kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AutoDiff.kt

@@ -1,5 +1,7 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.linear.Point
+import scientifik.kmath.structures.asBuffer
 import kotlin.math.pow
 import kotlin.math.sqrt
 
@@ -12,12 +14,26 @@ import kotlin.math.sqrt
  * Differentiable variable with value and derivative of differentiation ([deriv]) result
  * with respect to this variable.
  */
-open class Variable(val x: Double) {
+open class Variable(val value: Double) {
     constructor(x: Number) : this(x.toDouble())
 }
 
-class DerivationResult(x: Double, val deriv: Map<Variable, Double>): Variable(x) {
+class DerivationResult(value: Double, val deriv: Map<Variable, Double>) : Variable(value) {
     fun deriv(variable: Variable) = deriv[variable] ?: 0.0
+
+    /**
+     * compute divergence
+     */
+    fun div() = deriv.values.sum()
+
+    /**
+     * Compute a gradient for variables in given order
+     */
+    fun grad(vararg variables: Variable): Point<Double> = if (variables.isEmpty()) {
+        error("Variable order is not provided for gradient construction")
+    } else {
+        variables.map(::deriv).toDoubleArray().asBuffer()
+    }
 }
 
 /**
@@ -38,7 +54,7 @@ fun deriv(body: AutoDiffField.() -> Variable): DerivationResult =
         val result = body()
         result.d = 1.0 // computing derivative w.r.t result
         runBackwardPass()
-        DerivationResult(result.x, derivatives)
+        DerivationResult(result.value, derivatives)
     }
 
 
@@ -61,19 +77,21 @@ abstract class AutoDiffField : Field<Variable> {
      */
     abstract var Variable.d: Double
 
+    abstract fun variable(value: Double): Variable
+
     // Overloads for Double constants
 
-    operator fun Number.plus(that: Variable): Variable = derive(Variable(this.toDouble() + that.x)) { z ->
+    operator fun Number.plus(that: Variable): Variable = derive(variable(this.toDouble() + that.value)) { z ->
         that.d += z.d
     }
 
     operator fun Variable.plus(b: Number): Variable = b.plus(this)
 
-    operator fun Number.minus(that: Variable): Variable = derive(Variable(this.toDouble() - that.x)) { z ->
+    operator fun Number.minus(that: Variable): Variable = derive(variable(this.toDouble() - that.value)) { z ->
         that.d -= z.d
     }
 
-    operator fun Variable.minus(that: Number): Variable = derive(Variable(this.x - that.toDouble())) { z ->
+    operator fun Variable.minus(that: Number): Variable = derive(variable(this.value - that.toDouble())) { z ->
         this.d += z.d
     }
 }
@@ -89,10 +107,22 @@ private class AutoDiffContext : AutoDiffField() {
 
     internal val derivatives = HashMap<Variable, Double>()
 
+
+    /**
+     * A variable coupled with its derivative. For internal use only
+     */
+    class VariableWithDeriv(x: Double, var d: Double = 0.0): Variable(x)
+
+    override fun variable(value: Double): Variable  = VariableWithDeriv(value)
+
     override var Variable.d: Double
-        get() = derivatives[this] ?: 0.0
+        get() = (this as? VariableWithDeriv)?.d ?: derivatives[this] ?: 0.0
         set(value) {
-            derivatives[this] = value
+            if(this is VariableWithDeriv){
+                d = value
+            }else {
+                derivatives[this] = value
+            }
         }
 
     @Suppress("UNCHECKED_CAST")
@@ -117,25 +147,25 @@ private class AutoDiffContext : AutoDiffField() {
 
 
     override fun add(a: Variable, b: Variable): Variable =
-        derive(Variable(a.x + b.x)) { z ->
+        derive(variable(a.value + b.value)) { z ->
             a.d += z.d
             b.d += z.d
         }
 
     override fun multiply(a: Variable, b: Variable): Variable =
-        derive(Variable(a.x * b.x)) { z ->
+        derive(variable(a.value * b.value)) { z ->
-            a.d += z.d * b.x
+            a.d += z.d * b.value
-            b.d += z.d * a.x
+            b.d += z.d * a.value
         }
 
     override fun divide(a: Variable, b: Variable): Variable =
-        derive(Variable(a.x / b.x)) { z ->
+        derive(Variable(a.value / b.value)) { z ->
-            a.d += z.d / b.x
+            a.d += z.d / b.value
-            b.d -= z.d * a.x / (b.x * b.x)
+            b.d -= z.d * a.value / (b.value * b.value)
         }
 
     override fun multiply(a: Variable, k: Number): Variable =
-        derive(Variable(k.toDouble() * a.x)) { z ->
+        derive(variable(k.toDouble() * a.value)) { z ->
             a.d += z.d * k.toDouble()
         }
 
@@ -146,41 +176,41 @@ private class AutoDiffContext : AutoDiffField() {
 // Extensions for differentiation of various basic mathematical functions
 
