Update of symbolic operations

CHANGELOG.md

@@ -2,6 +2,8 @@
 
 ## [Unreleased]
 ### Added
+- `NamedMatrix` - matrix with symbol-based indexing
+- `Expression` with default arguments
 - Type-aliases for numbers like `Float64`
 - 2D optimal trajectory computation in a separate module `kmath-trajectory`
 - Autodiff for generic algebra elements in core!

build.gradle.kts

@@ -15,7 +15,7 @@ allprojects {
     }
 
     group = "space.kscience"
-    version = "0.3.1-dev-8"
+    version = "0.3.1-dev-9"
 }
 
 subprojects {

examples/src/main/kotlin/space/kscience/kmath/fit/chiSquared.kt

@@ -10,7 +10,6 @@ import kotlinx.html.h3
 import space.kscience.kmath.commons.optimization.CMOptimizer
 import space.kscience.kmath.distributions.NormalDistribution
 import space.kscience.kmath.expressions.autodiff
-import space.kscience.kmath.expressions.chiSquaredExpression
 import space.kscience.kmath.expressions.symbol
 import space.kscience.kmath.operations.asIterable
 import space.kscience.kmath.operations.toList
@@ -22,6 +21,7 @@ import space.kscience.kmath.random.RandomGenerator
 import space.kscience.kmath.real.DoubleVector
 import space.kscience.kmath.real.map
 import space.kscience.kmath.real.step
+import space.kscience.kmath.stat.chiSquaredExpression
 import space.kscience.plotly.*
 import space.kscience.plotly.models.ScatterMode
 import space.kscience.plotly.models.TraceValues

examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt

@@ -15,10 +15,7 @@ import space.kscience.kmath.expressions.binding
 import space.kscience.kmath.expressions.symbol
 import space.kscience.kmath.operations.asIterable
 import space.kscience.kmath.operations.toList
-import space.kscience.kmath.optimization.QowOptimizer
+import space.kscience.kmath.optimization.*
-import space.kscience.kmath.optimization.chiSquaredOrNull
-import space.kscience.kmath.optimization.fitWith
-import space.kscience.kmath.optimization.resultPoint
 import space.kscience.kmath.random.RandomGenerator
 import space.kscience.kmath.real.map
 import space.kscience.kmath.real.step
@@ -32,6 +29,8 @@ import kotlin.math.sqrt
 private val a by symbol
 private val b by symbol
 private val c by symbol
+private val d by symbol
+private val e by symbol
 
 
 /**
@@ -64,16 +63,22 @@ suspend fun main() {
     val result = XYErrorColumnarData.of(x, y, yErr).fitWith(
         QowOptimizer,
         Double.autodiff,
-        mapOf(a to 0.9, b to 1.2, c to 2.0)
+        mapOf(a to 0.9, b to 1.2, c to 2.0, e to 1.0, d to 1.0, e to 0.0),
+        OptimizationParameters(a, b, c, d)
     ) { arg ->
         //bind variables to autodiff context
         val a by binding
         val b by binding
         //Include default value for c if it is not provided as a parameter
         val c = bindSymbolOrNull(c) ?: one
-        a * arg.pow(2) + b * arg + c
+        val d by binding
+        val e by binding
+
+        a * arg.pow(2) + b * arg + c + d * arg.pow(3) + e / arg
     }
 
+    println("Resulting chi2/dof: ${result.chiSquaredOrNull}/${result.dof}")
+
     //display a page with plot and numerical results
     val page = Plotly.page {
         plot {
@@ -89,7 +94,7 @@ suspend fun main() {
             scatter {
                 mode = ScatterMode.lines
                 x(x)
-                y(x.map { result.model(result.resultPoint + (Symbol.x to it)) })
+                y(x.map { result.model(result.startPoint + result.resultPoint + (Symbol.x to it)) })
                 name = "fit"
             }
         }
@@ -98,7 +103,7 @@ suspend fun main() {
             +"Fit result: ${result.resultPoint}"
         }
         h3 {
-            +"Chi2/dof = ${result.chiSquaredOrNull!! / (x.size - 3)}"
+            +"Chi2/dof = ${result.chiSquaredOrNull!! / result.dof}"
         }
     }
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/ExpressionWithDefault.kt

