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[WIP] Optimization

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This commit is contained in:
Alexander Nozik 2021-05-24 17:02:12 +03:00
parent 3ec674c61b
commit 88e94a7fd9
15 changed files with 119 additions and 166 deletions
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1
examples/src/main/kotlin/space/kscience/kmath/commons/fit/fitWithAutoDiff.kt
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@ -8,7 +8,6 @@ package space.kscience.kmath.commons.fit
import kotlinx.html.br
import kotlinx.html.h3
import space.kscience.kmath.commons.optimization.chiSquared
import space.kscience.kmath.commons.optimization.minimize
import space.kscience.kmath.distributions.NormalDistribution
import space.kscience.kmath.expressions.symbol
import space.kscience.kmath.optimization.FunctionOptimization

103
kmath-commons/src/main/kotlin/space/kscience/kmath/commons/optimization/CMOptimization.kt
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@ -13,7 +13,6 @@ import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunctionGradient
import org.apache.commons.math3.optim.nonlinear.scalar.gradient.NonLinearConjugateGradientOptimizer
import space.kscience.kmath.expressions.derivative
import space.kscience.kmath.expressions.withSymbols
import space.kscience.kmath.misc.Symbol
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.optimization.*
import kotlin.reflect.KClass
@ -21,9 +20,15 @@ import kotlin.reflect.KClass
public operator fun PointValuePair.component1(): DoubleArray = point
public operator fun PointValuePair.component2(): Double = value
public class CMOptimizerFactory(public val optimizerBuilder: () -> MultivariateOptimizer) : OptimizationFeature
public class CMOptimizer(public val optimizerBuilder: () -> MultivariateOptimizer): OptimizationFeature{
override fun toString(): String = "CMOptimizer($optimizerBuilder)"
}
public class CMOptimizerData(public val data: List<OptimizationData>) : OptimizationFeature {
public constructor(vararg data: OptimizationData) : this(data.toList())
override fun toString(): String = "CMOptimizerData($data)"
}
@OptIn(UnstableKMathAPI::class)
@ -31,59 +36,69 @@ public class CMOptimization : Optimizer<FunctionOptimization<Double>> {
override suspend fun process(
problem: FunctionOptimization<Double>,
): FunctionOptimization<Double> = withSymbols(problem.parameters) {
val convergenceChecker: ConvergenceChecker<PointValuePair> = SimpleValueChecker(
DEFAULT_RELATIVE_TOLERANCE,
DEFAULT_ABSOLUTE_TOLERANCE,
DEFAULT_MAX_ITER
)
): FunctionOptimization<Double> {
val startPoint = problem.getFeature<OptimizationStartPoint<Double>>()?.point
?: error("Starting point not defined in $problem")
val cmOptimizer: MultivariateOptimizer = problem.getFeature<CMOptimizerFactory>()?.optimizerBuilder?.invoke()
?: NonLinearConjugateGradientOptimizer(
NonLinearConjugateGradientOptimizer.Formula.FLETCHER_REEVES,
convergenceChecker
val parameters = problem.getFeature<OptimizationParameters>()?.symbols
?: problem.getFeature<OptimizationStartPoint<Double>>()?.point?.keys
?:startPoint.keys
withSymbols(parameters) {
val convergenceChecker: ConvergenceChecker<PointValuePair> = SimpleValueChecker(
DEFAULT_RELATIVE_TOLERANCE,
DEFAULT_ABSOLUTE_TOLERANCE,
DEFAULT_MAX_ITER
)
val optimizationData: HashMap<KClass<out OptimizationData>, OptimizationData> = HashMap()
val cmOptimizer: MultivariateOptimizer = problem.getFeature<CMOptimizer>()?.optimizerBuilder?.invoke()
?: NonLinearConjugateGradientOptimizer(
NonLinearConjugateGradientOptimizer.Formula.FLETCHER_REEVES,
convergenceChecker
)
fun addOptimizationData(data: OptimizationData) {
optimizationData[data::class] = data
}
val optimizationData: HashMap<KClass<out OptimizationData>, OptimizationData> = HashMap()
addOptimizationData(MaxEval.unlimited())
addOptimizationData(InitialGuess(problem.initialGuess.toDoubleArray()))
fun exportOptimizationData(): List<OptimizationData> = optimizationData.values.toList()
val objectiveFunction = ObjectiveFunction {
val args = problem.initialGuess + it.toMap()
problem.expression(args)
}
addOptimizationData(objectiveFunction)
val gradientFunction = ObjectiveFunctionGradient {
val args = problem.initialGuess + it.toMap()
DoubleArray(symbols.size) { index ->
problem.expression.derivative(symbols[index])(args)
fun addOptimizationData(data: OptimizationData) {
optimizationData[data::class] = data
}
}
addOptimizationData(gradientFunction)
val logger = problem.getFeature<OptimizationLog>()
addOptimizationData(MaxEval.unlimited())
addOptimizationData(InitialGuess(startPoint.toDoubleArray()))
for (feature in problem.features) {
when (feature) {
is CMOptimizerData -> feature.data.forEach { addOptimizationData(it) }
is FunctionOptimizationTarget -> when(feature){
FunctionOptimizationTarget.MAXIMIZE -> addOptimizationData(GoalType.MAXIMIZE)
FunctionOptimizationTarget.MINIMIZE -> addOptimizationData(GoalType.MINIMIZE)
fun exportOptimizationData(): List<OptimizationData> = optimizationData.values.toList()
val objectiveFunction = ObjectiveFunction {
val args = startPoint + it.toMap()
problem.expression(args)
}
addOptimizationData(objectiveFunction)
val gradientFunction = ObjectiveFunctionGradient {
val args = startPoint + it.toMap()
DoubleArray(symbols.size) { index ->
problem.expression.derivative(symbols[index])(args)
}
else -> logger?.log { "The feature $feature is unused in optimization" }
}
}
addOptimizationData(gradientFunction)
val (point, value) = cmOptimizer.optimize(*optimizationData.values.toTypedArray())
return problem.withFeatures(FunctionOptimizationResult(point.toMap(), value))
val logger = problem.getFeature<OptimizationLog>()
for (feature in problem.features) {
when (feature) {
is CMOptimizerData -> feature.data.forEach { addOptimizationData(it) }
is FunctionOptimizationTarget -> when (feature) {
FunctionOptimizationTarget.MAXIMIZE -> addOptimizationData(GoalType.MAXIMIZE)
FunctionOptimizationTarget.MINIMIZE -> addOptimizationData(GoalType.MINIMIZE)
}
else -> logger?.log { "The feature $feature is unused in optimization" }
}
}
val (point, value) = cmOptimizer.optimize(*optimizationData.values.toTypedArray())
return problem.withFeatures(OptimizationResult(point.toMap()), OptimizationValue(value))
}
}
public companion object {

