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Symbol identity is always a string

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This commit is contained in:
Alexander Nozik 2020-10-21 11:38:28 +03:00
parent 6386f2b894
commit ae07652d9e
4 changed files with 73 additions and 81 deletions
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4
kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
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@ -25,13 +25,13 @@ public class DerivativeStructureField(
*/
public inner class DerivativeStructureSymbol(symbol: Symbol, value: Double) :
DerivativeStructure(bindings.size, order, bindings.keys.indexOf(symbol), value), Symbol {
override val identity: Any = symbol.identity
override val identity: String = symbol.identity
}
/**
* Identity-based symbol bindings map
*/
private val variables: Map<Any?, DerivativeStructureSymbol> = bindings.entries.associate { (key, value) ->
private val variables: Map<String, DerivativeStructureSymbol> = bindings.entries.associate { (key, value) ->
key.identity to DerivativeStructureSymbol(key, value)
}

2
kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/Expression.kt
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@ -12,7 +12,7 @@ public interface Symbol {
* Identity object for the symbol. Two symbols with the same identity are considered to be the same symbol.
* By default uses object identity
*/
public val identity: Any get() = this
public val identity: String
}
/**

140
kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt
View File

@ -12,20 +12,7 @@ import kotlin.contracts.contract
*/
/**
* A [Symbol] with bound value
*/
public interface BoundSymbol<out T> : Symbol {
public val value: T
}
/**
* Bind a [Symbol] to a [value] and produce [BoundSymbol]
*/
public fun <T> Symbol.bind(value: T): BoundSymbol<T> = object : BoundSymbol<T> {
override val identity = this@bind.identity
override val value: T = value
}
public open class AutoDiffValue<out T>(public val value: T)
/**
* Represents result of [withAutoDiff] call.
@ -36,10 +23,10 @@ public fun <T> Symbol.bind(value: T): BoundSymbol<T> = object : BoundSymbol<T> {
* @property context The field over [T].
*/
public class DerivationResult<T : Any>(
override val value: T,
private val derivativeValues: Map<Any, T>,
public val value: T,
private val derivativeValues: Map<String, T>,
public val context: Field<T>,
) : BoundSymbol<T> {
) {
/**
* Returns derivative of [variable] or returns [Ring.zero] in [context].
*/
@ -76,8 +63,8 @@ public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T
* @return the result of differentiation.
*/
public fun <T : Any, F : Field<T>> F.withAutoDiff(
bindings: Collection<BoundSymbol<T>>,
body: AutoDiffField<T, F>.() -> BoundSymbol<T>,
bindings: Map<Symbol, T>,
body: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
): DerivationResult<T> {
contract { callsInPlace(body, InvocationKind.EXACTLY_ONCE) }
@ -86,14 +73,14 @@ public fun <T : Any, F : Field<T>> F.withAutoDiff(
public fun <T : Any, F : Field<T>> F.withAutoDiff(
vararg bindings: Pair<Symbol, T>,
body: AutoDiffField<T, F>.() -> BoundSymbol<T>,
): DerivationResult<T> = withAutoDiff(bindings.map { it.first.bind(it.second) }, body)
body: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
): DerivationResult<T> = withAutoDiff(bindings.toMap(), body)
/**
* Represents field in context of which functions can be derived.
*/
public abstract class AutoDiffField<T : Any, F : Field<T>>
: Field<BoundSymbol<T>>, ExpressionAlgebra<T, BoundSymbol<T>> {
: Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>> {
public abstract val context: F
@ -101,7 +88,7 @@ public abstract class AutoDiffField<T : Any, F : Field<T>>
* A variable accessing inner state of derivatives.
* Use this value in inner builders to avoid creating additional derivative bindings.
*/
public abstract var BoundSymbol<T>.d: T
public abstract var AutoDiffValue<T>.d: T
/**
* Performs update of derivative after the rest of the formula in the back-pass.
@ -116,21 +103,21 @@ public abstract class AutoDiffField<T : Any, F : Field<T>>
*/
public abstract fun <R> derive(value: R, block: F.(R) -> Unit): R
public inline fun const(block: F.() -> T): BoundSymbol<T> = const(context.block())
public inline fun const(block: F.() -> T): AutoDiffValue<T> = const(context.block())
// Overloads for Double constants
override operator fun Number.plus(b: BoundSymbol<T>): BoundSymbol<T> =
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 BoundSymbol<T>.plus(b: Number): BoundSymbol<T> = b.plus(this)
override operator fun AutoDiffValue<T>.plus(b: Number): AutoDiffValue<T> = b.plus(this)
override operator fun Number.minus(b: BoundSymbol<T>): BoundSymbol<T> =
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 BoundSymbol<T>.minus(b: Number): BoundSymbol<T> =
override operator fun AutoDiffValue<T>.minus(b: Number): AutoDiffValue<T> =
derive(const { this@minus.value - one * b.toDouble() }) { z -> this@minus.d += z.d }
}
@ -139,14 +126,14 @@ public abstract class AutoDiffField<T : Any, F : Field<T>>
*/
private class AutoDiffContext<T : Any, F : Field<T>>(
override val context: F,
bindings: Collection<BoundSymbol<T>>,
bindings: Map<Symbol, T>,
) : AutoDiffField<T, F>() {
// 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<Any, T> = hashMapOf()
override val zero: BoundSymbol<T> get() = const(context.zero)
override val one: BoundSymbol<T> get() = const(context.one)
private val derivatives: MutableMap<AutoDiffValue<T>, T> = hashMapOf()
override val zero: AutoDiffValue<T> get() = const(context.zero)
override val one: AutoDiffValue<T> get() = const(context.one)
/**
* Differentiable variable with value and derivative of differentiation ([withAutoDiff]) result
@ -155,17 +142,23 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
* @param T the non-nullable type of value.
* @property value The value of this variable.
*/
private class AutoDiffVariableWithDeriv<T : Any>(override val value: T, var d: T) : BoundSymbol<T>
private class AutoDiffVariableWithDeriv<T : Any>(
override val identity: String,
value: T,
var d: T,
) : AutoDiffValue<T>(value), Symbol
private val bindings: Map<Any, BoundSymbol<T>> = bindings.associateBy { it.identity }
private val bindings: Map<String, AutoDiffVariableWithDeriv<T>> = bindings.entries.associate {
it.key.identity to AutoDiffVariableWithDeriv(it.key.identity, it.value, context.zero)
}
override fun bindOrNull(symbol: Symbol): BoundSymbol<T>? = bindings[symbol.identity]
