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Igor Dunaev 2024-04-25 20:55:54 +03:00
parent 8fa42450b2
commit 4f2ebb17ff
2 changed files with 68 additions and 67 deletions
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3
examples/src/main/kotlin/space/kscience/kmath/series/emdDemo.kt
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@ -6,11 +6,12 @@
package space.kscience.kmath.series
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 = with(Double.seriesAlgebra()) {
fun main(): Unit = (Double.seriesAlgebra()) {
val signal = DoubleArray(800) {
sin(it.toDouble() / 10.0) + 3.5 * sin(it.toDouble() / 60.0)
}.asBuffer().moveTo(0)

132
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/EmpiricalModeDecomposition.kt
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@ -12,7 +12,6 @@ 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.last
import space.kscience.kmath.structures.slice
import kotlin.math.sign
/**
@ -30,22 +29,23 @@ 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> (
public class EmpiricalModeDecomposition<BA, L: Number> (
private val seriesAlgebra: SeriesAlgebra<Double, *, BA, L>,
private val sConditionThreshold: Int = 15,
private val maxSiftIterations: Int = 20,
private val siftingDelta: Double = 1e-2,
private val nModes: Int = 6
) where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L : Number {
) where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> {
/**
* Take a signal, construct an upper and a lower envelope, find the mean value of two,
* Take a signal, construct an upper and a lower envelopes, find the mean value of two,
* represented as a series.
* @param signal Signal to compute on
*
* @return null is returned if the signal has not enough extrema to construct envelopes.
* @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>? = with(seriesAlgebra) {
private fun findMean(signal: Series<Double>): Series<Double>? = (seriesAlgebra) {
val interpolator = SplineInterpolator(Float64Field)
fun generateEnvelope(extrema: List<Int>): Series<Double> {
val envelopeFunction = interpolator.interpolate(
@ -59,12 +59,12 @@ public class EmpiricalModeDecomposition<BA, L> (
// need to make the interpolator yield values outside boundaries?
}
}
val maxima = signal.maxima()
val minima = signal.minima()
val maxima = signal.paddedMaxima()
val minima = signal.paddedMinima()
return if (maxima.size < 3 || minima.size < 3) null else {
val upperEnvelope = generateEnvelope(maxima)
val lowerEnvelope = generateEnvelope(minima)
return (upperEnvelope + lowerEnvelope).map { it * 0.5 }
return upperEnvelope.zip(lowerEnvelope) { upper, lower -> upper + lower / 2.0 }
}
}
@ -76,15 +76,16 @@ public class EmpiricalModeDecomposition<BA, L> (
* @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 = with(seriesAlgebra) {
private fun sift(signal: Series<Double>): SiftingResult = (seriesAlgebra) {
val mean = findMean(signal) ?: return SiftingResult.NotEnoughExtrema
val protoMode = signal.zip(mean) { s, m -> s - m }
val sNumber = if (protoMode.sCondition()) 1 else 0
return if (maxSiftIterations == 1) SiftingResult.MaxIterationsReached(protoMode)
else if (sNumber >= sConditionThreshold) SiftingResult.SNumberReached(protoMode)
else if (relativeDifference(signal, protoMode) < siftingDelta * signal.size) {
SiftingResult.DeltaReached(protoMode)
} else siftInner(protoMode, 2, sNumber)
return when {
maxSiftIterations == 1 -> SiftingResult.MaxIterationsReached(protoMode)
sNumber >= sConditionThreshold -> SiftingResult.SNumberReached(protoMode)
relativeDifference(protoMode, signal) < siftingDelta * signal.size -> SiftingResult.DeltaReached(protoMode)
else -> siftInner(protoMode, 2, sNumber)
}
}
/**
@ -94,14 +95,16 @@ public class EmpiricalModeDecomposition<BA, L> (
prevMode: Series<Double>,
iterationNumber: Int,
sNumber: Int
): SiftingResult = with(seriesAlgebra) {
): SiftingResult = (seriesAlgebra) {
val mean = findMean(prevMode) ?: return SiftingResult.SignalFlattened(prevMode)
val mode = prevMode.zip(mean) { p, m -> p - m }
val newSNumber = if (mode.sCondition()) sNumber + 1 else sNumber
return if (iterationNumber >= maxSiftIterations) SiftingResult.MaxIterationsReached(mode)
else if (sNumber >= sConditionThreshold) SiftingResult.SNumberReached(mode)
else if (relativeDifference(prevMode, mode) < siftingDelta * mode.size) SiftingResult.DeltaReached(mode)
else siftInner(mode, iterationNumber + 1, newSNumber)
return when {
iterationNumber >= maxSiftIterations -> SiftingResult.MaxIterationsReached(mode)
sNumber >= sConditionThreshold -> SiftingResult.SNumberReached(mode)
relativeDifference(mode, prevMode) < siftingDelta * mode.size -> SiftingResult.DeltaReached(mode)
else -> siftInner(mode, iterationNumber + 1, newSNumber)
}
}
/**
@ -112,20 +115,17 @@ public class EmpiricalModeDecomposition<BA, L> (
* 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 = with(seriesAlgebra) {
public fun decompose(signal: Series<Double>): EMDecompositionResult = (seriesAlgebra) {
val modes = mutableListOf<Series<Double>>()
val mode = when(val r = sift(signal)) {
SiftingResult.NotEnoughExtrema ->
return EMDecompositionResult(EMDTerminationReason.SIGNAL_TOO_FLAT, modes)
