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Separate double-based integrator for a Simpson rule

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This commit is contained in:
Alexander Nozik 2021-05-22 20:17:52 +03:00
parent a24c8dcbce
commit ec7a971df7
2 changed files with 51 additions and 3 deletions
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3
build.gradle.kts
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@ -10,13 +10,12 @@ allprojects {
maven("http://logicrunch.research.it.uu.se/maven") {
isAllowInsecureProtocol = true
}
maven("https://maven.pkg.jetbrains.space/public/p/kotlinx-html/maven")
maven("https://oss.sonatype.org/content/repositories/snapshots")
mavenCentral()
}
group = "space.kscience"
version = "0.3.0-dev-11"
version = "0.3.0-dev-12"
}
subprojects {

49
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt
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@ -5,6 +5,8 @@
package space.kscience.kmath.integration
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.Field
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.operations.sum
@ -15,6 +17,7 @@ import space.kscience.kmath.operations.sum
* [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.
*/
@UnstableKMathAPI
public class SimpsonIntegrator<T : Any>(
public val algebra: Field<T>,
) : UnivariateIntegrator<T> {
@ -55,4 +58,50 @@ public class SimpsonIntegrator<T : Any>(
}
}
@UnstableKMathAPI
public val <T : Any> Field<T>.simpsonIntegrator: SimpsonIntegrator<T> get() = SimpsonIntegrator(this)
/**
* Use double pass Simpson rule integration with a fixed number of points.
* Requires [UnivariateIntegrandRanges] or [IntegrationRange] and [IntegrandMaxCalls]
* [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 object DoubleSimpsonIntegrator : UnivariateIntegrator<Double> {
private fun integrateRange(
integrand: UnivariateIntegrand<Double>, range: ClosedRange<Double>, numPoints: Int,
): Double {
val h: Double = (range.endInclusive - range.start) / (numPoints - 1)
val values = DoubleArray(numPoints) { i ->
integrand.function(range.start + i * h)
}// equally distributed point
fun simpson(index: Int) = h / 3 * (values[index - 1] + 4 * values[index] + values[index + 1])
var res = 0.0
res += simpson(1) / 1.5 //border points with 1.5 factor
for (i in 2 until (values.size - 2)) {
//each half-interval is computed twice, therefore /2
res += simpson(i) / 2
}
res += simpson(values.size - 2) / 1.5 //border points with 1.5 factor
return res
}
override fun integrate(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
val ranges = integrand.getFeature<UnivariateIntegrandRanges>()
return if (ranges != null) {
val res = ranges.ranges.sumOf { integrateRange(integrand, it.first, it.second) }
integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + ranges.ranges.sumOf { it.second })
} else {
val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
require(numPoints >= 4) { "Simpson integrator requires at least 4 nodes" }
val range = integrand.getFeature<IntegrationRange>()?.range ?: 0.0..1.0
val res = integrateRange(integrand, range, numPoints)
integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + numPoints)
}
}
}
public val DoubleField.simpsonIntegrator: DoubleSimpsonIntegrator get() = DoubleSimpsonIntegrator