Safe modification of autodiff
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@ -1,5 +1,7 @@
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package scientifik.kmath.operations
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import scientifik.kmath.linear.Point
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import scientifik.kmath.structures.asBuffer
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import kotlin.math.pow
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import kotlin.math.sqrt
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@ -12,12 +14,26 @@ import kotlin.math.sqrt
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* Differentiable variable with value and derivative of differentiation ([deriv]) result
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* with respect to this variable.
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*/
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open class Variable(val x: Double) {
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open class Variable(val value: Double) {
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constructor(x: Number) : this(x.toDouble())
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}
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class DerivationResult(x: Double, val deriv: Map<Variable, Double>): Variable(x) {
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class DerivationResult(value: Double, val deriv: Map<Variable, Double>) : Variable(value) {
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fun deriv(variable: Variable) = deriv[variable] ?: 0.0
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/**
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* compute divergence
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*/
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fun div() = deriv.values.sum()
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/**
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* Compute a gradient for variables in given order
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*/
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fun grad(vararg variables: Variable): Point<Double> = if (variables.isEmpty()) {
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error("Variable order is not provided for gradient construction")
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} else {
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variables.map(::deriv).toDoubleArray().asBuffer()
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}
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}
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/**
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@ -38,7 +54,7 @@ fun deriv(body: AutoDiffField.() -> Variable): DerivationResult =
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val result = body()
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result.d = 1.0 // computing derivative w.r.t result
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runBackwardPass()
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DerivationResult(result.x, derivatives)
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DerivationResult(result.value, derivatives)
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}
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@ -61,19 +77,21 @@ abstract class AutoDiffField : Field<Variable> {
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*/
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abstract var Variable.d: Double
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abstract fun variable(value: Double): Variable
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// Overloads for Double constants
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operator fun Number.plus(that: Variable): Variable = derive(Variable(this.toDouble() + that.x)) { z ->
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operator fun Number.plus(that: Variable): Variable = derive(variable(this.toDouble() + that.value)) { z ->
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that.d += z.d
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}
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operator fun Variable.plus(b: Number): Variable = b.plus(this)
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operator fun Number.minus(that: Variable): Variable = derive(Variable(this.toDouble() - that.x)) { z ->
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operator fun Number.minus(that: Variable): Variable = derive(variable(this.toDouble() - that.value)) { z ->
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that.d -= z.d
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}
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operator fun Variable.minus(that: Number): Variable = derive(Variable(this.x - that.toDouble())) { z ->
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operator fun Variable.minus(that: Number): Variable = derive(variable(this.value - that.toDouble())) { z ->
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this.d += z.d
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}
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}
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@ -89,11 +107,23 @@ private class AutoDiffContext : AutoDiffField() {
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internal val derivatives = HashMap<Variable, Double>()
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/**
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* A variable coupled with its derivative. For internal use only
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*/
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class VariableWithDeriv(x: Double, var d: Double = 0.0): Variable(x)
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override fun variable(value: Double): Variable = VariableWithDeriv(value)
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override var Variable.d: Double
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get() = derivatives[this] ?: 0.0
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get() = (this as? VariableWithDeriv)?.d ?: derivatives[this] ?: 0.0
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set(value) {
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if(this is VariableWithDeriv){
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d = value
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}else {
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derivatives[this] = value
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}
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}
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@Suppress("UNCHECKED_CAST")
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override fun <R> derive(value: R, block: (R) -> Unit): R {
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@ -117,25 +147,25 @@ private class AutoDiffContext : AutoDiffField() {
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override fun add(a: Variable, b: Variable): Variable =
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derive(Variable(a.x + b.x)) { z ->
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derive(variable(a.value + b.value)) { z ->
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a.d += z.d
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b.d += z.d
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}
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override fun multiply(a: Variable, b: Variable): Variable =
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derive(Variable(a.x * b.x)) { z ->
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a.d += z.d * b.x
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b.d += z.d * a.x
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derive(variable(a.value * b.value)) { z ->
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a.d += z.d * b.value
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b.d += z.d * a.value
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}
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override fun divide(a: Variable, b: Variable): Variable =
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derive(Variable(a.x / b.x)) { z ->
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a.d += z.d / b.x
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b.d -= z.d * a.x / (b.x * b.x)
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derive(Variable(a.value / b.value)) { z ->
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a.d += z.d / b.value
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b.d -= z.d * a.value / (b.value * b.value)
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}
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override fun multiply(a: Variable, k: Number): Variable =
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derive(Variable(k.toDouble() * a.x)) { z ->
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derive(variable(k.toDouble() * a.value)) { z ->
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a.d += z.d * k.toDouble()
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}
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@ -146,41 +176,41 @@ private class AutoDiffContext : AutoDiffField() {
