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comparison PsiCLASS-1.0.2/samtools-0.1.19/bcftools/em.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 <stdlib.h>
2 #include <string.h>
3 #include <math.h>
4 #include "bcf.h"
5 #include "kmin.h"
6
7 static double g_q2p[256];
8
9 #define ITER_MAX 50
10 #define ITER_TRY 10
11 #define EPS 1e-5
12
13 extern double kf_gammaq(double, double);
14
15 /*
16 Generic routines
17 */
18 // get the 3 genotype likelihoods
19 static double *get_pdg3(const bcf1_t *b)
20 {
21 double *pdg;
22 const uint8_t *PL = 0;
23 int i, PL_len = 0;
24 // initialize g_q2p if necessary
25 if (g_q2p[0] == 0.)
26 for (i = 0; i < 256; ++i)
27 g_q2p[i] = pow(10., -i / 10.);
28 // set PL and PL_len
29 for (i = 0; i < b->n_gi; ++i) {
30 if (b->gi[i].fmt == bcf_str2int("PL", 2)) {
31 PL = (const uint8_t*)b->gi[i].data;
32 PL_len = b->gi[i].len;
33 break;
34 }
35 }
36 if (i == b->n_gi) return 0; // no PL
37 // fill pdg
38 pdg = malloc(3 * b->n_smpl * sizeof(double));
39 for (i = 0; i < b->n_smpl; ++i) {
40 const uint8_t *pi = PL + i * PL_len;
41 double *p = pdg + i * 3;
42 p[0] = g_q2p[pi[2]]; p[1] = g_q2p[pi[1]]; p[2] = g_q2p[pi[0]];
43 }
44 return pdg;
45 }
46
47 // estimate site allele frequency in a very naive and inaccurate way
48 static double est_freq(int n, const double *pdg)
49 {
50 int i, gcnt[3], tmp1;
51 // get a rough estimate of the genotype frequency
52 gcnt[0] = gcnt[1] = gcnt[2] = 0;
53 for (i = 0; i < n; ++i) {
54 const double *p = pdg + i * 3;
55 if (p[0] != 1. || p[1] != 1. || p[2] != 1.) {
56 int which = p[0] > p[1]? 0 : 1;
57 which = p[which] > p[2]? which : 2;
58 ++gcnt[which];
59 }
60 }
61 tmp1 = gcnt[0] + gcnt[1] + gcnt[2];
62 return (tmp1 == 0)? -1.0 : (.5 * gcnt[1] + gcnt[2]) / tmp1;
63 }
64
65 /*
66 Single-locus EM
67 */
68
69 typedef struct {
70 int beg, end;
71 const double *pdg;
72 } minaux1_t;
73
74 static double prob1(double f, void *data)
75 {
76 minaux1_t *a = (minaux1_t*)data;
77 double p = 1., l = 0., f3[3];
78 int i;
79 // printf("brent %lg\n", f);
80 if (f < 0 || f > 1) return 1e300;
81 f3[0] = (1.-f)*(1.-f); f3[1] = 2.*f*(1.-f); f3[2] = f*f;
82 for (i = a->beg; i < a->end; ++i) {
83 const double *pdg = a->pdg + i * 3;
84 p *= pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2];
85 if (p < 1e-200) l -= log(p), p = 1.;
86 }
87 return l - log(p);
88 }
89
90 // one EM iteration for allele frequency estimate
91 static double freq_iter(double *f, const double *_pdg, int beg, int end)
92 {
93 double f0 = *f, f3[3], err;
94 int i;
95 // printf("em %lg\n", *f);
96 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
97 for (i = beg, f0 = 0.; i < end; ++i) {
98 const double *pdg = _pdg + i * 3;
99 f0 += (pdg[1] * f3[1] + 2. * pdg[2] * f3[2])
100 / (pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2]);
101 }
102 f0 /= (end - beg) * 2;
103 err = fabs(f0 - *f);
104 *f = f0;
105 return err;
106 }
107
108 /* The following function combines EM and Brent's method. When the signal from
109 * the data is strong, EM is faster but sometimes, EM may converge very slowly.
110 * When this happens, we switch to Brent's method. The idea is learned from
111 * Rasmus Nielsen.
