, (double)sum);
129 for (sum = 0., k = 1; k <= ma->M; ++k) sum += k * ma->phi[ma->M - k] / ma->M;
130 fprintf(stderr, "theta=%lf\n", (double)sum);
131 bcf_p1_indel_prior(ma, MC_DEF_INDEL);
132 return 0;
133 }
134
135 bcf_p1aux_t *bcf_p1_init(int n, uint8_t *ploidy)
136 {
137 bcf_p1aux_t *ma;
138 int i;
139 ma = calloc(1, sizeof(bcf_p1aux_t));
140 ma->n1 = -1;
141 ma->n = n; ma->M = 2 * n;
142 if (ploidy) {
143 ma->ploidy = malloc(n);
144 memcpy(ma->ploidy, ploidy, n);
145 for (i = 0, ma->M = 0; i < n; ++i) ma->M += ploidy[i];
146 if (ma->M == 2 * n) {
147 free(ma->ploidy);
148 ma->ploidy = 0;
149 }
150 }
151 ma->q2p = calloc(256, sizeof(double));
152 ma->pdg = calloc(3 * ma->n, sizeof(double));
153 ma->phi = calloc(ma->M + 1, sizeof(double));
154 ma->phi_indel = calloc(ma->M + 1, sizeof(double));
155 ma->phi1 = calloc(ma->M + 1, sizeof(double));
156 ma->phi2 = calloc(ma->M + 1, sizeof(double));
157 ma->z = calloc(ma->M + 1, sizeof(double));
158 ma->zswap = calloc(ma->M + 1, sizeof(double));
159 ma->z1 = calloc(ma->M + 1, sizeof(double)); // actually we do not need this large
160 ma->z2 = calloc(ma->M + 1, sizeof(double));
161 ma->afs = calloc(ma->M + 1, sizeof(double));
162 ma->afs1 = calloc(ma->M + 1, sizeof(double));
163 ma->lf = calloc(ma->M + 1, sizeof(double));
164 for (i = 0; i < 256; ++i)
165 ma->q2p[i] = pow(10., -i / 10.);
166 for (i = 0; i <= ma->M; ++i) ma->lf[i] = lgamma(i + 1);
167 bcf_p1_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
168 return ma;
169 }
170
171 int bcf_p1_get_M(bcf_p1aux_t *b) { return b->M; }
172
173 int bcf_p1_set_n1(bcf_p1aux_t *b, int n1)
174 {
175 if (n1 == 0 || n1 >= b->n) return -1;
176 if (b->M != b->n * 2) {
177 fprintf(stderr, "[%s] unable to set `n1' when there are haploid samples.\n", __func__);
178 return -1;
179 }
180 b->n1 = n1;
181 return 0;
182 }
183
184 void bcf_p1_set_ploidy(bcf1_t *b, bcf_p1aux_t *ma)
185 {
186 // bcf_p1aux_t fields are not visible outside of prob1.c, hence this wrapper.
187 // Ideally, this should set ploidy per site to allow pseudo-autosomal regions
188 b->ploidy = ma->ploidy;
189 }
190
191 void bcf_p1_destroy(bcf_p1aux_t *ma)
192 {
193 if (ma) {
194 int k;
195 free(ma->lf);
196 if (ma->hg && ma->n1 > 0) {
197 for (k = 0; k <= 2*ma->n1; ++k) free(ma->hg[k]);
198 free(ma->hg);
199 }
200 free(ma->ploidy); free(ma->q2p); free(ma->pdg);
201 free(ma->phi); free(ma->phi_indel); free(ma->phi1); free(ma->phi2);
202 free(ma->z); free(ma->zswap); free(ma->z1); free(ma->z2);
203 free(ma->afs); free(ma->afs1);
204 free(ma);
205 }
206 }
207
208 extern double kf_gammap(double s, double z);
209 int test16(bcf1_t *b, anno16_t *a);
210
211 // Wigginton 2005, PMID: 15789306
212 // written by Jan Wigginton
213 double calc_hwe(int obs_hom1, int obs_hom2, int obs_hets)
214 {
215 if (obs_hom1 + obs_hom2 + obs_hets == 0 ) return 1;
216
217 assert(obs_hom1 >= 0 && obs_hom2 >= 0 && obs_hets >= 0);
218
219 int obs_homc = obs_hom1 < obs_hom2 ? obs_hom2 : obs_hom1;
220 int obs_homr = obs_hom1 < obs_hom2 ? obs_hom1 : obs_hom2;
221
222 int rare_copies = 2 * obs_homr + obs_hets;
223 int genotypes = obs_hets + obs_homc + obs_homr;
224
225 double *het_probs = (double*) calloc(rare_copies+1, sizeof(double));
226
227 /* start at midpoint */
228 int mid = rare_copies * (2 * genotypes - rare_copies) / (2 * genotypes);
229
230 /* check to ensure that midpoint and rare alleles have same parity */
231 if ((rare_copies & 1) ^ (mid & 1)) mid++;
232
233 int curr_hets = mid;
234 int curr_homr = (rare_copies - mid) / 2;
