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Field element integration

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This commit is contained in:
Alexander Nozik 2021-04-16 15:50:33 +03:00
parent 1582ac2c29
commit 65a8d8f581
13 changed files with 172 additions and 65 deletions
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1
CHANGELOG.md
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@ -9,6 +9,7 @@
- bindSymbolOrNull
- Blocking chains and Statistics
- Multiplatform integration
- Integration for any Field element
### Changed
- Exponential operations merged with hyperbolic functions

14
examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
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@ -20,22 +20,22 @@ internal class BigIntBenchmark {
val jvmNumber = JBigIntegerField.number(Int.MAX_VALUE)
@Benchmark
fun kmAdd(blackhole: Blackhole) = BigIntField{
fun kmAdd(blackhole: Blackhole) = BigIntField {
blackhole.consume(kmNumber + kmNumber + kmNumber)
}
@Benchmark
fun jvmAdd(blackhole: Blackhole) = JBigIntegerField{
blackhole.consume(jvmNumber + jvmNumber+ jvmNumber)
fun jvmAdd(blackhole: Blackhole) = JBigIntegerField {
blackhole.consume(jvmNumber + jvmNumber + jvmNumber)
}
@Benchmark
fun kmMultiply(blackhole: Blackhole) = BigIntField{
blackhole.consume(kmNumber*kmNumber*kmNumber)
fun kmMultiply(blackhole: Blackhole) = BigIntField {
blackhole.consume(kmNumber * kmNumber * kmNumber)
}
@Benchmark
fun jvmMultiply(blackhole: Blackhole) = JBigIntegerField{
blackhole.consume(jvmNumber*jvmNumber*jvmNumber)
fun jvmMultiply(blackhole: Blackhole) = JBigIntegerField {
blackhole.consume(jvmNumber * jvmNumber * jvmNumber)
}
}

16
examples/src/main/kotlin/space/kscience/kmath/functions/integrate.kt Normal file
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@ -0,0 +1,16 @@
package space.kscience.kmath.functions
import space.kscience.kmath.integration.GaussIntegrator
import space.kscience.kmath.integration.value
import kotlin.math.pow
fun main() {
//Define a function
val function: UnivariateFunction<Double> = { x -> 3 * x.pow(2) + 2 * x + 1 }
//get the result of the integration
val result = GaussIntegrator.legendre(0.0..10.0, function = function)
//the value is nullable because in some cases the integration could not succeed
println(result.value)
}

22
examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt Normal file
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@ -0,0 +1,22 @@
package space.kscience.kmath.functions
import space.kscience.kmath.integration.GaussIntegrator
import space.kscience.kmath.integration.UnivariateIntegrand
import space.kscience.kmath.integration.value
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.nd
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.invoke
fun main(): Unit = DoubleField {
nd(2, 2) {
//Define a function in a nd space
val function: UnivariateFunction<StructureND<Double>> = { x -> 3 * x.pow(2) + 2 * x + 1 }
//get the result of the integration
val result: UnivariateIntegrand<StructureND<Double>> = GaussIntegrator.legendre(this, 0.0..10.0, function = function)
//the value is nullable because in some cases the integration could not succeed
println(result.value)
}
}

2
kmath-commons/src/main/kotlin/space/kscience/kmath/commons/integration/CMIntegrator.kt
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@ -36,7 +36,7 @@ public class CMIntegrator(
IntegrandValue(res) +
IntegrandAbsoluteAccuracy(integrator.absoluteAccuracy) +
IntegrandRelativeAccuracy(integrator.relativeAccuracy) +
IntegrandCalls(integrator.evaluations + integrand.calls)
IntegrandCallsPerformed(integrator.evaluations + integrand.calls)
}

2
kmath-commons/src/main/kotlin/space/kscience/kmath/commons/integration/GaussRuleIntegrator.kt
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@ -22,7 +22,7 @@ public class GaussRuleIntegrator(
val integrator: GaussIntegrator = getIntegrator(range)
//TODO check performance
val res: Double = integrator.integrate(integrand.function)
return integrand + IntegrandValue(res) + IntegrandCalls(integrand.calls + numpoints)
return integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + numpoints)
}
private fun getIntegrator(range: ClosedRange<Double>): GaussIntegrator {

