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Author SHA1 Message Date
5efd5e8304 Part 3 2024-05-20 16:57:19 +03:00
d2c8423b6f Part 2 2024-05-04 23:25:22 +03:00
2a2c5e8765 Part 1 2024-05-04 20:32:23 +03:00
2 changed files with 70 additions and 58 deletions

View File

@ -5,20 +5,24 @@
package space.kscience.kmath.series
import space.kscience.kmath.operations.algebra
import space.kscience.kmath.operations.bufferAlgebra
import space.kscience.kmath.structures.*
import space.kscience.kmath.operations.invoke
import space.kscience.plotly.*
import space.kscience.plotly.models.Scatter
import kotlin.math.sin
fun main(): Unit = (Double.seriesAlgebra()) {
private val customAlgebra = (Double.algebra.bufferAlgebra) { SeriesAlgebra(this) { it.toDouble() } }
fun main(): Unit = (customAlgebra) {
val signal = DoubleArray(800) {
sin(it.toDouble() / 10.0) + 3.5 * sin(it.toDouble() / 60.0)
}.asBuffer().moveTo(0)
val emd = empiricalModeDecomposition(
sConditionThreshold = 1,
maxSiftIterations = 15,
siftingDelta = 1e-2,
nModes = 4
).decompose(signal)
println("EMD: ${emd.modes.size} modes extracted, terminated because ${emd.terminatedBecause}")
@ -26,7 +30,7 @@ fun main(): Unit = (Double.seriesAlgebra()) {
fun Plot.series(name: String, buffer: Buffer<Double>, block: Scatter.() -> Unit = {}) {
this.scatter {
this.name = name
this.x.numbers = buffer.offsetIndices
this.x.numbers = buffer.labels
this.y.doubles = buffer.toDoubleArray()
block()
}

View File

@ -8,11 +8,8 @@ package space.kscience.kmath.series
import space.kscience.kmath.interpolation.SplineInterpolator
import space.kscience.kmath.interpolation.interpolate
import space.kscience.kmath.operations.*
import space.kscience.kmath.operations.Float64BufferOps.Companion.div
import space.kscience.kmath.operations.Float64BufferOps.Companion.pow
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.asBuffer
import kotlin.math.sign
import space.kscience.kmath.structures.last
/**
* Empirical mode decomposition of a signal represented as a [Series].
@ -29,13 +26,13 @@ import kotlin.math.sign
* @param nModes how many modes should be extracted at most. The algorithm may return fewer modes if it was not
* possible to extract more modes from the signal.
*/
public class EmpiricalModeDecomposition<BA, L: Number> (
private val seriesAlgebra: SeriesAlgebra<Double, *, BA, L>,
public class EmpiricalModeDecomposition<T: Comparable<T>, A: Field<T>, BA, L: T> (
private val seriesAlgebra: SeriesAlgebra<T, A, BA, L>,
private val sConditionThreshold: Int = 15,
private val maxSiftIterations: Int = 20,
private val siftingDelta: Double = 1e-2,
private val siftingDelta: T,
private val nModes: Int = 6
) where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> {
) where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> {
/**
* Take a signal, construct an upper and a lower envelopes, find the mean value of two,
@ -45,37 +42,38 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
* @return mean [Series] or `null`. `null` is returned in case
* the signal does not have enough extrema to construct envelopes.
*/
private fun findMean(signal: Series<Double>): Series<Double>? = (seriesAlgebra) {
val interpolator = SplineInterpolator(Float64Field)
fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: DoubleArray): Series<Double> {
private fun findMean(signal: Series<T>): Series<T>? = (seriesAlgebra) {
val interpolator = SplineInterpolator(elementAlgebra)
val makeBuffer = elementAlgebra.bufferFactory
fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: Buffer<T>): Series<T> {
val envelopeFunction = interpolator.interpolate(
Buffer(extrema.size) { signal.labels[extrema[it]].toDouble() },
paddedExtremeValues.asBuffer()
makeBuffer(extrema.size) { signal.labels[extrema[it]] },
paddedExtremeValues
)
return signal.mapWithLabel { _, label ->
// For some reason PolynomialInterpolator is exclusive and the right boundary
// TODO Notify interpolator authors
envelopeFunction(label.toDouble()) ?: paddedExtremeValues.last()
envelopeFunction(label) ?: paddedExtremeValues.last()
// need to make the interpolator yield values outside boundaries?
