first DTW method realization
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/*
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* Copyright 2018-2023 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.series
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import space.kscience.kmath.structures.DoubleBuffer
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import kotlin.math.abs
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public const val LEFT_OFFSET : Int = -1
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public const val BOTTOM_OFFSET : Int = 1
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public const val DIAGONAL_OFFSET : Int = 0
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// TODO: Change container for alignMatrix to kmath special ND structure
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public data class DynamicTimeWarpingData(val totalCost : Double = 0.0,
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val alignMatrix : Array<BooleanArray> = Array(0) {BooleanArray(0)}) {
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override fun equals(other: Any?): Boolean {
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if (this === other) return true
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if (other == null || this::class != other::class) return false
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other as DynamicTimeWarpingData
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if (totalCost != other.totalCost) return false
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if (!alignMatrix.contentDeepEquals(other.alignMatrix)) return false
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return true
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}
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override fun hashCode(): Int {
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var result = totalCost.hashCode()
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result = 31 * result + alignMatrix.contentDeepHashCode()
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return result
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}
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}
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/**
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* costMatrix calculates special matrix of costs alignment for two series.
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* Formula: costMatrix[i, j] = euqlidNorm(series1(i), series2(j)) + min(costMatrix[i - 1, j],
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* costMatrix[i, j - 1],
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* costMatrix[i - 1, j - 1]).
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* There is special cases for i = 0 or j = 0.
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*/
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public fun costMatrix(series1 : DoubleBuffer, series2 : DoubleBuffer) : Array<DoubleArray> {
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val dtwMatrix: Array<DoubleArray> = Array(series1.size){ row ->
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DoubleArray(series2.size) { col ->
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abs(series1[row] - series2[col])
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}
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}
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for (i in dtwMatrix.indices) {
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for (j in dtwMatrix[i].indices) {
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dtwMatrix[i][j] += when {
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i == 0 && j == 0 -> 0.0
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i == 0 -> dtwMatrix[i][j-1]
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j == 0 -> dtwMatrix[i-1][j]
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else -> minOf(
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dtwMatrix[i][j-1],
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dtwMatrix[i-1][j],
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dtwMatrix[i-1][j-1]
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)
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}
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}
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}
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return dtwMatrix
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}
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/**
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* PathIndices class for better code perceptibility.
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* Special fun moveOption represent offset for indices. Arguments of this function
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* is flags for bottom, diagonal or left offsets respectively.
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*/
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public data class PathIndices (var id_x: Int, var id_y: Int) {
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public fun moveOption (direction: Int) {
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when(direction) {
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BOTTOM_OFFSET -> id_x--
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DIAGONAL_OFFSET -> {
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id_x--
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id_y--
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}
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LEFT_OFFSET -> id_y--
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else -> throw Exception("There is no such offset flag!")
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}
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}
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}
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/**
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* Final DTW method realization. Returns alignment matrix
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* for two series comparing and penalty for this alignment.
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*/
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public fun dynamicTimeWarping(series1 : DoubleBuffer, series2 : DoubleBuffer) : DynamicTimeWarpingData {
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var cost = 0.0
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var pathLength = 0
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val costMatrix = costMatrix(series1, series2)
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val alignMatrix : Array<BooleanArray> = Array(costMatrix.size) { BooleanArray(costMatrix.first().size) }
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val indexes = PathIndices(alignMatrix.lastIndex, alignMatrix.last().lastIndex)
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with(indexes) {
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alignMatrix[id_x][id_y] = true
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cost += costMatrix[id_x][id_y]
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pathLength++
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while (id_x != 0 || id_y != 0) {
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when {
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id_x == 0 || costMatrix[id_x][id_y] == costMatrix[id_x][id_y - 1] + abs(series1[id_x] - series2[id_y]) -> {
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moveOption(LEFT_OFFSET)
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}
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id_y == 0 || costMatrix[id_x][id_y] == costMatrix[id_x - 1][id_y] + abs(series1[id_x] - series2[id_y]) -> {
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moveOption(BOTTOM_OFFSET)
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}
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costMatrix[id_x][id_y] == costMatrix[id_x - 1][id_y - 1] + abs(series1[id_x] - series2[id_y]) -> {
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moveOption(DIAGONAL_OFFSET)
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}
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}
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alignMatrix[id_x][id_y] = true
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cost += costMatrix[id_x][id_y]
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pathLength++
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}
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cost /= pathLength
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}
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return DynamicTimeWarpingData(cost, alignMatrix)
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}
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