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// Extensions for differentiation of various basic mathematical functions
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// x ^ 2
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fun AutoDiffField.sqr(x: Variable): Variable = derive(Variable(x.x * x.x)) { z ->
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x.d += z.d * 2 * x.x
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fun AutoDiffField.sqr(x: Variable): Variable = derive(variable(x.value * x.value)) { z ->
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x.d += z.d * 2 * x.value
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}
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// x ^ 1/2
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fun AutoDiffField.sqrt(x: Variable): Variable = derive(Variable(sqrt(x.x))) { z ->
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x.d += z.d * 0.5 / z.x
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fun AutoDiffField.sqrt(x: Variable): Variable = derive(variable(sqrt(x.value))) { z ->
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x.d += z.d * 0.5 / z.value
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}
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// x ^ y (const)
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fun AutoDiffField.pow(x: Variable, y: Double): Variable = derive(Variable(x.x.pow(y))) { z ->
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x.d += z.d * y * x.x.pow(y - 1)
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fun AutoDiffField.pow(x: Variable, y: Double): Variable = derive(variable(x.value.pow(y))) { z ->
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x.d += z.d * y * x.value.pow(y - 1)
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}
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fun AutoDiffField.pow(x: Variable, y: Int): Variable = pow(x, y.toDouble())
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// exp(x)
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fun AutoDiffField.exp(x: Variable): Variable = derive(Variable(kotlin.math.exp(x.x))) { z ->
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x.d += z.d * z.x
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fun AutoDiffField.exp(x: Variable): Variable = derive(variable(kotlin.math.exp(x.value))) { z ->
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x.d += z.d * z.value
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}
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// ln(x)
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fun AutoDiffField.ln(x: Variable): Variable = derive(Variable(kotlin.math.ln(x.x))) { z ->
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x.d += z.d / x.x
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fun AutoDiffField.ln(x: Variable): Variable = derive(Variable(kotlin.math.ln(x.value))) { z ->
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x.d += z.d / x.value
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}
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// x ^ y (any)
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fun AutoDiffField.pow(x: Variable, y: Variable): Variable = exp(y * ln(x))
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// sin(x)
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fun AutoDiffField.sin(x: Variable): Variable = derive(Variable(kotlin.math.sin(x.x))) { z ->
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x.d += z.d * kotlin.math.cos(x.x)
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fun AutoDiffField.sin(x: Variable): Variable = derive(variable(kotlin.math.sin(x.value))) { z ->
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x.d += z.d * kotlin.math.cos(x.value)
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}
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// cos(x)
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fun AutoDiffField.cos(x: Variable): Variable = derive(Variable(kotlin.math.cos(x.x))) { z ->
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x.d -= z.d * kotlin.math.sin(x.x)
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fun AutoDiffField.cos(x: Variable): Variable = derive(variable(kotlin.math.cos(x.value))) { z ->
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x.d -= z.d * kotlin.math.sin(x.value)
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}
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@ -37,6 +37,11 @@ interface Buffer<T> {
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companion object {
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inline fun real(size: Int, initializer: (Int) -> Double): DoubleBuffer {
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val array = DoubleArray(size) { initializer(it) }
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return DoubleBuffer(array)
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}
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/**
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* Create a boxing buffer of given type
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*/
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@ -1,15 +1,17 @@
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package scientifik.kmath.operations
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import scientifik.kmath.structures.asBuffer
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import kotlin.math.PI
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertTrue
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class AutoDiffTest {
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@Test
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fun testPlusX2() {
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val x = Variable(3) // diff w.r.t this x at 3
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val y = deriv { x + x }
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assertEquals(6.0, y.x) // y = x + x = 6
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assertEquals(6.0, y.value) // y = x + x = 6
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assertEquals(2.0, y.deriv(x)) // dy/dx = 2
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}
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@ -19,7 +21,7 @@ class AutoDiffTest {
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val x = Variable(2)
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val y = Variable(3)
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val z = deriv { x + y }
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assertEquals(5.0, z.x) // z = x + y = 5
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assertEquals(5.0, z.value) // z = x + y = 5
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assertEquals(1.0, z.deriv(x)) // dz/dx = 1
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assertEquals(1.0, z.deriv(y)) // dz/dy = 1
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}
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@ -30,7 +32,7 @@ class AutoDiffTest {
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val x = Variable(7)
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val y = Variable(3)
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val z = deriv { x - y }
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assertEquals(4.0, z.x) // z = x - y = 4
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assertEquals(4.0, z.value) // z = x - y = 4
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assertEquals(1.0, z.deriv(x)) // dz/dx = 1
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assertEquals(-1.0, z.deriv(y)) // dz/dy = -1
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}
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@ -39,7 +41,7 @@ class AutoDiffTest {
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fun testMulX2() {
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val x = Variable(3) // diff w.r.t this x at 3
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val y = deriv { x * x }
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assertEquals(9.0, y.x) // y = x * x = 9
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assertEquals(9.0, y.value) // y = x * x = 9
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assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
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}
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@ -47,7 +49,7 @@ class AutoDiffTest {
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fun testSqr() {
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val x = Variable(3)
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val y = deriv { sqr(x) }
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assertEquals(9.0, y.x) // y = x ^ 2 = 9
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assertEquals(9.0, y.value) // y = x ^ 2 = 9
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assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
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}
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@ -55,7 +57,7 @@ class AutoDiffTest {
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fun testSqrSqr() {