}
}
// Extrema padding (experimental) TODO padding needs a dedicated function
val maxima = listOf(0) + signal.peaks() + (signal.size - 1)
val maxValues = DoubleArray(maxima.size) { signal[maxima[it]] }
val maxValues = makeBuffer(maxima.size) { signal[maxima[it]] }
if (maxValues[0] < maxValues[1]) {
maxValues[0] = maxValues[1]
}
if (maxValues.last() < maxValues[maxValues.lastIndex - 1]) {
maxValues[maxValues.lastIndex] = maxValues[maxValues.lastIndex - 1]
if (maxValues.last() < maxValues[maxValues.size - 2]) {
maxValues[maxValues.size - 1] = maxValues[maxValues.size - 2]
}
val minima = listOf(0) + signal.troughs() + (signal.size - 1)
val minValues = DoubleArray(minima.size) { signal[minima[it]] }
val minValues = makeBuffer(minima.size) { signal[minima[it]] }
if (minValues[0] > minValues[1]) {
minValues[0] = minValues[1]
}
if (minValues.last() > minValues[minValues.lastIndex - 1]) {
minValues[minValues.lastIndex] = minValues[minValues.lastIndex - 1]
if (minValues.last() > minValues[minValues.size - 2]) {
minValues[minValues.size - 1] = minValues[minValues.size - 2]
}
return if (maxima.size < 3 || minima.size < 3) null else { // maybe make an early return?
val upperEnvelope = generateEnvelope(maxima, maxValues)
@ -92,13 +90,13 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
* @return [SiftingResult.NotEnoughExtrema] is returned if the signal has too few extrema to extract a mode.
* Success of an appropriate type (See [SiftingResult.Success] class) is returned otherwise.
*/
private fun sift(signal: Series<Double>): SiftingResult = siftInner(signal, 1, 0)
private fun sift(signal: Series<T>): SiftingResult = siftInner(signal, 1, 0)
/**
* Compute a single iteration of the sifting process.
*/
private tailrec fun siftInner(
prevMode: Series<Double>,
prevMode: Series<T>,
iterationNumber: Int,
sNumber: Int
): SiftingResult = (seriesAlgebra) {
@ -106,11 +104,12 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
return if (iterationNumber == 1) SiftingResult.NotEnoughExtrema
else SiftingResult.SignalFlattened(prevMode)
val mode = prevMode.zip(mean) { p, m -> p - m }
val newSNumber = if (mode.sCondition()) sNumber + 1 else sNumber
val newSNumber = if (sCondition(mode)) sNumber + 1 else sNumber
return when {
iterationNumber >= maxSiftIterations -> SiftingResult.MaxIterationsReached(mode)
sNumber >= sConditionThreshold -> SiftingResult.SNumberReached(mode)
relativeDifference(mode, prevMode) < siftingDelta * mode.size -> SiftingResult.DeltaReached(mode)
relativeDifference(mode, prevMode) < (elementAlgebra) { siftingDelta * mode.size } ->
SiftingResult.DeltaReached(mode)
else -> siftInner(mode, iterationNumber + 1, newSNumber)
}
}
@ -123,8 +122,8 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
* Modes returned in a list which contains as many modes as it was possible
* to extract before triggering one of the termination conditions.
*/
public fun decompose(signal: Series<Double>): EMDecompositionResult = (seriesAlgebra) {
val modes = mutableListOf<Series<Double>>()
public fun decompose(signal: Series<T>): EMDecompositionResult<T> = (seriesAlgebra) {
val modes = mutableListOf<Series<T>>()
var residual = signal
repeat(nModes) {
val nextMode = when(val r = sift(residual)) {
@ -132,14 +131,15 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
return EMDecompositionResult(
if (it == 0) EMDTerminationReason.SIGNAL_TOO_FLAT
else EMDTerminationReason.ALL_POSSIBLE_MODES_EXTRACTED,
modes
modes,
residual
)
is SiftingResult.Success -> r.result
is SiftingResult.Success<*> -> r.result
}
modes.add(nextMode)
modes.add(nextMode as Series<T>) // TODO remove unchecked cast
residual = residual.zip(nextMode) { l, r -> l - r }
}
return EMDecompositionResult(EMDTerminationReason.MAX_MODES_REACHED, modes)
return EMDecompositionResult(EMDTerminationReason.MAX_MODES_REACHED, modes, residual)
}
}
@ -157,13 +157,13 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
* @param nModes how many modes should be extracted at most. The algorithm may return fewer modes if it was not
* possible to extract more modes from the signal.
*/
public fun <L: Number, BA> SeriesAlgebra<Double, *, BA, L>.empiricalModeDecomposition(
public fun <T: Comparable<T>, L: T, A: Field<T>, BA> SeriesAlgebra<T, A, BA, L>.empiricalModeDecomposition(
sConditionThreshold: Int = 15,
maxSiftIterations: Int = 20,
siftingDelta: Double = 1e-2,
siftingDelta: T,
nModes: Int = 3
): EmpiricalModeDecomposition<BA, L>
where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> = EmpiricalModeDecomposition(
): EmpiricalModeDecomposition<T, A, BA, L>
where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> = EmpiricalModeDecomposition(
seriesAlgebra = this,
sConditionThreshold = sConditionThreshold,
maxSiftIterations = maxSiftIterations,
@ -174,12 +174,15 @@ where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> = EmpiricalModeD
/**
* Brute force count all zeros in the series.