is SiftingResult.Success -> r.result
}
modes.add(mode)
var residual = signal.zip(mode) { l, r -> l - r }
repeat(nModes - 1) {
var residual = signal
repeat(nModes) {
val nextMode = when(val r = sift(residual)) {
SiftingResult.NotEnoughExtrema ->
return EMDecompositionResult(EMDTerminationReason.ALL_POSSIBLE_MODES_EXTRACTED, modes)
return EMDecompositionResult(
if (it == 0) EMDTerminationReason.SIGNAL_TOO_FLAT
else EMDTerminationReason.ALL_POSSIBLE_MODES_EXTRACTED,
modes
)
is SiftingResult.Success -> r.result
}
modes.add(nextMode)
@ -149,13 +149,13 @@ public class EmpiricalModeDecomposition<BA, L> (
* @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, BA> SeriesAlgebra<Double, *, BA, L>.empiricalModeDecomposition(
public fun <L: Number, BA> SeriesAlgebra<Double, *, BA, L>.empiricalModeDecomposition(
sConditionThreshold: Int = 15,
maxSiftIterations: Int = 20,
siftingDelta: Double = 1e-2,
nModes: Int = 3
): EmpiricalModeDecomposition<BA, L>
where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L: Number = EmpiricalModeDecomposition(
where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> = EmpiricalModeDecomposition(
seriesAlgebra = this,
sConditionThreshold = sConditionThreshold,
maxSiftIterations = maxSiftIterations,
@ -168,22 +168,25 @@ where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L: Number = Emp
*/
private fun Series<Double>.countZeros(): Int {
require(size >= 2) { "Expected series with at least 2 elements, but got $size elements" }
return fold(Pair(get(0), 0)) { acc: Pair<Double, Int>, it: Double ->
if (sign(acc.first) != sign(it)) Pair(it, acc.second + 1) else Pair(it, acc.second)
}.second
data class SignCounter(val prevSign: Double, val zeroCount: Int)
return fold(SignCounter(sign(get(0)), 0)) { acc: SignCounter, it: Double ->
val currentSign = sign(it)
if (acc.prevSign != currentSign) SignCounter(currentSign, acc.zeroCount + 1)
else SignCounter(currentSign, acc.zeroCount)
}.zeroCount
}
/**
* Compute relative difference of two series.
*/
private fun <L, BA> SeriesAlgebra<Double, *, BA, L>.relativeDifference(
private fun <BA> SeriesAlgebra<Double, *, BA, *>.relativeDifference(
current: Series<Double>,
previous: Series<Double>
):Double where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>>, L: Number {
return (current - previous).pow(2)
):Double where BA: BufferAlgebra<Double, *>, BA: RingOps<Buffer<Double>> =
(current - previous).pow(2)
.div(previous pow 2)
.fold(0.0) { acc, d -> acc + d } // to avoid unnecessary boxing, but i may be wrong
}
.fold(0.0) { acc, d -> acc + d } // TODO replace with Series<>.sum() method when it's implemented
private fun <T: Comparable<T>> isExtreme(prev: T, elem: T, next: T): Boolean =
(elem > prev && elem > next) || (elem < prev && elem < next)
@ -193,43 +196,40 @@ private fun <T: Comparable<T>> isExtreme(prev: T, elem: T, next: T): Boolean =
*/
private fun Series<Double>.countExtrema(): Int {
require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
return slice(1..< size - 1).asIterable().foldIndexed(0) { index, acc, it ->
if (isExtreme(get(index), it, get(index + 2))) acc + 1 else acc
}
return (1 .. size - 2).count { isExtreme(this[it - 1], this[it], this[it + 1]) }
}
/**
* Retrieve indices of knot points for spline interpolation matching the predicate.
* The first and the last points of a series are always included.
*/
private fun <T: Comparable<T>> Series<T>.knotPoints(predicate: (T, T, T) -> Boolean): List<Int> {
require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
val points = mutableListOf(0)
for (index in 1 .. size - 2) {
val left = this[index - 1]
val middle = this[index]
val right = this[index + 1]
if (predicate(left, middle, right)) points.add(index)
}
points.add(size - 1)
return points
}
/**
* Retrieve indices of knot points used to construct an upper envelope,
* namely maxima together with the first last point in a series.
*/
private fun<T> Series<T>.maxima(): List<Int> where T: Comparable<T> {
require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
val maxima = mutableListOf(0)
slice(1..< size - 1).asIterable().forEachIndexed { index, it ->
if (it > get(index) && it > get(index + 2)) { // weird offset, is there a way to do it better?
maxima.add(index + 1)
}
}
maxima.add(size - 1)
return maxima
}
private fun <T: Comparable<T>> Series<T>.paddedMaxima(): List<Int> =
knotPoints { left, middle, right -> (middle > left && middle > right) }
/**
* Retrieve indices of knot points used to construct a lower envelope,
* namely minima together with the first last point in a series.
*/
private fun<T> Series<T>.minima(): List<Int> where T: Comparable<T> {
require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
val minima = mutableListOf(0)
slice(1..< size - 1).asIterable().forEachIndexed { index, it ->
if (it < get(index) && it < get(index + 2)) { // weird offset, is there a way to do it better?
minima.add(index + 1)
}
}
minima.add(size - 1)
return minima
}
private fun <T: Comparable<T>> Series<T>.paddedMinima(): List<Int> =
knotPoints { left, middle, right -> (middle < left && middle < right) }
/**
* Check whether the numbers of zeroes and extrema of a series differ by no more than 1.