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#include <stdio.h>
#include "decode.h"
#include "scrappie_stdlib.h"
#include "util.h"
#define NBASE 4
#define BIG_FLOAT 1.e30f
float viterbi_backtrace(float const *score, size_t n, const_scrappie_imatrix traceback, int * seq){
RETURN_NULL_IF(NULL == score, NAN);
RETURN_NULL_IF(NULL == seq, NAN);
const size_t nblock = traceback->nc;
for(size_t i=0 ; i < nblock ; i++){
// Initialise entries to stay
seq[i] = -1;
}
int last_state = argmaxf(score, n);
float logscore = score[last_state];
for(size_t i=0 ; i < nblock ; i++){
const size_t ri = nblock - i - 1;
const int state = traceback->data.f[ri * traceback->stride + last_state];
if(state >= 0){
seq[ri] = last_state;
last_state = state;
}
}
return logscore;
}
float viterbi_local_backtrace(float const *score, size_t n, const_scrappie_imatrix traceback, int * seq){
RETURN_NULL_IF(NULL == score, NAN);
RETURN_NULL_IF(NULL == seq, NAN);
const size_t nblock = traceback->nc;
for(size_t i=0 ; i <= nblock ; i++){
// Initialise entries to stay
seq[i] = -1;
}
int last_state = argmaxf(score, n + 2);
float logscore = score[last_state];
for(size_t i=0 ; i < nblock ; i++){
const size_t ri = nblock - i - 1;
const int state = traceback->data.f[ri * traceback->stride + last_state];
if(state >= 0){
seq[ri + 1] = last_state;
last_state = state;
}
}
seq[0] = last_state;
// Transcode start to stay
for(size_t i=0 ; i < nblock ; i++){
if(seq[i] == n){
seq[i] = -1;
} else {
break;
}
}
// Transcode end to stay
for(int i=nblock ; i >= 0 ; i--){
if(seq[i] == n + 1){
seq[i] = -1;
} else {
break;
}
}
return logscore;
}
float argmax_decoder(const_scrappie_matrix logpost, int *seq) {
RETURN_NULL_IF(NULL == logpost, NAN);
RETURN_NULL_IF(NULL == seq, NAN);
const int nblock = logpost->nc;
const int nstate = logpost->nr;
assert(nstate > 0);
const int stride = logpost->stride;
assert(stride > 0);
int offset;
float logscore = 0;
int imax;
for (int blk = 0; blk < nblock; blk++) {
offset = blk * stride;
imax = argmaxf(logpost->data.f + offset, nstate);
logscore += logpost->data.f[offset + imax];
seq[blk] = (imax == nstate - 1) ? -1 : imax;
}
return logscore;
}
float decode_transducer(const_scrappie_matrix logpost, float stay_pen, float skip_pen, float local_pen, int *seq,
bool allow_slip) {
float logscore = NAN;
RETURN_NULL_IF(NULL == logpost, logscore);
RETURN_NULL_IF(NULL == seq, logscore);
const int nblock = logpost->nc;
const int nstate = logpost->nr;
const int nhistory = nstate - 1;
assert((nhistory % 4) == 0);
const int32_t nhistoryq = nhistory / 4;
const __m128i nhistoryqv = _mm_set1_epi32(nhistoryq);
assert((nhistoryq % 4) == 0);
const int32_t nhistoryqq = nhistoryq / 4;
const __m128i nhistoryqqv = _mm_set1_epi32(nhistoryqq);
assert((nhistoryqq % 4) == 0);
const int32_t nhistoryqqq = nhistoryqq / 4;
const __m128i nhistoryqqqv = _mm_set1_epi32(nhistoryqqq);
if (allow_slip) {
assert((nhistoryqqq % 4) == 0);
}
// Forwards memory + traceback
scrappie_matrix score = make_scrappie_matrix(nhistory + 2, 1);
scrappie_matrix prev_score = make_scrappie_matrix(nhistory + 2, 1);
scrappie_matrix tmp = make_scrappie_matrix(nhistory, 1);
scrappie_imatrix itmp = make_scrappie_imatrix(nhistory, 1);
scrappie_imatrix traceback = make_scrappie_imatrix(nhistory + 2, nblock);
if(NULL == score || NULL == prev_score || NULL == tmp || NULL == itmp || NULL == traceback){
goto cleanup;
}
// Initialise
for (int i = 0; i < nhistoryq; i++) {
score->data.v[i] = _mm_set1_ps(-BIG_FLOAT);
}
score->data.f[nhistory] = 0.0f;
score->data.f[nhistory + 1] = -BIG_FLOAT;
// Forwards Viterbi iteration
for (int blk = 0; blk < nblock; blk++) {
const size_t offsetTq = blk * traceback->nrq;
const size_t offsetT = offsetTq * 4;
const size_t offsetPq = blk * logpost->nrq;
const size_t offsetP = offsetPq * 4;
// Swap score and previous score
{
scrappie_matrix tmptr = score;
score = prev_score;
prev_score = tmptr;
}
// Stay
const __m128 stay_m128 =
_mm_set1_ps(logpost->data.f[offsetP + nhistory] - stay_pen);
const __m128i negone_m128i = _mm_set1_epi32(-1);
for (int i = 0; i < nhistoryq; i++) {
// Traceback for stay is negative
score->data.v[i] = prev_score->data.v[i] + stay_m128;
traceback->data.v[offsetTq + i] = negone_m128i;
}
// Step
// Following three loops find maximum over suffix and record index
for (int i = 0; i < nhistoryqq; i++) {
tmp->data.v[i] = prev_score->data.v[i];
itmp->data.v[i] = _mm_setzero_si128();
}
for (int r = 1; r < NBASE; r++) {
const size_t offset = r * nhistoryqq;
const __m128i itmp_fill = _mm_set1_epi32(r);
for (int i = 0; i < nhistoryqq; i++) {
__m128i mask = _mm_castps_si128(_mm_cmplt_ps(tmp->data.v[i],
prev_score->data.
v[offset + i]));
tmp->data.v[i] =
_mm_max_ps(tmp->data.v[i], prev_score->data.v[offset + i]);
itmp->data.v[i] =
_mm_or_si128(_mm_andnot_si128(mask, itmp->data.v[i]),
_mm_and_si128(mask, itmp_fill));
}
}
const __m128i c0123_m128i = _mm_setr_epi32(0, 1, 2, 3);
for (int i = 0; i < nhistoryqq; i++) {
itmp->data.v[i] =
_mm_add_epi32(_mm_mullo_epi32(itmp->data.v[i], nhistoryqv),
_mm_add_epi32(c0123_m128i,
_mm_set1_epi32(i * 4)));
}
for (int pref = 0; pref < nhistoryq; pref++) {
const size_t i = pref;
const __m128 step_score =
logpost->data.v[offsetPq + i] + _mm_set1_ps(tmp->data.f[pref]);
__m128i mask =
_mm_castps_si128(_mm_cmplt_ps(score->data.v[i], step_score));
score->data.v[i] = _mm_max_ps(score->data.v[i], step_score);
traceback->data.v[offsetTq + i] =
_mm_or_si128(_mm_andnot_si128
(mask, traceback->data.v[offsetTq + i]),
_mm_and_si128(mask,
_mm_set1_epi32(itmp->data.f[pref])));
}
// Skip
const __m128 skip_penv = _mm_set1_ps(skip_pen);
for (int i = 0; i < nhistoryqqq; i++) {
tmp->data.v[i] = prev_score->data.v[i];
itmp->data.v[i] = _mm_setzero_si128();
}
for (int r = 1; r < NBASE * NBASE; r++) {
const size_t offset = r * nhistoryqqq;
const __m128i itmp_fill = _mm_set1_epi32(r);
for (int i = 0; i < nhistoryqqq; i++) {
__m128i mask = _mm_castps_si128(_mm_cmplt_ps(tmp->data.v[i],
prev_score->data.