@@ -0,0 +1,31 @@
+/*
+ * Copyright 2018-2023 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.expressions
+
+public class ExpressionWithDefault<T>(
+    private val origin: Expression<T>,
+    private val defaultArgs: Map<Symbol, T>,
+) : Expression<T> {
+    override fun invoke(arguments: Map<Symbol, T>): T = origin.invoke(defaultArgs + arguments)
+}
+
+public fun <T> Expression<T>.withDefaultArgs(defaultArgs: Map<Symbol, T>): ExpressionWithDefault<T> =
+    ExpressionWithDefault(this, defaultArgs)
+
+
+public class DiffExpressionWithDefault<T>(
+    private val origin: DifferentiableExpression<T>,
+    private val defaultArgs: Map<Symbol, T>,
+) : DifferentiableExpression<T> {
+
+    override fun invoke(arguments: Map<Symbol, T>): T = origin.invoke(defaultArgs + arguments)
+
+    override fun derivativeOrNull(symbols: List<Symbol>): Expression<T>? =
+        origin.derivativeOrNull(symbols)?.withDefaultArgs(defaultArgs)
+}
+
+public fun <T> DifferentiableExpression<T>.withDefaultArgs(defaultArgs: Map<Symbol, T>): DiffExpressionWithDefault<T> =
+    DiffExpressionWithDefault(this, defaultArgs)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/NamedMatrix.kt

@@ -0,0 +1,37 @@
+/*
+ * Copyright 2018-2023 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.
+ */
+
+@file:OptIn(UnstableKMathAPI::class)
+
+package space.kscience.kmath.expressions
+
+import space.kscience.kmath.linear.Matrix
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.structures.getOrNull
+
+public class NamedMatrix<T>(public val values: Matrix<T>, public val indexer: SymbolIndexer) : Matrix<T> by values {
+    public operator fun get(i: Symbol, j: Symbol): T = get(indexer.indexOf(i), indexer.indexOf(j))
+
+    public companion object {
+
+        public fun toStringWithSymbols(values: Matrix<*>, indexer: SymbolIndexer): String = buildString {
+            appendLine(indexer.symbols.joinToString(separator = "\t", prefix = "\t\t"))
+            indexer.symbols.forEach { i ->
+                append(i.identity + "\t")
+                values.rows.getOrNull(indexer.indexOf(i))?.let { row ->
+                    indexer.symbols.forEach { j ->
+                        append(row.getOrNull(indexer.indexOf(j)).toString())
+                        append("\t")
+                    }
+                    appendLine()
+                }
+            }
+        }
+    }
+}
+
+public fun <T> Matrix<T>.named(indexer: SymbolIndexer): NamedMatrix<T> = NamedMatrix(this, indexer)
+
+public fun <T> Matrix<T>.named(symbols: List<Symbol>): NamedMatrix<T> = named(SimpleSymbolIndexer(symbols))

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

@@ -6,8 +6,8 @@
 package space.kscience.kmath.optimization
 
 import space.kscience.kmath.expressions.DifferentiableExpression
+import space.kscience.kmath.expressions.NamedMatrix
 import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.linear.Matrix
 import space.kscience.kmath.misc.*
 import kotlin.reflect.KClass
 
@@ -32,7 +32,10 @@ public interface OptimizationPrior<T> : OptimizationFeature, DifferentiableExpre
     override val key: FeatureKey<OptimizationFeature> get() = OptimizationPrior::class
 }
 
-public class OptimizationCovariance<T>(public val covariance: Matrix<T>) : OptimizationFeature {
+/**
+ * Covariance matrix for
+ */
+public class OptimizationCovariance<T>(public val covariance: NamedMatrix<T>) : OptimizationFeature {
     override fun toString(): String = "Covariance($covariance)"
 }
 
@@ -57,10 +60,20 @@ public class OptimizationLog(private val loggable: Loggable) : Loggable by logga
     override fun toString(): String = "Log($loggable)"
 }
 
