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Adapted Needleman-Wunsch algorithm for general array alignment implemented in Haxe (3).
/**
Adapted Needleman-Wunsch algorithm for general array alignment
If NeedlemanWunsch is used as entry point the unit tests are executed
Copyright (c) 2013, Jonas Malaco Filho
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
This is a BSD 2-clause license. Information available at:
http://opensource.org/licenses/BSD-2-Clause.
**/
class NeedlemanWunsch<T> {
public var alignedA( default, null ): Array<Null<T>>;
public var alignedB( default, null ): Array<Null<T>>;
public var distance( default, null ): Float;
public var length( default, null ): Int;
/**
Global alignment of two arrays, using a modified version of the quadratic running time
Needleman-Wunsch algorithm with gap penalties
Params:
dist( a, b ) should give the (edit) distance between a and b
skip( a, b, c ) should give (an estimate of) the penalty incured when skipping b
a (nullable) is the previous element
c (nullable) is the next element
Return:
A Alignment<T> object, with both a and b aligned arrays and the (edit) distance computed
**/
public static function globalAlignment<T>( a: Array<T>, b: Array<T>, dist: T -> T -> Float,
?skip: Null<T> -> T -> Null<T> -> Float): NeedlemanWunsch<T> {
// array lengths
var n = a.length;
var m = b.length;
// F (?) matrix initialization, size( F ) = n+1, m+1
// *** the corresponding a and b elements for Fij are a[i - 1] and b[i - 1] ***
var F = buildMatrix( n + 1, m + 1, function ( i, j ) return Math.POSITIVE_INFINITY );
// pre-computed distance matrix, size( D ) = n+1, m+1
var D = buildMatrix( n + 1, m + 1, function ( i, j ) return i*j != 0 ? dist( a[i - 1], b[j - 1] ) : Math.NaN );
// default gap penalty function is cte 1. (as in Levenshtein distance)
if ( skip == null )
skip = function ( a, b, c ) return 1.;
// basis
F[0][0] = 0.;
for ( i in 1...n+1 )
F[i][0] = F[i - 1][0] + skip( ( i > 1 ? a[i - 2] : null ), a[i - 1], ( i < n ? a[i] : null ) );
for ( j in 1...m+1 )
F[0][j] = F[0][j - 1] + skip( ( j > 1 ? b[j - 2] : null ), b[j - 1], ( j < m ? b[j] : null ) );
// recursion
// for i,j <=> a[i - 1],b[j - 1] there are 3 possible outcomes:
// move down and left, a[i - 1] aligns with b[j - 1], AKA "match"
// move down, a[i - 1] aligns with a gap in b, AKA "skipA" (one element of a is discarted), AKA "delete"
// move left, b[j - 1] aligns with a gap in a, AKA "skipB" (one element of b is discarted), AKA "insert"
for ( i in 1...n+1 )
for ( j in 1...m+1 ) {
var match = F[i - 1][j - 1] + D[i][j];
var skipA = F[i - 1][j] + skip( ( i > 1 ? a[i - 2] : null ), a[i - 1], ( i < n ? a[i] : null ) );
var skipB = F[i][j - 1] + skip( ( j > 1 ? b[j - 2] : null ), b[j - 1], ( j < m ? b[j] : null ) );
F[i][j] = Math.min( match, Math.min( skipA, skipB ) );
}
// trace( F.join( '\n' ) );
if ( !Math.isFinite( F[n][m] ) )
throw 'Supplied distance or skip penalty functions resulted in infeasible alignment';
// alignment
var aligA = new List();
var aligB = new List();
var i = n;
var j = m;
while ( i > 0 && j > 0 ) {
if ( Math.isFinite( F[i - 1][j - 1] ) && F[i][j] == F[i - 1][j - 1] + D[i][j] ) {
// results from match
aligA.push( a[--i] );
aligB.push( b[--j] );
}
else if ( Math.isFinite( F[i - 1][j] )
&& F[i][j] == F[i - 1][j] + skip( ( i > 1 ? a[i - 2] : null ), a[i - 1], ( i < n ? a[i] : null ) ) ) {
// results from skipA
aligA.push( a[--i] );
aligB.push( null );
}
else if ( Math.isFinite( F[i][j - 1] )
&& F[i][j] == F[i][j - 1] + skip( ( j > 1 ? b[j - 2] : null ), b[j - 1], ( j < m ? b[j] : null ) ) ) {
// results from skipB
aligA.push( null );
aligB.push( b[--j] );
}
else