v[offset + i]));
tmp->data.v[i] =
_mm_max_ps(tmp->data.v[i], prev_score->data.v[offset + i]);
itmp->data.v[i] =
_mm_or_si128(_mm_andnot_si128(mask, itmp->data.v[i]),
_mm_and_si128(mask, itmp_fill));
}
}
for (int i = 0; i < nhistoryqqq; i++) {
itmp->data.v[i] =
_mm_add_epi32(_mm_mullo_epi32(itmp->data.v[i], nhistoryqqv),
_mm_add_epi32(c0123_m128i,
_mm_set1_epi32(i * 4)));
}
for (int pref = 0; pref < nhistoryqq; pref++) {
for (int i = 0; i < NBASE; i++) {
const size_t oi = pref * NBASE + i;
// This cycling through prefixes
const __m128 skip_score = logpost->data.v[offsetPq + oi]
+ _mm_set1_ps(tmp->data.f[pref])
- skip_penv;
__m128i mask =
_mm_castps_si128(_mm_cmplt_ps
(score->data.v[oi], skip_score));
score->data.v[oi] = _mm_max_ps(score->data.v[oi], skip_score);
traceback->data.v[offsetTq + oi] =
_mm_or_si128(_mm_andnot_si128
(mask, traceback->data.v[offsetTq + oi]),
_mm_and_si128(mask,
_mm_set1_epi32(itmp->
data.f[pref])));
}
}
// Slip
if (allow_slip) {
const int32_t nhistoryqqqq = nhistoryqqq / 4;
const __m128 slip_penv = _mm_set1_ps(2.0 * skip_pen);
for (int i = 0; i < nhistoryqqqq; i++) {
tmp->data.v[i] = prev_score->data.v[i];
itmp->data.v[i] = _mm_setzero_si128();
}
for (int r = 1; r < NBASE * NBASE * NBASE; r++) {
const size_t offset = r * nhistoryqqqq;
const __m128i itmp_fill = _mm_set1_epi32(r);
for (int i = 0; i < nhistoryqqqq; i++) {
__m128i mask = _mm_castps_si128(_mm_cmplt_ps(tmp->data.v[i],
prev_score->
data.v[offset +
i]));
tmp->data.v[i] =
_mm_max_ps(tmp->data.v[i],
prev_score->data.v[offset + i]);
itmp->data.v[i] =
_mm_or_si128(_mm_andnot_si128(mask, itmp->data.v[i]),
_mm_and_si128(mask, itmp_fill));
}
}
for (int i = 0; i < nhistoryqqqq; i++) {
itmp->data.v[i] =
_mm_add_epi32(_mm_mullo_epi32
(itmp->data.v[i], nhistoryqqqv),
_mm_add_epi32(c0123_m128i,
_mm_set1_epi32(i * 4)));
}
for (int pref = 0; pref < nhistoryqqq; pref++) {
for (int i = 0; i < NBASE * NBASE; i++) {
const size_t oi = pref * NBASE * NBASE + i;
// This cycling through prefixes
const __m128 skip_score = logpost->data.v[offsetPq + oi]
+ _mm_set1_ps(tmp->data.f[pref])
- slip_penv;
__m128i mask =
_mm_castps_si128(_mm_cmplt_ps
(score->data.v[oi], skip_score));
score->data.v[oi] =
_mm_max_ps(score->data.v[oi], skip_score);
traceback->data.v[offsetTq + oi] =
_mm_or_si128(_mm_andnot_si128
(mask, traceback->data.v[offsetTq + oi]),
_mm_and_si128(mask,
_mm_set1_epi32(itmp->data.f
[pref])));
}
}
}
// Remain in start state (stay or local penalty)
score->data.f[nhistory] = prev_score->data.f[nhistory]
+ fmaxf(-local_pen, logpost->data.f[offsetP + nhistory] - stay_pen);
traceback->data.f[offsetT + nhistory] = nhistory;
// Exit start state
for(int hst=0 ; hst < nhistory ; hst++){
const float scoref = prev_score->data.f[nhistory] + logpost->data.f[offsetP + hst];
if(scoref > score->data.f[hst]){
score->data.f[hst] = scoref;
traceback->data.f[offsetT + hst] = nhistory;
}
}
// Remain in end state (stay or local penalty)
score->data.f[nhistory + 1] = prev_score->data.f[nhistory + 1]
+ fmax(-local_pen, logpost->data.f[offsetP + nhistory] - stay_pen);
traceback->data.f[offsetT + nhistory + 1] = nhistory + 1;
// Enter end state
for(int hst=0 ; hst < nhistory ; hst++){
const float scoref = prev_score->data.f[hst] - local_pen;
if(scoref > score->data.f[nhistory + 1]){
score->data.f[nhistory + 1] = scoref;
traceback->data.f[offsetT + nhistory + 1] = hst;
}
}
}
// Viterbi traceback
logscore = viterbi_local_backtrace(score->data.f, nhistory, traceback, seq);
assert(validate_ivector(seq, nblock, -1, nhistory - 1, __FILE__, __LINE__));
cleanup:
traceback = free_scrappie_imatrix(traceback);
itmp = free_scrappie_imatrix(itmp);
tmp = free_scrappie_matrix(tmp);
prev_score = free_scrappie_matrix(prev_score);
score = free_scrappie_matrix(score);
return logscore;
}
int overlap(int k1, int k2, int nkmer) {
// Neither k1 nor k2 can be stays
assert(k1 >= 0);
assert(k2 >= 0);
int kmer_mask = nkmer - 1;
int overlap = 0;
do {
kmer_mask >>= 2;
k1 &= kmer_mask;
k2 >>= 2;
overlap += 1;
} while (k1 != k2);
return overlap;
}
size_t position_highest_bit(size_t x) {
size_t i = 0;
for (; x != 0; i++, x >>= 1) ;
return i;
}
size_t first_nonnegative(const int *seq, size_t n) {
RETURN_NULL_IF(NULL == seq, n);
size_t st;
for (st = 0; st < n && seq[st] < 0; st++) ;
return st;
}
bool iskmerhomopolymer(int kmer, int klen) {
const int b = kmer & 3;
for (int k = 1; k < klen; k++) {
kmer >>= 2;
if (b != (kmer & 3)) {
return false;
}
}
return true;
}
const char base_lookup[4] = { 'A', 'C', 'G', 'T' };
// This method assumes a model which outputs single bases
char *ctc_remove_stays_and_repeats(const int *seq, size_t n, int *pos) {
RETURN_NULL_IF(NULL == seq, NULL);
RETURN_NULL_IF(NULL == pos, NULL);
// Determine length of final sequence
int length = 0;
if (seq[0] >= 0) { length += 1; }
for (size_t blk = 1; blk < n; blk++) {
if (seq[blk] >= 0 && seq[blk - 1] != seq[blk]) {
length += 1;
}
}
// Initialise basespace sequence with terminating null
char *bases = calloc(length + 1, sizeof(char));
RETURN_NULL_IF(NULL == bases, NULL);
int loc = -1;
int prev = -2;
for (size_t blk = 0; blk < n; blk++) {
int this = seq[blk];
if (this >= 0 && this != prev) {
bases[loc] = base_lookup[this];
prev = this;
loc += 1;
}
if (NULL != pos) {
pos[blk] = loc;
}
}
return bases;
}
char *overlapper(const int *seq, size_t n, int nkmer, int *pos) {
RETURN_NULL_IF(NULL == seq, NULL);
const size_t kmer_len = position_highest_bit(nkmer) / 2;
// Determine length of final sequence
size_t length = kmer_len;
// Find first non-stay
const size_t st = first_nonnegative(seq, n);
RETURN_NULL_IF(st == n, NULL);
int kprev = seq[st];
for (size_t k = st + 1; k < n; k++) {
if (seq[k] < 0) {
// Short-cut stays
continue;
}
assert(seq[k] >= 0);
length += overlap(kprev, seq[k], nkmer);
kprev = seq[k];
assert(kprev >= 0);
}
// Initialise basespace sequence with terminating null
char *bases = calloc(length + 1, sizeof(char));
RETURN_NULL_IF(NULL == bases, NULL);
// Fill with first kmer
for (size_t kmer = seq[st], k = 1; k <= kmer_len; k++) {
size_t b = kmer & 3;
kmer >>= 2;
bases[kmer_len - k] = base_lookup[b];
}
if(NULL != pos){
// Initial pos array if required -- start at beginning
pos[0] = 0;
}
for (size_t last_idx = kmer_len - 1, kprev = seq[st], k = st + 1; k < n; k++) {
if (seq[k] < 0) {
// Short-cut stays
if (NULL != pos) {
pos[k] = pos[k - 1];
}
continue;
}
int ol = overlap(kprev, seq[k], nkmer);
if (NULL != pos) {
pos[k] = pos[k - 1] + ol;
}
kprev = seq[k];
for (size_t kmer = seq[k], i = 0; i < ol; i++) {
size_t b = kmer & 3;
kmer >>= 2;
bases[last_idx + ol - i] = base_lookup[b];
}
last_idx += ol;
}
return bases;
}
int calibrated_dwell(int hdwell, int inhomo, const dwell_model dm) {
const int b = inhomo & 3;
return (int)roundf(((float)hdwell - dm.base_adj[b]) / dm.scale);
}
char *dwell_corrected_overlapper(const int *seq, const int *dwell, int n,
int nkmer, const dwell_model dm) {
RETURN_NULL_IF(NULL == seq, NULL);
RETURN_NULL_IF(NULL == dwell, NULL);
const int kmer_len = position_highest_bit(nkmer) / 2;
// Determine length of final sequence
int length = kmer_len;
// Find first non-stay
const int st = first_nonnegative(seq, n);
assert(st != n);
int kprev = seq[st];
int inhomo = -1;
int hdwell = 0;
for (int k = st + 1; k < n; k++) {
/* Simple state machine tagged by inhomo
* inhomo < 0 -- not in a homopolymer
* inhomo >= 0 -- in homopolymer and value is homopolymer state
*/
if (seq[k] < 0) {
// State is stay. Short circuit rest of logic
if (inhomo >= 0) {
// Accumate dwell if in homopolymer
hdwell += dwell[k];
}
continue;
}
if (seq[k] == inhomo) {
// Not stay but still in same homopolymer
hdwell += dwell[k];
continue;
}
if (inhomo >= 0) {
// Changed state. Leave homopolymer
length += calibrated_dwell(hdwell, inhomo, dm);
inhomo = -1;
hdwell = 0;
}
assert(seq[k] >= 0);
length += overlap(kprev, seq[k], nkmer);
kprev = seq[k];
assert(kprev >= 0);
if (iskmerhomopolymer(kprev, kmer_len)) {
// Entered a new homopolymer
inhomo = kprev;
hdwell = dwell[k];
}
}
if (inhomo >= 0) {
// Correction for final homopolymer
length += calibrated_dwell(hdwell, inhomo, dm);
}
// Initialise basespace sequence with terminating null
char *bases = calloc(length + 1, sizeof(char));
// Fill with first kmer
for (int kmer = seq[st], k = 1; k <= kmer_len; k++) {
int b = kmer & 3;
kmer >>= 2;
bases[kmer_len - k] = base_lookup[b];
}
int last_idx = kmer_len - 1;
inhomo = -1;
hdwell = 0;
for (int kprev = seq[st], k = st + 1; k < n; k++) {
if (seq[k] < 0) {
// State is stay.