235 int curr_homc = genotypes - curr_hets - curr_homr;
236
237 het_probs[mid] = 1.0;
238 double sum = het_probs[mid];
239 for (curr_hets = mid; curr_hets > 1; curr_hets -= 2)
240 {
241 het_probs[curr_hets - 2] = het_probs[curr_hets] * curr_hets * (curr_hets - 1.0) / (4.0 * (curr_homr + 1.0) * (curr_homc + 1.0));
242 sum += het_probs[curr_hets - 2];
243
244 /* 2 fewer heterozygotes for next iteration -> add one rare, one common homozygote */
245 curr_homr++;
246 curr_homc++;
247 }
248
249 curr_hets = mid;
250 curr_homr = (rare_copies - mid) / 2;
251 curr_homc = genotypes - curr_hets - curr_homr;
252 for (curr_hets = mid; curr_hets <= rare_copies - 2; curr_hets += 2)
253 {
254 het_probs[curr_hets + 2] = het_probs[curr_hets] * 4.0 * curr_homr * curr_homc /((curr_hets + 2.0) * (curr_hets + 1.0));
255 sum += het_probs[curr_hets + 2];
256
257 /* add 2 heterozygotes for next iteration -> subtract one rare, one common homozygote */
258 curr_homr--;
259 curr_homc--;
260 }
261 int i;
262 for (i = 0; i <= rare_copies; i++) het_probs[i] /= sum;
263
264 /* p-value calculation for p_hwe */
265 double p_hwe = 0.0;
266 for (i = 0; i <= rare_copies; i++)
267 {
268 if (het_probs[i] > het_probs[obs_hets])
269 continue;
270 p_hwe += het_probs[i];
271 }
272
273 p_hwe = p_hwe > 1.0 ? 1.0 : p_hwe;
274 free(het_probs);
275 return p_hwe;
276
277 }
278
279
280 static void _bcf1_set_ref(bcf1_t *b, int idp)
281 {
282 kstring_t s;
283 int old_n_gi = b->n_gi;
284 s.m = b->m_str; s.l = b->l_str - 1; s.s = b->str;
285 kputs(":GT", &s); kputc('\0', &s);
286 b->m_str = s.m; b->l_str = s.l; b->str = s.s;
287 bcf_sync(b);
288
289 // Call GTs
290 int isample, an = 0;
291 for (isample = 0; isample < b->n_smpl; isample++)
292 {
293 if ( idp>=0 && ((uint16_t*)b->gi[idp].data)[isample]==0 )
294 ((uint8_t*)b->gi[old_n_gi].data)[isample] = 1<<7;
295 else
296 {
297 ((uint8_t*)b->gi[old_n_gi].data)[isample] = 0;
298 an += b->ploidy ? b->ploidy[isample] : 2;
299 }
300 }
301 bcf_fit_alt(b,1);
302 b->qual = 999;
303
304 // Prepare BCF for output: ref, alt, filter, info, format
305 memset(&s, 0, sizeof(kstring_t)); kputc('\0', &s);
306 kputs(b->ref, &s); kputc('\0', &s);
307 kputs(b->alt, &s); kputc('\0', &s); kputc('\0', &s);
308 {
309 ksprintf(&s, "AN=%d;", an);
310 kputs(b->info, &s);
311 anno16_t a;
312 int has_I16 = test16(b, &a) >= 0? 1 : 0;
313 if (has_I16 )
314 {
315 if ( a.is_tested) ksprintf(&s, ";PV4=%.2g,%.2g,%.2g,%.2g", a.p[0], a.p[1], a.p[2], a.p[3]);
316 ksprintf(&s, ";DP4=%d,%d,%d,%d;MQ=%d", a.d[0], a.d[1], a.d[2], a.d[3], a.mq);
317 }
318 kputc('\0', &s);
319 rm_info(&s, "I16=");
320 rm_info(&s, "QS=");
321 }
322 kputs(b->fmt, &s); kputc('\0', &s);
323 free(b->str);
324 b->m_str = s.m; b->l_str = s.l; b->str = s.s;
325 bcf_sync(b);
326 }
327
328 int call_multiallelic_gt(bcf1_t *b, bcf_p1aux_t *ma, double threshold, int var_only)
329 {
330 int nals = 1;
331 char *p;
332 for (p=b->alt; *p; p++)
333 {
334 if ( *p=='X' || p[0]=='.' ) break;
335 if ( p[0]==',' ) nals++;
336 }
337 if ( b->alt[0] && !*p ) nals++;
338
339 if ( nals>4 )
340 {
341 if ( *b->ref=='N' ) return 0;
342 fprintf(stderr,"Not ready for this, more than 4 alleles at %d: %s, %s\n", b->pos+1, b->ref,b->alt);
343 exit(1);
344 }
345
346 // find PL, DV and DP FORMAT indexes
347 uint8_t *pl = NULL;
348 int i, npl = 0, idp = -1, idv = -1;
349 for (i = 0; i < b->n_gi; ++i)
350 {
351 if (b->gi[i].fmt == bcf_str2int("PL", 2))
352 {
353 pl = (uint8_t*)b->gi[i].data;
354 npl = b->gi[i].len;
355 }
