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smith_waterman.go
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/
smith_waterman.go
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package scoring
import (
"fmt"
"os"
"unicode"
)
// smithWaterman calculates a simularity score between s1 and s2
// by smith-waterman algorithm. smith-waterman algorithm is one of
// local alignment algorithms and it uses dynamic programming.
//
// In this smith-waterman algorithm, we use the affine gap penalty.
// Please see https://en.wikipedia.org/wiki/Gap_penalty#Affine for additional
// information about the affine gap penalty.
//
// We calculate the gap penalty by the Gotoh's algorithm, which optimizes
// the calculation from O(M^2N) to O(MN).
// Please see ftp://150.128.97.71/pub/Bioinformatica/gotoh1982.pdf for more details.
func smithWaterman(s1, s2 []rune) (int, [2]int) {
if len(s1) == 0 {
// If the length of s1 is 0, also the length of s2 is 0.
return 0, [2]int{-1, -1}
}
const (
openGap int32 = 5 // Gap opening penalty.
extGap int32 = 1 // Gap extension penalty.
matchScore int32 = 5
mismatchScore int32 = 1
firstCharBonus int32 = 3 // The first char of s1 is equal to s2's one.
)
// The scoring matrix.
H := make([][]int32, len(s1)+1)
// A matrix that calculates gap penalties for s2 until each position (i, j).
// Note that, we don't need a matrix for s1 because s1 contains all runes
// of s2 so that s1 is not inserted gaps.
D := make([][]int32, len(s1)+1)
for i := 0; i <= len(s1); i++ {
H[i] = make([]int32, len(s2)+1)
D[i] = make([]int32, len(s2)+1)
}
for i := 0; i <= len(s1); i++ {
D[i][0] = -openGap - int32(i)*extGap
}
// Calculate bonuses for each rune of s1.
bonus := make([]int32, len(s1))
bonus[0] = firstCharBonus
prevCh := s1[0]
prevIsDelimiter := isDelimiter(prevCh)
for i, r := range s1[1:] {
isDelimiter := isDelimiter(r)
if prevIsDelimiter && !isDelimiter {
bonus[i] = firstCharBonus
}
prevIsDelimiter = isDelimiter
}
var maxScore int32
var maxI int
var maxJ int
for i := 1; i <= len(s1); i++ {
for j := 1; j <= len(s2); j++ {
var score int32
if s1[i-1] != s2[j-1] {
score = H[i-1][j-1] - mismatchScore
} else {
score = H[i-1][j-1] + matchScore + bonus[i-1]
}
H[i][j] += max(D[i-1][j], score, 0)
D[i][j] = max(H[i-1][j]-openGap, D[i-1][j]-extGap)
// Update the max score.
// Don't pick a position that is less than the length of s2.
if H[i][j] > maxScore && i >= j {
maxScore = H[i][j]
maxI = i - 1
maxJ = j - 1
}
}
}
if isDebug() {
fmt.Printf("max score = %d (%d, %d)\n\n", maxScore, maxI, maxJ)
printSlice := func(m [][]int32) {
fmt.Printf("%4c ", '|')
for i := 0; i < len(s2); i++ {
fmt.Printf("%3c ", s2[i])
}
fmt.Printf("\n-------------------------\n")
fmt.Print(" | ")
for i := 0; i <= len(s1); i++ {
if i != 0 {
fmt.Printf("%3c| ", s1[i-1])
}
for j := 0; j <= len(s2); j++ {
fmt.Printf("%3d ", m[i][j])
}
fmt.Println()
}
fmt.Println()
}
printSlice(H)
printSlice(D)
}
// Determine the matched position.
var from, to int
cnt := 1
// maxJ is the last index of s2.
// If maxJ is equal to the length of s2, it means there are no matched runes after maxJ.
if maxJ == len(s2)-1 {
to = maxI
} else {
j := maxJ + 1
for i := maxI + 1; i < len(s1); i++ {
if unicode.ToLower(s1[i]) == unicode.ToLower(s2[j]) {
cnt++
j++
if j == len(s2) {
to = i + 1
break
}
}
}
}
for i := maxI - 1; i > 0; i-- {
if cnt == len(s2) {
from = i + 1
break
}
if unicode.ToLower(s1[i]) == unicode.ToLower(s2[len(s2)-1-cnt]) {
cnt++
}
}
// We adjust scores by the weight per one rune.
return int(float32(maxScore) * (float32(maxScore) / float32(len(s1)))), [2]int{from, to}
}
func isDebug() bool {
return os.Getenv("DEBUG") != ""
}
var delimiterRunes = map[rune]interface{}{
'(': nil,
'[': nil,
'{': nil,
'/': nil,
'-': nil,
'_': nil,
'.': nil,
}
func isDelimiter(r rune) bool {
if _, ok := delimiterRunes[r]; ok {
return true
}
return unicode.IsSpace(r)
}