if (inhomo >= 0) {
// Accumate dwell if in homopolymer
hdwell += dwell[k];
}
continue;
}
if (seq[k] == inhomo) {
// Not stay but still in same homopolymer
hdwell += dwell[k];
continue;
}
if (inhomo >= 0) {
// Changed state. Leave homopolymer
int hlen = calibrated_dwell(hdwell, inhomo, dm);
char hbase = base_lookup[inhomo & 3];
for (int i = 0; i < hlen; i++, last_idx++) {
bases[last_idx + 1] = hbase;
}
inhomo = -1;
hdwell = 0;
}
int ol = overlap(kprev, seq[k], nkmer);
kprev = seq[k];
for (int kmer = seq[k], i = 0; i < ol; i++) {
int b = kmer & 3;
kmer >>= 2;
bases[last_idx + ol - i] = base_lookup[b];
}
last_idx += ol;
if (iskmerhomopolymer(kprev, kmer_len)) {
// Entered a new homopolymer
inhomo = kprev;
hdwell += dwell[k];
}
}
if (inhomo >= 0) {
// Correction for final homopolymer
int hlen = calibrated_dwell(hdwell, inhomo, dm);
char hbase = base_lookup[inhomo & 3];
for (int i = 0; i < hlen; i++, last_idx++) {
bases[last_idx] = hbase;
}
}
if (last_idx + 1 != length) {
printf("last_idx %d length %d\n\n", last_idx, length);
assert(last_idx + 1 == length);
}
return bases;
}
char *homopolymer_dwell_correction(const event_table et, const int *seq,
size_t nstate, size_t basecall_len) {
RETURN_NULL_IF(NULL == et.event, NULL);
RETURN_NULL_IF(NULL == seq, NULL);
const int nev = et.end - et.start;
const int evoffset = et.start;
assert(et.event[nev + evoffset - 1].start >= et.event[evoffset].start);
int *dwell = calloc(nev, sizeof(int));
RETURN_NULL_IF(NULL == dwell, NULL);
for (int ev = 0; ev < nev; ev++) {
dwell[ev] = et.event[ev + evoffset].length;
}
/* Calibrate scaling factor for homopolymer estimation.
* Simple mean of the dwells of all 'step' movements in
* the basecall. Steps within homopolymers are ignored.
* A more complex calibration could be used.
*/
int tot_step_dwell = 0;
int nstep = 0;
for (int ev = 0, ppos = -2, evdwell = 0, pstate = -1; ev < nev; ev++) {
// Sum over dwell of all steps excluding those within homopolymers
if (et.event[ev + evoffset].pos == ppos) {
// Stay. Accumulate dwell
evdwell += dwell[ev];
continue;
}
if (et.event[ev + evoffset].pos == ppos + 1
&& et.event[ev + evoffset].state != pstate) {
// Have a step that is not within a homopolymer
tot_step_dwell += evdwell;
nstep += 1;
}
evdwell = dwell[ev];
ppos = et.event[ev + evoffset].pos;
pstate = et.event[ev + evoffset].state;
}
// Estimate of scale with a prior with weight equal to a single observation.
const float start_delta = (float)(et.event[nev + evoffset - 1].start
- et.event[evoffset ].start);
const float prior_scale =
(et.event[nev + evoffset - 1].length + start_delta) / (float)basecall_len;
const float homo_scale = (prior_scale + tot_step_dwell) / (1.0 + nstep);
const dwell_model dm = { homo_scale, {0.0f, 0.0f, 0.0f, 0.0f} };
char *newbases =
dwell_corrected_overlapper(seq, dwell, nev, nstate - 1, dm);
free(dwell);
return newbases;
}
void colmaxf(float * x, int nr, int nc, int * idx){
assert(nr > 0);
assert(nc > 0);
RETURN_NULL_IF(NULL == x,);
RETURN_NULL_IF(NULL == idx,);
for(int r=0 ; r < nr ; r++){
// Initialise
idx[r] = 0;
}
for(int c=1 ; c < nc ; c++){
const size_t offset2 = c * nr;
for(int r=0 ; r<nr ; r++){
if(x[offset2 + r] > x[idx[r] * nr + r]){
idx[r] = c;
}
}
}
}
float sloika_viterbi(const_scrappie_matrix logpost, float stay_pen, float skip_pen, float local_pen, int *seq){
float logscore = NAN;
RETURN_NULL_IF(NULL == logpost, logscore);
RETURN_NULL_IF(NULL == seq, logscore);
const int nbase = 4;
const size_t nblock = logpost->nc;
const size_t nst = logpost->nr;
const size_t nhst = nst - 1;
const size_t nstep = nbase;
const size_t nskip = nbase * nbase;
assert(nhst % nstep == 0);
assert(nhst % nskip == 0);
const size_t step_rem = nhst / nstep;
const size_t skip_rem = nhst / nskip;
float * cscore = calloc(nhst + 2, sizeof(float));
float * pscore = calloc(nhst + 2, sizeof(float));
int * step_idx = calloc(step_rem, sizeof(int));
int * skip_idx = calloc(skip_rem, sizeof(int));
scrappie_imatrix traceback = make_scrappie_imatrix(nhst + 2, nblock);
if(NULL != cscore && NULL != pscore && NULL != step_idx && NULL != skip_idx && NULL != traceback){
// Initialise -- must begin in start state
for(size_t i=0 ; i < (nhst + 2) ; i++){
cscore[i] = -BIG_FLOAT;
}
cscore[nhst] = 0.0f;
// Forwards Viterbi
for(size_t i=0 ; i < nblock ; i++){
const size_t lpoffset = i * logpost->stride;
const size_t toffset = i * traceback->stride;
{ // Swap vectors
float * tmp = pscore;
pscore = cscore;
cscore = tmp;
}
// Step indices
colmaxf(pscore, step_rem, nstep, step_idx);
// Skip indices
colmaxf(pscore, skip_rem, nskip, skip_idx);
// Update score for step and skip
for(size_t hst=0 ; hst < nhst ; hst++){
size_t step_prefix = hst / nstep;
size_t skip_prefix = hst / nskip;
size_t step_hst = step_prefix + step_idx[step_prefix] * step_rem;
size_t skip_hst = skip_prefix + skip_idx[skip_prefix] * skip_rem;
float step_score = pscore[step_hst];
float skip_score = pscore[skip_hst] - skip_pen;
if(step_score > skip_score){
// Arbitrary assumption here! Should be >= ?
cscore[hst] = step_score;
traceback->data.f[toffset + hst] = step_hst;
} else {
cscore[hst] = skip_score;
traceback->data.f[toffset + hst] = skip_hst;
}
cscore[hst] += logpost->data.f[lpoffset + hst];
}
// Stay
for(size_t hst=0 ; hst < nhst ; hst++){
const float score = pscore[hst] + logpost->data.f[lpoffset + nhst] - stay_pen;
if(score > cscore[hst]){
// Arbitrary assumption here! Should be >= ?