2
kmath-core/api/kmath-core.api
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@ -1791,6 +1791,7 @@ public final class space/kscience/kmath/structures/IntBufferKt {
}
public final class space/kscience/kmath/structures/ListBuffer : space/kscience/kmath/structures/Buffer {
public fun <init> (ILkotlin/jvm/functions/Function1;)V
public fun <init> (Ljava/util/List;)V
public fun get (I)Ljava/lang/Object;
public final fun getList ()Ljava/util/List;
@ -1865,6 +1866,7 @@ public final class space/kscience/kmath/structures/MutableBuffer$Companion {
public final class space/kscience/kmath/structures/MutableListBuffer : space/kscience/kmath/structures/MutableBuffer {
public static final synthetic fun box-impl (Ljava/util/List;)Lspace/kscience/kmath/structures/MutableListBuffer;
public static fun constructor-impl (ILkotlin/jvm/functions/Function1;)Ljava/util/List;
public static fun constructor-impl (Ljava/util/List;)Ljava/util/List;
public fun copy ()Lspace/kscience/kmath/structures/MutableBuffer;
public static fun copy-impl (Ljava/util/List;)Lspace/kscience/kmath/structures/MutableBuffer;

9
kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt
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@ -194,6 +194,9 @@ public interface MutableBuffer<T> : Buffer<T> {
* @property list The underlying list.
*/
public class ListBuffer<T>(public val list: List<T>) : Buffer<T> {
public constructor(size: Int, initializer: (Int) -> T) : this(List(size, initializer))
override val size: Int get() = list.size
override operator fun get(index: Int): T = list[index]
@ -213,8 +216,10 @@ public fun <T> List<T>.asBuffer(): ListBuffer<T> = ListBuffer(this)
*/
@JvmInline
public value class MutableListBuffer<T>(public val list: MutableList<T>) : MutableBuffer<T> {
override val size: Int
get() = list.size
public constructor(size: Int, initializer: (Int) -> T) : this(MutableList(size, initializer))
override val size: Int get() = list.size
override operator fun get(index: Int): T = list[index]

27
kmath-functions/build.gradle.kts
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@ -15,16 +15,23 @@ kotlin.sourceSets.commonMain {
}
readme {
description = "Functions and interpolation"
maturity = ru.mipt.npm.gradle.Maturity.PROTOTYPE
description = "Functions, integration and interpolation"
maturity = ru.mipt.npm.gradle.Maturity.EXPERIMENTAL
propertyByTemplate("artifact", rootProject.file("docs/templates/ARTIFACT-TEMPLATE.md"))
feature("piecewise", "src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt", "Piecewise functions.")
feature("polynomials", "src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt", "Polynomial functions.")
feature("linear interpolation",
"src/commonMain/kotlin/space/kscience/kmath/interpolation/LinearInterpolator.kt",
"Linear XY interpolator.")
feature("spline interpolation",
"src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt",
"Cubic spline XY interpolator.")
feature("piecewise", "src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt") {
"Piecewise functions."
}
feature("polynomials", "src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt") {
"Polynomial functions."
}
feature("linear interpolation", "src/commonMain/kotlin/space/kscience/kmath/interpolation/LinearInterpolator.kt") {
"Linear XY interpolator."
}
feature("spline interpolation", "src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt") {
"Cubic spline XY interpolator."
}
feature("integration") {
"Univariate and multivariate quadratures"
}
}

