Generification of autodiff and chi2

kmath-commons/build.gradle.kts

@@ -7,6 +7,6 @@ dependencies {
     api(project(":kmath-core"))
     api(project(":kmath-coroutines"))
     api(project(":kmath-prob"))
-//    api(project(":kmath-functions"))
+    api(project(":kmath-functions"))
     api("org.apache.commons:commons-math3:3.6.1")
 }

kmath-commons/src/test/kotlin/kscience/kmath/commons/optimization/OptimizeTest.kt

@@ -46,7 +46,7 @@ internal class OptimizeTest {
 
         val sigma = 1.0
         val generator = Distribution.normal(0.0, sigma)
-        val chain = generator.sample(RandomGenerator.default(1126))
+        val chain = generator.sample(RandomGenerator.default(112667))
         val x = (1..100).map { it.toDouble() }
         val y = x.map { it ->
             it.pow(2) + it + 1 + chain.nextDouble()
@@ -54,7 +54,8 @@ internal class OptimizeTest {
         val yErr = x.map { sigma }
         with(CMFit) {
             val chi2 = chiSquared(x.asBuffer(), y.asBuffer(), yErr.asBuffer()) { x ->
-                bind(a) * x.pow(2) + bind(b) * x + bind(c)
+                val cWithDefault = bindOrNull(c)?: one
+                bind(a) * x.pow(2) + bind(b) * x + cWithDefault
             }
 
             val result = chi2.minimize(a to 1.5, b to 0.9, c to 1.0)

kmath-functions/src/commonMain/kotlin/kscience/kmath/functions/Polynomial.kt

@@ -8,13 +8,13 @@ import kotlin.contracts.contract
 import kotlin.math.max
 import kotlin.math.pow
 
-// TODO make `inline`, when KT-41771 gets fixed
 /**
  * Polynomial coefficients without fixation on specific context they are applied to
  * @param coefficients constant is the leftmost coefficient
  */
 public inline class Polynomial<T : Any>(public val coefficients: List<T>)
 
+@Suppress("FunctionName")
 public fun <T : Any> Polynomial(vararg coefficients: T): Polynomial<T> = Polynomial(coefficients.toList())
 
 public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { index, acc, d -> acc + d.pow(index) }
@@ -33,14 +33,6 @@ public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring
     res
 }
 
-/**
- * Represent a polynomial as a context-dependent function
- */
-public fun <T : Any, C : Ring<T>> Polynomial<T>.asMathFunction(): MathFunction<T, C, T> =
-    object : MathFunction<T, C, T> {
-        override fun C.invoke(arg: T): T = value(this, arg)
-    }
-
 /**
  * Represent the polynomial as a regular context-less function
  */
@@ -49,7 +41,7 @@ public fun <T : Any, C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T =
 /**
  * An algebra for polynomials
  */
-public class PolynomialSpace<T : Any, C : Ring<T>>(public val ring: C) : Space<Polynomial<T>> {
+public class PolynomialSpace<T : Any, C : Ring<T>>(private val ring: C) : Space<Polynomial<T>> {
     public override val zero: Polynomial<T> = Polynomial(emptyList())
 
     public override fun add(a: Polynomial<T>, b: Polynomial<T>): Polynomial<T> {

kmath-functions/src/commonMain/kotlin/kscience/kmath/functions/functions.kt

@@ -1,34 +0,0 @@
-package kscience.kmath.functions
-
-import kscience.kmath.operations.Algebra
-import kscience.kmath.operations.RealField
-
-// TODO make fun interface when KT-41770 is fixed
-/**
- * A regular function that could be called only inside specific algebra context
- * @param T source type
- * @param C source algebra constraint
- * @param R result type
- */
-public /*fun*/ interface MathFunction<T, C : Algebra<T>, R> {
-    public operator fun C.invoke(arg: T): R
-}
-
-public fun <R> MathFunction<Double, RealField, R>.invoke(arg: Double): R = RealField.invoke(arg)
-
-/**
- * A suspendable function defined in algebraic context
- */
-// TODO make fun interface, when the new JVM IR is enabled
-public interface SuspendableMathFunction<T, C : Algebra<T>, R> {
-    public suspend operator fun C.invoke(arg: T): R
-}
-
-public suspend fun <R> SuspendableMathFunction<Double, RealField, R>.invoke(arg: Double): R = RealField.invoke(arg)
-
-/**
- * A parametric function with parameter
- */
-public fun interface ParametricFunction<T, P, C : Algebra<T>> {
-    public operator fun C.invoke(arg: T, parameter: P): T
-}

kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/Fit.kt

@@ -0,0 +1,36 @@
+package kscience.kmath.prob
+
+import kscience.kmath.expressions.AutoDiffProcessor
+import kscience.kmath.expressions.DifferentiableExpression
+import kscience.kmath.expressions.ExpressionAlgebra
+import kscience.kmath.operations.ExtendedField
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.indices
+
+public object Fit {
+
+    /**
+     * Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic differentiation
+     */
+    public fun <T : Any, I : Any, A> chiSquared(
+        autoDiff: AutoDiffProcessor<T, I, A>,
+        x: Buffer<T>,
+        y: Buffer<T>,
+        yErr: Buffer<T>,
+        model: A.(I) -> I,
+    ): DifferentiableExpression<T> where A : ExtendedField<I>, A : ExpressionAlgebra<T, I> {
+        require(x.size == y.size) { "X and y buffers should be of the same size" }
+        require(y.size == yErr.size) { "Y and yErr buffer should of the same size" }
+        return autoDiff.process {
+            var sum = zero
+            x.indices.forEach {
+                val xValue = const(x[it])
+                val yValue = const(y[it])
+                val yErrValue = const(yErr[it])
+                val modelValue = model(xValue)
+                sum += ((yValue - modelValue) / yErrValue).pow(2)
+            }
+            sum
+        }
+    }
+}

kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/OptimizationProblem.kt

@@ -0,0 +1,91 @@
+package kscience.kmath.commons.optimization
+
+import kscience.kmath.expressions.DifferentiableExpression
+import kscience.kmath.expressions.Expression
+import kscience.kmath.expressions.Symbol
+
+public interface OptimizationFeature
+
+public class OptimizationResult<T>(
+    public val point: Map<Symbol, T>,
+    public val value: T,
+    public val features: Set<OptimizationFeature> = emptySet(),
+) {
+    override fun toString(): String {
+        return "OptimizationResult(point=$point, value=$value)"
+    }
+}
+
+public operator fun <T> OptimizationResult<T>.plus(
+    feature: OptimizationFeature,
+): OptimizationResult<T> = OptimizationResult(point, value, features + feature)
+
+/**
+ * A configuration builder for optimization problem
+ */
+public interface OptimizationProblem<T : Any> {
+    /**
+     * Define the initial guess for the optimization problem
+     */
+    public fun initialGuess(map: Map<Symbol, T>): Unit
+
+    /**
+     * Set an objective function expression
+     */
+    public fun expression(expression: Expression<T>): Unit
+
+    /**
+     * Set a differentiable expression as objective function as function and gradient provider
+     */
+    public fun diffExpression(expression: DifferentiableExpression<T>): Unit
+
+    /**
+     * Update the problem from previous optimization run
+     */
+    public fun update(result: OptimizationResult<T>)
+
+    /**
+     * Make an optimization run
+     */
+    public fun optimize(): OptimizationResult<T>
+}
+
+public interface OptimizationProblemFactory<T : Any, out P : OptimizationProblem<T>> {
+    public fun build(symbols: List<Symbol>): P
+
+}
+
+public operator fun <T : Any, P : OptimizationProblem<T>> OptimizationProblemFactory<T, P>.invoke(
+    symbols: List<Symbol>,
+    block: P.() -> Unit,
+): P = build(symbols).apply(block)
+
+
+/**
+ * Optimize expression without derivatives using specific [OptimizationProblemFactory]
+ */
+public fun <T : Any, F : OptimizationProblem<T>> Expression<T>.optimizeWith(
+    factory: OptimizationProblemFactory<T, F>,
+    vararg symbols: Symbol,
+    configuration: F.() -> Unit,
+): OptimizationResult<T> {
+    require(symbols.isNotEmpty()) { "Must provide a list of symbols for optimization" }
+    val problem = factory(symbols.toList(),configuration)
+    problem.expression(this)
+    return problem.optimize()
+}
+
+/**
+ * Optimize differentiable expression using specific [OptimizationProblemFactory]
+ */
+public fun <T : Any, F : OptimizationProblem<T>>  DifferentiableExpression<T>.optimizeWith(
+    factory: OptimizationProblemFactory<T, F>,
+    vararg symbols: Symbol,
+    configuration: F.() -> Unit,
+): OptimizationResult<T> {
+    require(symbols.isNotEmpty()) { "Must provide a list of symbols for optimization" }
+    val problem = factory(symbols.toList(), configuration)
+    problem.diffExpression(this)
+    return problem.optimize()
+}
+