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@ -11,7 +11,7 @@ import space.kscience.kmath.operations.*
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import space.kscience.kmath.operations.Float64BufferOps.Companion.div
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import space.kscience.kmath.operations.Float64BufferOps.Companion.pow
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.structures.last
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import space.kscience.kmath.structures.asBuffer
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import kotlin.math.sign
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/**
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@ -47,24 +47,40 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
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*/
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private fun findMean(signal: Series<Double>): Series<Double>? = (seriesAlgebra) {
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val interpolator = SplineInterpolator(Float64Field)
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fun generateEnvelope(extrema: List<Int>): Series<Double> {
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fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: DoubleArray): Series<Double> {
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val envelopeFunction = interpolator.interpolate(
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Buffer(extrema.size) { signal.labels[extrema[it]].toDouble() },
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Buffer(extrema.size) { signal[extrema[it]] }
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paddedExtremeValues.asBuffer()
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)
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return signal.mapWithLabel { _, label ->
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// For some reason PolynomialInterpolator is exclusive and the right boundary
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// TODO Notify interpolator authors
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envelopeFunction(label.toDouble()) ?: signal.last()
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envelopeFunction(label.toDouble()) ?: paddedExtremeValues.last()
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// need to make the interpolator yield values outside boundaries?
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}
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}
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val maxima = signal.paddedMaxima()
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val minima = signal.paddedMinima()
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return if (maxima.size < 3 || minima.size < 3) null else {
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val upperEnvelope = generateEnvelope(maxima)
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val lowerEnvelope = generateEnvelope(minima)
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return upperEnvelope.zip(lowerEnvelope) { upper, lower -> upper + lower / 2.0 }
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// Extrema padding (experimental) TODO padding needs a dedicated function
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val maxima = listOf(0) + signal.peaks() + (signal.size - 1)
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val maxValues = DoubleArray(maxima.size) { signal[maxima[it]] }
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if (maxValues[0] < maxValues[1]) {
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maxValues[0] = maxValues[1]
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}
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if (maxValues.last() < maxValues[maxValues.lastIndex - 1]) {
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maxValues[maxValues.lastIndex] = maxValues[maxValues.lastIndex - 1]
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}
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val minima = listOf(0) + signal.troughs() + (signal.size - 1)
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val minValues = DoubleArray(minima.size) { signal[minima[it]] }
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if (minValues[0] > minValues[1]) {
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minValues[0] = minValues[1]
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}
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if (minValues.last() > minValues[minValues.lastIndex - 1]) {
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minValues[minValues.lastIndex] = minValues[minValues.lastIndex - 1]
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}
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return if (maxima.size < 3 || minima.size < 3) null else { // maybe make an early return?
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val upperEnvelope = generateEnvelope(maxima, maxValues)
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val lowerEnvelope = generateEnvelope(minima, minValues)
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return (upperEnvelope + lowerEnvelope).map { it * 0.5 }
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}
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}
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@ -76,27 +92,19 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
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* @return [SiftingResult.NotEnoughExtrema] is returned if the signal has too few extrema to extract a mode.
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* Success of an appropriate type (See [SiftingResult.Success] class) is returned otherwise.
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*/
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private fun sift(signal: Series<Double>): SiftingResult = (seriesAlgebra) {
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val mean = findMean(signal) ?: return SiftingResult.NotEnoughExtrema
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val protoMode = signal.zip(mean) { s, m -> s - m }
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val sNumber = if (protoMode.sCondition()) 1 else 0
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return when {
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maxSiftIterations == 1 -> SiftingResult.MaxIterationsReached(protoMode)
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sNumber >= sConditionThreshold -> SiftingResult.SNumberReached(protoMode)
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relativeDifference(protoMode, signal) < siftingDelta * signal.size -> SiftingResult.DeltaReached(protoMode)
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else -> siftInner(protoMode, 2, sNumber)
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}
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}
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private fun sift(signal: Series<Double>): SiftingResult = siftInner(signal, 1, 0)
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/**
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* Compute a single iteration of the sifting process.
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*/
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private fun siftInner(
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private tailrec fun siftInner(
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prevMode: Series<Double>,
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iterationNumber: Int,
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sNumber: Int
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): SiftingResult = (seriesAlgebra) {
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val mean = findMean(prevMode) ?: return SiftingResult.SignalFlattened(prevMode)
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val mean = findMean(prevMode) ?:
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return if (iterationNumber == 1) SiftingResult.NotEnoughExtrema
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else SiftingResult.SignalFlattened(prevMode)
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val mode = prevMode.zip(mean) { p, m -> p - m }
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val newSNumber = if (mode.sCondition()) sNumber + 1 else sNumber
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return when {
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@ -188,49 +196,14 @@ private fun <BA> SeriesAlgebra<Double, *, BA, *>.relativeDifference(
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.div(previous pow 2)
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.fold(0.0) { acc, d -> acc + d } // TODO replace with Series<>.sum() method when it's implemented
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private fun <T: Comparable<T>> isExtreme(prev: T, elem: T, next: T): Boolean =
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(elem > prev && elem > next) || (elem < prev && elem < next)
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/**
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* Brute force count all extrema of a series.
