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@ -6,11 +6,12 @@
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package space.kscience.kmath.series
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import space.kscience.kmath.structures.*
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import space.kscience.kmath.operations.invoke
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import space.kscience.plotly.*
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import space.kscience.plotly.models.Scatter
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import kotlin.math.sin
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fun main(): Unit = with(Double.seriesAlgebra()) {
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fun main(): Unit = (Double.seriesAlgebra()) {
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val signal = DoubleArray(800) {
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sin(it.toDouble() / 10.0) + 3.5 * sin(it.toDouble() / 60.0)
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}.asBuffer().moveTo(0)
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@ -12,7 +12,6 @@ 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.slice
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import kotlin.math.sign
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/**
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@ -30,22 +29,23 @@ import kotlin.math.sign
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* @param nModes how many modes should be extracted at most. The algorithm may return fewer modes if it was not
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* possible to extract more modes from the signal.
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*/
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public class EmpiricalModeDecomposition<BA, L> (
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public class EmpiricalModeDecomposition<BA, L: Number> (
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private val seriesAlgebra: SeriesAlgebra<Double, *, BA, L>,
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private val sConditionThreshold: Int = 15,
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private val maxSiftIterations: Int = 20,
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private val siftingDelta: Double = 1e-2,
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private val nModes: Int = 6
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) where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L : Number {
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) where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> {
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/**
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* Take a signal, construct an upper and a lower envelope, find the mean value of two,
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* Take a signal, construct an upper and a lower envelopes, find the mean value of two,
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* represented as a series.
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* @param signal Signal to compute on
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*
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* @return null is returned if the signal has not enough extrema to construct envelopes.
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* @return mean [Series] or `null`. `null` is returned in case
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* the signal does not have enough extrema to construct envelopes.
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*/
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private fun findMean(signal: Series<Double>): Series<Double>? = with(seriesAlgebra) {
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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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val envelopeFunction = interpolator.interpolate(
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@ -59,12 +59,12 @@ public class EmpiricalModeDecomposition<BA, L> (
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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.maxima()
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val minima = signal.minima()
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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 + lowerEnvelope).map { it * 0.5 }
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return upperEnvelope.zip(lowerEnvelope) { upper, lower -> upper + lower / 2.0 }
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}
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}
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@ -76,15 +76,16 @@ public class EmpiricalModeDecomposition<BA, L> (
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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 = with(seriesAlgebra) {
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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 if (maxSiftIterations == 1) SiftingResult.MaxIterationsReached(protoMode)
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else if (sNumber >= sConditionThreshold) SiftingResult.SNumberReached(protoMode)
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else if (relativeDifference(signal, protoMode) < siftingDelta * signal.size) {
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SiftingResult.DeltaReached(protoMode)
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} else siftInner(protoMode, 2, sNumber)
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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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/**
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@ -94,14 +95,16 @@ public class EmpiricalModeDecomposition<BA, L> (
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prevMode: Series<Double>,
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iterationNumber: Int,
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sNumber: Int
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): SiftingResult = with(seriesAlgebra) {
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): SiftingResult = (seriesAlgebra) {
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val mean = findMean(prevMode) ?: return 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 if (iterationNumber >= maxSiftIterations) SiftingResult.MaxIterationsReached(mode)
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else if (sNumber >= sConditionThreshold) SiftingResult.SNumberReached(mode)
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else if (relativeDifference(prevMode, mode) < siftingDelta * mode.size) SiftingResult.DeltaReached(mode)
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else siftInner(mode, iterationNumber + 1, newSNumber)
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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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relativeDifference(mode, prevMode) < siftingDelta * mode.size -> SiftingResult.DeltaReached(mode)
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else -> siftInner(mode, iterationNumber + 1, newSNumber)
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}
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}
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/**
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@ -112,20 +115,17 @@ public class EmpiricalModeDecomposition<BA, L> (
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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 = with(seriesAlgebra) {
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public fun decompose(signal: Series<Double>): EMDecompositionResult = (seriesAlgebra) {
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val modes = mutableListOf<Series<Double>>()
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val mode = when(val r = sift(signal)) {
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SiftingResult.NotEnoughExtrema ->
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return EMDecompositionResult(EMDTerminationReason.SIGNAL_TOO_FLAT, modes)
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is SiftingResult.Success -> r.result
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}
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modes.add(mode)
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var residual = signal.zip(mode) { l, r -> l - r }
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repeat(nModes - 1) {
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var residual = signal
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repeat(nModes) {
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val nextMode = when(val r = sift(residual)) {
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SiftingResult.NotEnoughExtrema ->
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return EMDecompositionResult(EMDTerminationReason.ALL_POSSIBLE_MODES_EXTRACTED, modes)
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return EMDecompositionResult(
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if (it == 0) EMDTerminationReason.SIGNAL_TOO_FLAT
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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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}
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modes.add(nextMode)
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@ -149,13 +149,13 @@ public class EmpiricalModeDecomposition<BA, L> (
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* @param nModes how many modes should be extracted at most. The algorithm may return fewer modes if it was not
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* possible to extract more modes from the signal.