throw 'Internal error in alignment reconstruction; F=\n' + F.join( '\n' );
}
while ( i > 0 || j > 0 ) {
aligA.push( i > 0 ? a[--i] : null );
aligB.push( j > 0 ? b[--j] : null );
}
return new NeedlemanWunsch( Lambda.array( aligA ), Lambda.array( aligB ), F[n][m] );
}
static function buildMatrix<A>( n: Int, m: Int, init: Int -> Int -> A ) {
var M = [];
for ( i in 0...n ) {
var _i = n - 1 - i;
M[_i] = [];
for ( j in 0...m ) {
var _j = m - 1 - j;
M[_i][_j] = init( _i, _j );
}
}
return M;
}
function new( a: Array<Null<T>>, b: Array<Null<T>>, dist: Float ) {
if ( a.length != b.length )
throw 'a.length != b.length';
alignedA = a;
alignedB = b;
length = alignedA.length;
distance = dist;
}
// Testing entry point
static function main() {
var runner = new haxe.unit.TestRunner();
runner.add( new NeedlemanWunschTest() );
runner.run();
}
}
class NeedlemanWunschTest extends haxe.unit.TestCase {
// Tests
// Test alignment using Levenshtein distance penalties
function testLevenshteinDistance() {
var dist = function ( a, b ) return a==b ? 0 : 1;
var skip = function ( a, b, c ) return 1;
assertEquals( '3|kitten_|sitting', stAl( 'kitten', 'sitting', dist, skip ) );
assertEquals( '6|industry|interest', stAl( 'industry', 'interest', dist, skip ) );
assertEquals( '3|horse|ror__', stAl( 'horse', 'ror', dist, skip ) );
assertEquals( '1|start|_tart', stAl( 'start', 'tart', dist, skip ) );
assertEquals( '1|finish|finis_', stAl( 'finish', 'finis', dist, skip ) );
assertEquals( '1|skipped|ski_ped', stAl( 'skipped', 'skiped', dist, skip ) );
}
// Test different skip functions, specially one that does not allow
// gaps in the beginning or end
function testSkipFunction() {
var dist = function ( a, b ) return a==b ? 0 : 1;
var skip = function ( a, b, c ) {
if ( a == null )
return Math.POSITIVE_INFINITY;
else if ( c == null )
return Math.POSITIVE_INFINITY;
else if ( b == a || b == c )
return 0.;
else
return 1.;
};
assertEquals( '2|start|t_art', stAl( 'start', 'tart', dist, skip ) );
assertEquals( '2|finish|fini_s', stAl( 'finish', 'finis', dist, skip ) );
assertEquals( '0|skipped|ski_ped', stAl( 'skipped', 'skiped', dist, skip ) );
// expect exception if b is only one char long and a has more than one char
assertRaises( null, stAl( 'ar', 'b', dist, skip ) );
assertEquals( '1|a|b', stAl( 'a', 'b', dist, skip ) );
}
// Helpers
// Assert exception
macro static function assertRaises( expected: haxe.macro.Expr, test: haxe.macro.Expr ) {
return macro {
var _exp: Null<Dynamic> = $expected;
var err = _exp != null? 'Expected exception ' + _exp: 'Expected exception';
var done = false;
try {
$test;
done = true;
}
catch ( e: Dynamic ) {
if ( _exp != null && Std.string( e ) != Std.string( _exp ) )
throw err;
}
if ( done )
throw err;
};
}
// Global alignment of strings
static function stAl( a: String, b: String, dist: Int -> Int -> Float, skip: Int -> Int -> Int -> Float ): String {
var _a = stAr( a );
var _b = stAr( b );
var nwa = NeedlemanWunsch.globalAlignment( _a, _b, dist, skip );
return stRes( nwa );
}
// String to Array<Int>
static function stAr( s: String ): Array<Int> {
var bytes = haxe.io.Bytes.ofString( s );
var a = [];
for ( i in 0...bytes.length ) {
a.push( bytes.get( i ) );
}
return a;
}
// Array<Int> to String
static function arSt( a: Array<Int>, ?nullValue = '_' ): String {
var bytes = haxe.io.Bytes.alloc( a.length );
var nl = nullValue.charCodeAt( 0 );
for ( i in 0...a.length )
bytes.set( i, a[i] == null ? nl : a[i] );
return bytes.toString();
}
// Alignment results printer
static function stRes( x: NeedlemanWunsch<Int>, ?sep='|', ?nl='_' ): String {
return '${x.distance}$sep${arSt( x.alignedA, nl )}$sep${arSt( x.alignedB, nl )}';
}
}
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