112 */
113 static double freqml(double f0, int beg, int end, const double *pdg)
114 {
115 int i;
116 double f;
117 for (i = 0, f = f0; i < ITER_TRY; ++i)
118 if (freq_iter(&f, pdg, beg, end) < EPS) break;
119 if (i == ITER_TRY) { // haven't converged yet; try Brent's method
120 minaux1_t a;
121 a.beg = beg; a.end = end; a.pdg = pdg;
122 kmin_brent(prob1, f0 == f? .5*f0 : f0, f, (void*)&a, EPS, &f);
123 }
124 return f;
125 }
126
127 // one EM iteration for genotype frequency estimate
128 static double g3_iter(double g[3], const double *_pdg, int beg, int end)
129 {
130 double err, gg[3];
131 int i;
132 gg[0] = gg[1] = gg[2] = 0.;
133 // printf("%lg,%lg,%lg\n", g[0], g[1], g[2]);
134 for (i = beg; i < end; ++i) {
135 double sum, tmp[3];
136 const double *pdg = _pdg + i * 3;
137 tmp[0] = pdg[0] * g[0]; tmp[1] = pdg[1] * g[1]; tmp[2] = pdg[2] * g[2];
138 sum = (tmp[0] + tmp[1] + tmp[2]) * (end - beg);
139 gg[0] += tmp[0] / sum; gg[1] += tmp[1] / sum; gg[2] += tmp[2] / sum;
140 }
141 err = fabs(gg[0] - g[0]) > fabs(gg[1] - g[1])? fabs(gg[0] - g[0]) : fabs(gg[1] - g[1]);
142 err = err > fabs(gg[2] - g[2])? err : fabs(gg[2] - g[2]);
143 g[0] = gg[0]; g[1] = gg[1]; g[2] = gg[2];
144 return err;
145 }
146
147 // perform likelihood ratio test
148 static double lk_ratio_test(int n, int n1, const double *pdg, double f3[3][3])
149 {
150 double r;
151 int i;
152 for (i = 0, r = 1.; i < n1; ++i) {
153 const double *p = pdg + i * 3;
154 r *= (p[0] * f3[1][0] + p[1] * f3[1][1] + p[2] * f3[1][2])
155 / (p[0] * f3[0][0] + p[1] * f3[0][1] + p[2] * f3[0][2]);
156 }
157 for (; i < n; ++i) {
158 const double *p = pdg + i * 3;
159 r *= (p[0] * f3[2][0] + p[1] * f3[2][1] + p[2] * f3[2][2])
160 / (p[0] * f3[0][0] + p[1] * f3[0][1] + p[2] * f3[0][2]);
161 }
162 return r;
163 }
164
165 // x[0]: ref frequency
166 // x[1..3]: alt-alt, alt-ref, ref-ref frequenc
167 // x[4]: HWE P-value
168 // x[5..6]: group1 freq, group2 freq
169 // x[7]: 1-degree P-value
170 // x[8]: 2-degree P-value
171 int bcf_em1(const bcf1_t *b, int n1, int flag, double x[10])
172 {
173 double *pdg;
174 int i, n, n2;
175 if (b->n_alleles < 2) return -1; // one allele only
176 // initialization
177 if (n1 < 0 || n1 > b->n_smpl) n1 = 0;
178 if (flag & 1<<7) flag |= 7<<5; // compute group freq if LRT is required
179 if (flag & 0xf<<1) flag |= 0xf<<1;
180 n = b->n_smpl; n2 = n - n1;
181 pdg = get_pdg3(b);
182 if (pdg == 0) return -1;
183 for (i = 0; i < 10; ++i) x[i] = -1.; // set to negative
184 {
185 if ((x[0] = est_freq(n, pdg)) < 0.) {
186 free(pdg);
187 return -1; // no data
188 }
189 x[0] = freqml(x[0], 0, n, pdg);
190 }
191 if (flag & (0xf<<1|3<<8)) { // estimate the genotype frequency and test HWE
192 double *g = x + 1, f3[3], r;
193 f3[0] = g[0] = (1 - x[0]) * (1 - x[0]);
194 f3[1] = g[1] = 2 * x[0] * (1 - x[0]);
195 f3[2] = g[2] = x[0] * x[0];
196 for (i = 0; i < ITER_MAX; ++i)
197 if (g3_iter(g, pdg, 0, n) < EPS) break;
198 // Hardy-Weinberg equilibrium (HWE)
199 for (i = 0, r = 1.; i < n; ++i) {
200 double *p = pdg + i * 3;
201 r *= (p[0] * g[0] + p[1] * g[1] + p[2] * g[2]) / (p[0] * f3[0] + p[1] * f3[1] + p[2] * f3[2]);
202 }
203 x[4] = kf_gammaq(.5, log(r));
204 }
205 if ((flag & 7<<5) && n1 > 0 && n1 < n) { // group frequency
206 x[5] = freqml(x[0], 0, n1, pdg);
207 x[6] = freqml(x[0], n1, n, pdg);
208 }
209 if ((flag & 1<<7) && n1 > 0 && n1 < n) { // 1-degree P-value