2
kmath-commons/src/main/kotlin/space/kscience/kmath/commons/optimization/cmFit.kt
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@ -9,7 +9,7 @@ import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
import space.kscience.kmath.commons.expressions.DerivativeStructureField
import space.kscience.kmath.expressions.DifferentiableExpression
import space.kscience.kmath.expressions.Expression
import space.kscience.kmath.misc.Symbol
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.optimization.*
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.asBuffer

6
kmath-core/src/commonMain/kotlin/space/kscience/kmath/data/XYErrorColumnarData.kt
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@ -5,10 +5,10 @@
package space.kscience.kmath.data
import space.kscience.kmath.misc.Symbol
import space.kscience.kmath.misc.Symbol.Companion.z
import space.kscience.kmath.data.XYErrorColumnarData.Companion
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.expressions.symbol
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.misc.symbol
import space.kscience.kmath.structures.Buffer

4
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt
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@ -51,7 +51,7 @@ public class GaussIntegrator<T : Any>(
}
}
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = with(algebra) {
override fun process(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = with(algebra) {
val f = integrand.function
val (points, weights) = buildRule(integrand)
var res = zero
@ -95,7 +95,7 @@ public fun <T : Any> GaussIntegrator<T>.integrate(
val ranges = UnivariateIntegrandRanges(
(0 until intervals).map { i -> (range.start + rangeSize * i)..(range.start + rangeSize * (i + 1)) to order }
)
return integrate(
return process(
UnivariateIntegrand(
function,
IntegrationRange(range),

