12 KSTREAM_INIT(gzFile, gzread, 16384)
14 #define MC_MAX_EM_ITER 16
15 #define MC_EM_EPS 1e-5
16 #define MC_DEF_INDEL 0.15
18 unsigned char seq_nt4_table[256] = {
19 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
20 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
21 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 /*'-'*/, 4, 4,
22 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
23 4, 0, 4, 1, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4,
24 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
25 4, 0, 4, 1, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4,
26 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
27 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
28 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
29 4, 4, 4, 4, 4, 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
37 struct __bcf_p1aux_t {
38 int n, M, n1, is_indel;
39 uint8_t *ploidy; // haploid or diploid ONLY
40 double *q2p, *pdg; // pdg -> P(D|g)
41 double *phi, *phi_indel;
42 double *z, *zswap; // aux for afs
43 double *z1, *z2, *phi1, *phi2; // only calculated when n1 is set
44 double **hg; // hypergeometric distribution
45 double *lf; // log factorial
47 double *afs, *afs1; // afs: accumulative AFS; afs1: site posterior distribution
48 const uint8_t *PL; // point to PL
52 void bcf_p1_indel_prior(bcf_p1aux_t *ma, double x)
55 for (i = 0; i < ma->M; ++i)
56 ma->phi_indel[i] = ma->phi[i] * x;
57 ma->phi_indel[ma->M] = 1. - ma->phi[ma->M] * x;
60 static void init_prior(int type, double theta, int M, double *phi)
63 if (type == MC_PTYPE_COND2) {
64 for (i = 0; i <= M; ++i)
65 phi[i] = 2. * (i + 1) / (M + 1) / (M + 2);
66 } else if (type == MC_PTYPE_FLAT) {
67 for (i = 0; i <= M; ++i)
68 phi[i] = 1. / (M + 1);
71 for (i = 0, sum = 0.; i < M; ++i)
72 sum += (phi[i] = theta / (M - i));
77 void bcf_p1_init_prior(bcf_p1aux_t *ma, int type, double theta)
79 init_prior(type, theta, ma->M, ma->phi);
80 bcf_p1_indel_prior(ma, MC_DEF_INDEL);
83 void bcf_p1_init_subprior(bcf_p1aux_t *ma, int type, double theta)
85 if (ma->n1 <= 0 || ma->n1 >= ma->M) return;
86 init_prior(type, theta, 2*ma->n1, ma->phi1);
87 init_prior(type, theta, 2*(ma->n - ma->n1), ma->phi2);
90 int bcf_p1_read_prior(bcf_p1aux_t *ma, const char *fn)
97 memset(&s, 0, sizeof(kstring_t));
98 fp = strcmp(fn, "-")? gzopen(fn, "r") : gzdopen(fileno(stdin), "r");
100 memset(ma->phi, 0, sizeof(double) * (ma->M + 1));
101 while (ks_getuntil(ks, '\n', &s, &dret) >= 0) {
102 if (strstr(s.s, "[afs] ") == s.s) {
104 for (k = 0; k <= ma->M; ++k) {
107 x = strtol(p, &p, 10);
108 if (x != k && (errno == EINVAL || errno == ERANGE)) return -1;
111 if (y == 0. && (errno == EINVAL || errno == ERANGE)) return -1;
112 ma->phi[ma->M - k] += y;
119 for (sum = 0., k = 0; k <= ma->M; ++k) sum += ma->phi[k];
120 fprintf(pysamerr, "[prior]");
121 for (k = 0; k <= ma->M; ++k) ma->phi[k] /= sum;
122 for (k = 0; k <= ma->M; ++k) fprintf(pysamerr, " %d:%.3lg", k, ma->phi[ma->M - k]);
123 fputc('\n', pysamerr);
124 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));
125 fprintf(pysamerr, "[%s] heterozygosity=%lf, ", __func__, (double)sum);
126 for (sum = 0., k = 1; k <= ma->M; ++k) sum += k * ma->phi[ma->M - k] / ma->M;
127 fprintf(pysamerr, "theta=%lf\n", (double)sum);