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*/
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public fun <L, BA> SeriesAlgebra<Double, *, BA, L>.empiricalModeDecomposition(
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public fun <L: Number, BA> SeriesAlgebra<Double, *, BA, L>.empiricalModeDecomposition(
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sConditionThreshold: Int = 15,
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maxSiftIterations: Int = 20,
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siftingDelta: Double = 1e-2,
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nModes: Int = 3
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): EmpiricalModeDecomposition<BA, L>
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where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L: Number = EmpiricalModeDecomposition(
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where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> = EmpiricalModeDecomposition(
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seriesAlgebra = this,
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sConditionThreshold = sConditionThreshold,
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maxSiftIterations = maxSiftIterations,
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@ -168,22 +168,25 @@ where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L: Number = Emp
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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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return fold(Pair(get(0), 0)) { acc: Pair<Double, Int>, it: Double ->
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if (sign(acc.first) != sign(it)) Pair(it, acc.second + 1) else Pair(it, acc.second)
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}.second
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data class SignCounter(val prevSign: Double, val zeroCount: Int)
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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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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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}
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/**
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* Compute relative difference of two series.
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*/
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private fun <L, BA> SeriesAlgebra<Double, *, BA, L>.relativeDifference(
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private fun <BA> SeriesAlgebra<Double, *, BA, *>.relativeDifference(
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current: Series<Double>,
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previous: Series<Double>
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):Double where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L: Number {
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return (current - previous).pow(2)
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):Double where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> =
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(current - previous).pow(2)
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.div(previous pow 2)
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.fold(0.0) { acc, d -> acc + d } // to avoid unnecessary boxing, but i may be wrong
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}
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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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@ -193,43 +196,40 @@ private fun <T: Comparable<T>> isExtreme(prev: T, elem: T, next: T): Boolean =
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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 slice(1..< size - 1).asIterable().foldIndexed(0) { index, acc, it ->
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if (isExtreme(get(index), it, get(index + 2))) acc + 1 else acc
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}
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return (1 .. size - 2).count { isExtreme(this[it - 1], this[it], this[it + 1]) }
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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> Series<T>.maxima(): List<Int> where T: Comparable<T> {
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require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
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val maxima = mutableListOf(0)
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slice(1..< size - 1).asIterable().forEachIndexed { index, it ->
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if (it > get(index) && it > get(index + 2)) { // weird offset, is there a way to do it better?
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maxima.add(index + 1)
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}
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}
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maxima.add(size - 1)
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return maxima
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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> Series<T>.minima(): List<Int> where T: Comparable<T> {
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require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
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val minima = mutableListOf(0)
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slice(1..< size - 1).asIterable().forEachIndexed { index, it ->
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if (it < get(index) && it < get(index + 2)) { // weird offset, is there a way to do it better?
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minima.add(index + 1)
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}
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}
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minima.add(size - 1)
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return minima
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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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