forked from kscience/kmath
Initial optimization implementation for CM
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@ -8,6 +8,9 @@
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- Automatic README generation for features (#139)
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- Native support for `memory`, `core` and `dimensions`
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- `kmath-ejml` to supply EJML SimpleMatrix wrapper.
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- A separate `Symbol` entity, which is used for global unbound symbol.
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- A `Symbol` indexing scope.
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- Basic optimization API for Commons-math.
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### Changed
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- Package changed from `scientifik` to `kscience.kmath`.
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@ -16,6 +19,7 @@
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- `Polynomial` secondary constructor made function.
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- Kotlin version: 1.3.72 -> 1.4.20-M1
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- `kmath-ast` doesn't depend on heavy `kotlin-reflect` library.
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- Full autodiff refactoring based on `Symbol`
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### Deprecated
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package kscience.kmath.commons.optimization
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import kscience.kmath.expressions.*
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import org.apache.commons.math3.optim.*
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import org.apache.commons.math3.optim.nonlinear.scalar.GoalType
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import org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
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import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction
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import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunctionGradient
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import org.apache.commons.math3.optim.nonlinear.scalar.gradient.NonLinearConjugateGradientOptimizer
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import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.NelderMeadSimplex
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import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
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public typealias ParameterSpacePoint = Map<Symbol, Double>
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public class OptimizationResult(public val point: ParameterSpacePoint, public val value: Double)
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public operator fun PointValuePair.component1(): DoubleArray = point
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public operator fun PointValuePair.component2(): Double = value
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public object Optimization {
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public const val DEFAULT_RELATIVE_TOLERANCE: Double = 1e-4
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public const val DEFAULT_ABSOLUTE_TOLERANCE: Double = 1e-4
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public const val DEFAULT_MAX_ITER: Int = 1000
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}
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private fun SymbolIndexer.objectiveFunction(expression: Expression<Double>) = ObjectiveFunction {
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val args = it.toMap()
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expression(args)
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}
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private fun SymbolIndexer.objectiveFunctionGradient(
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expression: DifferentiableExpression<Double>,
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) = ObjectiveFunctionGradient {
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val args = it.toMap()
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DoubleArray(symbols.size) { index ->
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expression.derivative(symbols[index])(args)
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}
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}
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private fun SymbolIndexer.initialGuess(point: ParameterSpacePoint) = InitialGuess(point.toArray())
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/**
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* Optimize expression without derivatives
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*/
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public fun Expression<Double>.optimize(
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startingPoint: ParameterSpacePoint,
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goalType: GoalType = GoalType.MAXIMIZE,
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vararg additionalArguments: OptimizationData,
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optimizerBuilder: () -> MultivariateOptimizer = {
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SimplexOptimizer(
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SimpleValueChecker(
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Optimization.DEFAULT_RELATIVE_TOLERANCE,
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Optimization.DEFAULT_ABSOLUTE_TOLERANCE,
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Optimization.DEFAULT_MAX_ITER
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)
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)
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},
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): OptimizationResult = withSymbols(startingPoint.keys) {
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val optimizer = optimizerBuilder()
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val objectiveFunction = objectiveFunction(this@optimize)
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val (point, value) = optimizer.optimize(
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objectiveFunction,
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initialGuess(startingPoint),
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goalType,
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MaxEval.unlimited(),
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NelderMeadSimplex(symbols.size, 1.0),
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*additionalArguments
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)
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OptimizationResult(point.toMap(), value)
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}
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/**
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* Optimize differentiable expression
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*/
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public fun DifferentiableExpression<Double>.optimize(
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startingPoint: ParameterSpacePoint,
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goalType: GoalType = GoalType.MAXIMIZE,
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vararg additionalArguments: OptimizationData,
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optimizerBuilder: () -> NonLinearConjugateGradientOptimizer = {
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NonLinearConjugateGradientOptimizer(
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NonLinearConjugateGradientOptimizer.Formula.FLETCHER_REEVES,
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SimpleValueChecker(
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Optimization.DEFAULT_RELATIVE_TOLERANCE,
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Optimization.DEFAULT_ABSOLUTE_TOLERANCE,
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Optimization.DEFAULT_MAX_ITER
