Update integration API

examples/src/main/kotlin/space/kscience/kmath/functions/integrate.kt

@@ -1,7 +1,8 @@
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.integration.GaussIntegrator
+import space.kscience.kmath.integration.integrate
 import space.kscience.kmath.integration.value
+import space.kscience.kmath.operations.DoubleField
 import kotlin.math.pow
 
 fun main() {
@@ -9,7 +10,7 @@ fun main() {
     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)
+    val result = DoubleField.integrate(0.0..10.0, function = function)
 
     //the value is nullable because in some cases the integration could not succeed
     println(result.value)

examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt

@@ -1,7 +1,6 @@
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.integration.GaussIntegrator
-import space.kscience.kmath.integration.UnivariateIntegrand
+import space.kscience.kmath.integration.integrate
 import space.kscience.kmath.integration.value
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.nd
@@ -10,11 +9,17 @@ import space.kscience.kmath.operations.invoke
 
 fun main(): Unit = DoubleField {
     nd(2, 2) {
+
+        //Produce a diagonal StructureND
+        fun diagonal(v: Double) = produce { (i, j) ->
+            if (i == j) v else 0.0
+        }
+
         //Define a function in a nd space
-        val function: UnivariateFunction<StructureND<Double>> = { x -> 3 * x.pow(2) + 2 * x + 1 }
+        val function: (Double) -> StructureND<Double> = { x: Double -> 3 * number(x).pow(2) + 2 * diagonal(x) + 1 }
 
         //get the result of the integration
-        val result: UnivariateIntegrand<StructureND<Double>> = GaussIntegrator.legendre(this, 0.0..10.0, function = function)
+        val result = integrate(0.0..10.0, function = function)
 
         //the value is nullable because in some cases the integration could not succeed
         println(result.value)

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt

@@ -5,7 +5,6 @@
 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.structures.*
 
@@ -15,12 +14,10 @@ import space.kscience.kmath.structures.*
  */
 public class GaussIntegrator<T : Any>(
     public val algebra: Field<T>,
-    public val bufferFactory: BufferFactory<T>,
 ) : UnivariateIntegrator<T> {
 
-    private fun buildRule(integrand: UnivariateIntegrand<T>): Pair<Buffer<T>, Buffer<T>> {
-        val factory = integrand.getFeature<GaussIntegratorRuleFactory<T>>()
-            ?: GenericGaussLegendreRuleFactory(algebra, bufferFactory)
+    private fun buildRule(integrand: UnivariateIntegrand<T>): Pair<Buffer<Double>, Buffer<Double>> {
+        val factory = integrand.getFeature<GaussIntegratorRuleFactory>() ?: GaussLegendreRuleFactory
         val numPoints = integrand.getFeature<IntegrandMaxCalls>()?.maxCalls ?: 100
         val range = integrand.getFeature<IntegrationRange<Double>>()?.range ?: 0.0..1.0
         return factory.build(numPoints, range)
@@ -32,9 +29,9 @@ public class GaussIntegrator<T : Any>(
         var res = zero
         var c = zero
         for (i in points.indices) {
-            val x: T = points[i]
-            val w: T = weights[i]
-            val y: T = w * f(x) - c
+            val x = points[i]
+            val weight = weights[i]
+            val y: T = weight * f(x) - c
             val t = res + y
             c = t - res - y
             res = t
@@ -44,68 +41,38 @@ public class GaussIntegrator<T : Any>(
 
     public companion object {
 
+    }
+}
+
 /**
  * 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]
+ * * [GaussIntegratorRuleFactory] - A factory for computing the Gauss integration rule. By default uses [GaussLegendreRuleFactory]
  * * [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,
+@UnstableKMathAPI
+public fun <T : Any> Field<T>.integrate(
     vararg features: IntegrandFeature,
-            function: (T) -> T,
-        ): UnivariateIntegrand<T> =
-            GaussIntegrator(algebra, bufferFactory).integrate(UnivariateIntegrand(function, *features))
+    function: (Double) -> T,
+): UnivariateIntegrand<T> = GaussIntegrator(this).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]
+ * Use [GaussIntegrator.Companion.integrate] to integrate the function in the current algebra with given [range] and [numPoints]
  */
 @UnstableKMathAPI
-        public fun  <T : Any> legendre(
-            algebra: Field<T>,
+public fun <T : Any> Field<T>.integrate(
     range: ClosedRange<Double>,
     numPoints: Int = 100,
-            bufferFactory: BufferFactory<T> = ::ListBuffer,
     vararg features: IntegrandFeature,
-            function: (T) -> T,
-        ): UnivariateIntegrand<T> = GaussIntegrator(algebra, bufferFactory).integrate(
+    function: (Double) -> T,
+): UnivariateIntegrand<T> = GaussIntegrator(this).integrate(
     UnivariateIntegrand(
         function,
         IntegrationRange(range),
-                DoubleGaussLegendreRuleFactory,
+        GaussLegendreRuleFactory,
         IntegrandMaxCalls(numPoints),
         *features
     )
 )
-
-        /**
-         * 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
-            )
-        )
-    }
-}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt

@@ -5,22 +5,20 @@
 
 package space.kscience.kmath.integration
 
-import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.operations.Field
-import space.kscience.kmath.structures.*
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.map
 import kotlin.jvm.Synchronized
 import kotlin.math.ulp
 import kotlin.native.concurrent.ThreadLocal
 
-public interface GaussIntegratorRuleFactory<T : Any> : IntegrandFeature {
-    public val algebra: Field<T>
-    public val bufferFactory: BufferFactory<T>
-
-    public fun build(numPoints: Int): Pair<Buffer<T>, Buffer<T>>
+public interface GaussIntegratorRuleFactory : IntegrandFeature {
+    public fun build(numPoints: Int): Pair<Buffer<Double>, Buffer<Double>>
 
     public companion object {
         public fun double(numPoints: Int, range: ClosedRange<Double>): Pair<Buffer<Double>, Buffer<Double>> =
-            DoubleGaussLegendreRuleFactory.build(numPoints, range)
+            GaussLegendreRuleFactory.build(numPoints, range)
     }
 }
 
@@ -28,24 +26,23 @@ public interface GaussIntegratorRuleFactory<T : Any> : IntegrandFeature {
  * Create an integration rule by scaling existing normalized rule
  *
  */
-public fun <T : Any> GaussIntegratorRuleFactory<T>.build(
+public fun GaussIntegratorRuleFactory.build(
     numPoints: Int,
     range: ClosedRange<Double>,
-): Pair<Buffer<T>, Buffer<T>> {
+): Pair<Buffer<Double>, Buffer<Double>> {
     val normalized = build(numPoints)
-    with(algebra) {
     val length = range.endInclusive - range.start
 
-        val points = normalized.first.map(bufferFactory) {
-            number(range.start + length / 2) + number(length / 2) * it
+    val points = normalized.first.map(::DoubleBuffer) {
+        range.start + length / 2 + length / 2 * it
     }
 
-        val weights = normalized.second.map(bufferFactory) {
+    val weights = normalized.second.map(::DoubleBuffer) {
         it * length / 2
     }
 
     return points to weights
-    }
+
 }
 
 
@@ -56,11 +53,7 @@ public fun <T : Any> GaussIntegratorRuleFactory<T>.build(
  *
  */
 @ThreadLocal
-public object DoubleGaussLegendreRuleFactory : GaussIntegratorRuleFactory<Double> {
-
-    override val algebra: Field<Double> get() = DoubleField
-
-    override val bufferFactory: BufferFactory<Double> get() = ::DoubleBuffer
+public object GaussLegendreRuleFactory : GaussIntegratorRuleFactory {
 
     private val cache = HashMap<Int, Pair<Buffer<Double>, Buffer<Double>>>()
 
@@ -172,21 +165,3 @@ public object DoubleGaussLegendreRuleFactory : 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
-    }
-}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt

@@ -5,14 +5,13 @@
 
 package space.kscience.kmath.integration
 
-import space.kscience.kmath.functions.UnivariateFunction
 import space.kscience.kmath.misc.UnstableKMathAPI
 import kotlin.jvm.JvmInline
 import kotlin.reflect.KClass
 
 public class UnivariateIntegrand<T : Any> internal constructor(
     private val features: Map<KClass<*>, IntegrandFeature>,
-    public val function: UnivariateFunction<T>,
+    public val function: (Double) -> T,
 ) : Integrand {
 
     @Suppress("UNCHECKED_CAST")
@@ -27,7 +26,7 @@ public class UnivariateIntegrand<T : Any> internal constructor(
 
 @Suppress("FunctionName")
 public fun <T : Any> UnivariateIntegrand(
-    function: (T) -> T,
+    function: (Double) -> T,
     vararg features: IntegrandFeature,
 ): UnivariateIntegrand<T> = UnivariateIntegrand(features.associateBy { it::class }, function)
 

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/GaussIntegralTest.kt

@@ -5,15 +5,18 @@
 
 package space.kscience.kmath.integration
 
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.DoubleField
 import kotlin.math.PI
 import kotlin.math.sin
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
+@OptIn(UnstableKMathAPI::class)
 class GaussIntegralTest {
     @Test
     fun gaussSin() {
-        val res = GaussIntegrator.legendre(0.0..2 * PI) { x ->
+        val res = DoubleField.integrate(0.0..2 * PI) { x ->
             sin(x)
         }
         assertEquals(0.0, res.value!!, 1e-4)
@@ -21,7 +24,7 @@ class GaussIntegralTest {
 
     @Test
     fun gaussUniform() {
-        val res = GaussIntegrator.legendre(0.0..100.0,300) { x ->
+        val res = DoubleField.integrate(0.0..100.0,300) { x ->
             if(x in 30.0..50.0){
                 1.0
             } else {