[WIP] optimization refactoring

kmath-commons/src/main/kotlin/space/kscience/kmath/commons/optimization/CMOptimization.kt

@@ -35,7 +35,7 @@ public class CMOptimizerData(public val data: List<OptimizationData>) : Optimiza
 @OptIn(UnstableKMathAPI::class)
 public class CMOptimization : Optimizer<FunctionOptimization<Double>> {
 
-    override suspend fun process(
+    override suspend fun optimize(
         problem: FunctionOptimization<Double>,
     ): FunctionOptimization<Double> {
         val startPoint = problem.getFeature<OptimizationStartPoint<Double>>()?.point

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/FunctionOptimization.kt

@@ -67,12 +67,12 @@ public fun <T> FunctionOptimization<T>.withFeatures(
 /**
  * Optimize differentiable expression using specific [optimizer] form given [startingPoint]
  */
-public suspend fun <T : Any> DifferentiableExpression<T, Expression<T>>.optimizeWith(
+public suspend fun <T : Any> DifferentiableExpression<T>.optimizeWith(
     optimizer: Optimizer<FunctionOptimization<T>>,
     startingPoint: Map<Symbol, T>,
     vararg features: OptimizationFeature,
 ): FunctionOptimization<T> {
     val problem = FunctionOptimization<T>(FeatureSet.of(OptimizationStartPoint(startingPoint), *features), this)
-    return optimizer.process(problem)
+    return optimizer.optimize(problem)
 }
 

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/OptimizationProblem.kt

@@ -40,7 +40,3 @@ public class OptimizationParameters(public val symbols: List<Symbol>): Optimizat
 }
 
 
-public interface Optimizer<P : OptimizationProblem> {
-    public suspend fun process(problem: P): P
-}
-

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/Optimizer.kt

@@ -0,0 +1,10 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.optimization
+
+public interface Optimizer<P : OptimizationProblem> {
+    public suspend fun optimize(problem: P): P
+}

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/XYOptimization.kt

@@ -12,39 +12,63 @@ import space.kscience.kmath.expressions.Expression
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.misc.FeatureSet
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.Field
-import space.kscience.kmath.operations.invoke
+import kotlin.math.pow
 
-public fun interface PointToCurveDistance<T> {
-    public fun distance(problem: XYOptimization<T>, index: Int): DifferentiableExpression<T, Expression<T>>
+public interface PointToCurveDistance : OptimizationFeature {
+    public fun distance(problem: XYOptimization, index: Int): DifferentiableExpression<Double>
 
     public companion object {
-        public fun <T> byY(
-            algebra: Field<T>,
-        ): PointToCurveDistance<T> = PointToCurveDistance { problem, index ->
-            algebra {
+        public val byY: PointToCurveDistance = object : PointToCurveDistance {
+            override fun distance(problem: XYOptimization, index: Int): DifferentiableExpression<Double> {
+
                 val x = problem.data.x[index]
                 val y = problem.data.y[index]
-                
-                val model = problem.model(args + (Symbol.x to x))
-                model - y
+                return object : DifferentiableExpression<Double> {
+                    override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double>? =
+                        problem.model.derivativeOrNull(symbols)
+
+                    override fun invoke(arguments: Map<Symbol, Double>): Double =
+                        problem.model(arguments + (Symbol.x to x)) - y
+                }
             }
+
+            override fun toString(): String = "PointToCurveDistanceByY"
+
         }
 
-
-//        val default = PointToCurveDistance<Double>{args, data, index ->
-//
-//        }
     }
 }
 
-
-public class XYOptimization<T>(
+public class XYOptimization(
     override val features: FeatureSet<OptimizationFeature>,
-    public val data: XYColumnarData<T, T, T>,
-    public val model: DifferentiableExpression<T, Expression<T>>,
+    public val data: XYColumnarData<Double, Double, Double>,
+    public val model: DifferentiableExpression<Double>,
 ) : OptimizationProblem
 
+
+public suspend fun Optimizer<FunctionOptimization<Double>>.maximumLogLikelihood(problem: XYOptimization): XYOptimization {
+    val distanceBuilder = problem.getFeature() ?: PointToCurveDistance.byY
+    val likelihood: DifferentiableExpression<Double> = object : DifferentiableExpression<Double> {
+        override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double>? {
+            TODO("Not yet implemented")
+        }
+
+        override fun invoke(arguments: Map<Symbol, Double>): Double {
+            var res = 0.0
+            for (index in 0 until problem.data.size) {
+                val d = distanceBuilder.distance(problem, index).invoke(arguments)
+                val sigma: Double = TODO()
+                res -= (d / sigma).pow(2)
+            }
+            return res
+        }
+
+    }
+    val functionOptimization = FunctionOptimization(problem.features, likelihood)
+    val result = optimize(functionOptimization)
+    return XYOptimization(result.features, problem.data, problem.model)
+}
+
 //
 //@UnstableKMathAPI
 //public interface XYFit<T> : OptimizationProblem {