forked from kscience/kmath
Part 2
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@ -9,8 +9,7 @@ import space.kscience.kmath.interpolation.SplineInterpolator
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import space.kscience.kmath.interpolation.interpolate
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import space.kscience.kmath.operations.*
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.structures.asBuffer
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import kotlin.math.sign
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import space.kscience.kmath.structures.last
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/**
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* Empirical mode decomposition of a signal represented as a [Series].
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@ -45,35 +44,36 @@ public class EmpiricalModeDecomposition<A: Field<Double>, 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(elementAlgebra)
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fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: Array<Double>): Series<Double> {
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val makeBuffer = elementAlgebra.bufferFactory
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fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: Buffer<Double>): Series<Double> {
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val envelopeFunction = interpolator.interpolate(
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Buffer(extrema.size) { signal.labels[extrema[it]] as Double },
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paddedExtremeValues.asBuffer()
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Buffer(extrema.size) { signal.labels[extrema[it]].toDouble() },
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paddedExtremeValues
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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 as Double) ?: paddedExtremeValues.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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// 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 = Array(maxima.size) { signal[maxima[it]] }
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val maxValues = makeBuffer(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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if (maxValues.last() < maxValues[maxValues.size - 2]) {
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maxValues[maxValues.size - 1] = maxValues[maxValues.size - 2]
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}
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val minima = listOf(0) + signal.troughs() + (signal.size - 1)
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val minValues = Array(minima.size) { signal[minima[it]] }
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val minValues = makeBuffer(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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if (minValues.last() > minValues[minValues.size - 2]) {
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minValues[minValues.size - 1] = minValues[minValues.size - 2]
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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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@ -104,7 +104,7 @@ public class EmpiricalModeDecomposition<A: Field<Double>, BA, L: Number> (
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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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val newSNumber = if (sCondition(mode)) sNumber + 1 else sNumber
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return when {
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iterationNumber >= maxSiftIterations -> SiftingResult.MaxIterationsReached(mode)
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sNumber >= sConditionThreshold -> SiftingResult.SNumberReached(mode)
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@ -121,7 +121,7 @@ public class EmpiricalModeDecomposition<A: Field<Double>, BA, L: Number> (
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* Modes returned in a list which contains as many modes as it was possible
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* to extract before triggering one of the termination conditions.
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*/
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public fun decompose(signal: Series<Double>): EMDecompositionResult = (seriesAlgebra) {
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public fun decompose(signal: Series<Double>): EMDecompositionResult<Double> = (seriesAlgebra) {
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val modes = mutableListOf<Series<Double>>()
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var residual = signal
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repeat(nModes) {
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@ -132,9 +132,9 @@ public class EmpiricalModeDecomposition<A: Field<Double>, BA, L: Number> (
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else EMDTerminationReason.ALL_POSSIBLE_MODES_EXTRACTED,
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modes
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)
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is SiftingResult.Success -> r.result
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is SiftingResult.Success<*> -> r.result
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}
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modes.add(nextMode)
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modes.add(nextMode as Series<Double>) // TODO remove unchecked cast
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residual = residual.zip(nextMode) { l, r -> l - r }
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}
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return EMDecompositionResult(EMDTerminationReason.MAX_MODES_REACHED, modes)
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@ -172,12 +172,15 @@ where BA: BufferAlgebra<Double, A>, BA: FieldOps<Buffer<Double>> = EmpiricalMode
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/**
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* Brute force count all zeros in the series.
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*/
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private fun Series<Double>.countZeros(): Int {
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require(size >= 2) { "Expected series with at least 2 elements, but got $size elements" }
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data class SignCounter(val prevSign: Double, val zeroCount: Int)
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private fun <T: Comparable<T>, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.countZeros(
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signal: Series<T>
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): Int where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> {
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require(signal.size >= 2) { "Expected series with at least 2 elements, but got ${signal.size} elements" }
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data class SignCounter(val prevSign: Int, val zeroCount: Int)
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fun strictSign(arg: T): Int = if (arg > elementAlgebra.zero) 1 else -1
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return fold(SignCounter(sign(get(0)), 0)) { acc: SignCounter, it: Double ->
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val currentSign = sign(it)
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return signal.fold(SignCounter(strictSign(signal[0]), 0)) { acc, it ->
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val currentSign = strictSign(it)
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if (acc.prevSign != currentSign) SignCounter(currentSign, acc.zeroCount + 1)
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else SignCounter(currentSign, acc.zeroCount)
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}.zeroCount
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@ -189,7 +192,7 @@ private fun Series<Double>.countZeros(): Int {
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private fun <T, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.relativeDifference(
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current: Series<T>,
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previous: Series<T>
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):T where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> = (bufferAlgebra) {
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): T where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> = (bufferAlgebra) {
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((current - previous) * (current - previous))
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.div(previous * previous)
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.fold(elementAlgebra.zero) { acc, it -> acc + it}
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@ -198,7 +201,7 @@ private fun <T, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.relativeDifference(
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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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private fun <T: Comparable<T>> Series<T>.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 peaks().size + troughs().size
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}
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@ -207,7 +210,10 @@ private fun Series<Double>.countExtrema(): Int {
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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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*/
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private fun Series<Double>.sCondition(): Boolean = (countExtrema() - countZeros()) in -1..1
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private fun <T: Comparable<T>, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.sCondition(
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signal: Series<T>
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): Boolean where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> =
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(signal.countExtrema() - countZeros(signal)) in -1..1
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internal sealed interface SiftingResult {
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@ -215,33 +221,33 @@ internal sealed interface SiftingResult {
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* Represents a condition when a mode has been successfully
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* extracted in a sifting process.
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*/
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open class Success(val result: Series<Double>): SiftingResult
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open class Success<T>(val result: Series<T>): SiftingResult
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/**
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* Returned when no termination condition was reached and the proto-mode
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* has become too flat (with not enough extrema to build envelopes)
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* after several sifting iterations.
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*/
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class SignalFlattened(result: Series<Double>) : Success(result)
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class SignalFlattened<T>(result: Series<T>) : Success<T>(result)
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/**
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* Returned when sifting process has been terminated due to the
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* S-number condition being reached.
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*/
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class SNumberReached(result: Series<Double>) : Success(result)
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class SNumberReached<T>(result: Series<T>) : Success<T>(result)
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/**
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* Returned when sifting process has been terminated due to the
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* delta condition (Cauchy criterion) being reached.
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*/
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class DeltaReached(result: Series<Double>) : Success(result)
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class DeltaReached<T>(result: Series<T>) : Success<T>(result)
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/**
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* Returned when sifting process has been terminated after
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* executing the maximum number of iterations (specified when creating an instance
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* of [EmpiricalModeDecomposition]).
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*/
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class MaxIterationsReached(result: Series<Double>): Success(result)
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class MaxIterationsReached<T>(result: Series<T>): Success<T>(result)
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/**
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* Returned when the submitted signal has not enough extrema to build envelopes,
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@ -273,7 +279,7 @@ public enum class EMDTerminationReason {
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ALL_POSSIBLE_MODES_EXTRACTED
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}
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public data class EMDecompositionResult(
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public data class EMDecompositionResult<T>(
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val terminatedBecause: EMDTerminationReason,
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val modes: List<Series<Double>>
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val modes: List<Series<T>>
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)
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