override fun bindOrNull(symbol: Symbol): AutoDiffVariableWithDeriv<T>? = bindings[symbol.identity]
override fun const(value: T): BoundSymbol<T> = AutoDiffVariableWithDeriv(value, context.zero)
override fun const(value: T): AutoDiffValue<T> = AutoDiffValue(value)
override var BoundSymbol<T>.d: T
get() = (this as? AutoDiffVariableWithDeriv)?.d ?: derivatives[identity] ?: context.zero
set(value) = if (this is AutoDiffVariableWithDeriv) d = value else derivatives[identity] = value
override var AutoDiffValue<T>.d: T
get() = (this as? AutoDiffVariableWithDeriv)?.d ?: derivatives[this] ?: context.zero
set(value) = if (this is AutoDiffVariableWithDeriv) d = value else derivatives[this] = value
@Suppress("UNCHECKED_CAST")
override fun <R> derive(value: R, block: F.(R) -> Unit): R {
@ -187,34 +180,34 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
// Basic math (+, -, *, /)
override fun add(a: BoundSymbol<T>, b: BoundSymbol<T>): BoundSymbol<T> =
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: BoundSymbol<T>, b: BoundSymbol<T>): BoundSymbol<T> =
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: BoundSymbol<T>, b: BoundSymbol<T>): BoundSymbol<T> =
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: BoundSymbol<T>, k: Number): BoundSymbol<T> =
override fun multiply(a: AutoDiffValue<T>, k: Number): AutoDiffValue<T> =
derive(const { k.toDouble() * a.value }) { z ->
a.d += z.d * k.toDouble()
}
inline fun derivate(function: AutoDiffField<T, F>.() -> BoundSymbol<T>): DerivationResult<T> {
inline fun derivate(function: AutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T> {
val result = function()
result.d = context.one // computing derivative w.r.t result
runBackwardPass()
return DerivationResult(result.value, derivatives, context)
return DerivationResult(result.value, bindings.mapValues { it.value.d }, context)
}
}
@ -223,11 +216,11 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
*/
public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
public val field: F,
public val function: AutoDiffField<T, F>.() -> BoundSymbol<T>,
public val function: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
) : DifferentiableExpression<T> {
public override operator fun invoke(arguments: Map<Symbol, T>): T {
val bindings = arguments.entries.map { it.key.bind(it.value) }
return AutoDiffContext(field, bindings).function().value
//val bindings = arguments.entries.map { it.key.bind(it.value) }
return AutoDiffContext(field, arguments).function().value
}
/**
@ -237,8 +230,8 @@ public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
val dSymbol = orders.entries.singleOrNull { it.value == 1 }
?: error("SimpleAutoDiff supports only first order derivatives")
return Expression { arguments ->
val bindings = arguments.entries.map { it.key.bind(it.value) }
val derivationResult = AutoDiffContext(field, bindings).derivate(function)
//val bindings = arguments.entries.map { it.key.bind(it.value) }
val derivationResult = AutoDiffContext(field, arguments).derivate(function)
derivationResult.derivative(dSymbol.key)
}
}
@ -248,82 +241,81 @@ public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
// Extensions for differentiation of various basic mathematical functions
// x ^ 2
public fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { x.value * x.value }) { z -> x.d += z.d * 2 * x.value }
// x ^ 1/2
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { sqrt(x.value) }) { z -> x.d += z.d * 0.5 / z.value }
// x ^ y (const)
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(
x: BoundSymbol<T>,
x: AutoDiffValue<T>,
y: Double,
): BoundSymbol<T> =
): AutoDiffValue<T> =
derive(const { power(x.value, y) }) { z -> x.d += z.d * y * power(x.value, y - 1) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(
x: BoundSymbol<T>,
x: AutoDiffValue<T>,
y: Int,
): BoundSymbol<T> =
pow(x, y.toDouble())
): AutoDiffValue<T> = pow(x, y.toDouble())
// exp(x)
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { exp(x.value) }) { z -> x.d += z.d * z.value }
// ln(x)
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { ln(x.value) }) { z -> x.d += z.d / x.value }
// x ^ y (any)
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(
x: BoundSymbol<T>,
y: BoundSymbol<T>,
): BoundSymbol<T> =
x: AutoDiffValue<T>,
y: AutoDiffValue<T>,
): AutoDiffValue<T> =
exp(y * ln(x))
// sin(x)
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { sin(x.value) }) { z -> x.d += z.d * cos(x.value) }
// cos(x)
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { cos(x.value) }) { z -> x.d -= z.d * sin(x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tan(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tan(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { tan(x.value) }) { z ->
val c = cos(x.value)
x.d += z.d / (c * c)
}
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asin(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asin(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { asin(x.value) }) { z -> x.d += z.d / sqrt(one - x.value * x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acos(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acos(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { acos(x.value) }) { z -> x.d -= z.d / sqrt(one - x.value * x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atan(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atan(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { atan(x.value) }) { z -> x.d += z.d / (one + x.value * x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sinh(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { sin(x.value) }) { z -> x.d += z.d * cosh(x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cosh(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { cos(x.value) }) { z -> x.d += z.d * sinh(x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tanh(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { tan(x.value) }) { z ->
val c = cosh(x.value)
x.d += z.d / (c * c)
}
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asinh(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { asinh(x.value) }) { z -> x.d += z.d / sqrt(one + x.value * x.value) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acosh(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { acosh(x.value) }) { z -> x.d += z.d / (sqrt((x.value - one) * (x.value + one))) }
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atanh(x: BoundSymbol<T>): BoundSymbol<T> =
public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
derive(const { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) }