128 bcf_p1_indel_prior(ma, MC_DEF_INDEL);
132 bcf_p1aux_t *bcf_p1_init(int n, uint8_t *ploidy)
136 ma = calloc(1, sizeof(bcf_p1aux_t));
138 ma->n = n; ma->M = 2 * n;
140 ma->ploidy = malloc(n);
141 memcpy(ma->ploidy, ploidy, n);
142 for (i = 0, ma->M = 0; i < n; ++i) ma->M += ploidy[i];
143 if (ma->M == 2 * n) {
148 ma->q2p = calloc(256, sizeof(double));
149 ma->pdg = calloc(3 * ma->n, sizeof(double));
150 ma->phi = calloc(ma->M + 1, sizeof(double));
151 ma->phi_indel = calloc(ma->M + 1, sizeof(double));
152 ma->phi1 = calloc(ma->M + 1, sizeof(double));
153 ma->phi2 = calloc(ma->M + 1, sizeof(double));
154 ma->z = calloc(ma->M + 1, sizeof(double));
155 ma->zswap = calloc(ma->M + 1, sizeof(double));
156 ma->z1 = calloc(ma->M + 1, sizeof(double)); // actually we do not need this large
157 ma->z2 = calloc(ma->M + 1, sizeof(double));
158 ma->afs = calloc(ma->M + 1, sizeof(double));
159 ma->afs1 = calloc(ma->M + 1, sizeof(double));
160 ma->lf = calloc(ma->M + 1, sizeof(double));
161 for (i = 0; i < 256; ++i)
162 ma->q2p[i] = pow(10., -i / 10.);
163 for (i = 0; i <= ma->M; ++i) ma->lf[i] = lgamma(i + 1);
164 bcf_p1_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
168 int bcf_p1_set_n1(bcf_p1aux_t *b, int n1)
170 if (n1 == 0 || n1 >= b->n) return -1;
171 if (b->M != b->n * 2) {
172 fprintf(pysamerr, "[%s] unable to set `n1' when there are haploid samples.\n", __func__);
179 void bcf_p1_destroy(bcf_p1aux_t *ma)
184 if (ma->hg && ma->n1 > 0) {
185 for (k = 0; k <= 2*ma->n1; ++k) free(ma->hg[k]);
188 free(ma->ploidy); free(ma->q2p); free(ma->pdg);
189 free(ma->phi); free(ma->phi_indel); free(ma->phi1); free(ma->phi2);
190 free(ma->z); free(ma->zswap); free(ma->z1); free(ma->z2);
191 free(ma->afs); free(ma->afs1);
196 static int cal_pdg(const bcf1_t *b, bcf_p1aux_t *ma)
200 p = alloca(b->n_alleles * sizeof(long));
201 memset(p, 0, sizeof(long) * b->n_alleles);
202 for (j = 0; j < ma->n; ++j) {
203 const uint8_t *pi = ma->PL + j * ma->PL_len;
204 double *pdg = ma->pdg + j * 3;
205 pdg[0] = ma->q2p[pi[2]]; pdg[1] = ma->q2p[pi[1]]; pdg[2] = ma->q2p[pi[0]];
206 for (i = 0; i < b->n_alleles; ++i)
207 p[i] += (int)pi[(i+1)*(i+2)/2-1];
209 for (i = 0; i < b->n_alleles; ++i) p[i] = p[i]<<4 | i;
210 for (i = 1; i < b->n_alleles; ++i) // insertion sort
211 for (j = i; j > 0 && p[j] < p[j-1]; --j)
212 tmp = p[j], p[j] = p[j-1], p[j-1] = tmp;
213 for (i = b->n_alleles - 1; i >= 0; --i)
214 if ((p[i]&0xf) == 0) break;
218 int bcf_p1_call_gt(const bcf_p1aux_t *ma, double f0, int k)
221 double max, f3[3], *pdg = ma->pdg + k * 3;
222 int q, i, max_i, ploidy;
223 ploidy = ma->ploidy? ma->ploidy[k] : 2;
225 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
227 f3[0] = 1. - f0; f3[1] = 0; f3[2] = f0;
229 for (i = 0, sum = 0.; i < 3; ++i)
230 sum += (g[i] = pdg[i] * f3[i]);
231 for (i = 0, max = -1., max_i = 0; i < 3; ++i) {
233 if (g[i] > max) max = g[i], max_i = i;
236 if (max < 1e-308) max = 1e-308;
237 q = (int)(-4.343 * log(max) + .499);
244 static void mc_cal_y_core(bcf_p1aux_t *ma, int beg)
246 double *z[2], *tmp, *pdg;
247 int _j, last_min, last_max;
248 assert(beg == 0 || ma->M == ma->n*2);
252 memset(z[0], 0, sizeof(double) * (ma->M + 1));
253 memset(z[1], 0, sizeof(double) * (ma->M + 1));
