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Merge branch 'dev' into nd4j

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Alexander Nozik 2020-10-29 19:58:35 +03:00 committed by GitHub
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4 changed files with 48 additions and 39 deletions
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42
kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt
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@ -12,16 +12,22 @@ import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
*/
public class DerivativeStructureField(
public val order: Int,
private val bindings: Map<Symbol, Double>
bindings: Map<Symbol, Double>,
) : ExtendedField<DerivativeStructure>, ExpressionAlgebra<Double, DerivativeStructure> {
public override val zero: DerivativeStructure by lazy { DerivativeStructure(bindings.size, order) }
public override val one: DerivativeStructure by lazy { DerivativeStructure(bindings.size, order, 1.0) }
public val numberOfVariables: Int = bindings.size
public override val zero: DerivativeStructure by lazy { DerivativeStructure(numberOfVariables, order) }
public override val one: DerivativeStructure by lazy { DerivativeStructure(numberOfVariables, order, 1.0) }
/**
* A class that implements both [DerivativeStructure] and a [Symbol]
*/
public inner class DerivativeStructureSymbol(symbol: Symbol, value: Double) :
DerivativeStructure(bindings.size, order, bindings.keys.indexOf(symbol), value), Symbol {
public inner class DerivativeStructureSymbol(
size: Int,
index: Int,
symbol: Symbol,
value: Double,
) : DerivativeStructure(size, order, index, value), Symbol {
override val identity: String = symbol.identity
override fun toString(): String = identity
override fun equals(other: Any?): Boolean = this.identity == (other as? Symbol)?.identity
@ -31,27 +37,26 @@ public class DerivativeStructureField(
/**
* Identity-based symbol bindings map
*/
private val variables: Map<String, DerivativeStructureSymbol> = bindings.entries.associate { (key, value) ->
key.identity to DerivativeStructureSymbol(key, value)
}
private val variables: Map<String, DerivativeStructureSymbol> = bindings.entries.mapIndexed { index, (key, value) ->
key.identity to DerivativeStructureSymbol(numberOfVariables, index, key, value)
}.toMap()
override fun const(value: Double): DerivativeStructure = DerivativeStructure(bindings.size, order, value)
override fun const(value: Double): DerivativeStructure = DerivativeStructure(numberOfVariables, order, value)
public override fun bindOrNull(symbol: Symbol): DerivativeStructureSymbol? = variables[symbol.identity]
public fun bind(symbol: Symbol): DerivativeStructureSymbol = variables.getValue(symbol.identity)
//public fun Number.const(): DerivativeStructure = const(toDouble())
override fun symbol(value: String): DerivativeStructureSymbol = bind(StringSymbol(value))
public fun DerivativeStructure.derivative(parameter: Symbol, order: Int = 1): Double {
return derivative(mapOf(parameter to order))
public fun DerivativeStructure.derivative(symbols: List<Symbol>): Double {
require(symbols.size <= order) { "The order of derivative ${symbols.size} exceeds computed order $order" }
val ordersCount = symbols.map { it.identity }.groupBy { it }.mapValues { it.value.size }
return getPartialDerivative(*variables.keys.map { ordersCount[it] ?: 0 }.toIntArray())
}
public fun DerivativeStructure.derivative(orders: Map<Symbol, Int>): Double {
return getPartialDerivative(*bindings.keys.map { orders[it] ?: 0 }.toIntArray())
}
public fun DerivativeStructure.derivative(vararg symbols: Symbol): Double = derivative(symbols.toList())
public fun DerivativeStructure.derivative(vararg orders: Pair<Symbol, Int>): Double = derivative(mapOf(*orders))
public override fun add(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.add(b)
public override fun multiply(a: DerivativeStructure, k: Number): DerivativeStructure = when (k) {
@ -97,6 +102,7 @@ public class DerivativeStructureField(
}
}
/**
* A constructs that creates a derivative structure with required order on-demand
*/
@ -109,7 +115,7 @@ public class DerivativeStructureExpression(
/**
* Get the derivative expression with given orders
*/
public override fun derivativeOrNull(orders: Map<Symbol, Int>): Expression<Double> = Expression { arguments ->
with(DerivativeStructureField(orders.values.maxOrNull() ?: 0, arguments)) { function().derivative(orders) }
public override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double> = Expression { arguments ->
with(DerivativeStructureField(symbols.size, arguments)) { function().derivative(symbols) }
}
}