+/**
+ * Free parameters of the optimization
+ */
 public class OptimizationParameters(public val symbols: List<Symbol>) : OptimizationFeature {
     public constructor(vararg symbols: Symbol) : this(listOf(*symbols))
 
     override fun toString(): String = "Parameters($symbols)"
 }
 
+/**
+ * Maximum allowed number of iterations
+ */
+public class OptimizationIterations(public val maxIterations: Int) : OptimizationFeature {
+    override fun toString(): String = "Iterations($maxIterations)"
+}
+
 

kmath-optimization/src/commonMain/kotlin/space/kscience/kmath/optimization/QowOptimizer.kt

@@ -5,10 +5,7 @@
 
 package space.kscience.kmath.optimization
 
-import space.kscience.kmath.expressions.DifferentiableExpression
+import space.kscience.kmath.expressions.*
-import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.expressions.SymbolIndexer
-import space.kscience.kmath.expressions.derivative
 import space.kscience.kmath.linear.*
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.misc.log
@@ -16,6 +13,7 @@ import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.DoubleL2Norm
 import space.kscience.kmath.operations.algebra
 import space.kscience.kmath.structures.DoubleBuffer
+import kotlin.math.abs
 
 
 public class QowRuns(public val runs: Int) : OptimizationFeature {
@@ -40,18 +38,24 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
     @OptIn(UnstableKMathAPI::class)
     private class QoWeight(
         val problem: XYFit,
-        val parameters: Map<Symbol, Double>,
+        val freeParameters: Map<Symbol, Double>,
-    ) : Map<Symbol, Double> by parameters, SymbolIndexer {
+    ) : SymbolIndexer {
-        override val symbols: List<Symbol> = parameters.keys.toList()
+        val size get() = freeParameters.size
+
+        override val symbols: List<Symbol> = freeParameters.keys.toList()
 
         val data get() = problem.data
 
+        val allParameters by lazy {
+            problem.startPoint + freeParameters
+        }
+
         /**
          * Derivatives of the spectrum over parameters. First index in the point number, second one - index of parameter
          */
         val derivs: Matrix<Double> by lazy {
             linearSpace.buildMatrix(problem.data.size, symbols.size) { d, s ->
-                problem.distance(d).derivative(symbols[s])(parameters)
+                problem.distance(d).derivative(symbols[s]).invoke(allParameters)
             }
         }
 
@@ -60,29 +64,31 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
          */
         val dispersion: Point<Double> by lazy {
             DoubleBuffer(problem.data.size) { d ->
-                1.0/problem.weight(d).invoke(parameters)
+                1.0 / problem.weight(d).invoke(allParameters)
             }
         }
 
-        val prior: DifferentiableExpression<Double>? get() = problem.getFeature<OptimizationPrior<Double>>()
+        val prior: DifferentiableExpression<Double>?
+            get() = problem.getFeature<OptimizationPrior<Double>>()?.withDefaultArgs(allParameters)
 
-        override fun toString(): String = parameters.toString()
+        override fun toString(): String = freeParameters.toString()
     }
 
     /**
      * The signed distance from the model to the [d]-th point of data.
      */
-    private fun QoWeight.distance(d: Int, parameters: Map<Symbol, Double>): Double = problem.distance(d)(parameters)
+    private fun QoWeight.distance(d: Int, parameters: Map<Symbol, Double>): Double =
+        problem.distance(d)(allParameters + parameters)
 
 
     /**
      * The derivative of [distance]
      */
     private fun QoWeight.distanceDerivative(symbol: Symbol, d: Int, parameters: Map<Symbol, Double>): Double =
-        problem.distance(d).derivative(symbol)(parameters)
+        problem.distance(d).derivative(symbol).invoke(allParameters + parameters)
 
     /**
-     * Теоретическая ковариация весовых функций.
+     * Theoretical covariance of weight functions
      *
      * D(\phi)=E(\phi_k(\theta_0) \phi_l(\theta_0))= disDeriv_k * disDeriv_l /sigma^2
      */
@@ -92,7 +98,7 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
         }
 