10
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/Integrand.kt
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@ -5,18 +5,20 @@
package space.kscience.kmath.integration
import space.kscience.kmath.misc.FeatureSet
import space.kscience.kmath.misc.Featured
import kotlin.reflect.KClass
public interface IntegrandFeature {
override fun toString(): String
}
public interface Integrand {
public val features: Set<IntegrandFeature>
public fun <T : IntegrandFeature> getFeature(type: KClass<T>): T?
public interface Integrand : Featured<IntegrandFeature> {
public val features: FeatureSet<IntegrandFeature>
override fun <T : IntegrandFeature> getFeature(type: KClass<out T>): T? = features.getFeature(type)
}
public inline fun <reified T : IntegrandFeature> Integrand.getFeature(): T? = getFeature(T::class)
public inline fun <reified T: IntegrandFeature> Integrand.getFeature(): T? = getFeature(T::class)
public class IntegrandValue<T : Any>(public val value: T) : IntegrandFeature {
override fun toString(): String = "Value($value)"

16
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/MultivariateIntegrand.kt
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@ -6,29 +6,21 @@
package space.kscience.kmath.integration
import space.kscience.kmath.linear.Point
import kotlin.reflect.KClass
import space.kscience.kmath.misc.FeatureSet
public class MultivariateIntegrand<T : Any> internal constructor(
private val featureMap: Map<KClass<*>, IntegrandFeature>,
override val features: FeatureSet<IntegrandFeature>,
public val function: (Point<T>) -> T,
) : Integrand {
override val features: Set<IntegrandFeature> get() = featureMap.values.toSet()
@Suppress("UNCHECKED_CAST")
override fun <T : IntegrandFeature> getFeature(type: KClass<T>): T? = featureMap[type] as? T
public operator fun <F : IntegrandFeature> plus(pair: Pair<KClass<out F>, F>): MultivariateIntegrand<T> =
MultivariateIntegrand(featureMap + pair, function)
public operator fun <F : IntegrandFeature> plus(feature: F): MultivariateIntegrand<T> =
plus(feature::class to feature)
MultivariateIntegrand(features.with(feature), function)
}
@Suppress("FunctionName")
public fun <T : Any> MultivariateIntegrand(
vararg features: IntegrandFeature,
function: (Point<T>) -> T,
): MultivariateIntegrand<T> = MultivariateIntegrand(features.associateBy { it::class }, function)
): MultivariateIntegrand<T> = MultivariateIntegrand(FeatureSet.of(*features), function)
public val <T : Any> MultivariateIntegrand<T>.value: T? get() = getFeature<IntegrandValue<T>>()?.value

4
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SimpsonIntegrator.kt
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@ -43,7 +43,7 @@ public class SimpsonIntegrator<T : Any>(
return res
}
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> {
override fun process(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> {
val ranges = integrand.getFeature<UnivariateIntegrandRanges>()
return if (ranges != null) {
val res = algebra.sum(ranges.ranges.map { integrateRange(integrand, it.first, it.second) })
@ -89,7 +89,7 @@ public object DoubleSimpsonIntegrator : UnivariateIntegrator<Double> {
return res
}
override fun integrate(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
override fun process(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
val ranges = integrand.getFeature<UnivariateIntegrandRanges>()
return if (ranges != null) {
val res = ranges.ranges.sumOf { integrateRange(integrand, it.first, it.second) }

4
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt
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@ -53,7 +53,7 @@ public class SplineIntegrator<T : Comparable<T>>(
public val algebra: Field<T>,
public val bufferFactory: MutableBufferFactory<T>,
) : UnivariateIntegrator<T> {
override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = algebra {
override fun process(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = algebra {
val range = integrand.getFeature<IntegrationRange>()?.range ?: 0.0..1.0
val interpolator: PolynomialInterpolator<T> = SplineInterpolator(algebra, bufferFactory)
@ -80,7 +80,7 @@ public class SplineIntegrator<T : Comparable<T>>(
*/
@UnstableKMathAPI
public object DoubleSplineIntegrator : UnivariateIntegrator<Double> {
override fun integrate(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
override fun process(integrand: UnivariateIntegrand<Double>): UnivariateIntegrand<Double> {
val range = integrand.getFeature<IntegrationRange>()?.range ?: 0.0..1.0
val interpolator: PolynomialInterpolator<Double> = SplineInterpolator(DoubleField, ::DoubleBuffer)

