Minor piecewise rework

examples/src/main/kotlin/space/kscience/kmath/functions/interpolate.kt

@@ -10,12 +10,14 @@ import space.kscience.kmath.interpolation.interpolatePolynomials
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.plotly.Plotly
+import space.kscience.plotly.UnstablePlotlyAPI
 import space.kscience.plotly.makeFile
 import space.kscience.plotly.models.functionXY
 import space.kscience.plotly.scatter
 import kotlin.math.PI
 import kotlin.math.sin
 
+@OptIn(UnstablePlotlyAPI::class)
 fun main() {
     val data = (0..10).map {
         val x = it.toDouble() / 5 * PI

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt

@@ -22,8 +22,20 @@ public fun interface Piecewise<T, R> {
 
 /**
  * Represents piecewise-defined function where all the sub-functions are polynomials.
+ * @param pieces An ordered list of range-polynomial pairs. The list does not in general guarantee that there are no "holes" in it.
  */
-public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
+public class PiecewisePolynomial<T : Comparable<T>>(
+    public val pieces: List<Pair<ClosedRange<T>, Polynomial<T>>>,
+) : Piecewise<T, Polynomial<T>> {
+
+    public override fun findPiece(arg: T): Polynomial<T>? {
+        return if (arg < pieces.first().first.start || arg >= pieces.last().first.endInclusive)
+            null
+        else {
+            pieces.firstOrNull { arg in it.first }?.second
+        }
+    }
+}
 
 /**
  * A [Piecewise]  builder where all the pieces are ordered by the [Comparable] type instances.
@@ -31,7 +43,7 @@ public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
  * @param T the comparable piece key type.
  * @param delimiter the initial piecewise separator
  */
-public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) : PiecewisePolynomial<T> {
+public class PiecewiseBuilder<T : Comparable<T>>(delimiter: T) {
     private val delimiters: MutableList<T> = arrayListOf(delimiter)
     private val pieces: MutableList<Polynomial<T>> = arrayListOf()
 
@@ -59,17 +71,19 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) : Piece
         pieces.add(0, piece)
     }
 
-    public override fun findPiece(arg: T): Polynomial<T>? {
+    public fun build(): PiecewisePolynomial<T> {
-        if (arg < delimiters.first() || arg >= delimiters.last())
+        return PiecewisePolynomial(delimiters.zipWithNext { l, r -> l..r }.zip(pieces))
-            return null
-        else {
-            for (index in 1 until delimiters.size)
-                if (arg < delimiters[index]) return pieces[index - 1]
-            error("Piece not found")
-        }
     }
 }
 
+/**
+ * A builder for [PiecewisePolynomial]
+ */
+public fun <T : Comparable<T>> PiecewisePolynomial(
+    startingPoint: T,
+    builder: PiecewiseBuilder<T>.() -> Unit,
+): PiecewisePolynomial<T> = PiecewiseBuilder(startingPoint).apply(builder).build()
+
 /**
  * Return a value of polynomial function with given [ring] an given [arg] or null if argument is outside of piecewise
  * definition.

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt

@@ -5,10 +5,8 @@
 
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.operations.Group
+import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.*
-import space.kscience.kmath.operations.ScaleOperations
-import space.kscience.kmath.operations.invoke
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 import kotlin.math.max
@@ -32,7 +30,9 @@ public fun <T> Polynomial(vararg coefficients: T): Polynomial<T> = Polynomial(co
 /**
  * Evaluates the value of the given double polynomial for given double argument.
  */
-public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { index, acc, d -> acc + d.pow(index) }
+public fun Polynomial<Double>.value(arg: Double): Double = coefficients.reduceIndexed { index, acc, c ->
+    acc + c * arg.pow(index)
+}
 
 /**
  * Evaluates the value of the given polynomial for given argument.
@@ -52,7 +52,36 @@ public fun <T, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring {
  */
 public fun <T, C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T = { value(ring, it) }
 
-//public fun <T: Any>
+/**
+ * Create a polynomial witch represents differentiated version of this polynomial
+ */
+@UnstableKMathAPI
+public fun <T, A> Polynomial<T>.differentiate(
+    algebra: A,
+): Polynomial<T> where  A : Ring<T>, A : NumericAlgebra<T> = algebra {
+    Polynomial(coefficients.drop(1).mapIndexed { index, t -> number(index) * t })
+}
+
+/**
+ * Create a polynomial witch represents indefinite integral version of this polynomial
+ */
+@UnstableKMathAPI
+public fun <T, A> Polynomial<T>.integrate(
+    algebra: A,
+): Polynomial<T> where  A : Field<T>, A : NumericAlgebra<T> = algebra {
+    Polynomial(coefficients.mapIndexed { index, t -> t / number(index) })
+}
+
+/**
+ * Compute a definite integral of a given polynomial in a [range]
+ */
+@UnstableKMathAPI
+public fun <T : Comparable<T>, A> Polynomial<T>.integrate(
+    algebra: A,
+    range: ClosedRange<T>,
+): T where  A : Field<T>, A : NumericAlgebra<T> = algebra {
+    value(algebra, range.endInclusive) - value(algebra, range.start)
+}
 