22
kmath-commons/src/test/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpressionTest.kt
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@ -5,14 +5,15 @@ import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertFails
internal inline fun <R> diff(
internal inline fun diff(
order: Int,
vararg parameters: Pair<Symbol, Double>,
block: DerivativeStructureField.() -> R,
): R {
block: DerivativeStructureField.() -> Unit,
): Unit {
contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
return DerivativeStructureField(order, mapOf(*parameters)).run(block)
DerivativeStructureField(order, mapOf(*parameters)).run(block)
}
internal class AutoDiffTest {
@ -21,13 +22,16 @@ internal class AutoDiffTest {
@Test
fun derivativeStructureFieldTest() {
val res: Double = diff(3, x to 1.0, y to 1.0) {
diff(2, x to 1.0, y to 1.0) {
val x = bind(x)//by binding()
val y = symbol("y")
val z = x * (-sin(x * y) + y)
z.derivative(x)
val z = x * (-sin(x * y) + y) + 2.0
println(z.derivative(x))
println(z.derivative(y,x))
assertEquals(z.derivative(x, y), z.derivative(y, x))
//check that improper order cause failure
assertFails { z.derivative(x,x,y) }
}
println(res)
}
@Test
@ -40,5 +44,7 @@ internal class AutoDiffTest {
assertEquals(10.0, f(x to 1.0, y to 2.0))
assertEquals(6.0, f.derivative(x)(x to 1.0, y to 2.0))
assertEquals(2.0, f.derivative(x, x)(x to 1.234, y to -2.0))
assertEquals(2.0, f.derivative(x, y)(x to 1.0, y to 2.0))
}
}

3
kmath-commons/src/test/kotlin/kscience/kmath/commons/optimization/OptimizeTest.kt
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@ -6,7 +6,6 @@ import kscience.kmath.stat.Distribution
import kscience.kmath.stat.Fitting
import kscience.kmath.stat.RandomGenerator
import kscience.kmath.stat.normal
import kscience.kmath.structures.asBuffer
import org.junit.jupiter.api.Test
import kotlin.math.pow
@ -53,7 +52,7 @@ internal class OptimizeTest {
it.pow(2) + it + 1 + chain.nextDouble()
}
val yErr = x.map { sigma }
val chi2 = Fitting.chiSquared(x.asBuffer(), y.asBuffer(), yErr.asBuffer()) { x ->
val chi2 = Fitting.chiSquared(x, y, yErr) { x ->
val cWithDefault = bindOrNull(c) ?: one
bind(a) * x.pow(2) + bind(b) * x + cWithDefault
}

18
kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/DifferentiableExpression.kt
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@ -4,19 +4,17 @@ package kscience.kmath.expressions
* An expression that provides derivatives
*/
public interface DifferentiableExpression<T> : Expression<T> {
public fun derivativeOrNull(orders: Map<Symbol, Int>): Expression<T>?
public fun derivativeOrNull(symbols: List<Symbol>): Expression<T>?
}
public fun <T> DifferentiableExpression<T>.derivative(orders: Map<Symbol, Int>): Expression<T> =
derivativeOrNull(orders) ?: error("Derivative with orders $orders not provided")
public fun <T> DifferentiableExpression<T>.derivative(symbols: List<Symbol>): Expression<T> =
derivativeOrNull(symbols) ?: error("Derivative by symbols $symbols not provided")
public fun <T> DifferentiableExpression<T>.derivative(vararg orders: Pair<Symbol, Int>): Expression<T> =
derivative(mapOf(*orders))
public fun <T> DifferentiableExpression<T>.derivative(symbol: Symbol): Expression<T> = derivative(symbol to 1)
public fun <T> DifferentiableExpression<T>.derivative(vararg symbols: Symbol): Expression<T> =
derivative(symbols.toList())
public fun <T> DifferentiableExpression<T>.derivative(name: String): Expression<T> =
derivative(StringSymbol(name) to 1)
derivative(StringSymbol(name))
/**
* A [DifferentiableExpression] that defines only first derivatives
@ -25,8 +23,8 @@ public abstract class FirstDerivativeExpression<T> : DifferentiableExpression<T>
public abstract fun derivativeOrNull(symbol: Symbol): Expression<T>?
public override fun derivativeOrNull(orders: Map<Symbol, Int>): Expression<T>? {
val dSymbol = orders.entries.singleOrNull { it.value == 1 }?.key ?: return null
public override fun derivativeOrNull(symbols: List<Symbol>): Expression<T>? {
val dSymbol = symbols.firstOrNull() ?: return null
return derivativeOrNull(dSymbol)
}
}