105
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt
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@ -4,27 +4,31 @@
*/
package space.kscience.kmath.integration
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.indices
import space.kscience.kmath.operations.Field
import space.kscience.kmath.structures.*
/**
* A simple one-pass integrator based on Gauss rule
*/
public class GaussIntegrator<T : Comparable<T>> internal constructor(
public val algebra: Ring<T>,
private val points: Buffer<T>,
private val weights: Buffer<T>,
public class GaussIntegrator<T : Any>(
public val algebra: Field<T>,
public val bufferFactory: BufferFactory<T>,
) : UnivariateIntegrator<T> {
init {
require(points.size == weights.size) { "Inconsistent points and weights sizes" }
require(points.indices.all { i -> i == 0 || points[i] > points[i - 1] }) { "Integration nodes must be sorted" }
private fun buildRule(integrand: UnivariateIntegrand<T>): Pair<Buffer<T>, Buffer<T>> {
val factory = integrand.getFeature<GaussIntegratorRuleFactory<T>>()
?: GenericGaussLegendreRuleFactory(algebra, bufferFactory)
val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
val range = integrand.getFeature<IntegrationRange<Double>>()?.range ?: 0.0..1.0
return factory.build(numPoints, range)
}
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = with(algebra) {
val f = integrand.function
val (points, weights) = buildRule(integrand)
var res = zero
var c = zero
for (i in points.indices) {
@ -35,40 +39,73 @@ public class GaussIntegrator<T : Comparable<T>> internal constructor(
c = t - res - y
res = t
}
return integrand + IntegrandValue(res) + IntegrandCalls(integrand.calls + points.size)
return integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + points.size)
}
public companion object {
/**
* Integrate given [function] in a [range] with Gauss-Legendre quadrature with [numPoints] points.
* Integrate [T]-valued univariate function using provided set of [IntegrandFeature]
* Following features are evaluated:
* * [GaussIntegratorRuleFactory] - A factory for computing the Gauss integration rule. By default uses [GenericGaussLegendreRuleFactory]
* * [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 100 points.
*/
public fun <T : Any> integrate(
algebra: Field<T>,
bufferFactory: BufferFactory<T> = ::ListBuffer,
vararg features: IntegrandFeature,
function: (T) -> T,
): UnivariateIntegrand<T> =
GaussIntegrator(algebra, bufferFactory).integrate(UnivariateIntegrand(function, *features))
/**
* Integrate in real numbers
*/
public fun integrate(
vararg features: IntegrandFeature,
function: (Double) -> Double,
): UnivariateIntegrand<Double> = integrate(DoubleField, ::DoubleBuffer, features = features, function)
/**
* Integrate given [function] in a [range] with Gauss-Legendre quadrature with [numPoints] points.
* The [range] is automatically transformed into [T] using [Field.number]
*/
@UnstableKMathAPI
public fun <T : Any> legendre(
algebra: Field<T>,
range: ClosedRange<Double>,
numPoints: Int = 100,
ruleFactory: GaussIntegratorRuleFactory<Double> = GaussLegendreDoubleRuleFactory,
features: List<IntegrandFeature> = emptyList(),
function: (Double) -> Double,
): UnivariateIntegrand<Double> {
val (points, weights) = ruleFactory.build(numPoints, range)
return GaussIntegrator(DoubleField, points, weights).integrate(
UnivariateIntegrand(function, IntegrationRange(range))
bufferFactory: BufferFactory<T> = ::ListBuffer,
vararg features: IntegrandFeature,
function: (T) -> T,
): UnivariateIntegrand<T> = GaussIntegrator(algebra, bufferFactory).integrate(
UnivariateIntegrand(
function,
IntegrationRange(range),
DoubleGaussLegendreRuleFactory,
IntegrandMaxCalls(numPoints),
*features
)
}
)
// public fun integrate(
// borders: List<Double>,
// numPoints: Int = 10,
// ruleFactory: GaussIntegratorRuleFactory<Double> = GaussLegendreDoubleRuleFactory,
// features: List<IntegrandFeature> = emptyList(),
// function: (Double) -> Double,
// ): UnivariateIntegrand<Double> {
// require(borders.indices.all { i -> i == 0 || borders[i] > borders[i - 1] }){"Borders are not sorted"}
//
// val (points, weights) = ruleFactory.build(numPoints, range)
// return GaussIntegrator(DoubleField, points, weights).integrate(
// UnivariateIntegrand(function, IntegrationRange(range))
// )
// }
/**
* Integrate given [function] in a [range] with Gauss-Legendre quadrature with [numPoints] points.
*/
@UnstableKMathAPI
public fun legendre(
range: ClosedRange<Double>,
numPoints: Int = 100,
vararg features: IntegrandFeature,
function: (Double) -> Double,
): UnivariateIntegrand<Double> = GaussIntegrator(DoubleField, ::DoubleBuffer).integrate(
UnivariateIntegrand(
function,
IntegrationRange(range),
DoubleGaussLegendreRuleFactory,
IntegrandMaxCalls(numPoints),
*features
)
)
}
}

