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Update DifferentiableExpression by providing second type argument representing the result of differentiation

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Iaroslav Postovalov 2020-10-30 16:57:19 +07:00
parent ef7066b8c9
commit d14e437659
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6 changed files with 57 additions and 60 deletions
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1
examples/src/main/kotlin/kscience/kmath/ast/KotlingradSupport.kt
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@ -3,7 +3,6 @@ package kscience.kmath.ast
import kscience.kmath.asm.compile
import kscience.kmath.expressions.invoke
import kscience.kmath.expressions.symbol
import kscience.kmath.kotlingrad.DifferentiableMstExpression
import kscience.kmath.kotlingrad.derivative
import kscience.kmath.kotlingrad.differentiable
import kscience.kmath.operations.RealField

10
kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
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@ -95,10 +95,10 @@ public class DerivativeStructureField(
public override operator fun Number.plus(b: DerivativeStructure): DerivativeStructure = b + this
public override operator fun Number.minus(b: DerivativeStructure): DerivativeStructure = b - this
public companion object : AutoDiffProcessor<Double, DerivativeStructure, DerivativeStructureField> {
override fun process(function: DerivativeStructureField.() -> DerivativeStructure): DifferentiableExpression<Double> {
return DerivativeStructureExpression(function)
}
public companion object :
AutoDiffProcessor<Double, DerivativeStructure, DerivativeStructureField, Expression<Double>> {
public override fun process(function: DerivativeStructureField.() -> DerivativeStructure): DifferentiableExpression<Double, Expression<Double>> =
DerivativeStructureExpression(function)
}
}
@ -108,7 +108,7 @@ public class DerivativeStructureField(
*/
public class DerivativeStructureExpression(
public val function: DerivativeStructureField.() -> DerivativeStructure,
) : DifferentiableExpression<Double> {
) : DifferentiableExpression<Double, Expression<Double>> {
public override operator fun invoke(arguments: Map<Symbol, Double>): Double =
DerivativeStructureField(0, arguments).function().value

32
kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/DifferentiableExpression.kt
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@ -1,29 +1,37 @@
package kscience.kmath.expressions
/**
* An expression that provides derivatives
* Represents expression which structure can be differentiated.
*
* @param T the type this expression takes as argument and returns.
* @param R the type of expression this expression can be differentiated to.
*/
public interface DifferentiableExpression<T> : Expression<T> {
public fun derivativeOrNull(symbols: List<Symbol>): Expression<T>?
public interface DifferentiableExpression<T, R : Expression<T>> : Expression<T> {
/**
* Differentiates this expression by ordered collection of [symbols].
*/
public fun derivativeOrNull(symbols: List<Symbol>): R?
}
public fun <T> DifferentiableExpression<T>.derivative(symbols: List<Symbol>): Expression<T> =
public fun <T, R : Expression<T>> DifferentiableExpression<T, R>.derivative(symbols: List<Symbol>): R =
derivativeOrNull(symbols) ?: error("Derivative by symbols $symbols not provided")
public fun <T> DifferentiableExpression<T>.derivative(vararg symbols: Symbol): Expression<T> =
public fun <T, R : Expression<T>> DifferentiableExpression<T, R>.derivative(vararg symbols: Symbol): R =
derivative(symbols.toList())
public fun <T> DifferentiableExpression<T>.derivative(name: String): Expression<T> =
public fun <T, R : Expression<T>> DifferentiableExpression<T, R>.derivative(name: String): R =
derivative(StringSymbol(name))
/**
* A [DifferentiableExpression] that defines only first derivatives
*/
public abstract class FirstDerivativeExpression<T> : DifferentiableExpression<T> {
public abstract class FirstDerivativeExpression<T, R : Expression<T>> : DifferentiableExpression<T,R> {
/**
* Returns first derivative of this expression by given [symbol].
*/
public abstract fun derivativeOrNull(symbol: Symbol): R?
public abstract fun derivativeOrNull(symbol: Symbol): Expression<T>?
public override fun derivativeOrNull(symbols: List<Symbol>): Expression<T>? {
public final override fun derivativeOrNull(symbols: List<Symbol>): R? {
val dSymbol = symbols.firstOrNull() ?: return null
return derivativeOrNull(dSymbol)
}
@ -32,6 +40,6 @@ public abstract class FirstDerivativeExpression<T> : DifferentiableExpression<T>
/**
* A factory that converts an expression in autodiff variables to a [DifferentiableExpression]
*/
public interface AutoDiffProcessor<T : Any, I : Any, A : ExpressionAlgebra<T, I>> {
public fun process(function: A.() -> I): DifferentiableExpression<T>
public fun interface AutoDiffProcessor<T : Any, I : Any, A : ExpressionAlgebra<T, I>, R : Expression<T>> {
public fun process(function: A.() -> I): DifferentiableExpression<T, R>
}