8
kmath-core/src/commonTest/kotlin/kscience/kmath/expressions/SimpleAutoDiffTest.kt
View File

@ -12,23 +12,23 @@ import kotlin.test.assertTrue
class SimpleAutoDiffTest {
fun d(
vararg bindings: Pair<Symbol, Double>,
body: AutoDiffField<Double, RealField>.() -> BoundSymbol<Double>,
body: AutoDiffField<Double, RealField>.() -> AutoDiffValue<Double>,
): DerivationResult<Double> = RealField.withAutoDiff(bindings = bindings, body)
fun dx(
xBinding: Pair<Symbol, Double>,
body: AutoDiffField<Double, RealField>.(x: BoundSymbol<Double>) -> BoundSymbol<Double>,
body: AutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
): DerivationResult<Double> = RealField.withAutoDiff(xBinding) { body(bind(xBinding.first)) }
fun dxy(
xBinding: Pair<Symbol, Double>,
yBinding: Pair<Symbol, Double>,
body: AutoDiffField<Double, RealField>.(x: BoundSymbol<Double>, y: BoundSymbol<Double>) -> BoundSymbol<Double>,
body: AutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>, y: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
): DerivationResult<Double> = RealField.withAutoDiff(xBinding, yBinding) {
body(bind(xBinding.first), bind(yBinding.first))
}
fun diff(block: AutoDiffField<Double, RealField>.() -> BoundSymbol<Double>): SimpleAutoDiffExpression<Double, RealField> {
fun diff(block: AutoDiffField<Double, RealField>.() -> AutoDiffValue<Double>): SimpleAutoDiffExpression<Double, RealField> {
return SimpleAutoDiffExpression(RealField, block)
}