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[WIP] Interpolation fix

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This commit is contained in:
Alexander Nozik 2021-05-17 16:53:12 +03:00
parent 83b6d8fee0
commit 53a6d3543f
7 changed files with 120 additions and 46 deletions
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2
examples/build.gradle.kts
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@ -43,7 +43,7 @@ dependencies {
implementation("org.slf4j:slf4j-simple:1.7.30")
// plotting
implementation("space.kscience:plotlykt-server:0.4.0-dev-2")
implementation("space.kscience:plotlykt-server:0.4.0")
}
kotlin.sourceSets.all {

56
examples/src/main/kotlin/space/kscience/kmath/functions/interpolate.kt Normal file
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@ -0,0 +1,56 @@
/*
* 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 space.kscience.kmath.interpolation.SplineInterpolator
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.makeFile
import space.kscience.plotly.models.functionXY
import space.kscience.plotly.scatter
import kotlin.math.PI
import kotlin.math.sin
fun main() {
val data = (0..10).map {
val x = it.toDouble() / 5 * PI
x to sin(x)
}
val polynomial: PiecewisePolynomial<Double> = SplineInterpolator(
DoubleField, ::DoubleBuffer
).interpolatePolynomials(data)
val function = polynomial.asFunction(DoubleField, 0.0)
val cmInterpolate = org.apache.commons.math3.analysis.interpolation.SplineInterpolator().interpolate(
data.map { it.first }.toDoubleArray(),
data.map { it.second }.toDoubleArray()
)
println(function(2.0))
println(cmInterpolate.value(2.0))
//
// Plotly.plot {
// scatter {
// name = "interpolated"
// x.numbers = data.map { it.first }
// y.numbers = x.doubles.map { function(it) }
// }
// scatter {
// name = "original"
// functionXY(0.0..(2 * PI), 0.1) { sin(it) }
// }
// scatter {
// name = "cm"
// x.numbers = data.map { it.first }
// y.numbers = x.doubles.map { cmInterpolate.value(it) }
// }
// }.makeFile()
}

30
kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/_generated.kt
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@ -8,28 +8,18 @@
package space.kscience.kmath.ejml
import org.ejml.data.*
import org.ejml.dense.row.CommonOps_DDRM
import org.ejml.dense.row.CommonOps_FDRM
import org.ejml.dense.row.factory.DecompositionFactory_DDRM
import org.ejml.dense.row.factory.DecompositionFactory_FDRM
import org.ejml.sparse.FillReducing
import org.ejml.sparse.csc.CommonOps_DSCC
import org.ejml.sparse.csc.CommonOps_FSCC
import org.ejml.sparse.csc.factory.DecompositionFactory_DSCC
import org.ejml.sparse.csc.factory.DecompositionFactory_FSCC
import org.ejml.sparse.csc.factory.LinearSolverFactory_DSCC
import org.ejml.sparse.csc.factory.LinearSolverFactory_FSCC
import space.kscience.kmath.linear.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.structures.*
import space.kscience.kmath.misc.*
import kotlin.reflect.*
import org.ejml.dense.row.*
import org.ejml.dense.row.factory.*
import org.ejml.sparse.*
import org.ejml.sparse.csc.*
import org.ejml.sparse.csc.factory.*
import space.kscience.kmath.nd.*
import space.kscience.kmath.linear.Matrix
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.nd.StructureFeature
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.FloatField
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.structures.DoubleBuffer
import space.kscience.kmath.structures.FloatBuffer
import kotlin.reflect.KClass
import kotlin.reflect.cast
/**
* [EjmlVector] specialization for [Double].

10
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt
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@ -26,12 +26,12 @@ public fun interface Piecewise<T, R> {
public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
/**
* Basic [Piecewise] implementation where all the pieces are ordered by the [Comparable] type instances.
* A [Piecewise] builder where all the pieces are ordered by the [Comparable] type instances.
*
* @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 OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) : PiecewisePolynomial<T> {
private val delimiters: MutableList<T> = arrayListOf(delimiter)
private val pieces: MutableList<Polynomial<T>> = arrayListOf()
@ -64,9 +64,7 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
return null
else {
for (index in 1 until delimiters.size)
if (arg < delimiters[index])
return pieces[index - 1]
if (arg < delimiters[index]) return pieces[index - 1]
error("Piece not found")
}
}

18
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
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@ -19,7 +19,9 @@ import kotlin.math.pow
*
* @param coefficients constant is the leftmost coefficient.
*/
public class Polynomial<T : Any>(public val coefficients: List<T>)
public class Polynomial<T : Any>(public val coefficients: List<T>){
override fun toString(): String = "Polynomial$coefficients"
}
/**
* Returns a [Polynomial] instance with given [coefficients].
@ -34,19 +36,15 @@ public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { ind
/**
* Evaluates the value of the given polynomial for given argument.
* https://en.wikipedia.org/wiki/Horner%27s_method
*/
public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring {
if (coefficients.isEmpty()) return@ring zero
var res = coefficients.first()
var powerArg = arg
for (index in 1 until coefficients.size) {
res += coefficients[index] * powerArg
// recalculating power on each step to avoid power costs on long polynomials
powerArg *= arg
var result: T = coefficients.last()
for (j in coefficients.size - 2 downTo 0) {
result = (arg * result) + coefficients[j]
}
res
return result
}
/**

15
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt
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@ -34,19 +34,16 @@ public class SplineInterpolator<T : Comparable<T>>(
// Number of intervals. The number of data points is n + 1.
val n = points.size - 1
// Differences between knot points
val h = bufferFactory(points.size) { i -> points.x[i + 1] - points.x[i] }
val mu = bufferFactory(points.size - 1) { zero }
val z = bufferFactory(points.size) { zero }
val h = bufferFactory(n) { i -> points.x[i + 1] - points.x[i] }
val mu = bufferFactory(n) { zero }
val z = bufferFactory(n + 1) { zero }
for (i in 1 until n) {
val g = 2.0 * (points.x[i + 1] - points.x[i - 1]) - h[i - 1] * mu[i - 1]
mu[i] = h[i] / g
z[i] = (3.0 * (points.y[i + 1] * h[i - 1]
- points.x[i] * (points.x[i + 1] - points.x[i - 1])
+ points.y[i - 1] * h[i]) / (h[i - 1] * h[i])
- h[i - 1] * z[i - 1]
) / g
z[i] =
((points.y[i + 1] * h[i - 1] - points.y[i] * (points.x[i + 1] - points.x[i - 1]) + points.y[i - 1] * h[i]) * 3.0 /
(h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g
}
// cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants)

35
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/interpolation/SplineInterpolatorTest.kt Normal file
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@ -0,0 +1,35 @@
/*
* 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.interpolation
import space.kscience.kmath.functions.PiecewisePolynomial
import space.kscience.kmath.functions.asFunction
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.structures.DoubleBuffer
import kotlin.math.PI
import kotlin.math.sin
import kotlin.test.Test
import kotlin.test.assertEquals
internal class SplineInterpolatorTest {
@Test
fun testInterpolation() {
val data = (0..10).map {
val x = it.toDouble() / 5 * PI
x to sin(x)
}
val polynomial: PiecewisePolynomial<Double> = SplineInterpolator(
DoubleField, ::DoubleBuffer
).interpolatePolynomials(data)
val function = polynomial.asFunction(DoubleField)
assertEquals(null, function(-1.0))
assertEquals(sin(0.5), function(0.5)!!, 0.1)
assertEquals(sin(1.5), function(1.5)!!, 0.1)
assertEquals(sin(2.0), function(2.0)!!, 0.1)
}
}