Suboptimal implementation for countExtrema

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/EmpiricalModeDecomposition.kt

@@ -11,7 +11,7 @@ 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.last
+import space.kscience.kmath.structures.asBuffer
 import kotlin.math.sign
 
 /**
@@ -47,24 +47,40 @@ public class EmpiricalModeDecomposition<BA, L: Number> (
      */
     private fun findMean(signal: Series<Double>): Series<Double>? = (seriesAlgebra) {
         val interpolator = SplineInterpolator(Float64Field)
-        fun generateEnvelope(extrema: List<Int>): Series<Double> {
+        fun generateEnvelope(extrema: List<Int>, paddedExtremeValues: DoubleArray): Series<Double> {
             val envelopeFunction = interpolator.interpolate(
                 Buffer(extrema.size) { signal.labels[extrema[it]].toDouble() },
-                Buffer(extrema.size) { signal[extrema[it]] }
+                paddedExtremeValues.asBuffer()
             )
             return signal.mapWithLabel { _, label ->
                 // For some reason PolynomialInterpolator is exclusive and the right boundary
                 // TODO Notify interpolator authors
-                envelopeFunction(label.toDouble()) ?: signal.last()
+                envelopeFunction(label.toDouble()) ?: paddedExtremeValues.last()
                 // need to make the interpolator yield values outside boundaries?
             }
         }
-        val maxima = signal.paddedMaxima()
+        // Extrema padding (experimental) TODO padding needs a dedicated function
-        val minima = signal.paddedMinima()
+        val maxima = listOf(0) + signal.peaks() + (signal.size - 1)
-        return if (maxima.size < 3 || minima.size < 3) null else {
+        val maxValues = DoubleArray(maxima.size) { signal[maxima[it]] }
-            val upperEnvelope = generateEnvelope(maxima)
+        if (maxValues[0] < maxValues[1]) {
-            val lowerEnvelope = generateEnvelope(minima)
+            maxValues[0] = maxValues[1]
-            return upperEnvelope.zip(lowerEnvelope) { upper, lower -> upper + lower / 2.0 }
+        }
+        if (maxValues.last() < maxValues[maxValues.lastIndex - 1]) {
+            maxValues[maxValues.lastIndex] = maxValues[maxValues.lastIndex - 1]
+        }
+
+        val minima = listOf(0) + signal.troughs() + (signal.size - 1)
+        val minValues = DoubleArray(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]
+        }
+         return if (maxima.size < 3 || minima.size < 3) null else { // maybe make an early return?
+            val upperEnvelope = generateEnvelope(maxima, maxValues)
+            val lowerEnvelope = generateEnvelope(minima, minValues)
+            return (upperEnvelope + lowerEnvelope).map { it * 0.5 }
         }
     }
 
@@ -76,27 +92,19 @@ 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 = (seriesAlgebra) {
+    private fun sift(signal: Series<Double>): SiftingResult = siftInner(signal, 1, 0)
-        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 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)
-        }
-    }
 
     /**
      * Compute a single iteration of the sifting process.
      */
-    private fun siftInner(
+    private tailrec fun siftInner(
         prevMode: Series<Double>,
         iterationNumber: Int,
         sNumber: Int
     ): SiftingResult = (seriesAlgebra) {
-        val mean = findMean(prevMode) ?: return SiftingResult.SignalFlattened(prevMode)
+        val mean = findMean(prevMode) ?:
+            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
         return when {
@@ -188,49 +196,14 @@ private fun <BA> SeriesAlgebra<Double, *, BA, *>.relativeDifference(
         .div(previous pow 2)
         .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)
-
 /**
  * Brute force count all extrema of a series.
  */
 private fun Series<Double>.countExtrema(): Int {
     require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
-    return (1 .. size - 2).count { isExtreme(this[it - 1], this[it], this[it + 1]) }
+    return peaks().size + troughs().size
 }
 
-
-/**
- * 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: 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: 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.
  * This is a necessary condition of an empirical mode.

