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Part 2

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Igor Dunaev 2024-05-04 21:55:37 +03:00
parent 2a2c5e8765
commit d2c8423b6f
1 changed files with 37 additions and 31 deletions
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68
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/EmpiricalModeDecomposition.kt
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@ -9,8 +9,7 @@ import space.kscience.kmath.interpolation.SplineInterpolator
import space.kscience.kmath.interpolation.interpolate
import space.kscience.kmath.operations.*
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].
@ -45,35 +44,36 @@ public class EmpiricalModeDecomposition<A: Field<Double>, BA, L: Number> (
*/
private fun findMean(signal: Series<Double>): Series<Double>? = (seriesAlgebra) {
val interpolator = SplineInterpolator(elementAlgebra)
fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: Array<Double>): Series<Double> {
val makeBuffer = elementAlgebra.bufferFactory
fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: Buffer<Double>): Series<Double> {
val envelopeFunction = interpolator.interpolate(
Buffer(extrema.size) { signal.labels[extrema[it]] as Double },
paddedExtremeValues.asBuffer()
Buffer(extrema.size) { signal.labels[extrema[it]].toDouble() },
paddedExtremeValues
)
return signal.mapWithLabel { _, label ->
// For some reason PolynomialInterpolator is exclusive and the right boundary
// TODO Notify interpolator authors
envelopeFunction(label as Double) ?: paddedExtremeValues.last()
envelopeFunction(label.toDouble()) ?: 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 = Array(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 = Array(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)
@ -104,7 +104,7 @@ public class EmpiricalModeDecomposition<A: Field<Double>, 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)
@ -121,7 +121,7 @@ public class EmpiricalModeDecomposition<A: Field<Double>, 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) {
public fun decompose(signal: Series<Double>): EMDecompositionResult<Double> = (seriesAlgebra) {
val modes = mutableListOf<Series<Double>>()
var residual = signal
repeat(nModes) {
@ -132,9 +132,9 @@ public class EmpiricalModeDecomposition<A: Field<Double>, BA, L: Number> (
else EMDTerminationReason.ALL_POSSIBLE_MODES_EXTRACTED,
modes
)
is SiftingResult.Success -> r.result
is SiftingResult.Success<*> -> r.result
}
modes.add(nextMode)
modes.add(nextMode as Series<Double>) // TODO remove unchecked cast
residual = residual.zip(nextMode) { l, r -> l - r }
}
return EMDecompositionResult(EMDTerminationReason.MAX_MODES_REACHED, modes)
@ -172,12 +172,15 @@ where BA: BufferAlgebra<Double, A>, BA: FieldOps<Buffer<Double>> = EmpiricalMode
/**
* 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
@ -189,7 +192,7 @@ private fun Series<Double>.countZeros(): Int {
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) {
): 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}
@ -198,7 +201,7 @@ private fun <T, A: Ring<T>, BA> SeriesAlgebra<T, A, BA, *>.relativeDifference(
/**
* 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
}
@ -207,7 +210,10 @@ 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 {
@ -215,33 +221,33 @@ 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,
@ -273,7 +279,7 @@ 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>>
)