forked from kscience/kmath
Minor piecewise rework
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0898285542
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8a07140f7c
@ -10,12 +10,14 @@ import space.kscience.kmath.interpolation.interpolatePolynomials
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.structures.DoubleBuffer
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import space.kscience.plotly.Plotly
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import space.kscience.plotly.UnstablePlotlyAPI
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import space.kscience.plotly.makeFile
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import space.kscience.plotly.models.functionXY
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import space.kscience.plotly.scatter
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import kotlin.math.PI
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import kotlin.math.sin
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@OptIn(UnstablePlotlyAPI::class)
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fun main() {
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val data = (0..10).map {
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val x = it.toDouble() / 5 * PI
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@ -22,8 +22,20 @@ public fun interface Piecewise<T, R> {
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/**
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* Represents piecewise-defined function where all the sub-functions are polynomials.
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* @param pieces An ordered list of range-polynomial pairs. The list does not in general guarantee that there are no "holes" in it.
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*/
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public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
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public class PiecewisePolynomial<T : Comparable<T>>(
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public val pieces: List<Pair<ClosedRange<T>, Polynomial<T>>>,
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) : Piecewise<T, Polynomial<T>> {
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public override fun findPiece(arg: T): Polynomial<T>? {
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return if (arg < pieces.first().first.start || arg >= pieces.last().first.endInclusive)
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null
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else {
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pieces.firstOrNull { arg in it.first }?.second
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}
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}
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}
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/**
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* A [Piecewise] builder where all the pieces are ordered by the [Comparable] type instances.
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@ -31,7 +43,7 @@ public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
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* @param T the comparable piece key type.
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* @param delimiter the initial piecewise separator
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*/
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public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) : PiecewisePolynomial<T> {
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public class PiecewiseBuilder<T : Comparable<T>>(delimiter: T) {
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private val delimiters: MutableList<T> = arrayListOf(delimiter)
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private val pieces: MutableList<Polynomial<T>> = arrayListOf()
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@ -59,17 +71,19 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) : Piece
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pieces.add(0, piece)
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}
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public override fun findPiece(arg: T): Polynomial<T>? {
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if (arg < delimiters.first() || arg >= delimiters.last())
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return null
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else {
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for (index in 1 until delimiters.size)
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if (arg < delimiters[index]) return pieces[index - 1]
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error("Piece not found")
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}
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public fun build(): PiecewisePolynomial<T> {
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return PiecewisePolynomial(delimiters.zipWithNext { l, r -> l..r }.zip(pieces))
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}
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}
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/**
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* A builder for [PiecewisePolynomial]
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*/
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public fun <T : Comparable<T>> PiecewisePolynomial(
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startingPoint: T,
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builder: PiecewiseBuilder<T>.() -> Unit,
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): PiecewisePolynomial<T> = PiecewiseBuilder(startingPoint).apply(builder).build()
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/**
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* Return a value of polynomial function with given [ring] an given [arg] or null if argument is outside of piecewise
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* definition.
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@ -5,10 +5,8 @@
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package space.kscience.kmath.functions
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import space.kscience.kmath.operations.Group
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import space.kscience.kmath.operations.Ring
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import space.kscience.kmath.operations.ScaleOperations
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import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.*
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import kotlin.contracts.InvocationKind
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import kotlin.contracts.contract
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import kotlin.math.max
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@ -19,7 +17,7 @@ import kotlin.math.pow
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*
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* @param coefficients constant is the leftmost coefficient.
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*/
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public class Polynomial<T>(public val coefficients: List<T>){
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public class Polynomial<T>(public val coefficients: List<T>) {
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override fun toString(): String = "Polynomial$coefficients"
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}
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@ -32,7 +30,9 @@ public fun <T> Polynomial(vararg coefficients: T): Polynomial<T> = Polynomial(co
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/**
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* Evaluates the value of the given double polynomial for given double argument.
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*/
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public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { index, acc, d -> acc + d.pow(index) }
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public fun Polynomial<Double>.value(arg: Double): Double = coefficients.reduceIndexed { index, acc, c ->
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acc + c * arg.pow(index)
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}
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/**
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* Evaluates the value of the given polynomial for given argument.
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@ -50,9 +50,38 @@ public fun <T, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring {
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/**
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* Represent the polynomial as a regular context-less function.
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*/
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public fun <T , C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T = { value(ring, it) }
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public fun <T, C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T = { value(ring, it) }
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//public fun <T: Any>
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/**
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* Create a polynomial witch represents differentiated version of this polynomial
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*/
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@UnstableKMathAPI
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public fun <T, A> Polynomial<T>.differentiate(
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algebra: A,
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): Polynomial<T> where A : Ring<T>, A : NumericAlgebra<T> = algebra {
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Polynomial(coefficients.drop(1).mapIndexed { index, t -> number(index) * t })
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}
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/**
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* Create a polynomial witch represents indefinite integral version of this polynomial
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*/
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@UnstableKMathAPI
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public fun <T, A> Polynomial<T>.integrate(
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algebra: A,
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): Polynomial<T> where A : Field<T>, A : NumericAlgebra<T> = algebra {
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Polynomial(coefficients.mapIndexed { index, t -> t / number(index) })
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}
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/**
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* Compute a definite integral of a given polynomial in a [range]
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*/
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@UnstableKMathAPI
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public fun <T : Comparable<T>, A> Polynomial<T>.integrate(
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algebra: A,
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range: ClosedRange<T>,
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): T where A : Field<T>, A : NumericAlgebra<T> = algebra {
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value(algebra, range.endInclusive) - value(algebra, range.start)
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}
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/**
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* Space of polynomials.