210 double f[3], f3[3][3], tmp;
211 f[0] = x[0]; f[1] = x[5]; f[2] = x[6];
212 for (i = 0; i < 3; ++i)
213 f3[i][0] = (1-f[i])*(1-f[i]), f3[i][1] = 2*f[i]*(1-f[i]), f3[i][2] = f[i]*f[i];
214 tmp = log(lk_ratio_test(n, n1, pdg, f3));
215 if (tmp < 0) tmp = 0;
216 x[7] = kf_gammaq(.5, tmp);
217 }
218 if ((flag & 3<<8) && n1 > 0 && n1 < n) { // 2-degree P-value
219 double g[3][3], tmp;
220 for (i = 0; i < 3; ++i) memcpy(g[i], x + 1, 3 * sizeof(double));
221 for (i = 0; i < ITER_MAX; ++i)
222 if (g3_iter(g[1], pdg, 0, n1) < EPS) break;
223 for (i = 0; i < ITER_MAX; ++i)
224 if (g3_iter(g[2], pdg, n1, n) < EPS) break;
225 tmp = log(lk_ratio_test(n, n1, pdg, g));
226 if (tmp < 0) tmp = 0;
227 x[8] = kf_gammaq(1., tmp);
228 }
229 // free
230 free(pdg);
231 return 0;
232 }
233
234 /*
235 Two-locus EM (LD)
236 */
237
238 #define _G1(h, k) ((h>>1&1) + (k>>1&1))
239 #define _G2(h, k) ((h&1) + (k&1))
240
241 // 0: the previous site; 1: the current site
242 static int pair_freq_iter(int n, double *pdg[2], double f[4])
243 {
244 double ff[4];
245 int i, k, h;
246 // printf("%lf,%lf,%lf,%lf\n", f[0], f[1], f[2], f[3]);
247 memset(ff, 0, 4 * sizeof(double));
248 for (i = 0; i < n; ++i) {
249 double *p[2], sum, tmp;
250 p[0] = pdg[0] + i * 3; p[1] = pdg[1] + i * 3;
251 for (k = 0, sum = 0.; k < 4; ++k)
252 for (h = 0; h < 4; ++h)
253 sum += f[k] * f[h] * p[0][_G1(k,h)] * p[1][_G2(k,h)];
254 for (k = 0; k < 4; ++k) {
255 tmp = f[0] * (p[0][_G1(0,k)] * p[1][_G2(0,k)] + p[0][_G1(k,0)] * p[1][_G2(k,0)])
256 + f[1] * (p[0][_G1(1,k)] * p[1][_G2(1,k)] + p[0][_G1(k,1)] * p[1][_G2(k,1)])
257 + f[2] * (p[0][_G1(2,k)] * p[1][_G2(2,k)] + p[0][_G1(k,2)] * p[1][_G2(k,2)])
258 + f[3] * (p[0][_G1(3,k)] * p[1][_G2(3,k)] + p[0][_G1(k,3)] * p[1][_G2(k,3)]);
259 ff[k] += f[k] * tmp / sum;
260 }
261 }
262 for (k = 0; k < 4; ++k) f[k] = ff[k] / (2 * n);
263 return 0;
264 }
265
266 double bcf_pair_freq(const bcf1_t *b0, const bcf1_t *b1, double f[4])
267 {
268 const bcf1_t *b[2];
269 int i, j, n_smpl;
270 double *pdg[2], flast[4], r, f0[2];
271 // initialize others
272 if (b0->n_smpl != b1->n_smpl) return -1; // different number of samples
273 n_smpl = b0->n_smpl;
274 b[0] = b0; b[1] = b1;
275 f[0] = f[1] = f[2] = f[3] = -1.;
276 if (b[0]->n_alleles < 2 || b[1]->n_alleles < 2) return -1; // one allele only
277 pdg[0] = get_pdg3(b0); pdg[1] = get_pdg3(b1);
278 if (pdg[0] == 0 || pdg[1] == 0) {
279 free(pdg[0]); free(pdg[1]);
280 return -1;
281 }
282 // set the initial value
283 f0[0] = est_freq(n_smpl, pdg[0]);
284 f0[1] = est_freq(n_smpl, pdg[1]);
285 f[0] = (1 - f0[0]) * (1 - f0[1]); f[3] = f0[0] * f0[1];
286 f[1] = (1 - f0[0]) * f0[1]; f[2] = f0[0] * (1 - f0[1]);
287 // iteration
288 for (j = 0; j < ITER_MAX; ++j) {
289 double eps = 0;
290 memcpy(flast, f, 4 * sizeof(double));
291 pair_freq_iter(n_smpl, pdg, f);
292 for (i = 0; i < 4; ++i) {
293 double x = fabs(f[i] - flast[i]);
294 if (x > eps) eps = x;
295 }
296 if (eps < EPS) break;
297 }
298 // free
299 free(pdg[0]); free(pdg[1]);
300 { // calculate r^2
301 double p[2], q[2], D;
302 p[0] = f[0] + f[1]; q[0] = 1 - p[0];
303 p[1] = f[0] + f[2]; q[1] = 1 - p[1];
304 D = f[0] * f[3] - f[1] * f[2];
305 r = sqrt(D * D / (p[0] * p[1] * q[0] * q[1]));
306 // printf("R(%lf,%lf,%lf,%lf)=%lf\n", f[0], f[1], f[2], f[3], r);
307 if (isnan(r)) r = -1.;
308 }
309 return r;
310 }