4
kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/Expression.kt
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@ -22,7 +22,9 @@ public inline class StringSymbol(override val identity: String) : Symbol {
}
/**
* An elementary function that could be invoked on a map of arguments
* An elementary function that could be invoked on a map of arguments.
*
* @param T the type this expression takes as argument and returns.
*/
public fun interface Expression<T> {
/**

54
kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt
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@ -68,7 +68,7 @@ public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
): DerivationResult<T> {
contract { callsInPlace(body, InvocationKind.EXACTLY_ONCE) }
return SimpleAutoDiffField(this, bindings).derivate(body)
return SimpleAutoDiffField(this, bindings).differentiate(body)
}
public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
@ -83,12 +83,21 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
public val context: F,
bindings: Map<Symbol, T>,
) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>> {
public override val zero: AutoDiffValue<T>
get() = const(context.zero)
public override val one: AutoDiffValue<T>
get() = const(context.one)
// this stack contains pairs of blocks and values to apply them to
private var stack: Array<Any?> = arrayOfNulls<Any?>(8)
private var sp: Int = 0
private val derivatives: MutableMap<AutoDiffValue<T>, T> = hashMapOf()
private val bindings: Map<String, AutoDiffVariableWithDerivative<T>> = bindings.entries.associate {
it.key.identity to AutoDiffVariableWithDerivative(it.key.identity, it.value, context.zero)
}
/**
* Differentiable variable with value and derivative of differentiation ([simpleAutoDiff]) result
* with respect to this variable.
@ -106,11 +115,7 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
override fun hashCode(): Int = identity.hashCode()
}
private val bindings: Map<String, AutoDiffVariableWithDerivative<T>> = bindings.entries.associate {
it.key.identity to AutoDiffVariableWithDerivative(it.key.identity, it.value, context.zero)
}
override fun bindOrNull(symbol: Symbol): AutoDiffValue<T>? = bindings[symbol.identity]
public override fun bindOrNull(symbol: Symbol): AutoDiffValue<T>? = bindings[symbol.identity]
private fun getDerivative(variable: AutoDiffValue<T>): T =
(variable as? AutoDiffVariableWithDerivative)?.d ?: derivatives[variable] ?: context.zero
@ -119,7 +124,6 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
if (variable is AutoDiffVariableWithDerivative) variable.d = value else derivatives[variable] = value
}
@Suppress("UNCHECKED_CAST")
private fun runBackwardPass() {
while (sp > 0) {
@ -129,9 +133,6 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
}
}
override val zero: AutoDiffValue<T> get() = const(context.zero)
override val one: AutoDiffValue<T> get() = const(context.one)
override fun const(value: T): AutoDiffValue<T> = AutoDiffValue(value)
/**
@ -165,7 +166,7 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
}
internal fun derivate(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T> {
internal fun differentiate(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T> {
val result = function()
result.d = context.one // computing derivative w.r.t result
runBackwardPass()
@ -174,41 +175,41 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
// Overloads for Double constants
override operator fun Number.plus(b: AutoDiffValue<T>): AutoDiffValue<T> =
public override operator fun Number.plus(b: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { this@plus.toDouble() * one + b.value }) { z ->
b.d += z.d
}
override operator fun AutoDiffValue<T>.plus(b: Number): AutoDiffValue<T> = b.plus(this)
public override operator fun AutoDiffValue<T>.plus(b: Number): AutoDiffValue<T> = b.plus(this)
override operator fun Number.minus(b: AutoDiffValue<T>): AutoDiffValue<T> =
public override operator fun Number.minus(b: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { this@minus.toDouble() * one - b.value }) { z -> b.d -= z.d }
override operator fun AutoDiffValue<T>.minus(b: Number): AutoDiffValue<T> =
public override operator fun AutoDiffValue<T>.minus(b: Number): AutoDiffValue<T> =
derive(const { this@minus.value - one * b.toDouble() }) { z -> this@minus.d += z.d }
// Basic math (+, -, *, /)
override fun add(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
public override fun add(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { a.value + b.value }) { z ->
a.d += z.d
b.d += z.d
}
override fun multiply(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
public override fun multiply(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { a.value * b.value }) { z ->
a.d += z.d * b.value
b.d += z.d * a.value
}
override fun divide(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
public override fun divide(a: AutoDiffValue<T>, b: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { a.value / b.value }) { z ->
a.d += z.d / b.value
b.d -= z.d * a.value / (b.value * b.value)
}
override fun multiply(a: AutoDiffValue<T>, k: Number): AutoDiffValue<T> =
public override fun multiply(a: AutoDiffValue<T>, k: Number): AutoDiffValue<T> =
derive(const { k.toDouble() * a.value }) { z ->
a.d += z.d * k.toDouble()
}
@ -220,15 +221,15 @@ public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
public val field: F,
public val function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
) : FirstDerivativeExpression<T>() {
) : FirstDerivativeExpression<T, Expression<T>>() {
public override operator fun invoke(arguments: Map<Symbol, T>): T {
//val bindings = arguments.entries.map { it.key.bind(it.value) }
return SimpleAutoDiffField(field, arguments).function().value
}
override fun derivativeOrNull(symbol: Symbol): Expression<T> = Expression { arguments ->
public override fun derivativeOrNull(symbol: Symbol): Expression<T> = Expression { arguments ->
//val bindings = arguments.entries.map { it.key.bind(it.value) }
val derivationResult = SimpleAutoDiffField(field, arguments).derivate(function)
val derivationResult = SimpleAutoDiffField(field, arguments).differentiate(function)
derivationResult.derivative(symbol)
}
}
@ -236,12 +237,9 @@ public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
/**
* Generate [AutoDiffProcessor] for [SimpleAutoDiffExpression]
*/
public fun <T : Any, F : Field<T>> simpleAutoDiff(field: F): AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>> {
return object : AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>> {
override fun process(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DifferentiableExpression<T> {
return SimpleAutoDiffExpression(field, function)
}
}
public fun <T : Any, F : Field<T>> simpleAutoDiff(field: F): AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>, Expression<T>> =
AutoDiffProcessor { function ->
SimpleAutoDiffExpression(field, function)
}
// Extensions for differentiation of various basic mathematical functions