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@ -87,6 +116,9 @@ public class PolynomialSpace<T, C>(
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* Evaluates the polynomial for the given value [arg].
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*/
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public operator fun Polynomial<T>.invoke(arg: T): T = value(ring, arg)
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public fun Polynomial<T>.asFunction(): (T) -> T = asFunction(ring)
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}
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public inline fun <T, C, R> C.polynomial(block: PolynomialSpace<T, C>.() -> R): R where C : Ring<T>, C : ScaleOperations<T> {
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@ -6,7 +6,6 @@
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package space.kscience.kmath.interpolation
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import space.kscience.kmath.data.XYColumnarData
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import space.kscience.kmath.functions.OrderedPiecewisePolynomial
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import space.kscience.kmath.functions.PiecewisePolynomial
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import space.kscience.kmath.functions.Polynomial
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import space.kscience.kmath.misc.UnstableKMathAPI
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@ -28,7 +27,7 @@ public class LinearInterpolator<T : Comparable<T>>(public override val algebra:
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require(points.size > 0) { "Point array should not be empty" }
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insureSorted(points)
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OrderedPiecewisePolynomial(points.x[0]).apply {
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PiecewisePolynomial(points.x[0]) {
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for (i in 0 until points.size - 1) {
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val slope = (points.y[i + 1] - points.y[i]) / (points.x[i + 1] - points.x[i])
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val const = points.y[i] - slope * points.x[i]
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@ -6,7 +6,6 @@
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package space.kscience.kmath.interpolation
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import space.kscience.kmath.data.XYColumnarData
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import space.kscience.kmath.functions.OrderedPiecewisePolynomial
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import space.kscience.kmath.functions.PiecewisePolynomial
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import space.kscience.kmath.functions.Polynomial
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import space.kscience.kmath.misc.UnstableKMathAPI
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@ -50,7 +49,7 @@ public class SplineInterpolator<T : Comparable<T>>(
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// cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants)
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OrderedPiecewisePolynomial(points.x[points.size - 1]).apply {
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PiecewisePolynomial(points.x[points.size - 1]) {
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var cOld = zero
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for (j in n - 1 downTo 0) {
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@ -0,0 +1,17 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.functions
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import kotlin.test.Test
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import kotlin.test.assertEquals
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class PolynomialTest {
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@Test
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fun testIntegration() {
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val polynomial = Polynomial(1.0, -2.0, 1.0)
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assertEquals(0.0, polynomial.value(1.0), 0.001)
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}
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}
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@ -28,7 +28,6 @@ private fun <B : ClosedFloatingPointRange<Double>> TreeMap<Double, B>.getBin(val
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@UnstableKMathAPI
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public class TreeHistogram(
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override val context: TreeHistogramSpace,
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private val binMap: TreeMap<Double, out UnivariateBin>,
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) : UnivariateHistogram {
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override fun get(value: Double): UnivariateBin? = binMap.getBin(value)
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@ -79,15 +78,15 @@ public class TreeHistogramSpace(
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val count = binCounter.counter.value
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resBins[key] = UnivariateBin(binCounter.domain, count, sqrt(count))
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}
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return TreeHistogram(this, resBins)
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return TreeHistogram(resBins)
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}
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override fun add(
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a: UnivariateHistogram,
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b: UnivariateHistogram,
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): UnivariateHistogram {
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require(a.context == this) { "Histogram $a does not belong to this context" }
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require(b.context == this) { "Histogram $b does not belong to this context" }
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// require(a.context == this) { "Histogram $a does not belong to this context" }
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// require(b.context == this) { "Histogram $b does not belong to this context" }
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val bins = TreeMap<Double, UnivariateBin>().apply {
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(a.bins.map { it.domain } union b.bins.map { it.domain }).forEach { def ->
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put(def.center,
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@ -100,7 +99,7 @@ public class TreeHistogramSpace(
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)
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}
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}
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return TreeHistogram(this, bins)
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return TreeHistogram(bins)
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}
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override fun scale(a: UnivariateHistogram, value: Double): UnivariateHistogram {
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@ -116,7 +115,7 @@ public class TreeHistogramSpace(
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}
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}
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return TreeHistogram(this, bins)
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return TreeHistogram(bins)
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}
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override fun UnivariateHistogram.unaryMinus(): UnivariateHistogram = this * (-1)
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@ -7,8 +7,6 @@ package space.kscience.kmath.histogram
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import space.kscience.kmath.domains.UnivariateDomain
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.Group
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import space.kscience.kmath.operations.GroupElement
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.structures.asSequence
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@ -35,8 +33,7 @@ public class UnivariateBin(
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}
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@OptIn(UnstableKMathAPI::class)
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public interface UnivariateHistogram : Histogram<Double, UnivariateBin>,
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GroupElement<UnivariateHistogram, Group<UnivariateHistogram>> {
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public interface UnivariateHistogram : Histogram<Double, UnivariateBin>{
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public operator fun get(value: Double): UnivariateBin?
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public override operator fun get(point: Buffer<Double>): UnivariateBin? = get(point[0])
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