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val x = Variable(2)
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val y = deriv { sqr(sqr(x)) }
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assertEquals(16.0, y.x) // y = x ^ 4 = 16
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assertEquals(16.0, y.value) // y = x ^ 4 = 16
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assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32
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}
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@ -63,7 +65,7 @@ class AutoDiffTest {
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fun testX3() {
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val x = Variable(2) // diff w.r.t this x at 2
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val y = deriv { x * x * x }
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assertEquals(8.0, y.x) // y = x * x * x = 8
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assertEquals(8.0, y.value) // y = x * x * x = 8
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assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12
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}
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@ -72,7 +74,7 @@ class AutoDiffTest {
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val x = Variable(5)
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val y = Variable(2)
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val z = deriv { x / y }
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assertEquals(2.5, z.x) // z = x / y = 2.5
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assertEquals(2.5, z.value) // z = x / y = 2.5
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assertEquals(0.5, z.deriv(x)) // dz/dx = 1 / y = 0.5
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assertEquals(-1.25, z.deriv(y)) // dz/dy = -x / y^2 = -1.25
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}
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@ -81,7 +83,7 @@ class AutoDiffTest {
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fun testPow3() {
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val x = Variable(2) // diff w.r.t this x at 2
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val y = deriv { pow(x, 3) }
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assertEquals(8.0, y.x) // y = x ^ 3 = 8
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assertEquals(8.0, y.value) // y = x ^ 3 = 8
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assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12
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}
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@ -90,7 +92,7 @@ class AutoDiffTest {
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val x = Variable(2)
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val y = Variable(3)
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val z = deriv { pow(x, y) }
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assertApprox(8.0, z.x) // z = x ^ y = 8
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assertApprox(8.0, z.value) // z = x ^ y = 8
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assertApprox(12.0, z.deriv(x)) // dz/dx = y * x ^ (y - 1) = 12
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assertApprox(8.0 * kotlin.math.ln(2.0), z.deriv(y)) // dz/dy = x ^ y * ln(x)
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}
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@ -99,7 +101,7 @@ class AutoDiffTest {
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fun testFromPaper() {
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val x = Variable(3)
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val y = deriv { 2 * x + x * x * x }
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assertEquals(33.0, y.x) // y = 2 * x + x * x * x = 33
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assertEquals(33.0, y.value) // y = 2 * x + x * x * x = 33
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assertEquals(29.0, y.deriv(x)) // dy/dx = 2 + 3 * x * x = 29
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}
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@ -109,7 +111,7 @@ class AutoDiffTest {
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val y = deriv {
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Variable(1) * x
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}
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assertEquals(1.0, y.x) // y = x ^ n = 1
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assertEquals(1.0, y.value) // y = x ^ n = 1
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assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
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}
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@ -122,7 +124,7 @@ class AutoDiffTest {
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for (i in 1..n) res *= x
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res
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}
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assertEquals(1.0, y.x) // y = x ^ n = 1
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assertEquals(1.0, y.value) // y = x ^ n = 1
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assertEquals(n.toDouble(), y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
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}
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@ -130,7 +132,7 @@ class AutoDiffTest {
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fun testExample() {
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val x = Variable(2)
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val y = deriv { sqr(x) + 5 * x + 3 }
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assertEquals(17.0, y.x) // the value of result (y)
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assertEquals(17.0, y.value) // the value of result (y)
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assertEquals(9.0, y.deriv(x)) // dy/dx
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}
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@ -138,7 +140,7 @@ class AutoDiffTest {
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fun testSqrt() {
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val x = Variable(16)
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val y = deriv { sqrt(x) }
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assertEquals(4.0, y.x) // y = x ^ 1/2 = 4
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assertEquals(4.0, y.value) // y = x ^ 1/2 = 4
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assertEquals(1.0 / 8, y.deriv(x)) // dy/dx = 1/2 / x ^ 1/4 = 1/8
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}
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@ -146,7 +148,7 @@ class AutoDiffTest {
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fun testSin() {
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val x = Variable(PI / 6)
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val y = deriv { sin(x) }
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assertApprox(0.5, y.x) // y = sin(PI/6) = 0.5
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assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5
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assertApprox(kotlin.math.sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(PI/6) = sqrt(3)/2
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}
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@ -154,10 +156,19 @@ class AutoDiffTest {
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fun testCos() {
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val x = Variable(PI / 6)
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val y = deriv { cos(x) }
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assertApprox(kotlin.math.sqrt(3.0) / 2, y.x) // y = cos(PI/6) = sqrt(3)/2
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assertApprox(kotlin.math.sqrt(3.0) / 2, y.value) // y = cos(PI/6) = sqrt(3)/2
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assertApprox(-0.5, y.deriv(x)) // dy/dx = -sin(PI/6) = -0.5
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}
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@Test
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fun testDivGrad() {
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val x = Variable(1.0)
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val y = Variable(2.0)
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val res = deriv { x * x + y * y }
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assertEquals(6.0, res.div())
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assertTrue(res.grad(x, y).contentEquals(doubleArrayOf(2.0, 4.0).asBuffer()))
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}
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private fun assertApprox(a: Double, b: Double) {
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if ((a - b) > 1e-10) assertEquals(a, b)
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}
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