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0
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1 /* The MIT License
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2
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3 Copyright (c) 2003-2006, 2008-2010, by Heng Li <lh3lh3@live.co.uk>
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4
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5 Permission is hereby granted, free of charge, to any person obtaining
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6 a copy of this software and associated documentation files (the
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7 "Software"), to deal in the Software without restriction, including
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8 without limitation the rights to use, copy, modify, merge, publish,
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9 distribute, sublicense, and/or sell copies of the Software, and to
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10 permit persons to whom the Software is furnished to do so, subject to
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11 the following conditions:
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12
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13 The above copyright notice and this permission notice shall be
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14 included in all copies or substantial portions of the Software.
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15
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16 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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17 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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18 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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19 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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20 BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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21 ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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22 CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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23 SOFTWARE.
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24 */
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25
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26 #include <stdlib.h>
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27 #include <stdio.h>
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28 #include <string.h>
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29 #include <stdint.h>
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30 #include <math.h>
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31 #include "kprobaln.h"
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32
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33 /*****************************************
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34 * Probabilistic banded glocal alignment *
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35 *****************************************/
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36
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37 #define EI .25
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38 #define EM .33333333333
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39
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40 static float g_qual2prob[256];
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41
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42 #define set_u(u, b, i, k) { int x=(i)-(b); x=x>0?x:0; (u)=((k)-x+1)*3; }
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43
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44 kpa_par_t kpa_par_def = { 0.001, 0.1, 10 };
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45 kpa_par_t kpa_par_alt = { 0.0001, 0.01, 10 };
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46
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47 /*
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48 The topology of the profile HMM:
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49
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50 /\ /\ /\ /\
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51 I[1] I[k-1] I[k] I[L]
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52 ^ \ \ ^ \ ^ \ \ ^
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53 | \ \ | \ | \ \ |
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54 M[0] M[1] -> ... -> M[k-1] -> M[k] -> ... -> M[L] M[L+1]
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55 \ \/ \/ \/ /
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56 \ /\ /\ /\ /
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57 -> D[k-1] -> D[k] ->
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58
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59 M[0] points to every {M,I}[k] and every {M,I}[k] points M[L+1].
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60
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61 On input, _ref is the reference sequence and _query is the query
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62 sequence. Both are sequences of 0/1/2/3/4 where 4 stands for an
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63 ambiguous residue. iqual is the base quality. c sets the gap open
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64 probability, gap extension probability and band width.
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65
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66 On output, state and q are arrays of length l_query. The higher 30
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67 bits give the reference position the query base is matched to and the
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68 lower two bits can be 0 (an alignment match) or 1 (an