255 last_min = last_max = 0;
257 if (ma->M == ma->n * 2) {
259 for (_j = beg; _j < ma->n; ++_j) {
260 int k, j = _j - beg, _min = last_min, _max = last_max, M0;
263 pdg = ma->pdg + _j * 3;
264 p[0] = pdg[0]; p[1] = 2. * pdg[1]; p[2] = pdg[2];
265 for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
266 for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
268 if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
269 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];
270 for (k = _min < 2? 2 : _min; k <= _max; ++k)
271 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];
272 for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
273 ma->t += log(sum / (M * (M - 1.)));
274 for (k = _min; k <= _max; ++k) z[1][k] /= sum;
275 if (_min >= 1) z[1][_min-1] = 0.;
276 if (_min >= 2) z[1][_min-2] = 0.;
277 if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
278 if (_j == ma->n1 - 1) { // set pop1; ma->n1==-1 when unset
280 memcpy(ma->z1, z[1], sizeof(double) * (ma->n1 * 2 + 1));
282 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
283 last_min = _min; last_max = _max;
285 //for (_j = 0; _j < last_min; ++_j) z[0][_j] = 0.; // TODO: are these necessary?
286 //for (_j = last_max + 1; _j < ma->M; ++_j) z[0][_j] = 0.;
287 } else { // this block is very similar to the block above; these two might be merged in future
289 for (j = 0; j < ma->n; ++j) {
290 int k, M0, _min = last_min, _max = last_max;
292 pdg = ma->pdg + j * 3;
293 for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
294 for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
297 if (ma->ploidy[j] == 1) {
298 p[0] = pdg[0]; p[1] = pdg[2];
300 if (_min == 0) k = 0, z[1][k] = (M0+1-k) * p[0] * z[0][k];
301 for (k = _min < 1? 1 : _min; k <= _max; ++k)
302 z[1][k] = (M0+1-k) * p[0] * z[0][k] + k * p[1] * z[0][k-1];
303 for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
304 ma->t += log(sum / M);
305 for (k = _min; k <= _max; ++k) z[1][k] /= sum;
306 if (_min >= 1) z[1][_min-1] = 0.;
307 if (j < ma->n - 1) z[1][_max+1] = 0.;
308 } else if (ma->ploidy[j] == 2) {
309 p[0] = pdg[0]; p[1] = 2 * pdg[1]; p[2] = pdg[2];
311 if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
312 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];
313 for (k = _min < 2? 2 : _min; k <= _max; ++k)
314 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];
315 for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
316 ma->t += log(sum / (M * (M - 1.)));
317 for (k = _min; k <= _max; ++k) z[1][k] /= sum;
318 if (_min >= 1) z[1][_min-1] = 0.;
319 if (_min >= 2) z[1][_min-2] = 0.;
320 if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
322 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
323 last_min = _min; last_max = _max;
326 if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (ma->M + 1));
329 static void mc_cal_y(bcf_p1aux_t *ma)
331 if (ma->n1 > 0 && ma->n1 < ma->n && ma->M == ma->n * 2) { // NB: ma->n1 is ineffective when there are haploid samples
334 memset(ma->z1, 0, sizeof(double) * (2 * ma->n1 + 1));
335 memset(ma->z2, 0, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
336 ma->t1 = ma->t2 = 0.;
337 mc_cal_y_core(ma, ma->n1);
339 memcpy(ma->z2, ma->z, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
340 mc_cal_y_core(ma, 0);