23
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
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@ -5,33 +5,24 @@
package space.kscience.kmath.integration
import space.kscience.kmath.misc.FeatureSet
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.DoubleBuffer
import kotlin.reflect.KClass
public class UnivariateIntegrand<T> internal constructor(
private val featureMap: Map<KClass<*>, IntegrandFeature>,
override val features: FeatureSet<IntegrandFeature>,
public val function: (Double) -> T,
) : Integrand {
override val features: Set<IntegrandFeature> get() = featureMap.values.toSet()
@Suppress("UNCHECKED_CAST")
override fun <T : IntegrandFeature> getFeature(type: KClass<T>): T? = featureMap[type] as? T
public operator fun <F : IntegrandFeature> plus(pair: Pair<KClass<out F>, F>): UnivariateIntegrand<T> =
UnivariateIntegrand(featureMap + pair, function)
public operator fun <F : IntegrandFeature> plus(feature: F): UnivariateIntegrand<T> =
plus(feature::class to feature)
UnivariateIntegrand(features.with(feature), function)
}
@Suppress("FunctionName")
public fun <T : Any> UnivariateIntegrand(
function: (Double) -> T,
vararg features: IntegrandFeature,
): UnivariateIntegrand<T> = UnivariateIntegrand(features.associateBy { it::class }, function)
): UnivariateIntegrand<T> = UnivariateIntegrand(FeatureSet.of(*features), function)
public typealias UnivariateIntegrator<T> = Integrator<UnivariateIntegrand<T>>
@ -79,7 +70,7 @@ public val <T : Any> UnivariateIntegrand<T>.value: T get() = valueOrNull ?: erro
public fun <T : Any> UnivariateIntegrator<T>.integrate(
vararg features: IntegrandFeature,
function: (Double) -> T,
): UnivariateIntegrand<T> = integrate(UnivariateIntegrand(function, *features))
): UnivariateIntegrand<T> = process(UnivariateIntegrand(function, *features))
/**
* A shortcut method to integrate a [function] in [range] with additional [features].
@ -90,7 +81,7 @@ public fun <T : Any> UnivariateIntegrator<T>.integrate(
range: ClosedRange<Double>,
vararg features: IntegrandFeature,
function: (Double) -> T,
): UnivariateIntegrand<T> = integrate(UnivariateIntegrand(function, IntegrationRange(range), *features))
): UnivariateIntegrand<T> = process(UnivariateIntegrand(function, IntegrationRange(range), *features))
/**
* A shortcut method to integrate a [function] in [range] with additional [features].
@ -107,5 +98,5 @@ public fun <T : Any> UnivariateIntegrator<T>.integrate(
featureBuilder()
add(IntegrationRange(range))
}
return integrate(UnivariateIntegrand(function, *features.toTypedArray()))
return process(UnivariateIntegrand(function, *features.toTypedArray()))
}

10
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/FunctionOptimization.kt
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@ -10,12 +10,13 @@ import space.kscience.kmath.expressions.DifferentiableExpression
import space.kscience.kmath.expressions.Expression
import space.kscience.kmath.expressions.ExpressionAlgebra
import space.kscience.kmath.misc.FeatureSet
import space.kscience.kmath.misc.Symbol
import space.kscience.kmath.operations.ExtendedField
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.indices
public class FunctionOptimizationResult<T>(point: Map<Symbol, T>, public val value: T) : OptimizationResult<T>(point)
public class OptimizationValue<T>(public val value: T) : OptimizationFeature{
override fun toString(): String = "Value($value)"
}
public enum class FunctionOptimizationTarget : OptimizationFeature {
MAXIMIZE,
@ -25,9 +26,8 @@ public enum class FunctionOptimizationTarget : OptimizationFeature {
public class FunctionOptimization<T>(
override val features: FeatureSet<OptimizationFeature>,
public val expression: DifferentiableExpression<T, Expression<T>>,
public val initialGuess: Map<Symbol, T>,
public val parameters: Collection<Symbol>,
) : OptimizationProblem{
public companion object{
/**
* Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic differentiation
@ -65,7 +65,5 @@ public fun <T> FunctionOptimization<T>.withFeatures(
): FunctionOptimization<T> = FunctionOptimization(
features.with(*newFeature),
expression,
initialGuess,
parameters
)

