Separate double-based integrator for a Simpson rule
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@ -10,13 +10,12 @@ allprojects {
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maven("http://logicrunch.research.it.uu.se/maven") {
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maven("http://logicrunch.research.it.uu.se/maven") {
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isAllowInsecureProtocol = true
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isAllowInsecureProtocol = true
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}
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}
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maven("https://maven.pkg.jetbrains.space/public/p/kotlinx-html/maven")
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maven("https://oss.sonatype.org/content/repositories/snapshots")
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maven("https://oss.sonatype.org/content/repositories/snapshots")
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mavenCentral()
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mavenCentral()
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}
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}
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group = "space.kscience"
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group = "space.kscience"
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version = "0.3.0-dev-11"
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version = "0.3.0-dev-12"
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}
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}
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subprojects {
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subprojects {
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@ -5,6 +5,8 @@
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package space.kscience.kmath.integration
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package space.kscience.kmath.integration
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.operations.Field
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import space.kscience.kmath.operations.Field
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import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.operations.sum
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import space.kscience.kmath.operations.sum
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@ -15,6 +17,7 @@ import space.kscience.kmath.operations.sum
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* [IntegrationRange] - the univariate range of integration. By default uses 0..1 interval.
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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 10 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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*/
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*/
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@UnstableKMathAPI
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public class SimpsonIntegrator<T : Any>(
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public class SimpsonIntegrator<T : Any>(
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public val algebra: Field<T>,
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public val algebra: Field<T>,
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) : UnivariateIntegrator<T> {
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) : UnivariateIntegrator<T> {
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@ -55,4 +58,50 @@ public class SimpsonIntegrator<T : Any>(
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}
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}
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}
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}
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public val <T : Any> Field<T>.simpsonIntegrator: SimpsonIntegrator<T> get() = SimpsonIntegrator(this)
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@UnstableKMathAPI
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public val <T : Any> Field<T>.simpsonIntegrator: SimpsonIntegrator<T> get() = SimpsonIntegrator(this)
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/**
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* Use double pass Simpson rule integration with a fixed number of points.
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* Requires [UnivariateIntegrandRanges] or [IntegrationRange] and [IntegrandMaxCalls]
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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 10 points.
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*/
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public object DoubleSimpsonIntegrator : UnivariateIntegrator<Double> {
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private fun integrateRange(
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integrand: UnivariateIntegrand<Double>, range: ClosedRange<Double>, numPoints: Int,
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): Double {
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val h: Double = (range.endInclusive - range.start) / (numPoints - 1)
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val values = DoubleArray(numPoints) { i ->
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integrand.function(range.start + i * h)
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}// equally distributed point
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fun simpson(index: Int) = h / 3 * (values[index - 1] + 4 * values[index] + values[index + 1])
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var res = 0.0
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res += simpson(1) / 1.5 //border points with 1.5 factor
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for (i in 2 until (values.size - 2)) {
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//each half-interval is computed twice, therefore /2
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res += simpson(i) / 2
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}
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res += simpson(values.size - 2) / 1.5 //border points with 1.5 factor
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return res
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}
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override fun integrate(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
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val ranges = integrand.getFeature<UnivariateIntegrandRanges>()
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return if (ranges != null) {
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val res = ranges.ranges.sumOf { integrateRange(integrand, it.first, it.second) }
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integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + ranges.ranges.sumOf { it.second })
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} else {
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val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
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require(numPoints >= 4) { "Simpson integrator requires at least 4 nodes" }
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val range = integrand.getFeature<IntegrationRange>()?.range ?: 0.0..1.0
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val res = integrateRange(integrand, range, numPoints)
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integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + numPoints)
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}
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}
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}
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public val DoubleField.simpsonIntegrator: DoubleSimpsonIntegrator get() = DoubleSimpsonIntegrator
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