356 else if (b->gi[i].fmt == bcf_str2int("DP", 2)) idp=i;
357 else if (b->gi[i].fmt == bcf_str2int("DV", 2)) idv=i;
358 }
359 if ( nals==1 )
360 {
361 if ( !var_only ) _bcf1_set_ref(b, idp);
362 return 1;
363 }
364 if ( !pl ) return -1;
365
366 assert(ma->q2p[0] == 1);
367
368 // Init P(D|G)
369 int npdg = nals*(nals+1)/2;
370 double *pdg,*_pdg;
371 _pdg = pdg = malloc(sizeof(double)*ma->n*npdg);
372 for (i=0; i<ma->n; i++)
373 {
374 int j;
375 double sum = 0;
376 for (j=0; j<npdg; j++)
377 {
378 //_pdg[j] = pow(10,-0.1*pl[j]);
379 _pdg[j] = ma->q2p[pl[j]];
380 sum += _pdg[j];
381 }
382 if ( sum )
383 for (j=0; j<npdg; j++) _pdg[j] /= sum;
384 _pdg += npdg;
385 pl += npl;
386 }
387
388 if ((p = strstr(b->info, "QS=")) == 0) { fprintf(stderr,"INFO/QS is required with -m, exiting\n"); exit(1); }
389 double qsum[4];
390 if ( sscanf(p+3,"%lf,%lf,%lf,%lf",&qsum[0],&qsum[1],&qsum[2],&qsum[3])!=4 ) { fprintf(stderr,"Could not parse %s\n",p); exit(1); }
391
392
393 // Calculate the most likely combination of alleles, remembering the most and second most likely set
394 int ia,ib,ic, max_als=0, max_als2=0;
395 double ref_lk = 0, max_lk = INT_MIN, max_lk2 = INT_MIN, lk_sum = INT_MIN, lk_sums[3];
396 for (ia=0; ia<nals; ia++)
397 {
398 double lk_tot = 0;
399 int iaa = (ia+1)*(ia+2)/2-1;
400 int isample;
401 for (isample=0; isample<ma->n; isample++)
402 {
403 double *p = pdg + isample*npdg;
404 // assert( log(p[iaa]) <= 0 );
405 lk_tot += log(p[iaa]);
406 }
407 if ( ia==0 ) ref_lk = lk_tot;
408 if ( max_lk<lk_tot ) { max_lk2 = max_lk; max_als2 = max_als; max_lk = lk_tot; max_als = 1<<ia; }
409 else if ( max_lk2<lk_tot ) { max_lk2 = lk_tot; max_als2 = 1<<ia; }
410 lk_sum = lk_tot>lk_sum ? lk_tot + log(1+exp(lk_sum-lk_tot)) : lk_sum + log(1+exp(lk_tot-lk_sum));
411 }
412 lk_sums[0] = lk_sum;
413 if ( nals>1 )
414 {
415 for (ia=0; ia<nals; ia++)
416 {
417 if ( qsum[ia]==0 ) continue;
418 int iaa = (ia+1)*(ia+2)/2-1;
419 for (ib=0; ib<ia; ib++)
420 {
421 if ( qsum[ib]==0 ) continue;
422 double lk_tot = 0;
423 double fa = qsum[ia]/(qsum[ia]+qsum[ib]);
424 double fb = qsum[ib]/(qsum[ia]+qsum[ib]);
425 double fab = 2*fa*fb; fa *= fa; fb *= fb;
426 int isample, ibb = (ib+1)*(ib+2)/2-1, iab = iaa - ia + ib;
427 for (isample=0; isample<ma->n; isample++)
428 {
429 double *p = pdg + isample*npdg;
430 //assert( log(fa*p[iaa] + fb*p[ibb] + fab*p[iab]) <= 0 );
431 if ( b->ploidy && b->ploidy[isample]==1 )
432 lk_tot += log(fa*p[iaa] + fb*p[ibb]);
433 else
434 lk_tot += log(fa*p[iaa] + fb*p[ibb] + fab*p[iab]);
435 }
436 if ( max_lk<lk_tot ) { max_lk2 = max_lk; max_als2 = max_als; max_lk = lk_tot; max_als = 1<<ia|1<<ib; }
437 else if ( max_lk2<lk_tot ) { max_lk2 = lk_tot; max_als2 = 1<<ia|1<<ib; }
438 lk_sum = lk_tot>lk_sum ? lk_tot + log(1+exp(lk_sum-lk_tot)) : lk_sum + log(1+exp(lk_tot-lk_sum));
439 }
440 }
441 lk_sums[1] = lk_sum;
442 }
443 if ( nals>2 )
444 {
445 for (ia=0; ia<nals; ia++)
446 {
447 if ( qsum[ia]==0 ) continue;
448 int iaa = (ia+1)*(ia+2)/2-1;
449 for (ib=0; ib<ia; ib++)
450 {
451 if ( qsum[ib]==0 ) continue;
452 int ibb = (ib+1)*(ib+2)/2-1;
453 int iab = iaa - ia + ib;
454 for (ic=0; ic<ib; ic++)
455 {
456 if ( qsum[ic]==0 ) continue;
457 double lk_tot = 0;
458 double fa = qsum[ia]/(qsum[ia]+qsum[ib]+qsum[ic]);
459 double fb = qsum[ib]/(qsum[ia]+qsum[ib]+qsum[ic]);
460 double fc = qsum[ic]/(qsum[ia]+qsum[ib]+qsum[ic]);
461 double fab = 2*fa*fb, fac = 2*fa*fc, fbc = 2*fb*fc; fa *= fa; fb *= fb; fc *= fc;
462 int isample, icc = (ic+1)*(ic+2)/2-1;