cscore[hst] = score;
traceback->data.f[toffset + hst] = -1;
}
}
// Remain in start state -- local penalty or stay
cscore[nhst] = pscore[nhst] + fmaxf(-local_pen, logpost->data.f[lpoffset + nhst] - stay_pen);
traceback->data.f[toffset + nhst] = nhst;
// Exit start state
for(size_t hst=0 ; hst < nhst ; hst++){
const float score = pscore[nhst] + logpost->data.f[lpoffset + hst];
if(score > cscore[hst]){
cscore[hst] = score;
traceback->data.f[toffset + hst] = nhst;
}
}
// Remain in end state -- local penalty or stay
cscore[nhst + 1] = pscore[nhst + 1] + fmaxf(-local_pen, logpost->data.f[lpoffset + nhst] - stay_pen);
traceback->data.f[toffset + nhst + 1] = nhst + 1;
// Enter end state
for(size_t hst=0 ; hst < nhst ; hst++){
const float score = pscore[hst] - local_pen;
if(score > cscore[nhst + 1]){
cscore[nhst + 1] = score;
traceback->data.f[toffset + nhst + 1] = hst;
}
}
}
logscore = viterbi_local_backtrace(cscore, nhst, traceback, seq);
}
traceback = free_scrappie_imatrix(traceback);
free(skip_idx);
free(step_idx);
free(pscore);
free(cscore);
return logscore;
}
float decode_crf(const_scrappie_matrix trans, int * path){
RETURN_NULL_IF(NULL == trans, NAN);
RETURN_NULL_IF(NULL == path, NAN);
const size_t nblk = trans->nc;
const size_t nstate = roundf(sqrtf((float)trans->nr));
assert(nstate * nstate == trans->nr);
float * mem = calloc(2 * nstate, sizeof(float));
scrappie_imatrix tb = make_scrappie_imatrix(nstate, nblk);
if(NULL == mem || NULL == tb){
tb = free_scrappie_imatrix(tb);
free(mem);
return NAN;
}
float * curr = mem;
float * prev = mem + nstate;
// Forwards Viterbi pass
for(size_t blk=0 ; blk < nblk ; blk++){
const size_t offset = blk * trans->stride;
const size_t tboffset = blk * tb->stride;
{ // Swap
float * tmp = curr;
curr = prev;
prev = tmp;
}
for(size_t st1=0 ; st1 < nstate ; st1++){
// st1 is to-state (in -ACGT)
const size_t offsetS = offset + st1 * nstate;
curr[st1] = trans->data.f[offsetS + 0] + prev[0];
tb->data.f[tboffset + st1] = 0;
for(size_t st2=1 ; st2 < nstate ; st2++){
// st2 is from-state (in -ACGT)
const float score = trans->data.f[offsetS + st2] + prev[st2];
if(score > curr[st1]){
curr[st1] = score;
tb->data.f[tboffset + st1] = st2;
}
}
}
}
// Traceback
const float score = valmaxf(curr, nstate);
path[nblk] = argmaxf(curr, nstate);
for(size_t blk=nblk ; blk > 0 ; blk--){
const size_t offset = (blk - 1) * tb->stride;
path[blk - 1] = tb->data.f[offset + path[blk]];
}
tb = free_scrappie_imatrix(tb);
free(mem);
return score;
}
char * crfpath_to_basecall(int const * path, size_t npos, int * pos){
RETURN_NULL_IF(NULL == path, NULL);
RETURN_NULL_IF(NULL == pos, NULL);
int nbase = 0;
for(size_t pos=0 ; pos < npos ; pos++){
if(path[pos] < NBASE){
nbase += 1;
}
}
char * basecall = calloc(nbase + 1, sizeof(char));
RETURN_NULL_IF(NULL == basecall, NULL);
for(size_t pos=0, bpos=0 ; pos < npos ; pos++){
if(path[pos] < NBASE){
assert(bpos < nbase);
basecall[bpos] = base_lookup[path[pos]];
bpos += 1;
}
}
return basecall;
}
/** Posterior over states at each block
*
* @param trans. Constant scrappie matrix containing the (25) energies
* for each block. (order ACGT-, from state in minor, to state major).
*
* @returns scrappie matrix containing the posterior for nblk + 1
**/
scrappie_matrix posterior_crf(const_scrappie_matrix trans){
RETURN_NULL_IF(NULL == trans, NULL);
const size_t nstate = roundf(sqrtf((float)trans->nr));
assert(nstate * nstate == trans->nr);
const size_t nblk = trans->nc;
scrappie_matrix post = make_scrappie_matrix(nstate, nblk + 1);
RETURN_NULL_IF(NULL == post, NULL);
// Forwards pass
for(size_t st=0 ; st < nstate ; st++){
// Initialisation
post->data.f[st] = 0.0f;
}
for(size_t blk=0 ; blk < nblk ; blk++){
const size_t offset = blk * trans->stride;
const size_t offset_post = blk * post->stride;
const float * prev = post->data.f + offset_post;
float * curr = post->data.f + offset_post + post->stride;
for(size_t st1=0 ; st1 < nstate ; st1++){
const size_t offsetS = offset + st1 * nstate;
curr[st1] = trans->data.f[offsetS + 0] + prev[0];
for(size_t st2=1 ; st2 < nstate ; st2++){
curr[st1] = logsumexpf(curr[st1], trans->data.f[offsetS + st2] + prev[st2]);
}
}
}
// Backwards pass
float * tmpmem = malloc(2 * nstate * sizeof(float));
float * prev = tmpmem;
float * curr = tmpmem + nstate;
for(size_t st=0 ; st < nstate ; st++){
// Initialisation
curr[st] = 0.0f;
}
// Normalisation of last block
float tot = 0.0f;
for(size_t st=0 ; st < nstate ; st++){
tot = logsumexpf(tot, post->data.f[nblk * post->stride + st]);
}
for(size_t st=0 ; st < nstate ; st++){
post->data.f[nblk * post->stride + st] = expf(post->data.f[nblk * post->stride + st] - tot);
}
for(size_t blk=nblk ; blk > 0 ; blk--){
const size_t blkm1 = blk - 1;
const size_t offset = blkm1 * trans->stride;
const size_t offset_post = blkm1 * post->stride;
{ // Swap
float * tmp = curr;
curr = prev;
prev = tmp;
}
for(size_t st=0 ; st < nstate ; st++){
curr[st] = trans->data.f[offset + st] + prev[0];
}
for(size_t st1=1 ; st1 < nstate ; st1++){
const size_t offsetS = offset + st1 * nstate;
for(size_t st2=0 ; st2 < nstate ; st2++){
curr[st2] = logsumexpf(curr[st2], trans->data.f[offsetS + st2] + prev[st1]);
}
}
// Normalisation
float tot = 0.0f;
for(size_t st=0 ; st < nstate ; st++){
post->data.f[offset_post + st] += curr[st];
tot = logsumexpf(tot, post->data.f[offset_post + st]);
}
for(size_t st=0 ; st < nstate ; st++){
post->data.f[offset_post + st] = expf(post->data.f[offset_post + st] - tot);
}
}
free(tmpmem);
return post;
}
static float LARGE_VAL = 1e30f;
/** Map a signal to a predicted squiggle using variant of dynamic time-warping
*
* Uses a local mapping so not all of signal may be mapped and not every position of the
* predicted squiggle may be mapped to.
*
* @param signal `raw_table` containing signal to map
* @param rate Rate of translocation relative to squiggle model
* @param params `scrappie_matrix` containing predicted squiggle
* @param prob_back Probability of a backward movement.