342 x = expl(ma->t - (ma->t1 + ma->t2));
343 for (k = 0; k <= ma->M; ++k) ma->z[k] *= x;
344 } else mc_cal_y_core(ma, 0);
347 #define CONTRAST_TINY 1e-30
349 extern double kf_gammaq(double s, double z); // incomplete gamma function for chi^2 test
351 static inline double chi2_test(int a, int b, int c, int d)
354 x = (double)(a+b) * (c+d) * (b+d) * (a+c);
355 if (x == 0.) return 1;
357 return kf_gammaq(.5, .5 * z * z * (a+b+c+d) / x);
360 // chi2=(a+b+c+d)(ad-bc)^2/[(a+b)(c+d)(a+c)(b+d)]
361 static inline double contrast2_aux(const bcf_p1aux_t *p1, double sum, int k1, int k2, double x[3])
363 double p = p1->phi[k1+k2] * p1->z1[k1] * p1->z2[k2] / sum * p1->hg[k1][k2];
364 int n1 = p1->n1, n2 = p1->n - p1->n1;
365 if (p < CONTRAST_TINY) return -1;
366 if (.5*k1/n1 < .5*k2/n2) x[1] += p;
367 else if (.5*k1/n1 > .5*k2/n2) x[2] += p;
369 return p * chi2_test(k1, k2, (n1<<1) - k1, (n2<<1) - k2);
372 static double contrast2(bcf_p1aux_t *p1, double ret[3])
374 int k, k1, k2, k10, k20, n1, n2;
377 n1 = p1->n1; n2 = p1->n - p1->n1;
378 if (n1 <= 0 || n2 <= 0) return 0.;
379 if (p1->hg == 0) { // initialize the hypergeometric distribution
380 /* NB: the hg matrix may take a lot of memory when there are many samples. There is a way
381 to avoid precomputing this matrix, but it is slower and quite intricate. The following
382 computation in this block can be accelerated with a similar strategy, but perhaps this
383 is not a serious concern for now. */
384 double tmp = lgamma(2*(n1+n2)+1) - (lgamma(2*n1+1) + lgamma(2*n2+1));
385 p1->hg = calloc(2*n1+1, sizeof(void*));
386 for (k1 = 0; k1 <= 2*n1; ++k1) {
387 p1->hg[k1] = calloc(2*n2+1, sizeof(double));
388 for (k2 = 0; k2 <= 2*n2; ++k2)
389 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));
393 long double suml = 0;
394 for (k = 0; k <= p1->M; ++k) suml += p1->phi[k] * p1->z[k];
397 { // get the max k1 and k2
400 for (k = 0, max = 0, max_k = -1; k <= 2*n1; ++k) {
401 double x = p1->phi1[k] * p1->z1[k];
402 if (x > max) max = x, max_k = k;
405 for (k = 0, max = 0, max_k = -1; k <= 2*n2; ++k) {
406 double x = p1->phi2[k] * p1->z2[k];
407 if (x > max) max = x, max_k = k;
411 { // 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.
413 long double z = 0., L[2];
414 x[0] = x[1] = x[2] = 0; L[0] = L[1] = 0;
415 for (k1 = k10; k1 >= 0; --k1) {
416 for (k2 = k20; k2 >= 0; --k2) {
417 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
420 for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
421 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
425 ret[0] = x[0]; ret[1] = x[1]; ret[2] = x[2];
426 x[0] = x[1] = x[2] = 0;
427 for (k1 = k10 + 1; k1 <= 2*n1; ++k1) {
428 for (k2 = k20; k2 >= 0; --k2) {
429 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
432 for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
433 if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
437 ret[0] += x[0]; ret[1] += x[1]; ret[2] += x[2];
438 if (ret[0] + ret[1] + ret[2] < 0.95) { // in case of bad things happened
439 ret[0] = ret[1] = ret[2] = 0; L[0] = L[1] = 0;
440 for (k1 = 0, z = 0.; k1 <= 2*n1; ++k1)
441 for (k2 = 0; k2 <= 2*n2; ++k2)
442 if ((y = contrast2_aux(p1, sum, k1, k2, ret)) >= 0) z += y;
443 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...