 // x ^ 2
-fun AutoDiffField.sqr(x: Variable): Variable = derive(Variable(x.x * x.x)) { z ->
+fun AutoDiffField.sqr(x: Variable): Variable = derive(variable(x.value * x.value)) { z ->
-    x.d += z.d * 2 * x.x
+    x.d += z.d * 2 * x.value
 }
 
 // x ^ 1/2
-fun AutoDiffField.sqrt(x: Variable): Variable = derive(Variable(sqrt(x.x))) { z ->
+fun AutoDiffField.sqrt(x: Variable): Variable = derive(variable(sqrt(x.value))) { z ->
-    x.d += z.d * 0.5 / z.x
+    x.d += z.d * 0.5 / z.value
 }
 
 // x ^ y (const)
-fun AutoDiffField.pow(x: Variable, y: Double): Variable = derive(Variable(x.x.pow(y))) { z ->
+fun AutoDiffField.pow(x: Variable, y: Double): Variable = derive(variable(x.value.pow(y))) { z ->
-    x.d += z.d * y * x.x.pow(y - 1)
+    x.d += z.d * y * x.value.pow(y - 1)
 }
 
 fun AutoDiffField.pow(x: Variable, y: Int): Variable = pow(x, y.toDouble())
 
 // exp(x)
-fun AutoDiffField.exp(x: Variable): Variable = derive(Variable(kotlin.math.exp(x.x))) { z ->
+fun AutoDiffField.exp(x: Variable): Variable = derive(variable(kotlin.math.exp(x.value))) { z ->
-    x.d += z.d * z.x
+    x.d += z.d * z.value
 }
 
 // ln(x)
-fun AutoDiffField.ln(x: Variable): Variable = derive(Variable(kotlin.math.ln(x.x))) { z ->
+fun AutoDiffField.ln(x: Variable): Variable = derive(Variable(kotlin.math.ln(x.value))) { z ->
-    x.d += z.d / x.x
+    x.d += z.d / x.value
 }
 
 // x ^ y (any)
 fun AutoDiffField.pow(x: Variable, y: Variable): Variable = exp(y * ln(x))
 
 // sin(x)
-fun AutoDiffField.sin(x: Variable): Variable = derive(Variable(kotlin.math.sin(x.x))) { z ->
+fun AutoDiffField.sin(x: Variable): Variable = derive(variable(kotlin.math.sin(x.value))) { z ->
-    x.d += z.d * kotlin.math.cos(x.x)
+    x.d += z.d * kotlin.math.cos(x.value)
 }
 
 // cos(x)
-fun AutoDiffField.cos(x: Variable): Variable = derive(Variable(kotlin.math.cos(x.x))) { z ->
+fun AutoDiffField.cos(x: Variable): Variable = derive(variable(kotlin.math.cos(x.value))) { z ->
-    x.d -= z.d * kotlin.math.sin(x.x)
+    x.d -= z.d * kotlin.math.sin(x.value)
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt

@@ -37,6 +37,11 @@ interface Buffer<T> {
 
     companion object {
 
+        inline fun real(size: Int, initializer: (Int) -> Double): DoubleBuffer {
+            val array = DoubleArray(size) { initializer(it) }
+            return DoubleBuffer(array)
+        }
+
         /**
          * Create a boxing buffer of given type
          */

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/AutoDiffTest.kt

@@ -1,15 +1,17 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.structures.asBuffer
 import kotlin.math.PI
 import kotlin.test.Test
 import kotlin.test.assertEquals
+import kotlin.test.assertTrue
 
 class AutoDiffTest {
     @Test
     fun testPlusX2() {
         val x = Variable(3) // diff w.r.t this x at 3
         val y = deriv { x + x }
-        assertEquals(6.0, y.x) //    y  = x + x = 6
+        assertEquals(6.0, y.value) //    y  = x + x = 6
         assertEquals(2.0, y.deriv(x)) // dy/dx = 2
     }
 
@@ -19,7 +21,7 @@ class AutoDiffTest {
         val x = Variable(2)
         val y = Variable(3)
         val z = deriv { x + y }
-        assertEquals(5.0, z.x) //    z  = x + y = 5
+        assertEquals(5.0, z.value) //    z  = x + y = 5
         assertEquals(1.0, z.deriv(x)) // dz/dx = 1
         assertEquals(1.0, z.deriv(y)) // dz/dy = 1
     }
@@ -30,7 +32,7 @@ class AutoDiffTest {
         val x = Variable(7)
         val y = Variable(3)
         val z = deriv { x - y }
-        assertEquals(4.0, z.x)  //    z  = x - y = 4
+        assertEquals(4.0, z.value)  //    z  = x - y = 4
         assertEquals(1.0, z.deriv(x))  // dz/dx = 1
         assertEquals(-1.0, z.deriv(y)) // dz/dy = -1
     }
@@ -39,7 +41,7 @@ class AutoDiffTest {
     fun testMulX2() {
         val x = Variable(3) // diff w.r.t this x at 3
         val y = deriv { x * x }
-        assertEquals(9.0, y.x) //    y  = x * x = 9
+        assertEquals(9.0, y.value) //    y  = x * x = 9
         assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
     }
 