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69 insertion). q[i] gives the phred scaled posterior probability of
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70 state[i] being wrong.
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71 */
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72 int kpa_glocal(const uint8_t *_ref, int l_ref, const uint8_t *_query, int l_query, const uint8_t *iqual,
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73 const kpa_par_t *c, int *state, uint8_t *q)
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74 {
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75 double **f, **b = 0, *s, m[9], sI, sM, bI, bM, pb;
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76 float *qual, *_qual;
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77 const uint8_t *ref, *query;
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78 int bw, bw2, i, k, is_diff = 0, is_backward = 1, Pr;
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79
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80 /*** initialization ***/
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81 is_backward = state && q? 1 : 0;
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82 ref = _ref - 1; query = _query - 1; // change to 1-based coordinate
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83 bw = l_ref > l_query? l_ref : l_query;
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84 if (bw > c->bw) bw = c->bw;
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85 if (bw < abs(l_ref - l_query)) bw = abs(l_ref - l_query);
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86 bw2 = bw * 2 + 1;
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87 // allocate the forward and backward matrices f[][] and b[][] and the scaling array s[]
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88 f = calloc(l_query+1, sizeof(void*));
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89 if (is_backward) b = calloc(l_query+1, sizeof(void*));
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90 for (i = 0; i <= l_query; ++i) {
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91 f[i] = calloc(bw2 * 3 + 6, sizeof(double)); // FIXME: this is over-allocated for very short seqs
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92 if (is_backward) b[i] = calloc(bw2 * 3 + 6, sizeof(double));
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93 }
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94 s = calloc(l_query+2, sizeof(double)); // s[] is the scaling factor to avoid underflow
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95 // initialize qual
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96 _qual = calloc(l_query, sizeof(float));
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97 if (g_qual2prob[0] == 0)
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98 for (i = 0; i < 256; ++i)
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99 g_qual2prob[i] = pow(10, -i/10.);
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100 for (i = 0; i < l_query; ++i) _qual[i] = g_qual2prob[iqual? iqual[i] : 30];
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101 qual = _qual - 1;
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102 // initialize transition probability
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103 sM = sI = 1. / (2 * l_query + 2); // the value here seems not to affect results; FIXME: need proof
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104 m[0*3+0] = (1 - c->d - c->d) * (1 - sM); m[0*3+1] = m[0*3+2] = c->d * (1 - sM);
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105 m[1*3+0] = (1 - c->e) * (1 - sI); m[1*3+1] = c->e * (1 - sI); m[1*3+2] = 0.;
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106 m[2*3+0] = 1 - c->e; m[2*3+1] = 0.; m[2*3+2] = c->e;
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107 bM = (1 - c->d) / l_ref; bI = c->d / l_ref; // (bM+bI)*l_ref==1
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108 /*** forward ***/
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109 // f[0]
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110 set_u(k, bw, 0, 0);
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111 f[0][k] = s[0] = 1.;
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112 { // f[1]
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113 double *fi = f[1], sum;
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114 int beg = 1, end = l_ref < bw + 1? l_ref : bw + 1, _beg, _end;
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115 for (k = beg, sum = 0.; k <= end; ++k) {
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116 int u;
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117 double e = (ref[k] > 3 || query[1] > 3)? 1. : ref[k] == query[1]? 1. - qual[1] : qual[1] * EM;
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118 set_u(u, bw, 1, k);
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119 fi[u+0] = e * bM; fi[u+1] = EI * bI;
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120 sum += fi[u] + fi[u+1];
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121 }
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122 // rescale
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123 s[1] = sum;
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124 set_u(_beg, bw, 1, beg); set_u(_end, bw, 1, end); _end += 2;
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125 for (k = _beg; k <= _end; ++k) fi[k] /= sum;
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126 }
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127 // f[2..l_query]
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128 for (i = 2; i <= l_query; ++i) {
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129 double *fi = f[i], *fi1 = f[i-1], sum, qli = qual[i];
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130 int beg = 1, end = l_ref, x, _beg, _end;
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131 uint8_t qyi = query[i];