444 z = 1.0, ret[0] = ret[1] = ret[2] = 1./3;
450 static double mc_cal_afs(bcf_p1aux_t *ma, double *p_ref_folded, double *p_var_folded)
453 long double sum = 0., sum2;
454 double *phi = ma->is_indel? ma->phi_indel : ma->phi;
455 memset(ma->afs1, 0, sizeof(double) * (ma->M + 1));
458 for (k = 0, sum = 0.; k <= ma->M; ++k)
459 sum += (long double)phi[k] * ma->z[k];
460 for (k = 0; k <= ma->M; ++k) {
461 ma->afs1[k] = phi[k] * ma->z[k] / sum;
462 if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return -1.;
464 // compute folded variant probability
465 for (k = 0, sum = 0.; k <= ma->M; ++k)
466 sum += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
467 for (k = 1, sum2 = 0.; k < ma->M; ++k)
468 sum2 += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
469 *p_var_folded = sum2 / sum;
470 *p_ref_folded = (phi[k] + phi[ma->M - k]) / 2. * (ma->z[ma->M] + ma->z[0]) / sum;
471 // the expected frequency
472 for (k = 0, sum = 0.; k <= ma->M; ++k) {
473 ma->afs[k] += ma->afs1[k];
474 sum += k * ma->afs1[k];
479 int bcf_p1_cal(const bcf1_t *b, int do_contrast, bcf_p1aux_t *ma, bcf_p1rst_t *rst)
482 long double sum = 0.;
483 ma->is_indel = bcf_is_indel(b);
486 for (i = 0; i < b->n_gi; ++i) {
487 if (b->gi[i].fmt == bcf_str2int("PL", 2)) {
488 ma->PL = (uint8_t*)b->gi[i].data;
489 ma->PL_len = b->gi[i].len;
493 if (i == b->n_gi) return -1; // no PL
494 if (b->n_alleles < 2) return -1; // FIXME: find a better solution
496 rst->rank0 = cal_pdg(b, ma);
497 rst->f_exp = mc_cal_afs(ma, &rst->p_ref_folded, &rst->p_var_folded);
498 rst->p_ref = ma->afs1[ma->M];
499 for (k = 0, sum = 0.; k < ma->M; ++k)
501 rst->p_var = (double)sum;
502 // calculate f_flat and f_em
503 for (k = 0, sum = 0.; k <= ma->M; ++k)
504 sum += (long double)ma->z[k];
506 for (k = 0; k <= ma->M; ++k) {
507 double p = ma->z[k] / sum;
508 rst->f_flat += k * p;
510 rst->f_flat /= ma->M;
511 { // estimate equal-tail credible interval (95% level)
514 for (i = 0, p = 0.; i < ma->M; ++i)
515 if (p + ma->afs1[i] > 0.025) break;
516 else p += ma->afs1[i];
518 for (i = ma->M-1, p = 0.; i >= 0; --i)
519 if (p + ma->afs1[i] > 0.025) break;
520 else p += ma->afs1[i];
522 rst->cil = (double)(ma->M - h) / ma->M; rst->cih = (double)(ma->M - l) / ma->M;
524 rst->cmp[0] = rst->cmp[1] = rst->cmp[2] = rst->p_chi2 = -1.0;
525 if (do_contrast && rst->p_var > 0.5) // skip contrast2() if the locus is a strong non-variant
526 rst->p_chi2 = contrast2(ma, rst->cmp);
530 void bcf_p1_dump_afs(bcf_p1aux_t *ma)
533 fprintf(pysamerr, "[afs]");
534 for (k = 0; k <= ma->M; ++k)
535 fprintf(pysamerr, " %d:%.3lf", k, ma->afs[ma->M - k]);
536 fprintf(pysamerr, "\n");
537 memset(ma->afs, 0, sizeof(double) * (ma->M + 1));