463 int iac = iaa - ia + ic, ibc = ibb - ib + ic;
464 for (isample=0; isample<ma->n; isample++)
465 {
466 double *p = pdg + isample*npdg;
467 //assert( log(fa*p[iaa] + fb*p[ibb] + fc*p[icc] + fab*p[iab] + fac*p[iac] + fbc*p[ibc]) <= 0 );
468 if ( b->ploidy && b->ploidy[isample]==1 )
469 lk_tot += log(fa*p[iaa] + fb*p[ibb] + fc*p[icc]);
470 else
471 lk_tot += log(fa*p[iaa] + fb*p[ibb] + fc*p[icc] + fab*p[iab] + fac*p[iac] + fbc*p[ibc]);
472 }
473 if ( max_lk<lk_tot ) { max_lk2 = max_lk; max_als2 = max_als; max_lk = lk_tot; max_als = 1<<ia|1<<ib|1<<ic; }
474 else if ( max_lk2<lk_tot ) { max_lk2 = lk_tot; max_als2 = 1<<ia|1<<ib|1<<ic; }
475 lk_sum = lk_tot>lk_sum ? lk_tot + log(1+exp(lk_sum-lk_tot)) : lk_sum + log(1+exp(lk_tot-lk_sum));
476 }
477 }
478 }
479 lk_sums[2] = lk_sum;
480 }
481
482 // Should we add another allele, does it increase the likelihood significantly?
483 int n1=0, n2=0;
484 for (i=0; i<nals; i++) if ( max_als&1<<i) n1++;
485 for (i=0; i<nals; i++) if ( max_als2&1<<i) n2++;
486 if ( n2<n1 && kf_gammap(1,2.0*(max_lk-max_lk2))<threshold )
487 {
488 // the threshold not exceeded, use the second most likely set with fewer alleles
489 max_lk = max_lk2;
490 max_als = max_als2;
491 n1 = n2;
492 }
493 lk_sum = lk_sums[n1-1];
494
495 // Get the BCF record ready for GT and GQ
496 kstring_t s;
497 int old_n_gi = b->n_gi;
498 s.m = b->m_str; s.l = b->l_str - 1; s.s = b->str;
499 kputs(":GT:GQ", &s); kputc('\0', &s);
500 b->m_str = s.m; b->l_str = s.l; b->str = s.s;
501 bcf_sync(b);
502
503 // Call GTs
504 int isample, gts=0, ac[4] = {0,0,0,0};
505 int nRR = 0, nAA = 0, nRA = 0, max_dv = 0;
506 for (isample = 0; isample < b->n_smpl; isample++)
507 {
508 int ploidy = b->ploidy ? b->ploidy[isample] : 2;
509 double *p = pdg + isample*npdg;
510 int ia, als = 0;
511 double lk = 0, lk_s = 0;
512 for (ia=0; ia<nals; ia++)
513 {
514 if ( !(max_als&1<<ia) ) continue;
515 int iaa = (ia+1)*(ia+2)/2-1;
516 double _lk = p[iaa]*qsum[ia]*qsum[ia];
517 if ( _lk > lk ) { lk = _lk; als = ia<<3 | ia; }
518 lk_s += _lk;
519 }
520 if ( ploidy==2 )
521 {
522 for (ia=0; ia<nals; ia++)
523 {
524 if ( !(max_als&1<<ia) ) continue;
525 int iaa = (ia+1)*(ia+2)/2-1;
526 for (ib=0; ib<ia; ib++)
527 {
528 if ( !(max_als&1<<ib) ) continue;
529 int iab = iaa - ia + ib;
530 double _lk = 2*qsum[ia]*qsum[ib]*p[iab];
531 if ( _lk > lk ) { lk = _lk; als = ib<<3 | ia; }
532 lk_s += _lk;
533 }
534 }
535 }
536 lk = -log(1-lk/lk_s)/0.2302585;
537 int dp = 0;
538 if ( idp>=0 && (dp=((uint16_t*)b->gi[idp].data)[isample])==0 )
539 {
540 // no coverage
541 ((uint8_t*)b->gi[old_n_gi].data)[isample] = 1<<7;
542 ((uint8_t*)b->gi[old_n_gi+1].data)[isample] = 0;
543 continue;
544 }
545 if ( lk>99 ) lk = 99;
546 ((uint8_t*)b->gi[old_n_gi].data)[isample] = als;
547 ((uint8_t*)b->gi[old_n_gi+1].data)[isample] = (int)lk;
548
549 // For MDV annotation
550 int dv;
551 if ( als && idv>=0 && (dv=((uint16_t*)b->gi[idv].data)[isample]) )
552 {
553 if ( max_dv < dv ) max_dv = dv;
554 }
555
556 // For HWE annotation; multiple ALT alleles treated as one
557 if ( !als ) nRR++;
558 else if ( !(als>>3&7) || !(als&7) ) nRA++;
559 else nAA++;
560
561 gts |= 1<<(als>>3&7) | 1<<(als&7);
562 ac[ als>>3&7 ]++;
563 ac[ als&7 ]++;
564 }
565 free(pdg);
566 bcf_fit_alt(b,max_als);
567
568 // The VCF spec is ambiguous about QUAL: is it the probability of anything else
569 // (that is QUAL(non-ref) = P(ref)+P(any non-ref other than ALT)) or is it
570 // QUAL(non-ref)=P(ref) and QUAL(ref)=1-P(ref)? Assuming the latter.