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*/
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private fun Series<Double>.countExtrema(): Int {
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require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
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return (1 .. size - 2).count { isExtreme(this[it - 1], this[it], this[it + 1]) }
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return peaks().size + troughs().size
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}
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/**
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* Retrieve indices of knot points for spline interpolation matching the predicate.
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* The first and the last points of a series are always included.
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*/
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private fun <T: Comparable<T>> Series<T>.knotPoints(predicate: (T, T, T) -> Boolean): List<Int> {
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require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
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val points = mutableListOf(0)
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for (index in 1 .. size - 2) {
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val left = this[index - 1]
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val middle = this[index]
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val right = this[index + 1]
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if (predicate(left, middle, right)) points.add(index)
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}
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points.add(size - 1)
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return points
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}
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/**
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* Retrieve indices of knot points used to construct an upper envelope,
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* namely maxima together with the first last point in a series.
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*/
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private fun <T: Comparable<T>> Series<T>.paddedMaxima(): List<Int> =
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knotPoints { left, middle, right -> (middle > left && middle > right) }
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/**
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* Retrieve indices of knot points used to construct a lower envelope,
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* namely minima together with the first last point in a series.
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*/
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private fun <T: Comparable<T>> Series<T>.paddedMinima(): List<Int> =
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knotPoints { left, middle, right -> (middle < left && middle < right) }
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/**
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* Check whether the numbers of zeroes and extrema of a series differ by no more than 1.
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* This is a necessary condition of an empirical mode.
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@ -0,0 +1,89 @@
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/*
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* Copyright 2018-2024 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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public enum class PlateauEdgePolicy {
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/**
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* Midpoints of plateau are returned, edges not belonging to a plateau are ignored.
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*
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* A midpoint is the index closest to the average of indices of the left and right edges
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* of the plateau:
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*
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* `val midpoint = ((leftEdge + rightEdge) / 2).toInt`
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*/
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AVERAGE,
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/**
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* Both left and right edges are returned.
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*/
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KEEP_ALL_EDGES,
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/**
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* Only right edges are returned.
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*/
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KEEP_RIGHT_EDGES,
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/**
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* Only left edges are returned.
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*/
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KEEP_LEFT_EDGES,
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/**
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* Ignore plateau, only peaks (troughs) with values strictly greater (less)
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* than values of the adjacent points are returned.
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*/
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IGNORE
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}
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public fun <T: Comparable<T>> Series<T>.peaks(
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plateauEdgePolicy: PlateauEdgePolicy = PlateauEdgePolicy.AVERAGE
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): List<Int> = findPeaks(plateauEdgePolicy, { other -> this > other }, { other -> this >= other })
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public fun <T: Comparable<T>> Series<T>.troughs(
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plateauEdgePolicy: PlateauEdgePolicy = PlateauEdgePolicy.AVERAGE
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): List<Int> = findPeaks(plateauEdgePolicy, { other -> this < other }, { other -> this <= other })
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private fun <T: Comparable<T>> Series<T>.findPeaks(
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plateauPolicy: PlateauEdgePolicy = PlateauEdgePolicy.AVERAGE,
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cmpStrong: T.(T) -> Boolean,
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cmpWeak: T.(T) -> Boolean
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): List<Int> {
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require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
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if (plateauPolicy == PlateauEdgePolicy.AVERAGE) return peaksWithPlateau(cmpStrong)
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fun peakCriterion(left: T, middle: T, right: T): Boolean = when(plateauPolicy) {
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PlateauEdgePolicy.KEEP_LEFT_EDGES -> middle.cmpStrong(left) && middle.cmpWeak(right)
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PlateauEdgePolicy.KEEP_RIGHT_EDGES -> middle.cmpWeak(left) && middle.cmpStrong(right)
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PlateauEdgePolicy.KEEP_ALL_EDGES ->
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(middle.cmpStrong(left) && middle.cmpWeak(right)) || (middle.cmpWeak(left) && middle.cmpStrong(right))
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else -> middle.cmpStrong(right) && middle.cmpStrong(left)
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}
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val indices = mutableListOf<Int>()
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for (index in 1 .. size - 2) {
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val left = this[index - 1]
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val middle = this[index]
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val right = this[index + 1]
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if (peakCriterion(left, middle, right)) indices.add(index)
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}
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return indices
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}
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private fun <T: Comparable<T>> Series<T>.peaksWithPlateau(cmpStrong: T.(T) -> Boolean): List<Int> {
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val peaks = mutableListOf<Int>()
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tailrec fun peaksPlateauInner(index: Int) {
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val nextUnequal = (index + 1 ..< size).firstOrNull { this[it] != this[index] } ?: (size - 1)
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val newIndex = if (this[index].cmpStrong(this[index - 1]) && this[index].cmpStrong(this[nextUnequal])) {
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peaks.add((index + nextUnequal) / 2)
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nextUnequal
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} else index + 1
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if (newIndex < size - 1) peaksPlateauInner(newIndex)
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}
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peaksPlateauInner(1)
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return peaks
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}
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