* @param local_pen Penalty for local mapping (stay in start or ends state)
* @param skip_pen Penalty for skipping
* @param minscore Minimum possible emission for
* @param path [OUT] An array containing path. Length equal to that of FULL signal
* @param fwd [OUT]
*
* @returns score
**/
float squiggle_match_viterbi(const raw_table signal, float rate, const_scrappie_matrix params,
float prob_back, float local_pen, float skip_pen, float minscore,
int32_t * path_padded){
RETURN_NULL_IF(NULL == signal.raw, NAN);
RETURN_NULL_IF(NULL == params, NAN);
RETURN_NULL_IF(NULL == path_padded, NAN);
assert(signal.start < signal.end);
assert(signal.end <= signal.n);
assert(rate > 0.0f);
assert(prob_back >= 0.0f && prob_back <= 1.0f);
float final_score = NAN;
const float * rawsig = signal.raw + signal.start;
const size_t nsample = signal.end - signal.start;
const size_t ldp = params->stride;
const size_t npos = params->nc;
const size_t nfstate = npos + 2;
const size_t nstate = npos + nfstate;
const float move_back_pen = logf(prob_back);
const float stay_in_back_pen = logf(0.5f);
const float move_from_back_pen = logf(0.5f);
float * move_pen = calloc(nfstate, sizeof(float));
float * fwd = calloc(2 * nstate, sizeof(float));
float * scale = calloc(npos, sizeof(float));
float * stay_pen = calloc(nfstate, sizeof(float));
int32_t * traceback = calloc(nsample * nstate, sizeof(int32_t));
if(NULL == move_pen || NULL == fwd || NULL == scale ||
NULL == stay_pen || NULL == traceback){
goto clean;
}
for(size_t pos=0 ; pos < npos ; pos++){
// Create array of scales
scale[pos] = expf(params->data.f[pos * ldp + 1]);
}
for(size_t i=0 ; i < signal.n ; i++){
path_padded[i] = -1;
}
// Only deal with part of path that corresponds to trimmed signal
int32_t * path = path_padded + signal.start;
{
const float lograte = logf(rate);
float mean_move_pen = 0.0f;
float mean_stay_pen = 0.0f;
for(size_t pos=0 ; pos < npos ; pos++){
const float mp = (1.0f - prob_back) * plogisticf(params->data.f[pos * ldp + 2] + lograte);
move_pen[pos + 1] = logf(mp);
stay_pen[pos + 1] = log1pf(-mp - prob_back);
mean_move_pen += move_pen[pos + 1];
mean_stay_pen += stay_pen[pos + 1];
}
mean_move_pen /= npos;
mean_stay_pen /= npos;
move_pen[0] = mean_move_pen;
move_pen[nfstate - 1] = mean_move_pen;
stay_pen[0] = mean_stay_pen;
stay_pen[nfstate - 1] = mean_stay_pen;
}
for(size_t st=0 ; st < nstate ; st++){
// States are start .. positions .. end
fwd[st] = -LARGE_VAL;
}
// Must begin in start state
fwd[0] = 0.0;
for(size_t sample=0 ; sample < nsample ; sample++){
const size_t fwd_prev_off = (sample % 2) * nstate;
const size_t fwd_curr_off = ((sample + 1) % 2) * nstate;
const size_t tr_off = sample * nstate;
for(size_t st=0 ; st < nfstate ; st++){
// Stay in start, end or normal position
fwd[fwd_curr_off + st] = fwd[fwd_prev_off + st] + stay_pen[st];
traceback[tr_off + st] = st;
}
for(size_t st=0 ; st < npos ; st++){
// Stay in back position
const size_t idx = nfstate + st;
fwd[fwd_curr_off + idx] = fwd[fwd_prev_off + idx] + stay_in_back_pen;
traceback[tr_off + idx] = idx;
}
for(size_t st=1 ; st < nfstate ; st++){
// Move to next position
const float step_score = fwd[fwd_prev_off + st - 1] + move_pen[st - 1];
if(step_score > fwd[fwd_curr_off + st]){
fwd[fwd_curr_off + st] = step_score;
traceback[tr_off + st] = st - 1;
}
}
for(size_t st=2 ; st < nfstate ; st++){
// Skip to next position
const float skip_score = fwd[fwd_prev_off + st - 2] + move_pen[st - 2] - skip_pen;
if(skip_score > fwd[fwd_curr_off + st]){
fwd[fwd_curr_off + st] = skip_score;
traceback[tr_off + st] = st - 2;
}
}
for(size_t destpos=1 ; destpos < npos ; destpos++){
const size_t destst = destpos + 1;
// Move from start into sequence
const float score = fwd[fwd_prev_off] + move_pen[0] - local_pen * destpos;
if(score > fwd[fwd_curr_off + destst]){
fwd[fwd_curr_off + destst] = score;
traceback[tr_off + destst] = 0;
}
}
for(size_t origpos=0 ; origpos < (npos - 1) ; origpos++){
const size_t destst = nfstate - 1;
const size_t origst = origpos + 1;
const size_t deltapos = npos - 1 - origpos;
// Move from sequence into end
const float score = fwd[fwd_prev_off + origst] + move_pen[origst] - local_pen * deltapos;
if(score > fwd[fwd_curr_off + destst]){
fwd[fwd_curr_off + destst] = score;
traceback[tr_off + destst] = origst;
}
}
for(size_t st=1 ; st < npos ; st++){
// Move to back
const float back_score = fwd[fwd_prev_off + st + 1] + move_back_pen;
if(back_score > fwd[fwd_curr_off + nfstate + st - 1]){
fwd[fwd_curr_off + nfstate + st - 1] = back_score;
traceback[tr_off + nfstate + st - 1] = st + 1;
}
}
for(size_t st=1 ; st < npos ; st++){
// Move from back
const float back_score = fwd[fwd_prev_off + nfstate + st - 1] + move_from_back_pen;
if(back_score > fwd[fwd_curr_off + st + 1]){
fwd[fwd_curr_off + st + 1] = back_score;
traceback[tr_off + st + 1] = nfstate + st - 1;
}
}
for(size_t pos=0 ; pos < npos ; pos++){
// Add on score for samples
const float location = params->data.f[pos * ldp + 0];
const float logscale = params->data.f[pos * ldp + 1];
const float logscore = fmaxf(-minscore, loglaplace(rawsig[sample], location, scale[pos], logscale));
// State to add to is offset by one because of start state
fwd[fwd_curr_off + pos + 1] += logscore;
fwd[fwd_curr_off + nfstate + pos] += logscore;
}
// Score for start and end states
fwd[fwd_curr_off + 0] -= local_pen;
fwd[fwd_curr_off + nfstate - 1] -= local_pen;
}
// Score of best path and final states. Could be either last position or end state
const size_t fwd_offset = (nsample % 2) * nstate;
final_score = fmaxf(fwd[fwd_offset + nfstate - 2], fwd[fwd_offset + nfstate - 1]);
if(fwd[fwd_offset + nfstate - 2] > fwd[fwd_offset + nfstate - 1]){
path[nsample - 1] = nfstate - 2;
} else {
path[nsample - 1] = nfstate - 1;
}
for(size_t sample=1 ; sample < nsample ; sample++){
const size_t rs = nsample - sample;
const size_t tr_off = rs * nstate;
path[rs - 1] = traceback[tr_off + path[rs]];
}
// Correct path so start and end states are encoded as -1, other states as positions
{
size_t sample_min = 0;
size_t sample_max = nsample;
for(; sample_min < nsample ; sample_min++){
if(0 != path[sample_min]){
break;
}
path[sample_min] = -1;
}
for(; sample_max > 0 ; sample_max--){
if(nfstate - 1 != path[sample_max - 1]){
break;
}
path[sample_max - 1] = -1;
}
for(size_t sample=sample_min ; sample < sample_max ; sample++){
assert(path[sample] > 0);
if(path[sample] >= nfstate){
path[sample] -= nfstate;
} else {
path[sample] -= 1;
}
}
}
clean:
free(traceback);
free(stay_pen);
free(scale);
free(fwd);
free(move_pen);
return final_score;
}
/** Score a signal against a predicted squiggle using variant of dynamic time-warping
*
* Uses a local mapping so not all of signal may be mapped and not every position of the
* predicted squiggle may be mapped to.
*
* @param signal `raw_table` containing signal to map
* @param rate Read translocation rate relative to squiggle model
* @param params `scrappie_matrix` containing predicted squiggle
* @param prob_back Probability of a backward movement.
