Extrema padding (experimental)

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 }
         }
     }
 
@@ -186,43 +202,12 @@ private fun <T: Comparable<T>> isExtreme(prev: T, elem: T, next: T): Boolean =
 /**
  * Brute force count all extrema of a series.
  */
+@Deprecated("Does not match the algorithm currently in use.")
 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]) }
 }
 
-
-/**
- * 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.