     /**
-     * Экспериментальная ковариация весов. Формула (22) из
+     * Experimental covariance Eq (22) from
      * http://arxiv.org/abs/physics/0604127
      */
     private fun QoWeight.covarFExp(theta: Map<Symbol, Double>): Matrix<Double> =
@@ -115,10 +121,9 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
      * Equation derivatives for Newton run
      */
     private fun QoWeight.getEqDerivValues(
-        theta: Map<Symbol, Double> = parameters,
+        theta: Map<Symbol, Double> = freeParameters,
     ): Matrix<Double> = with(linearSpace) {
-        //Возвращает производную k-того Eq по l-тому параметру
+        //Derivative of k Eq over l parameter
-        //val res = Array(fitDim) { DoubleArray(fitDim) }
         val sderiv = buildMatrix(data.size, size) { d, s ->
             distanceDerivative(symbols[s], d, theta)
         }
@@ -140,16 +145,15 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
 
 
     /**
-     * Значения уравнений метода квазиоптимальных весов
+     * Quasi optimal weights equations values
      */
-    private fun QoWeight.getEqValues(theta: Map<Symbol, Double> = this): Point<Double> {
+    private fun QoWeight.getEqValues(theta: Map<Symbol, Double>): Point<Double> {
         val distances = DoubleBuffer(data.size) { d -> distance(d, theta) }
-
         return DoubleBuffer(size) { s ->
             val base = (0 until data.size).sumOf { d -> distances[d] * derivs[d, s] / dispersion[d] }
-            //Поправка на априорную вероятность
+            //Prior probability correction
             prior?.let { prior ->
-                base - prior.derivative(symbols[s])(theta) / prior(theta)
+                base - prior.derivative(symbols[s]).invoke(theta) / prior(theta)
             } ?: base
         }
     }
@@ -157,15 +161,13 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
 
     private fun QoWeight.newtonianStep(
         theta: Map<Symbol, Double>,
-        eqvalues: Point<Double>,
+        eqValues: Point<Double>,
     ): QoWeight = linearSpace {
-        with(this@newtonianStep) {
+        val start = theta.toPoint()
-            val start = theta.toPoint()
+        val invJacob = solver.inverse(getEqDerivValues(theta))
-            val invJacob = solver.inverse(this@newtonianStep.getEqDerivValues(theta))
 
-            val step = invJacob.dot(eqvalues)
+        val step = invJacob.dot(eqValues)
-            return QoWeight(problem, theta + (start - step).toMap())
+        return QoWeight(problem, theta + (start - step).toMap())
-        }
     }
 
     private fun QoWeight.newtonianRun(
@@ -177,10 +179,10 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
         val logger = problem.getFeature<OptimizationLog>()
 
         var dis: Double //discrepancy value
-        // Working with the full set of parameters
-        var par = problem.startPoint
 
-        logger?.log { "Starting newtonian iteration from: \n\t$par" }
+        var par = freeParameters
+
+        logger?.log { "Starting newtonian iteration from: \n\t$allParameters" }
 
         var eqvalues = getEqValues(par) //Values of the weight functions
 
@@ -193,48 +195,48 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
             logger?.log { "Starting step number $i" }
 
             val currentSolution = if (fast) {
-                //Берет значения матрицы в той точке, где считается вес
+                //Matrix values in the point of weight computation
-                newtonianStep(this, eqvalues)
+                newtonianStep(freeParameters, eqvalues)
             } else {
-                //Берет значения матрицы в точке par
+                //Matrix values in a current point
                 newtonianStep(par, eqvalues)
             }
             // здесь должен стоять учет границ параметров
             logger?.log { "Parameter values after step are: \n\t$currentSolution" }
 