571 b->qual = gts>1 ? -4.343*(ref_lk - lk_sum) : -4.343*log(1-exp(ref_lk - lk_sum));
572 if ( b->qual>999 ) b->qual = 999;
573
574 // Prepare BCF for output: ref, alt, filter, info, format
575 memset(&s, 0, sizeof(kstring_t)); kputc('\0', &s);
576 kputs(b->ref, &s); kputc('\0', &s);
577 kputs(b->alt, &s); kputc('\0', &s); kputc('\0', &s);
578 {
579 int an=0, nalts=0;
580 for (i=0; i<nals; i++)
581 {
582 an += ac[i];
583 if ( i>0 && ac[i] ) nalts++;
584 }
585 ksprintf(&s, "AN=%d;", an);
586 if ( nalts )
587 {
588 kputs("AC=", &s);
589 for (i=1; i<nals; i++)
590 {
591 if ( !(gts&1<<i) ) continue;
592 nalts--;
593 ksprintf(&s,"%d", ac[i]);
594 if ( nalts>0 ) kputc(',', &s);
595 }
596 kputc(';', &s);
597 }
598 kputs(b->info, &s);
599 anno16_t a;
600 int has_I16 = test16(b, &a) >= 0? 1 : 0;
601 if (has_I16 )
602 {
603 if ( a.is_tested) ksprintf(&s, ";PV4=%.2g,%.2g,%.2g,%.2g", a.p[0], a.p[1], a.p[2], a.p[3]);
604 ksprintf(&s, ";DP4=%d,%d,%d,%d;MQ=%d", a.d[0], a.d[1], a.d[2], a.d[3], a.mq);
605 ksprintf(&s, ";QBD=%e", b->qual/(a.d[0] + a.d[1] + a.d[2] + a.d[3]));
606 if ( max_dv ) ksprintf(&s, ";MDV=%d", max_dv);
607 }
608 if ( nAA+nRA )
609 {
610 double hwe = calc_hwe(nAA, nRR, nRA);
611 ksprintf(&s, ";HWE=%e", hwe);
612 }
613 kputc('\0', &s);
614 rm_info(&s, "I16=");
615 rm_info(&s, "QS=");
616 }
617 kputs(b->fmt, &s); kputc('\0', &s);
618 free(b->str);
619 b->m_str = s.m; b->l_str = s.l; b->str = s.s;
620 bcf_sync(b);
621
622 return gts;
623 }
624
625 static int cal_pdg(const bcf1_t *b, bcf_p1aux_t *ma)
626 {
627 int i, j;
628 long *p, tmp;
629 p = alloca(b->n_alleles * sizeof(long));
630 memset(p, 0, sizeof(long) * b->n_alleles);
631 for (j = 0; j < ma->n; ++j) {
632 const uint8_t *pi = ma->PL + j * ma->PL_len;
633 double *pdg = ma->pdg + j * 3;
634 pdg[0] = ma->q2p[pi[2]]; pdg[1] = ma->q2p[pi[1]]; pdg[2] = ma->q2p[pi[0]];
635 for (i = 0; i < b->n_alleles; ++i)
636 p[i] += (int)pi[(i+1)*(i+2)/2-1];
637 }
638 for (i = 0; i < b->n_alleles; ++i) p[i] = p[i]<<4 | i;
639 for (i = 1; i < b->n_alleles; ++i) // insertion sort
640 for (j = i; j > 0 && p[j] < p[j-1]; --j)
641 tmp = p[j], p[j] = p[j-1], p[j-1] = tmp;
642 for (i = b->n_alleles - 1; i >= 0; --i)
643 if ((p[i]&0xf) == 0) break;
644 return i;
645 }
646
647
648 int bcf_p1_call_gt(const bcf_p1aux_t *ma, double f0, int k)
649 {
650 double sum, g[3];
651 double max, f3[3], *pdg = ma->pdg + k * 3;
652 int q, i, max_i, ploidy;
653 ploidy = ma->ploidy? ma->ploidy[k] : 2;
654 if (ploidy == 2) {
655 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
656 } else {
657 f3[0] = 1. - f0; f3[1] = 0; f3[2] = f0;
658 }
659 for (i = 0, sum = 0.; i < 3; ++i)
660 sum += (g[i] = pdg[i] * f3[i]);
661 for (i = 0, max = -1., max_i = 0; i < 3; ++i) {
662 g[i] /= sum;
663 if (g[i] > max) max = g[i], max_i = i;
664 }
665 max = 1. - max;
666 if (max < 1e-308) max = 1e-308;
667 q = (int)(-4.343 * log(max) + .499);
668 if (q > 99) q = 99;
669 return q<<2|max_i;
670 }
671
672 #define TINY 1e-20
673
674 static void mc_cal_y_core(bcf_p1aux_t *ma, int beg)
675 {
676 double *z[2], *tmp, *pdg;
677 int _j, last_min, last_max;
678 assert(beg == 0 || ma->M == ma->n*2);
679 z[0] = ma->z;
680 z[1] = ma->zswap;
681 pdg = ma->pdg;
682 memset(z[0], 0, sizeof(double) * (ma->M + 1));
683 memset(z[1], 0, sizeof(double) * (ma->M + 1));
684 z[0][0] = 1.;
685 last_min = last_max = 0;
686 ma->t = 0.;
687 if (ma->M == ma->n * 2) {
688 int M = 0;
689 for (_j = beg; _j < ma->n; ++_j) {
690 int k, j = _j - beg, _min = last_min, _max = last_max, M0;
691 double p[3], sum;
692 M0 = M; M += 2;
693 pdg = ma->pdg + _j * 3;
694 p[0] = pdg[0]; p[1] = 2. * pdg[1]; p[2] = pdg[2];
695 for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