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132 x = i - bw; beg = beg > x? beg : x; // band start
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133 x = i + bw; end = end < x? end : x; // band end
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134 for (k = beg, sum = 0.; k <= end; ++k) {
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135 int u, v11, v01, v10;
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136 double e;
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137 e = (ref[k] > 3 || qyi > 3)? 1. : ref[k] == qyi? 1. - qli : qli * EM;
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138 set_u(u, bw, i, k); set_u(v11, bw, i-1, k-1); set_u(v10, bw, i-1, k); set_u(v01, bw, i, k-1);
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139 fi[u+0] = e * (m[0] * fi1[v11+0] + m[3] * fi1[v11+1] + m[6] * fi1[v11+2]);
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140 fi[u+1] = EI * (m[1] * fi1[v10+0] + m[4] * fi1[v10+1]);
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141 fi[u+2] = m[2] * fi[v01+0] + m[8] * fi[v01+2];
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142 sum += fi[u] + fi[u+1] + fi[u+2];
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143 // fprintf(stderr, "F (%d,%d;%d): %lg,%lg,%lg\n", i, k, u, fi[u], fi[u+1], fi[u+2]); // DEBUG
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144 }
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145 // rescale
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146 s[i] = sum;
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147 set_u(_beg, bw, i, beg); set_u(_end, bw, i, end); _end += 2;
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148 for (k = _beg, sum = 1./sum; k <= _end; ++k) fi[k] *= sum;
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149 }
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150 { // f[l_query+1]
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151 double sum;
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152 for (k = 1, sum = 0.; k <= l_ref; ++k) {
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153 int u;
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154 set_u(u, bw, l_query, k);
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155 if (u < 3 || u >= bw2*3+3) continue;
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156 sum += f[l_query][u+0] * sM + f[l_query][u+1] * sI;
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157 }
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158 s[l_query+1] = sum; // the last scaling factor
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159 }
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160 { // compute likelihood
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161 double p = 1., Pr1 = 0.;
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162 for (i = 0; i <= l_query + 1; ++i) {
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163 p *= s[i];
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164 if (p < 1e-100) Pr += -4.343 * log(p), p = 1.;
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165 }
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166 Pr1 += -4.343 * log(p * l_ref * l_query);
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167 Pr = (int)(Pr1 + .499);
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168 if (!is_backward) { // skip backward and MAP
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169 for (i = 0; i <= l_query; ++i) free(f[i]);
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170 free(f); free(s); free(_qual);
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171 return Pr;
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172 }
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173 }
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174 /*** backward ***/
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175 // b[l_query] (b[l_query+1][0]=1 and thus \tilde{b}[][]=1/s[l_query+1]; this is where s[l_query+1] comes from)
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176 for (k = 1; k <= l_ref; ++k) {
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177 int u;
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178 double *bi = b[l_query];
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179 set_u(u, bw, l_query, k);
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180 if (u < 3 || u >= bw2*3+3) continue;
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181 bi[u+0] = sM / s[l_query] / s[l_query+1]; bi[u+1] = sI / s[l_query] / s[l_query+1];
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182 }
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183 // b[l_query-1..1]
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184 for (i = l_query - 1; i >= 1; --i) {
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185 int beg = 1, end = l_ref, x, _beg, _end;
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186 double *bi = b[i], *bi1 = b[i+1], y = (i > 1), qli1 = qual[i+1];
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187 uint8_t qyi1 = query[i+1];
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188 x = i - bw; beg = beg > x? beg : x;
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189 x = i + bw; end = end < x? end : x;
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190 for (k = end; k >= beg; --k) {
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191 int u, v11, v01, v10;
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192 double e;
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193 set_u(u, bw, i, k); set_u(v11, bw, i+1, k+1); set_u(v10, bw, i+1, k); set_u(v01, bw, i, k+1);
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194 e = (k >= l_ref? 0 : (ref[k+1] > 3 || qyi1 > 3)? 1. : ref[k+1] == qyi1? 1. - qli1 : qli1 * EM) * bi1[v11];
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195 bi[u+0] = e * m[0] + EI * m[1] * bi1[v10+1] + m[2] * bi[v01+2]; // bi1[v11] has been foled into e.
