forked from kscience/kmath
Extrema padding (experimental)
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@ -11,7 +11,7 @@ import space.kscience.kmath.operations.*
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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.asBuffer
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import kotlin.math.sign
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/**
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@ -47,24 +47,40 @@ public class EmpiricalModeDecomposition<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(Float64Field)
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fun generateEnvelope(extrema: List<Int>): Series<Double> {
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fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: DoubleArray): Series<Double> {
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val envelopeFunction = interpolator.interpolate(
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Buffer(extrema.size) { signal.labels[extrema[it]].toDouble() },
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Buffer(extrema.size) { signal[extrema[it]] }
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paddedExtremeValues.asBuffer()
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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.toDouble()) ?: signal.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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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.zip(lowerEnvelope) { upper, lower -> upper + lower / 2.0 }
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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 = DoubleArray(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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}
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val minima = listOf(0) + signal.troughs() + (signal.size - 1)
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val minValues = DoubleArray(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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}
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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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val lowerEnvelope = generateEnvelope(minima, minValues)
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return (upperEnvelope + lowerEnvelope).map { it * 0.5 }
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}
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}
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@ -186,43 +202,12 @@ private fun <T: Comparable<T>> isExtreme(prev: T, elem: T, next: T): Boolean =
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/**
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* Brute force count all extrema of a series.
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*/
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@Deprecated("Does not match the algorithm currently in use.")
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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 (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: 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: 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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* This is a necessary condition of an empirical mode.
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