43
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/OptimizationProblem.kt
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@ -5,13 +5,15 @@
package space.kscience.kmath.optimization
import space.kscience.kmath.expressions.Symbol
import space.kscience.kmath.misc.FeatureSet
import space.kscience.kmath.misc.Featured
import space.kscience.kmath.misc.Loggable
import space.kscience.kmath.misc.Symbol
import kotlin.reflect.KClass
public interface OptimizationFeature
public interface OptimizationFeature {
override fun toString(): String
}
public interface OptimizationProblem : Featured<OptimizationFeature> {
public val features: FeatureSet<OptimizationFeature>
@ -20,31 +22,22 @@ public interface OptimizationProblem : Featured<OptimizationFeature> {
public inline fun <reified T : OptimizationFeature> OptimizationProblem.getFeature(): T? = getFeature(T::class)
public open class OptimizationResult<T>(public val point: Map<Symbol, T>) : OptimizationFeature
public open class OptimizationStartPoint<T>(public val point: Map<Symbol, T>) : OptimizationFeature {
override fun toString(): String = "StartPoint($point)"
}
public class OptimizationLog(private val loggable: Loggable) : Loggable by loggable, OptimizationFeature
public open class OptimizationResult<T>(public val point: Map<Symbol, T>) : OptimizationFeature {
override fun toString(): String = "Result($point)"
}
public class OptimizationLog(private val loggable: Loggable) : Loggable by loggable, OptimizationFeature {
override fun toString(): String = "Log($loggable)"
}
public class OptimizationParameters(public val symbols: List<Symbol>): OptimizationFeature{
override fun toString(): String = "Parameters($symbols)"
}
//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)
//public fun 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)
public interface Optimizer<P : OptimizationProblem> {
public suspend fun process(problem: P): P

21
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/XYFit.kt
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@ -10,8 +10,6 @@ import space.kscience.kmath.expressions.*
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.ExtendedField
import space.kscience.kmath.operations.Field
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.indices
@UnstableKMathAPI
public interface XYFit<T> : OptimizationProblem {
@ -59,15 +57,16 @@ public interface XYFit<T> : OptimizationProblem {
//}
/**
* Optimize differentiable expression using specific [OptimizationProblemFactory]
* Optimize differentiable expression using specific [Optimizer]
*/
public suspend fun <T : Any, F : FunctionOptimization<T>> DifferentiableExpression<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.function(this)
return problem.optimize()
optimizer: Optimizer<F>,
startingPoint: Map<Symbol,T>,
vararg features: OptimizationFeature
): OptimizationProblem {
// require(startingPoint.isNotEmpty()) { "Must provide a list of symbols for optimization" }
// val problem = factory(symbols.toList(), configuration)
// problem.function(this)
// return problem.optimize()
val problem = FunctionOptimization<T>()
}

32
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/minuit/Range.kt
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@ -1,32 +0,0 @@
/*
* Copyright 2015 Alexander Nozik.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package ru.inr.mass.minuit
/**
* A class representing a pair of double (x,y) or (lower,upper)
*
* @version $Id$
* @author Darksnake
*/
class Range
/**
*
* Constructor for Range.
*
* @param k a double.
* @param v a double.
*/
(k: Double, v: Double) : Pair<Double?, Double?>(k, v)

6
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/optimization/qow/QowFit.kt
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@ -7,12 +7,8 @@ package space.kscience.kmath.optimization.qow
import space.kscience.kmath.data.ColumnarData
import space.kscience.kmath.data.XYErrorColumnarData
import space.kscience.kmath.expressions.DifferentiableExpression
import space.kscience.kmath.expressions.Expression
import space.kscience.kmath.expressions.SymbolIndexer
import space.kscience.kmath.expressions.derivative
import space.kscience.kmath.expressions.*
import space.kscience.kmath.linear.*
import space.kscience.kmath.misc.Symbol
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.Field