* @param local_pen Penalty for local mapping (stay in start or ends state)
* @param skip_pen Penalty for skipping
* @param minscore Minimum possible emission for
*
* @returns score
**/
float squiggle_match_forward(const raw_table signal, float rate, const_scrappie_matrix params,
float prob_back, float local_pen, float skip_pen, float minscore){
RETURN_NULL_IF(NULL == signal.raw, NAN);
RETURN_NULL_IF(NULL == params, NAN);
assert(signal.start < signal.end);
assert(signal.end <= signal.n);
assert(prob_back >= 0.0f && prob_back <= 1.0f);
assert(rate > 0.0);
float final_score = NAN;
const float * rawsig = signal.raw + signal.start;
const size_t nsample = signal.end - signal.start;
const size_t ldp = params->stride;
const size_t npos = params->nc;
const size_t nfstate = npos + 2;
const size_t nstate = npos + nfstate;
const float move_back_pen = logf(prob_back);
const float stay_in_back_pen = logf(0.5f);
const float move_from_back_pen = logf(0.5f);
float * move_pen = calloc(nfstate, sizeof(float));
float * fwd = calloc(2 * nstate, sizeof(float));
float * scale = calloc(npos, sizeof(float));
float * stay_pen = calloc(nfstate, sizeof(float));
if(NULL == move_pen || NULL == fwd || NULL == scale ||
NULL == stay_pen){
goto clean;
}
for(size_t pos=0 ; pos < npos ; pos++){
// Create array of scales
scale[pos] = expf(params->data.f[pos * ldp + 1]);
}
{
const float lograte = logf(rate);
float mean_move_pen = 0.0f;
float mean_stay_pen = 0.0f;
for(size_t pos=0 ; pos < npos ; pos++){
const float mp = (1.0f - prob_back) * plogisticf(params->data.f[pos * ldp + 2] + lograte);
move_pen[pos + 1] = logf(mp);
stay_pen[pos + 1] = log1pf(-mp - prob_back);
mean_move_pen += move_pen[pos + 1];
mean_stay_pen += stay_pen[pos + 1];
}
mean_move_pen /= npos;
mean_stay_pen /= npos;
move_pen[0] = mean_move_pen;
move_pen[nfstate - 1] = mean_move_pen;
stay_pen[0] = mean_stay_pen;
stay_pen[nfstate - 1] = mean_stay_pen;
}
for(size_t st=0 ; st < nstate ; st++){
// States are start .. positions .. end
fwd[st] = -LARGE_VAL;
}
// Must begin in start state
fwd[0] = 0.0;
for(size_t sample=0 ; sample < nsample ; sample++){
const size_t fwd_prev_off = (sample % 2) * nstate;
const size_t fwd_curr_off = ((sample + 1) % 2) * nstate;
for(size_t st=0 ; st < nfstate ; st++){
// Stay in start, end or normal position
fwd[fwd_curr_off + st] = fwd[fwd_prev_off + st] + stay_pen[st];
}
for(size_t st=0 ; st < npos ; st++){
// Stay in back position
const size_t idx = nfstate + st;
fwd[fwd_curr_off + idx] = fwd[fwd_prev_off + idx] + stay_in_back_pen;
}
for(size_t st=1 ; st < nfstate ; st++){
// Move to next position
const float step_score = fwd[fwd_prev_off + st - 1] + move_pen[st - 1];
fwd[fwd_curr_off + st] = logsumexpf(fwd[fwd_curr_off + st], step_score);
}
for(size_t st=2 ; st < nfstate ; st++){
// Skip to next position
const float skip_score = fwd[fwd_prev_off + st - 2] + move_pen[st - 2] - skip_pen;
fwd[fwd_curr_off + st] = logsumexpf(fwd[fwd_curr_off + st], skip_score);
}
for(size_t destpos=1 ; destpos < npos ; destpos++){
const size_t destst = destpos + 1;
// Move from start into sequence
const float score = fwd[fwd_prev_off] + move_pen[0] - local_pen * destpos;
fwd[fwd_curr_off + destst] = logsumexpf(fwd[fwd_curr_off + destst], score);
}
for(size_t origpos=0 ; origpos < (npos - 1) ; origpos++){
const size_t destst = nfstate - 1;
const size_t origst = origpos + 1;
const size_t deltapos = npos - 1 - origpos;
// Move from sequence into end
const float score = fwd[fwd_prev_off + origst] + move_pen[origst] - local_pen * deltapos;
fwd[fwd_curr_off + destst] = logsumexpf(fwd[fwd_curr_off + destst], score);
}
for(size_t st=1 ; st < npos ; st++){
// Move to back
const float back_score = fwd[fwd_prev_off + st + 1] + move_back_pen;
fwd[fwd_curr_off + nfstate + st - 1] = logsumexpf(fwd[fwd_curr_off + nfstate + st - 1], back_score);
}
for(size_t st=1 ; st < npos ; st++){
// Move from back
const float back_score = fwd[fwd_prev_off + nfstate + st - 1] + move_from_back_pen;
fwd[fwd_curr_off + st + 1] = logsumexpf(fwd[fwd_curr_off + st + 1], back_score);
}
for(size_t pos=0 ; pos < npos ; pos++){
// Add on score for samples
const float location = params->data.f[pos * ldp + 0];
const float logscale = params->data.f[pos * ldp + 1];
const float logscore = fmaxf(-minscore, loglaplace(rawsig[sample], location, scale[pos], logscale));
// State to add to is offset by one because of start state
fwd[fwd_curr_off + pos + 1] += logscore;
fwd[fwd_curr_off + nfstate + pos] += logscore;
}
// Score for start and end states
fwd[fwd_curr_off + 0] -= local_pen;
fwd[fwd_curr_off + nfstate - 1] -= local_pen;
}
// Score of best path and final states. Could be either last position or end state
const size_t fwd_offset = (nsample % 2) * nstate;
final_score = logsumexpf(fwd[fwd_offset + nfstate - 2], fwd[fwd_offset + nfstate - 1]);
clean:
free(stay_pen);
free(scale);
free(fwd);
free(move_pen);
return final_score;
}
/** Viterbi score of sequence
*
* Local-global mapping through sequence calculating scores of best path from basecall posterior
*
* Internal states are seq0 ... seq, start, end
*
* @param logpost Log posterior probability of state at each block. Stay is last state.
* @param stay_pen Penalty for staying
* @param skip_pen Penalty for skipping
* @param local_pen Penalty for local mapping (stay in start or ends state)
* @param seq Sequence encoded into same history states as basecalls
* @param seqlen Length of seq
* @param path Viterbi path [out]. If NULL, no path is returned
*
* @returns score
**/
float map_to_sequence_viterbi(const_scrappie_matrix logpost, float stay_pen, float skip_pen,
float local_pen, int const *seq, size_t seqlen, int *path){
float logscore = NAN;
RETURN_NULL_IF(NULL == logpost, logscore);
RETURN_NULL_IF(NULL == seq, logscore);
const size_t nblock = logpost->nc;
const size_t nst = logpost->nr;
const size_t STAY = nst - 1;
const size_t nseqstate = seqlen + 2;
const size_t START_STATE = seqlen;
const size_t END_STATE = seqlen + 1;
// Memory.
float * cscore = calloc(nseqstate, sizeof(float));
float * pscore = calloc(nseqstate, sizeof(float));
scrappie_imatrix traceback = make_scrappie_imatrix(nseqstate, nblock);
if(NULL == cscore || NULL == pscore || NULL == traceback){
traceback = free_scrappie_imatrix(traceback);
free(pscore);
free(cscore);
return logscore;
}
// Initialise
for(size_t pos=0 ; pos < nseqstate ; pos++){
cscore[pos] = -BIG_FLOAT;
}
cscore[START_STATE] = 0.0;
// Forwards Viterbi
for(size_t blk=0 ; blk < nblock ; blk++){
const size_t lpoffset = blk * logpost->stride;
const size_t toffset = blk * traceback->stride;
{ // Swap vectors
float * tmp = pscore;
pscore = cscore;
cscore = tmp;
}
// Stay in start state (local penalty or stay)
cscore[START_STATE] = pscore[START_STATE] + fmaxf(-local_pen, logpost->data.f[lpoffset + STAY]);
traceback->data.f[toffset + START_STATE] = START_STATE;
// Stay in end state (local penalty or stay)
cscore[END_STATE] = pscore[END_STATE] + fmaxf(-local_pen, logpost->data.f[lpoffset + STAY]);
traceback->data.f[toffset + END_STATE] = END_STATE;
for(size_t pos=0 ; pos < seqlen ; pos++){
// Stay in ordinary state
cscore[pos] = pscore[pos] - stay_pen + logpost->data.f[lpoffset + STAY];
traceback->data.f[toffset + pos] = pos;
}
for(size_t pos=1 ; pos < seqlen ; pos++){
// Step
const size_t newstate = seq[pos];
const float step_score = pscore[pos - 1] + logpost->data.f[lpoffset + newstate];
if(step_score > cscore[pos]){
cscore[pos] = step_score;
traceback->data.f[toffset + pos] = pos - 1;
}
}
for(size_t pos=2 ; pos < seqlen ; pos++){
// Skip
const size_t newstate = seq[pos];
const float skip_score = pscore[pos - 2] - skip_pen + logpost->data.f[lpoffset + newstate];
if(skip_score > cscore[pos]){
cscore[pos] = skip_score;
traceback->data.f[toffset + pos] = pos - 2;
}
}
// Move directly from start to end without mapping
/*if(pscore[START_STATE] - local_pen > cscore[END_STATE]){
cscore[END_STATE] = pscore[START_STATE] - local_pen;
traceback->data.f[toffset + END_STATE] = START_STATE;
}*/
// Move from start into sequence
if(pscore[START_STATE] + logpost->data.f[lpoffset + seq[0]] > cscore[0]){
cscore[0] = pscore[START_STATE] + logpost->data.f[lpoffset + seq[0]];
traceback->data.f[toffset + 0] = START_STATE;
}
// Move from sequence into end
if(pscore[seqlen - 1] - local_pen > cscore[END_STATE]){
cscore[END_STATE] = pscore[seqlen - 1] - local_pen;
traceback->data.f[toffset + END_STATE] = seqlen - 1;
}
}
logscore = fmaxf(cscore[seqlen - 1], cscore[END_STATE]);
if(NULL != path){
path[nblock - 1] = (cscore[seqlen-1] > cscore[END_STATE]) ? (seqlen - 1) : END_STATE;
for(size_t blk=nblock - 1; blk > 0 ; blk--){
const size_t toffset = blk * traceback->stride;
path[blk - 1] = traceback->data.f[toffset + path[blk]];
}
for(size_t blk=0 ; blk < nblock ; blk++){
if(START_STATE == path[blk] || END_STATE == path[blk]){
path[blk] = -1;
}
}
}
traceback = free_scrappie_imatrix(traceback);
free(pscore);
free(cscore);
return logscore;
}
/** Forward score of sequence
*
* Local-Global mapping through sequence calculating sum of scores over all paths from basecall posterior
*
* @param logpost Log posterior probability of state at each block. Stay is last state.