696 for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
697 _max += 2;
698 if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
699 if (_min <= 1) k = 1, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1];
700 for (k = _min < 2? 2 : _min; k <= _max; ++k)
701 z[1][k] = (M0-k+1)*(M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1] + k*(k-1)* p[2] * z[0][k-2];
702 for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
703 ma->t += log(sum / (M * (M - 1.)));
704 for (k = _min; k <= _max; ++k) z[1][k] /= sum;
705 if (_min >= 1) z[1][_min-1] = 0.;
706 if (_min >= 2) z[1][_min-2] = 0.;
707 if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
708 if (_j == ma->n1 - 1) { // set pop1; ma->n1==-1 when unset
709 ma->t1 = ma->t;
710 memcpy(ma->z1, z[1], sizeof(double) * (ma->n1 * 2 + 1));
711 }
712 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
713 last_min = _min; last_max = _max;
714 }
715 //for (_j = 0; _j < last_min; ++_j) z[0][_j] = 0.; // TODO: are these necessary?
716 //for (_j = last_max + 1; _j < ma->M; ++_j) z[0][_j] = 0.;
717 } else { // this block is very similar to the block above; these two might be merged in future
718 int j, M = 0;
719 for (j = 0; j < ma->n; ++j) {
720 int k, M0, _min = last_min, _max = last_max;
721 double p[3], sum;
722 pdg = ma->pdg + j * 3;
723 for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
724 for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
725 M0 = M;
726 M += ma->ploidy[j];
727 if (ma->ploidy[j] == 1) {
728 p[0] = pdg[0]; p[1] = pdg[2];
729 _max++;
730 if (_min == 0) k = 0, z[1][k] = (M0+1-k) * p[0] * z[0][k];
731 for (k = _min < 1? 1 : _min; k <= _max; ++k)
732 z[1][k] = (M0+1-k) * p[0] * z[0][k] + k * p[1] * z[0][k-1];
733 for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
734 ma->t += log(sum / M);
735 for (k = _min; k <= _max; ++k) z[1][k] /= sum;
736 if (_min >= 1) z[1][_min-1] = 0.;
737 if (j < ma->n - 1) z[1][_max+1] = 0.;
738 } else if (ma->ploidy[j] == 2) {
739 p[0] = pdg[0]; p[1] = 2 * pdg[1]; p[2] = pdg[2];
740 _max += 2;
741 if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
742 if (_min <= 1) k = 1, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1];
743 for (k = _min < 2? 2 : _min; k <= _max; ++k)
744 z[1][k] = (M0-k+1)*(M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1] + k*(k-1)* p[2] * z[0][k-2];
745 for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
746 ma->t += log(sum / (M * (M - 1.)));
747 for (k = _min; k <= _max; ++k) z[1][k] /= sum;
748 if (_min >= 1) z[1][_min-1] = 0.;
749 if (_min >= 2) z[1][_min-2] = 0.;
750 if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
751 }
752 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
753 last_min = _min; last_max = _max;
754 }
755 }
756 if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (ma->M + 1));
757 if (bcf_p1_fp_lk)
758 gzwrite(bcf_p1_fp_lk, ma->z, sizeof(double) * (ma->M + 1));
759 }
760
761 static void mc_cal_y(bcf_p1aux_t *ma)
762 {
763 if (ma->n1 > 0 && ma->n1 < ma->n && ma->M == ma->n * 2) { // NB: ma->n1 is ineffective when there are haploid samples
764 int k;
765 long double x;
766 memset(ma->z1, 0, sizeof(double) * (2 * ma->n1 + 1));
767 memset(ma->z2, 0, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
768 ma->t1 = ma->t2 = 0.;
769 mc_cal_y_core(ma, ma->n1);
770 ma->t2 = ma->t;
771 memcpy(ma->z2, ma->z, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
772 mc_cal_y_core(ma, 0);
773 // rescale z
774 x = expl(ma->t - (ma->t1 + ma->t2));
775 for (k = 0; k <= ma->M; ++k) ma->z[k] *= x;
776 } else mc_cal_y_core(ma, 0);
777 }
778
779 #define CONTRAST_TINY 1e-30
780
