Use split interval for integration.
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6c215abf13
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@ -22,8 +22,8 @@ fun main() {
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return DoubleBuffer(x.size) { i ->
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val h = sigma[i] / 5
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val dVector = DoubleBuffer(x.size) { if (it == i) h else 0.0 }
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val f1 = invoke(x + dVector / 2)
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val f0 = invoke(x - dVector / 2)
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val f1 = this(x + dVector / 2)
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val f0 = this(x - dVector / 2)
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(f1 - f0) / h
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}
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}
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@ -28,7 +28,7 @@ public class CMIntegrator(
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val integrator = integratorBuilder(integrand)
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val maxCalls = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: defaultMaxCalls
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val remainingCalls = maxCalls - integrand.calls
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val range = integrand.getFeature<IntegrationRange<Double>>()?.range
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val range = integrand.getFeature<IntegrationRange>()?.range
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?: error("Integration range is not provided")
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val res = integrator.integrate(remainingCalls, integrand.function, range.start, range.endInclusive)
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@ -17,7 +17,7 @@ public class GaussRuleIntegrator(
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) : UnivariateIntegrator<Double> {
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override fun integrate(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
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val range = integrand.getFeature<IntegrationRange<Double>>()?.range
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val range = integrand.getFeature<IntegrationRange>()?.range
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?: error("Integration range is not provided")
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val integrator: GaussIntegrator = getIntegrator(range)
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//TODO check performance
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@ -8,6 +8,13 @@ import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.Field
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import space.kscience.kmath.structures.*
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/**
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* Set of univariate integration ranges. First components correspond to ranges themselves, second components to number of
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* integration nodes per range
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*/
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public class UnivariateIntegrandRanges(public val ranges: List<Pair<ClosedRange<Double>, Int>>) : IntegrandFeature {
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public constructor(vararg pairs: Pair<ClosedRange<Double>, Int>) : this(pairs.toList())
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}
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/**
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* A simple one-pass integrator based on Gauss rule
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@ -18,9 +25,29 @@ public class GaussIntegrator<T : Any>(
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private fun buildRule(integrand: UnivariateIntegrand<T>): Pair<Buffer<Double>, Buffer<Double>> {
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val factory = integrand.getFeature<GaussIntegratorRuleFactory>() ?: GaussLegendreRuleFactory
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val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
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val range = integrand.getFeature<IntegrationRange<Double>>()?.range ?: 0.0..1.0
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return factory.build(numPoints, range)
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val predefinedRanges = integrand.getFeature<UnivariateIntegrandRanges>()
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if (predefinedRanges == null || predefinedRanges.ranges.isEmpty()) {
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val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
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val range = integrand.getFeature<IntegrationRange>()?.range ?: 0.0..1.0
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return factory.build(numPoints, range)
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} else {
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val ranges = predefinedRanges.ranges
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var counter = 0
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val length = ranges.sumOf { it.second }
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val pointsArray = DoubleArray(length)
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val weightsArray = DoubleArray(length)
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for (range in ranges) {
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val rule = factory.build(range.second, range.first)
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repeat(rule.first.size) { i ->
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pointsArray[counter] = rule.first[i]
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weightsArray[counter] = rule.second[i]
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counter++
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}
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}
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return pointsArray.asBuffer() to weightsArray.asBuffer()
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}
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}
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override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = with(algebra) {
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@ -49,7 +76,8 @@ public class GaussIntegrator<T : Any>(
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* Following features are evaluated:
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* * [GaussIntegratorRuleFactory] - A factory for computing the Gauss integration rule. By default uses [GaussLegendreRuleFactory]
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* * [IntegrationRange] - the univariate range of integration. By default uses 0..1 interval.
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* * [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.
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* * [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.
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* * [UnivariateIntegrandRanges] - Set of ranges and number of points per range. Defaults to given [IntegrationRange] and [IntegrandMaxCalls]
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*/
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@UnstableKMathAPI
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public fun <T : Any> Field<T>.integrate(
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@ -64,15 +92,25 @@ public fun <T : Any> Field<T>.integrate(
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@UnstableKMathAPI
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public fun <T : Any> Field<T>.integrate(
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range: ClosedRange<Double>,
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numPoints: Int = 100,
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order: Int = 10,
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intervals: Int = 10,
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vararg features: IntegrandFeature,
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function: (Double) -> T,
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): UnivariateIntegrand<T> = GaussIntegrator(this).integrate(
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UnivariateIntegrand(
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function,
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IntegrationRange(range),
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GaussLegendreRuleFactory,
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IntegrandMaxCalls(numPoints),
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*features
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): UnivariateIntegrand<T> {
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require(range.endInclusive > range.start) { "The range upper bound should be higher than lower bound" }
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require(order > 1) { "The order of polynomial must be more than 1" }
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require(intervals > 0) { "Number of intervals must be positive" }
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val rangeSize = (range.endInclusive - range.start) / intervals
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val ranges = UnivariateIntegrandRanges(
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(0 until intervals).map { i -> (rangeSize * i)..(rangeSize * i + 1) to order }
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)
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)
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return GaussIntegrator(this).integrate(
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UnivariateIntegrand(
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function,
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IntegrationRange(range),
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GaussLegendreRuleFactory,
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ranges,
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*features
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)
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)
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}
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@ -33,7 +33,7 @@ public fun <T : Any> UnivariateIntegrand(
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public typealias UnivariateIntegrator<T> = Integrator<UnivariateIntegrand<T>>
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@JvmInline
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public value class IntegrationRange<T : Comparable<T>>(public val range: ClosedRange<T>) : IntegrandFeature
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public value class IntegrationRange(public val range: ClosedRange<Double>) : IntegrandFeature
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public val <T : Any> UnivariateIntegrand<T>.value: T? get() = getFeature<IntegrandValue<T>>()?.value
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