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)
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)
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},
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): OptimizationResult = withSymbols(startingPoint.keys) {
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val optimizer = optimizerBuilder()
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val objectiveFunction = objectiveFunction(this@optimize)
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val objectiveGradient = objectiveFunctionGradient(this@optimize)
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val (point, value) = optimizer.optimize(
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objectiveFunction,
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objectiveGradient,
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initialGuess(startingPoint),
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goalType,
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MaxEval.unlimited(),
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*additionalArguments
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)
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OptimizationResult(point.toMap(), value)
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}
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@ -0,0 +1,37 @@
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package kscience.kmath.commons.optimization
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import kscience.kmath.commons.expressions.DerivativeStructureExpression
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import kscience.kmath.expressions.Expression
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import kscience.kmath.expressions.Symbol
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import kscience.kmath.expressions.symbol
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import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
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import org.junit.jupiter.api.Test
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internal class OptimizeTest {
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val x by symbol
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val y by symbol
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val normal = DerivativeStructureExpression {
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val x = bind(x)
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val y = bind(y)
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exp(-x.pow(2)/2) + exp(-y.pow(2)/2)
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}
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val startingPoint: Map<Symbol, Double> = mapOf(x to 1.0, y to 1.0)
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@Test
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fun testOptimization() {
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val result = normal.optimize(startingPoint)
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println(result.point)
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println(result.value)
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}
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@Test
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fun testSimplexOptimization() {
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val result = (normal as Expression<Double>).optimize(startingPoint){
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SimplexOptimizer(1e-4,1e-4)
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}
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println(result.point)
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println(result.value)
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}
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}
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@ -35,7 +35,7 @@ public fun interface Expression<T> {
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}
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/**
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* Invlode an expression without parameters
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* Invoke an expression without parameters
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*/
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public operator fun <T> Expression<T>.invoke(): T = invoke(emptyMap())
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//This method exists to avoid resolution ambiguity of vararg methods
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@ -0,0 +1,45 @@
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package kscience.kmath.expressions
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/**
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* An environment to easy transform indexed variables to symbols and back.
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*/
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public interface SymbolIndexer {
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public val symbols: List<Symbol>
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public fun indexOf(symbol: Symbol): Int = symbols.indexOf(symbol)
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public operator fun <T> List<T>.get(symbol: Symbol): T {
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require(size == symbols.size) { "The input list size for indexer should be ${symbols.size} but $size found" }
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return get(this@SymbolIndexer.indexOf(symbol))
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}
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public operator fun <T> Array<T>.get(symbol: Symbol): T {
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require(size == symbols.size) { "The input array size for indexer should be ${symbols.size} but $size found" }
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return get(this@SymbolIndexer.indexOf(symbol))
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}
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public operator fun DoubleArray.get(symbol: Symbol): Double {
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require(size == symbols.size) { "The input array size for indexer should be ${symbols.size} but $size found" }
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return get(this@SymbolIndexer.indexOf(symbol))
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}
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public fun DoubleArray.toMap(): Map<Symbol, Double> {
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require(size == symbols.size) { "The input array size for indexer should be ${symbols.size} but $size found" }
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return symbols.indices.associate { symbols[it] to get(it) }
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}
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public fun <T> Map<Symbol, T>.toList(): List<T> = symbols.map { getValue(it) }
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public fun Map<Symbol, Double>.toArray(): DoubleArray = DoubleArray(symbols.size) { getValue(symbols[it]) }
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}
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public inline class SimpleSymbolIndexer(override val symbols: List<Symbol>) : SymbolIndexer
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/**
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* Execute the block with symbol indexer based on given symbol order
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*/
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public inline fun <R> withSymbols(vararg symbols: Symbol, block: SymbolIndexer.() -> R): R =
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with(SimpleSymbolIndexer(symbols.toList()), block)
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public inline fun <R> withSymbols(symbols: Collection<Symbol>, block: SymbolIndexer.() -> R): R =
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with(SimpleSymbolIndexer(symbols.toList()), block)
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