-            eqvalues = getEqValues(currentSolution)
+            eqvalues = getEqValues(currentSolution.freeParameters)
-            val currentDis = DoubleL2Norm.norm(eqvalues)// невязка после шага
+            val currentDis = DoubleL2Norm.norm(eqvalues)// discrepancy after the step
 
             logger?.log { "The discrepancy after step is: $currentDis." }
 
             if (currentDis >= dis && i > 1) {
-                //дополнительно проверяем, чтобы был сделан хотя бы один шаг
+                //Check if one step is made
                 flag = true
                 logger?.log { "The discrepancy does not decrease. Stopping iteration." }
+            } else if (abs(dis - currentDis) <= tolerance) {
+                flag = true
+                par = currentSolution.freeParameters
+                logger?.log { "Relative discrepancy tolerance threshold is reached. Stopping iteration." }
             } else {
-                par = currentSolution
+                par = currentSolution.freeParameters
                 dis = currentDis
             }
             if (i >= maxSteps) {
                 flag = true
                 logger?.log { "Maximum number of iterations reached. Stopping iteration." }
             }
-            if (dis <= tolerance) {
-                flag = true
-                logger?.log { "Tolerance threshold is reached. Stopping iteration." }
-            }
         }
 
         return QoWeight(problem, par)
     }
 
-    private fun QoWeight.covariance(): Matrix<Double> {
+    private fun QoWeight.covariance(): NamedMatrix<Double> {
         val logger = problem.getFeature<OptimizationLog>()
 
         logger?.log {
             """
-            Starting errors estimation using quasioptimal weights method. The starting weight is:
+            Starting errors estimation using quasi-optimal weights method. The starting weight is:
-                ${problem.startPoint}
+                $allParameters
              """.trimIndent()
         }
 
@@ -248,19 +250,27 @@ public object QowOptimizer : Optimizer<Double, XYFit> {
 //                valid = false
 //            }
 //        }
-        return covar
+        logger?.log {
+            "Covariance matrix:" + "\n" + NamedMatrix.toStringWithSymbols(covar, this)
+        }
+        return covar.named(symbols)
     }
 
     override suspend fun optimize(problem: XYFit): XYFit {
         val qowRuns = problem.getFeature<QowRuns>()?.runs ?: 2
+        val iterations = problem.getFeature<OptimizationIterations>()?.maxIterations ?: 50
 
+        val freeParameters: Map<Symbol, Double> = problem.getFeature<OptimizationParameters>()?.let { op ->
+            problem.startPoint.filterKeys { it in op.symbols }
+        } ?: problem.startPoint
 
-        var qow = QoWeight(problem, problem.startPoint)
+        var qow = QoWeight(problem, freeParameters)
-        var res = qow.newtonianRun()
+        var res = qow.newtonianRun(maxSteps = iterations)
         repeat(qowRuns - 1) {
-            qow = QoWeight(problem, res.parameters)
+            qow = QoWeight(problem, res.freeParameters)
-            res = qow.newtonianRun()
+            res = qow.newtonianRun(maxSteps = iterations)
         }
-        return res.problem.withFeature(OptimizationResult(res.parameters))
+        val covariance = res.covariance()
+        return res.problem.withFeature(OptimizationResult(res.freeParameters), OptimizationCovariance(covariance))
     }
 }

kmath-optimization/src/commonMain/kotlin/space/kscience/kmath/optimization/XYFit.kt

@@ -152,7 +152,7 @@ public suspend fun <I : Any, A> XYColumnarData<Double, Double, Double>.fitWith(
  */
 public val XYFit.chiSquaredOrNull: Double?
     get() {
-        val result = resultPointOrNull ?: return null
+        val result = startPoint + (resultPointOrNull ?: return null)
 
         return data.indices.sumOf { index ->
 
@@ -164,4 +164,7 @@ public val XYFit.chiSquaredOrNull: Double?
 
             ((y - mu) / yErr).pow(2)
         }
-    }
+    }
+
+public val XYFit.dof: Int
+    get() = data.size - (getFeature<OptimizationParameters>()?.symbols?.size ?: startPoint.size)

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/chiSquaredExpression.kt

@@ -1,10 +1,13 @@
 /*
- * Copyright 2018-2022 KMath contributors.
+ * Copyright 2018-2023 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.expressions
+package space.kscience.kmath.stat
 
+import space.kscience.kmath.expressions.AutoDiffProcessor
+import space.kscience.kmath.expressions.DifferentiableExpression
+import space.kscience.kmath.expressions.ExpressionAlgebra
 import space.kscience.kmath.operations.ExtendedField
 import space.kscience.kmath.operations.asIterable
 import space.kscience.kmath.structures.Buffer