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Simpson integrator

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This commit is contained in:
Alexander Nozik 2021-05-21 23:14:07 +03:00
parent 889244902b
commit 18509f1259
7 changed files with 85 additions and 12 deletions
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1
examples/src/main/kotlin/space/kscience/kmath/functions/interpolate.kt
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@ -35,7 +35,6 @@ fun main() {
data.map { it.second }.toDoubleArray()
)
Plotly.plot {
scatter {
name = "interpolated"

4
kmath-commons/src/main/kotlin/space/kscience/kmath/commons/integration/GaussRuleIntegrator.kt → kmath-commons/src/main/kotlin/space/kscience/kmath/commons/integration/CMGaussRuleIntegrator.kt
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@ -11,7 +11,7 @@ import space.kscience.kmath.integration.*
/**
* A simple one-pass integrator based on Gauss rule
*/
public class GaussRuleIntegrator(
public class CMGaussRuleIntegrator(
private val numpoints: Int,
private var type: GaussRule = GaussRule.LEGANDRE,
) : UnivariateIntegrator<Double> {
@ -76,7 +76,7 @@ public class GaussRuleIntegrator(
numPoints: Int = 100,
type: GaussRule = GaussRule.LEGANDRE,
function: (Double) -> Double,
): Double = GaussRuleIntegrator(numPoints, type).integrate(
): Double = CMGaussRuleIntegrator(numPoints, type).integrate(
UnivariateIntegrand(function, IntegrationRange(range))
).valueOrNull!!
}

36
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt
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@ -5,13 +5,37 @@
package space.kscience.kmath.integration
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.Field
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.BufferFactory
/**
* [IntegrationRange] - the univariate range of integration. By default uses 0..1 interval.
* [IntegrandMaxCalls] - the maximum number of function calls during integration. For non-iterative rules, always uses the maximum number of points. By default uses 10 points.
*/
public class SimpsonIntegrator<T : Any>(
public val algebra: Ring<T>,
public val algebra: Field<T>,
public val bufferFactory: BufferFactory<T>,
) : UnivariateIntegrator<T> {
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> {
TODO("Not yet implemented")
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = with(algebra) {
val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
require(numPoints >= 4)
val range = integrand.getFeature<IntegrationRange>()?.range ?: 0.0..1.0
val h: Double = (range.endInclusive - range.start) / (numPoints - 1)
val points: Buffer<T> = bufferFactory(numPoints) { i ->
integrand.function(range.start + i * h)
}// equally distributed point
fun simpson(index: Int) = h / 3 * (points[index - 1] + 4 * points[index] + points[index + 1])
var res = zero
res += simpson(1) / 1.5 //border points with 1.5 factor
for (i in 2 until (points.size - 2)) {
res += simpson(i) / 2
}
res += simpson(points.size - 2) / 1.5 //border points with 1.5 factor
return integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + points.size)
}
}
}
public inline val <reified T : Any> Field<T>.simpsonIntegrator: SimpsonIntegrator<T>
get() = SimpsonIntegrator(this, Buffer.Companion::auto)

12
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt Normal file
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@ -0,0 +1,12 @@
/*
* 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.integration
public class SplineIntegrator<T>: UnivariateIntegrator<T> {
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> {
TODO("Not yet implemented")
}
}

2
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
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@ -9,7 +9,7 @@ import space.kscience.kmath.misc.UnstableKMathAPI
import kotlin.jvm.JvmInline
import kotlin.reflect.KClass
public class UnivariateIntegrand<T : Any> internal constructor(
public class UnivariateIntegrand<T> internal constructor(
private val features: Map<KClass<*>, IntegrandFeature>,
public val function: (Double) -> T,
) : Integrand {

4
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/GaussIntegralTest.kt
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@ -19,7 +19,7 @@ class GaussIntegralTest {
val res = DoubleField.gaussIntegrator.integrate(0.0..2 * PI) { x ->
sin(x)
}
assertEquals(0.0, res.valueOrNull!!, 1e-2)
assertEquals(0.0, res.value, 1e-2)
}
@Test
@ -31,7 +31,7 @@ class GaussIntegralTest {
0.0
}
}
assertEquals(15.0, res.valueOrNull!!, 0.5)
assertEquals(15.0, res.value, 0.5)
}

38
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/SimpsonIntegralTest.kt Normal file
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@ -0,0 +1,38 @@
/*
* 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.integration
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.DoubleField
import kotlin.math.PI
import kotlin.math.sin
import kotlin.test.Test
import kotlin.test.assertEquals
@OptIn(UnstableKMathAPI::class)
class SimpsonIntegralTest {
@Test
fun gaussSin() {
val res = DoubleField.simpsonIntegrator.integrate(0.0..2 * PI, IntegrandMaxCalls(5)) { x ->
sin(x)
}
assertEquals(0.0, res.value, 1e-2)
}
@Test
fun gaussUniform() {
val res = DoubleField.simpsonIntegrator.integrate(35.0..100.0) { x ->
if(x in 30.0..50.0){
1.0
} else {
0.0
}
}
assertEquals(15.0, res.value, 0.5)
}
}