781 extern double kf_gammaq(double s, double z); // incomplete gamma function for chi^2 test
782
783 static inline double chi2_test(int a, int b, int c, int d)
784 {
785 double x, z;
786 x = (double)(a+b) * (c+d) * (b+d) * (a+c);
787 if (x == 0.) return 1;
788 z = a * d - b * c;
789 return kf_gammaq(.5, .5 * z * z * (a+b+c+d) / x);
790 }
791
792 // chi2=(a+b+c+d)(ad-bc)^2/[(a+b)(c+d)(a+c)(b+d)]
793 static inline double contrast2_aux(const bcf_p1aux_t *p1, double sum, int k1, int k2, double x[3])
794 {
795 double p = p1->phi[k1+k2] * p1->z1[k1] * p1->z2[k2] / sum * p1->hg[k1][k2];
796 int n1 = p1->n1, n2 = p1->n - p1->n1;
797 if (p < CONTRAST_TINY) return -1;
798 if (.5*k1/n1 < .5*k2/n2) x[1] += p;
799 else if (.5*k1/n1 > .5*k2/n2) x[2] += p;
800 else x[0] += p;
801 return p * chi2_test(k1, k2, (n1<<1) - k1, (n2<<1) - k2);
802 }
803
804 static double contrast2(bcf_p1aux_t *p1, double ret[3])
805 {
806 int k, k1, k2, k10, k20, n1, n2;
807 double sum;
808 // get n1 and n2
809 n1 = p1->n1; n2 = p1->n - p1->n1;
810 if (n1 <= 0 || n2 <= 0) return 0.;
811 if (p1->hg == 0) { // initialize the hypergeometric distribution
812 /* NB: the hg matrix may take a lot of memory when there are many samples. There is a way
813 to avoid precomputing this matrix, but it is slower and quite intricate. The following
814 computation in this block can be accelerated with a similar strategy, but perhaps this
815 is not a serious concern for now. */
816 double tmp = lgamma(2*(n1+n2)+1) - (lgamma(2*n1+1) + lgamma(2*n2+1));
817 p1->hg = calloc(2*n1+1, sizeof(void*));
818 for (k1 = 0; k1 <= 2*n1; ++k1) {
819 p1->hg[k1] = calloc(2*n2+1, sizeof(double));
820 for (k2 = 0; k2 <= 2*n2; ++k2)
821 p1->hg[k1][k2] = exp(lgamma(k1+k2+1) + lgamma(p1->M-k1-k2+1) - (lgamma(k1+1) + lgamma(k2+1) + lgamma(2*n1-k1+1) + lgamma(2*n2-k2+1) + tmp));
822 }
823 }
824 { // compute
825 long double suml = 0;
826 for (k = 0; k <= p1->M; ++k) suml += p1->phi[k] * p1->z[k];
827 sum = suml;
828 }
829 { // get the max k1 and k2
830 double max;
831 int max_k;
832 for (k = 0, max = 0, max_k = -1; k <= 2*n1; ++k) {
833 double x = p1->phi1[k] * p1->z1[k];
834 if (x > max) max = x, max_k = k;
835 }
836 k10 = max_k;
837 for (k = 0, max = 0, max_k = -1; k <= 2*n2; ++k) {
838 double x = p1->phi2[k] * p1->z2[k];
839 if (x > max) max = x, max_k = k;
840 }
841 k20 = max_k;
842 }
843 { // We can do the following with one nested loop, but that is an O(N^2) thing. The following code block is much faster for large N.
844 double x[3], y;
845 long double z = 0., L[2];
846 x[0] = x[1] = x[2] = 0; L[0] = L[1] = 0;
847 for (k1 = k10; k1 >= 0; --k1) {
848 for (k2 = k20; k2 >= 0; --k2) {
849 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
850 else z += y;
851 }
852 for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
853 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
854 else z += y;
855 }
856 }
857 ret[0] = x[0]; ret[1] = x[1]; ret[2] = x[2];
858 x[0] = x[1] = x[2] = 0;
859 for (k1 = k10 + 1; k1 <= 2*n1; ++k1) {
860 for (k2 = k20; k2 >= 0; --k2) {
861 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
862 else z += y;
863 }
864 for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
865 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
866 else z += y;
867 }
868 }
869 ret[0] += x[0]; ret[1] += x[1]; ret[2] += x[2];
870 if (ret[0] + ret[1] + ret[2] < 0.95) { // in case of bad things happened
871 ret[0] = ret[1] = ret[2] = 0; L[0] = L[1] = 0;
872 for (k1 = 0, z = 0.; k1 <= 2*n1; ++k1)
873 for (k2 = 0; k2 <= 2*n2; ++k2)
874 if ((y = contrast2_aux(p1, sum, k1, k2, ret)) >= 0) z += y;
875 if (ret[0] + ret[1] + ret[2] < 0.95) // It seems that this may be caused by floating point errors. I do not really understand why...