*/
private fun Series<Double>.countZeros(): Int {
require(size >= 2) { "Expected series with at least 2 elements, but got $size elements" }
data class SignCounter(val prevSign: Double, val zeroCount: Int)
private fun <T: Comparable<T>, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.countZeros(
signal: Series<T>
): Int where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> {
require(signal.size >= 2) { "Expected series with at least 2 elements, but got ${signal.size} elements" }
data class SignCounter(val prevSign: Int, val zeroCount: Int)
fun strictSign(arg: T): Int = if (arg > elementAlgebra.zero) 1 else -1
return fold(SignCounter(sign(get(0)), 0)) { acc: SignCounter, it: Double ->
val currentSign = sign(it)
return signal.fold(SignCounter(strictSign(signal[0]), 0)) { acc, it ->
val currentSign = strictSign(it)
if (acc.prevSign != currentSign) SignCounter(currentSign, acc.zeroCount + 1)
else SignCounter(currentSign, acc.zeroCount)
}.zeroCount
@ -188,18 +191,19 @@ private fun Series<Double>.countZeros(): Int {
/**
* Compute relative difference of two series.
*/
private fun <BA> SeriesAlgebra<Double, *, BA, *>.relativeDifference(
current: Series<Double>,
previous: Series<Double>
):Double where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> =
(current - previous).pow(2)
.div(previous pow 2)
.fold(0.0) { acc, d -> acc + d } // TODO replace with Series<>.sum() method when it's implemented
private fun <T, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.relativeDifference(
current: Series<T>,
previous: Series<T>
): T where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> = (bufferAlgebra) {
((current - previous) * (current - previous))
.div(previous * previous)
.fold(elementAlgebra.zero) { acc, it -> acc + it}
}
/**
* Brute force count all extrema of a series.
*/
private fun Series<Double>.countExtrema(): Int {
private fun <T: Comparable<T>> Series<T>.countExtrema(): Int {
require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
return peaks().size + troughs().size
}
@ -208,7 +212,10 @@ private fun Series<Double>.countExtrema(): Int {
* Check whether the numbers of zeroes and extrema of a series differ by no more than 1.
* This is a necessary condition of an empirical mode.
*/
private fun Series<Double>.sCondition(): Boolean = (countExtrema() - countZeros()) in -1..1
private fun <T: Comparable<T>, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.sCondition(
signal: Series<T>
): Boolean where BA: BufferAlgebra<T, A>, BA: FieldOps<Buffer<T>> =
(signal.countExtrema() - countZeros(signal)) in -1..1
internal sealed interface SiftingResult {
@ -216,33 +223,33 @@ internal sealed interface SiftingResult {
* Represents a condition when a mode has been successfully
* extracted in a sifting process.
*/
open class Success(val result: Series<Double>): SiftingResult
open class Success<T>(val result: Series<T>): SiftingResult
/**
* Returned when no termination condition was reached and the proto-mode
* has become too flat (with not enough extrema to build envelopes)
* after several sifting iterations.
*/
class SignalFlattened(result: Series<Double>) : Success(result)
class SignalFlattened<T>(result: Series<T>) : Success<T>(result)
/**
* Returned when sifting process has been terminated due to the
* S-number condition being reached.
*/
class SNumberReached(result: Series<Double>) : Success(result)
class SNumberReached<T>(result: Series<T>) : Success<T>(result)
/**
* Returned when sifting process has been terminated due to the
* delta condition (Cauchy criterion) being reached.
*/
class DeltaReached(result: Series<Double>) : Success(result)
class DeltaReached<T>(result: Series<T>) : Success<T>(result)
/**
* Returned when sifting process has been terminated after
* executing the maximum number of iterations (specified when creating an instance
* of [EmpiricalModeDecomposition]).
*/
class MaxIterationsReached(result: Series<Double>): Success(result)
class MaxIterationsReached<T>(result: Series<T>): Success<T>(result)
/**
* Returned when the submitted signal has not enough extrema to build envelopes,
@ -274,7 +281,8 @@ public enum class EMDTerminationReason {
ALL_POSSIBLE_MODES_EXTRACTED
}
public data class EMDecompositionResult(
public data class EMDecompositionResult<T>(
val terminatedBecause: EMDTerminationReason,
val modes: List<Series<Double>>
val modes: List<Series<T>>,
val residual: Series<T>
)