* @param stay_pen Penalty for staying
* @param skip_pen Penalty for skipping
* @param local_pen Penalty for local mapping (stay in start or ends state)
* @param seq Sequence encoded into same history states as basecalls
* @param seqlen Length of seq
*
* @returns score
**/
float map_to_sequence_forward(const_scrappie_matrix logpost, float stay_pen, float skip_pen,
float local_pen, int const *seq, size_t seqlen){
float logscore = NAN;
RETURN_NULL_IF(NULL == logpost, logscore);
RETURN_NULL_IF(NULL == seq, logscore);
const size_t nblock = logpost->nc;
const size_t nst = logpost->nr;
const size_t STAY = nst - 1;
const size_t nseqstate = seqlen + 2;
const size_t START_STATE = seqlen;
const size_t END_STATE = seqlen + 1;
// Memory.
float * cscore = calloc(nseqstate, sizeof(float));
float * pscore = calloc(nseqstate, sizeof(float));
if(NULL == cscore || NULL == pscore){
free(pscore);
free(cscore);
return logscore;
}
// Initialise
for(size_t pos=0 ; pos < nseqstate ; pos++){
cscore[pos] = -BIG_FLOAT;
}
cscore[START_STATE] = 0.0;
// Forwards pass
for(size_t blk=0 ; blk < nblock ; blk++){
const size_t lpoffset = blk * logpost->stride;
{ // Swap vectors
float * tmp = pscore;
pscore = cscore;
cscore = tmp;
}
// Stay in start state (local penalty or stay)
cscore[START_STATE] = pscore[START_STATE] + logsumexpf(-local_pen, logpost->data.f[lpoffset + STAY]);
// Stay in end state (local penalty or stay)
cscore[END_STATE] = pscore[END_STATE] + logsumexpf(-local_pen, logpost->data.f[lpoffset + STAY]);
for(size_t pos=0 ; pos < seqlen ; pos++){
// Stay
cscore[pos] = pscore[pos] - stay_pen + logpost->data.f[lpoffset + STAY];
}
for(size_t pos=1 ; pos < seqlen ; pos++){
// Step
const size_t newstate = seq[pos];
const float step_score = pscore[pos - 1] + logpost->data.f[lpoffset + newstate];
cscore[pos] = logsumexpf(cscore[pos], step_score);
}
for(size_t pos=2 ; pos < seqlen ; pos++){
// skip
const size_t newstate = seq[pos];
const float skip_score = pscore[pos - 2] - skip_pen + logpost->data.f[lpoffset + newstate];
cscore[pos] = logsumexpf(cscore[pos], skip_score);
}
// Move directly from start to end without mapping
//cscore[END_STATE] = logsumexpf(cscore[END_STATE], pscore[START_STATE] - local_pen);
// Move from start into sequence
cscore[0] = logsumexpf(cscore[0], pscore[START_STATE] + logpost->data.f[lpoffset + seq[0]]);
// Move from sequence into end
cscore[END_STATE] = logsumexpf(cscore[END_STATE], pscore[seqlen - 1] - local_pen);
}
logscore = logsumexpf(cscore[seqlen - 1], cscore[END_STATE]);
free(pscore);
free(cscore);
return logscore;
}
/** Check if sequences of lower and upper bounds are consistent
*
* @param low Array of lower bounds
* @param high Array of upper bounds
* @param nblock Number of blocks (bounds)
* @param seqlen Length of sequence (maximum upper bound)
*
* @returns bool
**/
bool are_bounds_sane(size_t const * low, size_t const * high, size_t nblock, size_t seqlen){
bool ret = true;
if(NULL == low || NULL == high){
warnx("One or more bounds are NULL\n");
// Early return since further tests make no sense
return false;
}
if(low[0] != 0){
warnx("First bound must include 0 (got %zu)\n", low[0]);
ret = false;
}
if(high[nblock - 1] != seqlen){
warnx("Last bound must equal seqlen %zu (got %zu)\n", seqlen, high[nblock - 1]);
ret = false;
}
for(size_t i=0 ; i < nblock ; i++){
if(low[i] > seqlen){
warnx("Low bound for block %zu exceeds length of sequence (got %zu but seqlen is %zu)\n", i, low[i], seqlen);
ret = false;
}
if(high[i] > seqlen){
warnx("High bound for block %zu exceeds length of sequence (got %zu but seqlen is %zu)\n", i, high[i], seqlen);
ret = false;
}
if(low[i] > high[i]){
warnx("Low bound for block %zu exceeds high bound [%zu , %zu).\n", i, low[i], high[i]);
ret = false;
}
}
for(size_t i=1 ; i < nblock ; i++){
if(low[i] > high[i - 1]){
// Allow case where step but not stay is possible (low[i] == high[i-1])
warnx("Blocks %zu and %zu don't overlap [%zu , %zu) -> [%zu , %zu)\n",
i - 1, i , low[i - 1], high[i - 1], low[i], high[i]);
ret = false;
}
if(low[i] < low[i - 1]){
warnx("Low bounds for blocks %zu and %zu aren't monotonic [%zu , %zu) -> [%zu , %zu)\n",
i - 1, i , low[i - 1], high[i - 1], low[i], high[i]);
ret = false;
}
if(high[i] < high[i - 1]){
warnx("High bounds for blocks %zu and %zu aren't monotonic [%zu , %zu) -> [%zu , %zu)\n",
i - 1, i , low[i - 1], high[i - 1], low[i], high[i]);
ret = false;
}
}
return ret;
}
/** Viterbi score of sequence, banded
*
* Local-Global mapping through sequence calculating scores of best path from basecall posterior (banded)
*
* @param logpost Log posterior probability of state at each block. Stay is last state.
