kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt

@@ -12,46 +12,51 @@ 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 override val zero: DerivativeStructure by lazy { DerivativeStructure(bindings.size, 0) }
+    public override val one: DerivativeStructure by lazy { DerivativeStructure(bindings.size, 0, 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
         override fun hashCode(): Int = identity.hashCode()
     }
 
+    public val numberOfVariables: Int = bindings.size
+
     /**
      * 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, 0, 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) }
     }
 }

kmath-commons/src/test/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpressionTest.kt

@@ -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))
     }
 }

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/DifferentiableExpression.kt

@@ -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)
     }
 }

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/Expression.kt

@@ -87,7 +87,7 @@ public fun <T, E> ExpressionAlgebra<T, E>.bind(symbol: Symbol): E =
 /**
  * A delegate to create a symbol with a string identity in this scope
  */
-public val symbol: ReadOnlyProperty<Any?, StringSymbol> =    ReadOnlyProperty { thisRef, property ->
+public val symbol: ReadOnlyProperty<Any?, StringSymbol> =    ReadOnlyProperty { _, property ->
     StringSymbol(property.name)
 }