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196 bi[u+1] = e * m[3] + EI * m[4] * bi1[v10+1];
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197 bi[u+2] = (e * m[6] + m[8] * bi[v01+2]) * y;
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198 // fprintf(stderr, "B (%d,%d;%d): %lg,%lg,%lg\n", i, k, u, bi[u], bi[u+1], bi[u+2]); // DEBUG
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199 }
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200 // rescale
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201 set_u(_beg, bw, i, beg); set_u(_end, bw, i, end); _end += 2;
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202 for (k = _beg, y = 1./s[i]; k <= _end; ++k) bi[k] *= y;
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203 }
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204 { // b[0]
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205 int beg = 1, end = l_ref < bw + 1? l_ref : bw + 1;
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206 double sum = 0.;
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207 for (k = end; k >= beg; --k) {
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208 int u;
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209 double e = (ref[k] > 3 || query[1] > 3)? 1. : ref[k] == query[1]? 1. - qual[1] : qual[1] * EM;
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210 set_u(u, bw, 1, k);
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211 if (u < 3 || u >= bw2*3+3) continue;
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212 sum += e * b[1][u+0] * bM + EI * b[1][u+1] * bI;
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213 }
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214 set_u(k, bw, 0, 0);
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215 pb = b[0][k] = sum / s[0]; // if everything works as is expected, pb == 1.0
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216 }
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217 is_diff = fabs(pb - 1.) > 1e-7? 1 : 0;
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218 /*** MAP ***/
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219 for (i = 1; i <= l_query; ++i) {
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220 double sum = 0., *fi = f[i], *bi = b[i], max = 0.;
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221 int beg = 1, end = l_ref, x, max_k = -1;
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222 x = i - bw; beg = beg > x? beg : x;
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223 x = i + bw; end = end < x? end : x;
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224 for (k = beg; k <= end; ++k) {
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225 int u;
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226 double z;
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227 set_u(u, bw, i, k);
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228 z = fi[u+0] * bi[u+0]; if (z > max) max = z, max_k = (k-1)<<2 | 0; sum += z;
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229 z = fi[u+1] * bi[u+1]; if (z > max) max = z, max_k = (k-1)<<2 | 1; sum += z;
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230 }
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231 max /= sum; sum *= s[i]; // if everything works as is expected, sum == 1.0
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232 if (state) state[i-1] = max_k;
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233 if (q) k = (int)(-4.343 * log(1. - max) + .499), q[i-1] = k > 100? 99 : k;
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234 #ifdef _MAIN
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235 fprintf(stderr, "(%.10lg,%.10lg) (%d,%d:%c,%c:%d) %lg\n", pb, sum, i-1, max_k>>2,
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236 "ACGT"[query[i]], "ACGT"[ref[(max_k>>2)+1]], max_k&3, max); // DEBUG
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237 #endif
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238 }
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239 /*** free ***/
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240 for (i = 0; i <= l_query; ++i) {
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241 free(f[i]); free(b[i]);
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242 }
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243 free(f); free(b); free(s); free(_qual);
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244 return Pr;
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245 }
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246
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247 #ifdef _MAIN
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248 #include <unistd.h>
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249 int main(int argc, char *argv[])
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250 {
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251 uint8_t conv[256], *iqual, *ref, *query;
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252 int c, l_ref, l_query, i, q = 30, b = 10, P;
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253 while ((c = getopt(argc, argv, "b:q:")) >= 0) {
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254 switch (c) {
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255 case 'b': b = atoi(optarg); break;
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256 case 'q': q = atoi(optarg); break;
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257 }
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258 }
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259 if (optind + 2 > argc) {
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260 fprintf(stderr, "Usage: %s [-q %d] [-b %d] <ref> <query>\n", argv[0], q, b); // example: acttc attc
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261 return 1;
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262 }
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263 memset(conv, 4, 256);
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264 conv['a'] = conv['A'] = 0; conv['c'] = conv['C'] = 1;
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265 conv['g'] = conv['G'] = 2; conv['t'] = conv['T'] = 3;
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266 ref = (uint8_t*)argv[optind]; query = (uint8_t*)argv[optind+1];
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267 l_ref = strlen((char*)ref); l_query = strlen((char*)query);
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268 for (i = 0; i < l_ref; ++i) ref[i] = conv[ref[i]];
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269 for (i = 0; i < l_query; ++i) query[i] = conv[query[i]];
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270 iqual = malloc(l_query);
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271 memset(iqual, q, l_query);
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272 kpa_par_def.bw = b;
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273 P = kpa_glocal(ref, l_ref, query, l_query, iqual, &kpa_par_alt, 0, 0);
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274 fprintf(stderr, "%d\n", P);
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275 free(iqual);
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276 return 0;
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277 }
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278 #endif
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