From ec7a971df71e4371c2720ffb77d2c3dafbd0c0bf Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sat, 22 May 2021 20:17:52 +0300
Subject: [PATCH] Separate double-based integrator for a Simpson rule

---
 build.gradle.kts                              |  3 +-
 .../kmath/integration/SimpsonIntegrator.kt    | 51 ++++++++++++++++++-
 2 files changed, 51 insertions(+), 3 deletions(-)

diff --git a/build.gradle.kts b/build.gradle.kts
index d44833445..ef9c60c55 100644
--- a/build.gradle.kts
+++ b/build.gradle.kts
@@ -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 {
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt
index 56647bace..baa9d4af8 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt
@@ -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>(
     }
 }
 
-public val <T : Any> Field<T>.simpsonIntegrator: SimpsonIntegrator<T> get() = SimpsonIntegrator(this)
\ No newline at end of file
+@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
\ No newline at end of file