 /**
  * Space of polynomials.
@@ -87,6 +116,9 @@ public class PolynomialSpace<T, C>(
      * Evaluates the polynomial for the given value [arg].
      */
     public operator fun Polynomial<T>.invoke(arg: T): T = value(ring, arg)
+
+    public fun Polynomial<T>.asFunction(): (T) -> T = asFunction(ring)
+
 }
 
 public inline fun <T, C, R> C.polynomial(block: PolynomialSpace<T, C>.() -> R): R where C : Ring<T>, C : ScaleOperations<T> {

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/LinearInterpolator.kt

@@ -6,7 +6,6 @@
 package space.kscience.kmath.interpolation
 
 import space.kscience.kmath.data.XYColumnarData
-import space.kscience.kmath.functions.OrderedPiecewisePolynomial
 import space.kscience.kmath.functions.PiecewisePolynomial
 import space.kscience.kmath.functions.Polynomial
 import space.kscience.kmath.misc.UnstableKMathAPI
@@ -28,7 +27,7 @@ public class LinearInterpolator<T : Comparable<T>>(public override val algebra:
         require(points.size > 0) { "Point array should not be empty" }
         insureSorted(points)
 
-        OrderedPiecewisePolynomial(points.x[0]).apply {
+        PiecewisePolynomial(points.x[0]) {
             for (i in 0 until points.size - 1) {
                 val slope = (points.y[i + 1] - points.y[i]) / (points.x[i + 1] - points.x[i])
                 val const = points.y[i] - slope * points.x[i]

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt

@@ -6,7 +6,6 @@
 package space.kscience.kmath.interpolation
 
 import space.kscience.kmath.data.XYColumnarData
-import space.kscience.kmath.functions.OrderedPiecewisePolynomial
 import space.kscience.kmath.functions.PiecewisePolynomial
 import space.kscience.kmath.functions.Polynomial
 import space.kscience.kmath.misc.UnstableKMathAPI
@@ -50,7 +49,7 @@ public class SplineInterpolator<T : Comparable<T>>(
 
         // cubic spline coefficients --  b is linear, c quadratic, d is cubic (original y's are constants)
 
-        OrderedPiecewisePolynomial(points.x[points.size - 1]).apply {
+        PiecewisePolynomial(points.x[points.size - 1]) {
             var cOld = zero
 
             for (j in n - 1 downTo 0) {

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/PolynomialTest.kt

@@ -0,0 +1,17 @@
+/*
+ * Copyright 2018-2021 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.functions
+
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class PolynomialTest {
+    @Test
+    fun testIntegration() {
+        val polynomial = Polynomial(1.0, -2.0, 1.0)
+        assertEquals(0.0, polynomial.value(1.0), 0.001)
+    }
+}

kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/TreeHistogramSpace.kt

@@ -28,7 +28,6 @@ private fun <B : ClosedFloatingPointRange<Double>> TreeMap<Double, B>.getBin(val
 
 @UnstableKMathAPI
 public class TreeHistogram(
-    override val context: TreeHistogramSpace,
     private val binMap: TreeMap<Double, out UnivariateBin>,
 ) : UnivariateHistogram {
     override fun get(value: Double): UnivariateBin? = binMap.getBin(value)
@@ -79,15 +78,15 @@ public class TreeHistogramSpace(
             val count = binCounter.counter.value
             resBins[key] = UnivariateBin(binCounter.domain, count, sqrt(count))
         }
-        return TreeHistogram(this, resBins)
+        return TreeHistogram(resBins)
     }
 
     override fun add(
         a: UnivariateHistogram,
         b: UnivariateHistogram,
     ): UnivariateHistogram {
-        require(a.context == this) { "Histogram $a does not belong to this context" }
+//        require(a.context == this) { "Histogram $a does not belong to this context" }
-        require(b.context == this) { "Histogram $b does not belong to this context" }
+//        require(b.context == this) { "Histogram $b does not belong to this context" }
         val bins = TreeMap<Double, UnivariateBin>().apply {
             (a.bins.map { it.domain } union b.bins.map { it.domain }).forEach { def ->
                 put(def.center,
@@ -100,7 +99,7 @@ public class TreeHistogramSpace(
                 )
             }
         }
-        return TreeHistogram(this, bins)
+        return TreeHistogram(bins)
     }
 
     override fun scale(a: UnivariateHistogram, value: Double): UnivariateHistogram {
@@ -116,7 +115,7 @@ public class TreeHistogramSpace(
             }
         }
 
-        return TreeHistogram(this, bins)
+        return TreeHistogram(bins)
     }
 
     override fun UnivariateHistogram.unaryMinus(): UnivariateHistogram = this * (-1)

kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/UnivariateHistogram.kt

@@ -7,8 +7,6 @@ package space.kscience.kmath.histogram
 
 import space.kscience.kmath.domains.UnivariateDomain
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.Group
-import space.kscience.kmath.operations.GroupElement
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.asSequence
 
@@ -35,8 +33,7 @@ public class UnivariateBin(
 }
 
 @OptIn(UnstableKMathAPI::class)
-public interface UnivariateHistogram : Histogram<Double, UnivariateBin>,
+public interface UnivariateHistogram : Histogram<Double, UnivariateBin>{
-    GroupElement<UnivariateHistogram, Group<UnivariateHistogram>> {
     public operator fun get(value: Double): UnivariateBin?
     public override operator fun get(point: Buffer<Double>): UnivariateBin? = get(point[0])