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/peakFinding.kt

@@ -0,0 +1,89 @@
+/*
+ * Copyright 2018-2024 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.series
+
+
+public enum class PlateauEdgePolicy  {
+    /**
+     * Midpoints of plateau are returned, edges not belonging to a plateau are ignored.
+     *
+     * A midpoint is the index closest to the average of indices of the left and right edges
+     * of the plateau:
+     *
+     * `val midpoint = ((leftEdge + rightEdge) / 2).toInt`
+     */
+     AVERAGE,
+
+    /**
+     * Both left and right edges are returned.
+     */
+    KEEP_ALL_EDGES,
+
+    /**
+     * Only right edges are returned.
+     */
+    KEEP_RIGHT_EDGES,
+
+    /**
+     * Only left edges are returned.
+     */
+    KEEP_LEFT_EDGES,
+
+    /**
+     * Ignore plateau, only peaks (troughs) with values strictly greater (less)
+     * than values of the adjacent points are returned.
+     */
+    IGNORE
+}
+
+
+public fun <T: Comparable<T>> Series<T>.peaks(
+    plateauEdgePolicy: PlateauEdgePolicy = PlateauEdgePolicy.AVERAGE
+): List<Int> = findPeaks(plateauEdgePolicy, { other -> this > other },  { other -> this >= other })
+
+public fun <T: Comparable<T>> Series<T>.troughs(
+    plateauEdgePolicy: PlateauEdgePolicy = PlateauEdgePolicy.AVERAGE
+): List<Int> = findPeaks(plateauEdgePolicy, { other -> this < other }, { other -> this <= other })
+
+
+private fun <T: Comparable<T>> Series<T>.findPeaks(
+    plateauPolicy: PlateauEdgePolicy = PlateauEdgePolicy.AVERAGE,
+    cmpStrong: T.(T) -> Boolean,
+    cmpWeak: T.(T) -> Boolean
+): List<Int> {
+    require(size >= 3) { "Expected series with at least 3 elements, but got $size elements" }
+    if (plateauPolicy == PlateauEdgePolicy.AVERAGE) return peaksWithPlateau(cmpStrong)
+    fun peakCriterion(left: T, middle: T, right: T): Boolean = when(plateauPolicy) {
+        PlateauEdgePolicy.KEEP_LEFT_EDGES -> middle.cmpStrong(left) && middle.cmpWeak(right)
+        PlateauEdgePolicy.KEEP_RIGHT_EDGES -> middle.cmpWeak(left) && middle.cmpStrong(right)
+        PlateauEdgePolicy.KEEP_ALL_EDGES ->
+            (middle.cmpStrong(left) && middle.cmpWeak(right)) || (middle.cmpWeak(left) && middle.cmpStrong(right))
+        else -> middle.cmpStrong(right) && middle.cmpStrong(left)
+    }
+    val indices = mutableListOf<Int>()
+    for (index in 1 .. size - 2) {
+        val left = this[index - 1]
+        val middle = this[index]
+        val right = this[index + 1]
+        if (peakCriterion(left, middle, right)) indices.add(index)
+    }
+    return indices
+}
+
+
+private fun <T: Comparable<T>> Series<T>.peaksWithPlateau(cmpStrong: T.(T) -> Boolean): List<Int> {
+    val peaks = mutableListOf<Int>()
+    tailrec fun peaksPlateauInner(index: Int) {
+        val nextUnequal = (index + 1 ..< size).firstOrNull { this[it] != this[index] } ?: (size - 1)
+        val newIndex = if (this[index].cmpStrong(this[index - 1]) && this[index].cmpStrong(this[nextUnequal])) {
+            peaks.add((index + nextUnequal) / 2)
+            nextUnequal
+        } else index + 1
+        if (newIndex < size - 1) peaksPlateauInner(newIndex)
+    }
+    peaksPlateauInner(1)
+    return peaks
+}