forked from biogo/biogo
/
complexity.go
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/
complexity.go
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// Copyright ©2013 The bíogo Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package complexity provides routines for evaluating sequence complexity.
package complexity
import (
"github.com/biogo/biogo/seq"
"compress/zlib"
"fmt"
"math"
)
const tableLength = 10000
var lnFacTable = genLnFac(tableLength)
func genLnFac(l int) (table []float64) {
table = make([]float64, l)
lnfac := 0.
for i := 1; i < l; i++ {
lnfac += math.Log(float64(i))
table[i] = lnfac
}
return
}
const ln2pi = 1.8378770664093454835606594728112352797227949472755668
func lnFac(x int) float64 {
if x < len(lnFacTable) {
return lnFacTable[x]
}
// use Sterling's approximation for queries outside the table:
return (float64(x)+0.5)*math.Log(float64(x)) - float64(x) + ln2pi/2
}
func logBaseK(logk, x float64) float64 {
return math.Log(x) / logk
}
// Entropic returns the entropic complexity of a segment of s defined by
// start and end.
func Entropic(s seq.Sequence, start, end int) (ce float64, err error) {
if start < s.Start() || end > s.End() {
err = fmt.Errorf("complex: index out of range")
return
}
if start == end {
return 0, nil
}
var N float64
k := s.Alphabet().Len()
logk := math.Log(float64(k))
n := make([]float64, k)
// tally classes
it := s.Alphabet().LetterIndex()
for i := start; i < end; i++ {
if ind := it[s.At(i).L]; ind >= 0 {
N++
n[ind]++
}
}
// -∑i=1..k((n_i/N)*log_k(n_i/N))
for i := 0; i < k; i++ {
if n[i] != 0 { // ignore zero counts
ce += n[i] * logBaseK(logk, n[i]/N)
}
}
ce = -ce / N
return
}
// WF returns the Wootton and Federhen complexity of a segment of s defined by
// start and end.
func WF(s seq.Sequence, start, end int) (cwf float64, err error) {
if start < s.Start() || end > s.End() {
err = fmt.Errorf("complex: index out of range")
return
}
if start == end {
return 0, nil
}
var N int
k := s.Alphabet().Len()
logk := math.Log(float64(k))
n := make([]int, k)
// tally classes
it := s.Alphabet().LetterIndex()
for i := start; i < end; i++ {
if ind := it[s.At(i).L]; ind >= 0 {
N++
n[ind]++
}
}
// 1/N*log_k(N!/∏i=1..k(n_i!))
cwf = lnFac(N)
for i := 0; i < k; i++ {
cwf -= lnFac(n[i])
}
cwf /= float64(N) * logk
return
}
type byteCounter int
func (b *byteCounter) Write(p []byte) (n int, err error) {
*b += byteCounter(len(p))
return len(p), nil
}
var overhead = calcOverhead()
func calcOverhead() byteCounter {
b := new(byteCounter)
z := zlib.NewWriter(b)
z.Write([]byte{0})
z.Close()
return *b - 1
}
// Z returns the zlib compression estimate of complexity of a segment of s defined by
// start and end.
func Z(s seq.Sequence, start, end int) (cz float64, err error) {
if start < s.Start() || end > s.End() {
err = fmt.Errorf("complex: index out of range")
return
}
if start == end {
return 0, nil
}
bc := new(byteCounter)
z := zlib.NewWriter(bc)
defer z.Close()
it := s.Alphabet().LetterIndex()
var N float64
for i := start; i < end; i++ {
if b := byte(s.At(i).L); it[b] >= 0 {
N++
z.Write([]byte{b})
}
}
z.Close()
cz = (float64(*bc - overhead)) / N
return
}