876 z = 1.0, ret[0] = ret[1] = ret[2] = 1./3;
877 }
878 return (double)z;
879 }
880 }
881
882 static double mc_cal_afs(bcf_p1aux_t *ma, double *p_ref_folded, double *p_var_folded)
883 {
884 int k;
885 long double sum = 0., sum2;
886 double *phi = ma->is_indel? ma->phi_indel : ma->phi;
887 memset(ma->afs1, 0, sizeof(double) * (ma->M + 1));
888 mc_cal_y(ma);
889 // compute AFS
890 for (k = 0, sum = 0.; k <= ma->M; ++k)
891 sum += (long double)phi[k] * ma->z[k];
892 for (k = 0; k <= ma->M; ++k) {
893 ma->afs1[k] = phi[k] * ma->z[k] / sum;
894 if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return -1.;
895 }
896 // compute folded variant probability
897 for (k = 0, sum = 0.; k <= ma->M; ++k)
898 sum += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
899 for (k = 1, sum2 = 0.; k < ma->M; ++k)
900 sum2 += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
901 *p_var_folded = sum2 / sum;
902 *p_ref_folded = (phi[k] + phi[ma->M - k]) / 2. * (ma->z[ma->M] + ma->z[0]) / sum;
903 // the expected frequency
904 for (k = 0, sum = 0.; k <= ma->M; ++k) {
905 ma->afs[k] += ma->afs1[k];
906 sum += k * ma->afs1[k];
907 }
908 return sum / ma->M;
909 }
910
911 int bcf_p1_cal(const bcf1_t *b, int do_contrast, bcf_p1aux_t *ma, bcf_p1rst_t *rst)
912 {
913 int i, k;
914 long double sum = 0.;
915 ma->is_indel = bcf_is_indel(b);
916 rst->perm_rank = -1;
917 // set PL and PL_len
918 for (i = 0; i < b->n_gi; ++i) {
919 if (b->gi[i].fmt == bcf_str2int("PL", 2)) {
920 ma->PL = (uint8_t*)b->gi[i].data;
921 ma->PL_len = b->gi[i].len;
922 break;
923 }
924 }
925 if (i == b->n_gi) return -1; // no PL
926 if (b->n_alleles < 2) return -1; // FIXME: find a better solution
927 //
928 rst->rank0 = cal_pdg(b, ma);
929 rst->f_exp = mc_cal_afs(ma, &rst->p_ref_folded, &rst->p_var_folded);
930 rst->p_ref = ma->afs1[ma->M];
931 for (k = 0, sum = 0.; k < ma->M; ++k)
932 sum += ma->afs1[k];
933 rst->p_var = (double)sum;
934 { // compute the allele count
935 double max = -1;
936 rst->ac = -1;
937 for (k = 0; k <= ma->M; ++k)
938 if (max < ma->z[k]) max = ma->z[k], rst->ac = k;
939 rst->ac = ma->M - rst->ac;
940 }
941 // calculate f_flat and f_em
942 for (k = 0, sum = 0.; k <= ma->M; ++k)
943 sum += (long double)ma->z[k];
944 rst->f_flat = 0.;
945 for (k = 0; k <= ma->M; ++k) {
946 double p = ma->z[k] / sum;
947 rst->f_flat += k * p;
948 }
949 rst->f_flat /= ma->M;
950 { // estimate equal-tail credible interval (95% level)
951 int l, h;
952 double p;
953 for (i = 0, p = 0.; i <= ma->M; ++i)
954 if (p + ma->afs1[i] > 0.025) break;
955 else p += ma->afs1[i];
956 l = i;
957 for (i = ma->M, p = 0.; i >= 0; --i)
958 if (p + ma->afs1[i] > 0.025) break;
959 else p += ma->afs1[i];
960 h = i;
961 rst->cil = (double)(ma->M - h) / ma->M; rst->cih = (double)(ma->M - l) / ma->M;
962 }
963 if (ma->n1 > 0) { // compute LRT
964 double max0, max1, max2;
965 for (k = 0, max0 = -1; k <= ma->M; ++k)
966 if (max0 < ma->z[k]) max0 = ma->z[k];
967 for (k = 0, max1 = -1; k <= ma->n1 * 2; ++k)
968 if (max1 < ma->z1[k]) max1 = ma->z1[k];
969 for (k = 0, max2 = -1; k <= ma->M - ma->n1 * 2; ++k)
970 if (max2 < ma->z2[k]) max2 = ma->z2[k];
971 rst->lrt = log(max1 * max2 / max0);
972 rst->lrt = rst->lrt < 0? 1 : kf_gammaq(.5, rst->lrt);
973 } else rst->lrt = -1.0;
974 rst->cmp[0] = rst->cmp[1] = rst->cmp[2] = rst->p_chi2 = -1.0;
975 if (do_contrast && rst->p_var > 0.5) // skip contrast2() if the locus is a strong non-variant
976 rst->p_chi2 = contrast2(ma, rst->cmp);
977 return 0;
978 }
979
980 void bcf_p1_dump_afs(bcf_p1aux_t *ma)
981 {
982 int k;
983 fprintf(stderr, "[afs]");
984 for (k = 0; k <= ma->M; ++k)
985 fprintf(stderr, " %d:%.3lf", k, ma->afs[ma->M - k]);
986 fprintf(stderr, "\n");
987 memset(ma->afs, 0, sizeof(double) * (ma->M + 1));
988 }