12
kmath-kotlingrad/src/main/kotlin/kscience/kmath/kotlingrad/DifferentiableMstExpression.kt
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@ -5,7 +5,6 @@ import kscience.kmath.ast.MST
import kscience.kmath.ast.MstAlgebra
import kscience.kmath.ast.MstExpression
import kscience.kmath.expressions.DifferentiableExpression
import kscience.kmath.expressions.StringSymbol
import kscience.kmath.expressions.Symbol
import kscience.kmath.operations.NumericAlgebra
@ -20,7 +19,7 @@ import kscience.kmath.operations.NumericAlgebra
* @property expr the underlying [MstExpression].
*/
public inline class DifferentiableMstExpression<T, A>(public val expr: MstExpression<T, A>) :
DifferentiableExpression<T> where A : NumericAlgebra<T>, T : Number {
DifferentiableExpression<T, MstExpression<T, A>> where A : NumericAlgebra<T>, T : Number {
public constructor(algebra: A, mst: MST) : this(MstExpression(algebra, mst))
/**
@ -47,15 +46,6 @@ public inline class DifferentiableMstExpression<T, A>(public val expr: MstExpres
)
}
public fun <T : Number, A : NumericAlgebra<T>> DifferentiableMstExpression<T, A>.derivative(symbols: List<Symbol>): MstExpression<T, A> =
derivativeOrNull(symbols)
public fun <T : Number, A : NumericAlgebra<T>> DifferentiableMstExpression<T, A>.derivative(vararg symbols: Symbol): MstExpression<T, A> =
derivative(symbols.toList())
public fun <T : Number, A : NumericAlgebra<T>> DifferentiableMstExpression<T, A>.derivative(name: String): MstExpression<T, A> =
derivative(StringSymbol(name))
/**
* Wraps this [MstExpression] into [DifferentiableMstExpression].
*/