* @param stay_pen Penalty for staying
* @param skip_pen Penalty for skipping
* @param local_pen Penalty for local mapping (stay in start or ends state)
* @param seq Sequence encoded into same history states as basecalls
* @param seqlen Length of seq
* @param poslow, poshigh Arrays of lowest and highest coordinate for each block. Low inclusive, high exclusive
*
* @returns score
**/
float map_to_sequence_viterbi_banded(const_scrappie_matrix logpost, float stay_pen, float skip_pen, float local_pen,
int const *seq, size_t seqlen, size_t const * poslow, size_t const * poshigh){
float logscore = NAN;
RETURN_NULL_IF(NULL == logpost, logscore);
RETURN_NULL_IF(NULL == seq, logscore);
RETURN_NULL_IF(NULL == poslow, logscore);
RETURN_NULL_IF(NULL == poshigh, logscore);
const size_t nblock = logpost->nc;
const size_t nst = logpost->nr;
const size_t STAY = nst - 1;
const size_t nseqstate = seqlen + 2;
const size_t START_STATE = seqlen;
const size_t END_STATE = seqlen + 1;
// Verify assumptions about bounds
RETURN_NULL_IF(!are_bounds_sane(poslow, poshigh, nblock, seqlen), logscore);
// Memeory. First state is stay in previous position
float * cscore = calloc(nseqstate, sizeof(float));
float * pscore = calloc(nseqstate, sizeof(float));
if(NULL == cscore || NULL == pscore){
free(pscore);
free(cscore);
return logscore;
}
// Initialise
for(size_t pos=0 ; pos < nseqstate ; pos++){
pscore[pos] = -BIG_FLOAT;
cscore[pos] = -BIG_FLOAT;
}
pscore[START_STATE] = 0.0;
// Forwards Viterbi
{ // First block
// Stay in start state (local penalty or stay)
cscore[START_STATE] = pscore[START_STATE] + fmaxf(-local_pen, logpost->data.f[STAY]);
// Stay in end state (local penalty or stay)
cscore[END_STATE] = pscore[END_STATE] + fmaxf(-local_pen, logpost->data.f[STAY]);
cscore[0] = fmaxf(cscore[0], pscore[0] + logpost->data.f[STAY] - stay_pen);
if(poshigh[0] > 0){
// Step
const size_t stepto = seq[1];
const float step_score = logpost->data.f[stepto];
cscore[1] = step_score;
}
if(poshigh[0] > 1){
// Skip
const size_t stepto = seq[2];
const float skip_score = logpost->data.f[stepto] - skip_pen;
cscore[2] = skip_score;
}
// Move directly from start to end without mapping -- always allow
cscore[END_STATE] = fmaxf(cscore[END_STATE], pscore[START_STATE] - local_pen);
// Move from start into sequence -- lower bound for first block must be zero
cscore[0] = fmaxf(cscore[0], pscore[START_STATE] + logpost->data.f[seq[0]]);
// Move from sequence into end
cscore[END_STATE] = fmaxf(cscore[END_STATE], pscore[seqlen - 1] - local_pen);
}
for(size_t blk=1 ; blk < nblock ; blk++){
const size_t lpoffset = blk * logpost->stride;
{ // Swap vectors
float * tmp = pscore;
pscore = cscore;
cscore = tmp;
}
// Stay in start state (local penalty or stay)
cscore[START_STATE] = pscore[START_STATE] + fmaxf(-local_pen, logpost->data.f[lpoffset + STAY]);
// Stay in end state (local penalty or stay)
cscore[END_STATE] = pscore[END_STATE] + fmaxf(-local_pen, logpost->data.f[lpoffset + STAY]);
for(size_t pos=poslow[blk] ; pos < poshigh[blk - 1] ; pos++){
// Stay
cscore[pos] = pscore[pos] - stay_pen + logpost->data.f[lpoffset + STAY];
}
const size_t min_step_idx = imax(poslow[blk], poslow[blk - 1] + 1);
const size_t max_step_idx = imin(poshigh[blk], poshigh[blk - 1] + 1);
for(size_t pos=min_step_idx ; pos < max_step_idx ; pos++){
// step -- pos is position going _to_
const size_t stepto = seq[pos];
const float step_score = pscore[pos - 1] + logpost->data.f[lpoffset + stepto];
cscore[pos] = fmaxf(step_score, cscore[pos]);
}
const size_t min_skip_idx = imax(poslow[blk], poslow[blk - 1] + 2);
const size_t max_skip_idx = imin(poshigh[blk], poshigh[blk - 1] + 2);
for(size_t pos=min_skip_idx ; pos < max_skip_idx ; pos++){
// skip -- pos is position going _to_
const size_t skipto = seq[pos];
const float skip_score = pscore[pos - 2] - skip_pen
+ logpost->data.f[lpoffset + skipto];
cscore[pos] = fmaxf(skip_score, cscore[pos]);
}
// Move directly from start to end without mapping -- always allow
//cscore[END_STATE] = fmaxf(cscore[END_STATE], pscore[START_STATE] - local_pen);
// Move from start into sequence -- only allowed if lower bound is zero
if(0 == poslow[blk]){
cscore[0] = fmaxf(cscore[0], pscore[START_STATE] + logpost->data.f[lpoffset + seq[0]]);
}
// Move from sequence into end
cscore[END_STATE] = fmaxf(cscore[END_STATE], pscore[seqlen - 1] - local_pen);
}
logscore = fmax(cscore[seqlen - 1], cscore[END_STATE]);
free(pscore);
free(cscore);
return logscore;
}
/** Forward score of sequence, banded
*
* Local-Global mapping through sequence calculating scores of best path from basecall posterior (banded)
*
* @param logpost Log posterior probability of state at each block. Stay is last state.
* @param stay_pen Penalty for staying
* @param skip_pen Penalty for skipping
* @param local_pen Penalty for local mapping (stay in start or ends state)
* @param seq Sequence encoded into same history states as basecalls
* @param seqlen Length of seq
* @param poslow, poshigh Arrays of lowest and highest coordinate for each block. Low inclusive, high exclusive
*
*
* @returns score
**/
float map_to_sequence_forward_banded(const_scrappie_matrix logpost, float stay_pen, float skip_pen, float local_pen,
int const *seq, size_t seqlen, size_t const * poslow, size_t const * poshigh){
float logscore = NAN;
RETURN_NULL_IF(NULL == logpost, logscore);
RETURN_NULL_IF(NULL == seq, logscore);
RETURN_NULL_IF(NULL == poslow, logscore);
RETURN_NULL_IF(NULL == poshigh, logscore);
const size_t nblock = logpost->nc;
const size_t nst = logpost->nr;
const size_t STAY = nst - 1;
const size_t nseqstate = seqlen + 2;
const size_t START_STATE = seqlen;
const size_t END_STATE = seqlen + 1;
// Verify assumptions about bounds
RETURN_NULL_IF(!are_bounds_sane(poslow, poshigh, nblock, seqlen), logscore);
// Memory. First state is stay in previous position
float * cscore = calloc(nseqstate, sizeof(float));
float * pscore = calloc(nseqstate, sizeof(float));
if(NULL == cscore || NULL == pscore){
free(pscore);
free(cscore);
return logscore;
}
// Initialise
for(size_t pos=0 ; pos < nseqstate ; pos++){
pscore[pos] = -BIG_FLOAT;
cscore[pos] = -BIG_FLOAT;
}
pscore[START_STATE] = 0.0f;
// Forwards pass
{ // First block
// Stay in start state (local penalty or stay)
cscore[START_STATE] = pscore[START_STATE] + logsumexpf(-local_pen, logpost->data.f[STAY]);
// Stay in end state (local penalty or stay)
cscore[END_STATE] = pscore[END_STATE] + logsumexpf(-local_pen, logpost->data.f[STAY]);
cscore[0] = logsumexpf(cscore[0], pscore[0] + logpost->data.f[STAY] - stay_pen);
if(poshigh[0] > 0){
// Step
const size_t stepto = seq[1];
const float step_score = logpost->data.f[stepto];
cscore[1] = step_score;
}
if(poshigh[0] > 1){
// Skip
const size_t stepto = seq[2];
const float skip_score = logpost->data.f[stepto] - skip_pen;
cscore[2] = skip_score;
}
// Move directly from start to end without mapping -- always allow
cscore[END_STATE] = logsumexpf(cscore[END_STATE], pscore[START_STATE] - local_pen);
// Move from start into sequence -- lower bound for first block must be zero
cscore[0] = logsumexpf(cscore[0], pscore[START_STATE] + logpost->data.f[seq[0]]);
// Move from sequence into end
cscore[END_STATE] = logsumexpf(cscore[END_STATE], pscore[seqlen - 1] - local_pen);
}
for(size_t blk=1 ; blk < nblock ; blk++){
const size_t lpoffset = blk * logpost->stride;
{ // Swap vectors
float * tmp = pscore;
pscore = cscore;
cscore = tmp;
}
// Stay in start state (local penalty or stay)
cscore[START_STATE] = pscore[START_STATE] + logsumexpf(-local_pen, logpost->data.f[lpoffset + STAY]);
// Stay in end state (local penalty or stay)
cscore[END_STATE] = pscore[END_STATE] + logsumexpf(-local_pen, logpost->data.f[lpoffset + STAY]);
for(size_t pos=poslow[blk] ; pos < poshigh[blk - 1] ; pos++){
// Stay
cscore[pos] = pscore[pos] - stay_pen + logpost->data.f[lpoffset + STAY];
}
const size_t min_step_idx = imax(poslow[blk], poslow[blk - 1] + 1);
const size_t max_step_idx = imin(poshigh[blk], poshigh[blk - 1] + 1);
for(size_t pos=min_step_idx ; pos < max_step_idx ; pos++){
// step -- pos is position going _to_
const size_t stepto = seq[pos];
const float step_score = pscore[pos - 1] + logpost->data.f[lpoffset + stepto];
cscore[pos] = logsumexpf(step_score, cscore[pos]);
}
const size_t min_skip_idx = imax(poslow[blk], poslow[blk - 1] + 2);
const size_t max_skip_idx = imin(poshigh[blk], poshigh[blk - 1] + 2);
for(size_t pos=min_skip_idx ; pos < max_skip_idx ; pos++){
// skip -- pos is position going _to_
const size_t skipto = seq[pos];
const float skip_score = pscore[pos - 2] - skip_pen
+ logpost->data.f[lpoffset + skipto];
cscore[pos] = logsumexpf(skip_score, cscore[pos]);
}
// Move directly from start to end without mapping -- always allow
//cscore[END_STATE] = logsumexpf(cscore[END_STATE], pscore[START_STATE] - local_pen);
// Move from start into sequence -- only allowed if lower bound is zero
if(0 == poslow[blk]){
cscore[0] = logsumexpf(cscore[0], pscore[START_STATE] + logpost->data.f[lpoffset + seq[0]]);
}
// Move from sequence into end
cscore[END_STATE] = logsumexpf(cscore[END_STATE], pscore[seqlen - 1] - local_pen);
}
logscore = logsumexpf(cscore[seqlen - 1], cscore[END_STATE]);
free(pscore);
free(cscore);
return logscore;
}
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