29
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt
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@ -12,7 +12,7 @@ import kotlin.jvm.Synchronized
import kotlin.math.ulp
import kotlin.native.concurrent.ThreadLocal
public interface GaussIntegratorRuleFactory<T : Any> {
public interface GaussIntegratorRuleFactory<T : Any> : IntegrandFeature {
public val algebra: Field<T>
public val bufferFactory: BufferFactory<T>
@ -20,7 +20,7 @@ public interface GaussIntegratorRuleFactory<T : Any> {
public companion object {
public fun double(numPoints: Int, range: ClosedRange<Double>): Pair<Buffer<Double>, Buffer<Double>> =
GaussLegendreDoubleRuleFactory.build(numPoints, range)
DoubleGaussLegendreRuleFactory.build(numPoints, range)
}
}
@ -28,16 +28,16 @@ public interface GaussIntegratorRuleFactory<T : Any> {
* Create an integration rule by scaling existing normalized rule
*
*/
public fun <T : Comparable<T>> GaussIntegratorRuleFactory<T>.build(
public fun <T : Any> GaussIntegratorRuleFactory<T>.build(
numPoints: Int,
range: ClosedRange<T>,
range: ClosedRange<Double>,
): Pair<Buffer<T>, Buffer<T>> {
val normalized = build(numPoints)
with(algebra) {
val length = range.endInclusive - range.start
val points = normalized.first.map(bufferFactory) {
range.start + length / 2 + length * it / 2
number(range.start + length / 2) + number(length / 2) * it
}
val weights = normalized.second.map(bufferFactory) {
@ -56,7 +56,7 @@ public fun <T : Comparable<T>> GaussIntegratorRuleFactory<T>.build(
*
*/
@ThreadLocal
public object GaussLegendreDoubleRuleFactory : GaussIntegratorRuleFactory<Double> {
public object DoubleGaussLegendreRuleFactory : GaussIntegratorRuleFactory<Double> {
override val algebra: Field<Double> get() = DoubleField
@ -173,3 +173,20 @@ public object GaussLegendreDoubleRuleFactory : GaussIntegratorRuleFactory<Double
override fun build(numPoints: Int): Pair<Buffer<Double>, Buffer<Double>> = getOrBuildRule(numPoints)
}
/**
* A generic Gauss-Legendre rule factory that wraps [DoubleGaussLegendreRuleFactory] in a generic way.
*/
public class GenericGaussLegendreRuleFactory<T : Any>(
override val algebra: Field<T>,
override val bufferFactory: BufferFactory<T>,
) : GaussIntegratorRuleFactory<T> {
override fun build(numPoints: Int): Pair<Buffer<T>, Buffer<T>> {
val (doublePoints, doubleWeights) = DoubleGaussLegendreRuleFactory.build(numPoints)
val points = doublePoints.map(bufferFactory) { algebra.number(it) }
val weights = doubleWeights.map(bufferFactory) { algebra.number(it) }
return points to weights
}
}

4
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/Integrand.kt
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@ -21,8 +21,8 @@ public class IntegrandRelativeAccuracy(public val accuracy: Double) : IntegrandF
public class IntegrandAbsoluteAccuracy(public val accuracy: Double) : IntegrandFeature
public class IntegrandCalls(public val calls: Int) : IntegrandFeature
public class IntegrandCallsPerformed(public val calls: Int) : IntegrandFeature
public val Integrand.calls: Int get() = getFeature<IntegrandCalls>()?.calls ?: 0
public val Integrand.calls: Int get() = getFeature<IntegrandCallsPerformed>()?.calls ?: 0
public class IntegrandMaxCalls(public val maxCalls: Int) : IntegrandFeature

4
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/GaussIntegralTest.kt
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@ -13,7 +13,7 @@ import kotlin.test.assertEquals
class GaussIntegralTest {
@Test
fun gaussSin() {
val res = GaussIntegrator.integrate(0.0..2 * PI) { x ->
val res = GaussIntegrator.legendre(0.0..2 * PI) { x ->
sin(x)
}
assertEquals(0.0, res.value!!, 1e-4)
@ -21,7 +21,7 @@ class GaussIntegralTest {
@Test
fun gaussUniform() {
val res = GaussIntegrator.integrate(0.0..100.0,300) { x ->
val res = GaussIntegrator.legendre(0.0..100.0,300) { x ->
if(x in 30.0..50.0){
1.0
} else {