@@ -47,7 +49,7 @@ class AutoDiffTest {
     fun testSqr() {
         val x = Variable(3)
         val y = deriv { sqr(x) }
-        assertEquals(9.0, y.x) //    y  = x ^ 2 = 9
+        assertEquals(9.0, y.value) //    y  = x ^ 2 = 9
         assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
     }
 
@@ -55,7 +57,7 @@ class AutoDiffTest {
     fun testSqrSqr() {
         val x = Variable(2)
         val y = deriv { sqr(sqr(x)) }
-        assertEquals(16.0, y.x) //     y = x ^ 4   = 16
+        assertEquals(16.0, y.value) //     y = x ^ 4   = 16
         assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32
     }
 
@@ -63,7 +65,7 @@ class AutoDiffTest {
     fun testX3() {
         val x = Variable(2) // diff w.r.t this x at 2
         val y = deriv { x * x * x }
-        assertEquals(8.0, y.x)  //    y  = x * x * x = 8
+        assertEquals(8.0, y.value)  //    y  = x * x * x = 8
         assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12
     }
 
@@ -72,7 +74,7 @@ class AutoDiffTest {
         val x = Variable(5)
         val y = Variable(2)
         val z = deriv { x / y }
-        assertEquals(2.5, z.x)   //     z =  x / y   = 2.5
+        assertEquals(2.5, z.value)   //     z =  x / y   = 2.5
         assertEquals(0.5, z.deriv(x))   // dz/dx =  1 / y   = 0.5
         assertEquals(-1.25, z.deriv(y)) // dz/dy = -x / y^2 = -1.25
     }
@@ -81,7 +83,7 @@ class AutoDiffTest {
     fun testPow3() {
         val x = Variable(2) // diff w.r.t this x at 2
         val y = deriv { pow(x, 3) }
-        assertEquals(8.0, y.x)  //    y  = x ^ 3     = 8
+        assertEquals(8.0, y.value)  //    y  = x ^ 3     = 8
         assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12
     }
 
@@ -90,7 +92,7 @@ class AutoDiffTest {
         val x = Variable(2)
         val y = Variable(3)
         val z = deriv { pow(x, y) }
-        assertApprox(8.0, z.x)           //     z = x ^ y = 8
+        assertApprox(8.0, z.value)           //     z = x ^ y = 8
         assertApprox(12.0, z.deriv(x))          // dz/dx = y * x ^ (y - 1) = 12
         assertApprox(8.0 * kotlin.math.ln(2.0), z.deriv(y)) // dz/dy = x ^ y * ln(x)
     }
@@ -99,7 +101,7 @@ class AutoDiffTest {
     fun testFromPaper() {
         val x = Variable(3)
         val y = deriv { 2 * x + x * x * x }
-        assertEquals(33.0, y.x)  //     y = 2 * x + x * x * x = 33
+        assertEquals(33.0, y.value)  //     y = 2 * x + x * x * x = 33
         assertEquals(29.0, y.deriv(x))  // dy/dx = 2 + 3 * x * x = 29
     }
 
@@ -109,7 +111,7 @@ class AutoDiffTest {
         val y = deriv {
             Variable(1) * x
         }
-        assertEquals(1.0, y.x)          //     y = x ^ n = 1
+        assertEquals(1.0, y.value)          //     y = x ^ n = 1
         assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
     }
 
@@ -122,7 +124,7 @@ class AutoDiffTest {
             for (i in 1..n) res *= x
             res
         }
-        assertEquals(1.0, y.x)          //     y = x ^ n = 1
+        assertEquals(1.0, y.value)          //     y = x ^ n = 1
         assertEquals(n.toDouble(), y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
     }
 
@@ -130,7 +132,7 @@ class AutoDiffTest {
     fun testExample() {
         val x = Variable(2)
         val y = deriv { sqr(x) + 5 * x + 3 }
-        assertEquals(17.0, y.x) // the value of result (y)
+        assertEquals(17.0, y.value) // the value of result (y)
         assertEquals(9.0, y.deriv(x))  // dy/dx
     }
 
@@ -138,7 +140,7 @@ class AutoDiffTest {
     fun testSqrt() {
         val x = Variable(16)
         val y = deriv { sqrt(x) }
-        assertEquals(4.0, y.x)     //     y = x ^ 1/2 = 4
+        assertEquals(4.0, y.value)     //     y = x ^ 1/2 = 4
         assertEquals(1.0 / 8, y.deriv(x)) // dy/dx = 1/2 / x ^ 1/4 = 1/8
     }
 
@@ -146,7 +148,7 @@ class AutoDiffTest {
     fun testSin() {
         val x = Variable(PI / 6)
         val y = deriv { sin(x) }
-        assertApprox(0.5, y.x)           //    y = sin(PI/6) = 0.5
+        assertApprox(0.5, y.value)           //    y = sin(PI/6) = 0.5
         assertApprox(kotlin.math.sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(PI/6) = sqrt(3)/2
     }
 
@@ -154,10 +156,19 @@ class AutoDiffTest {
     fun testCos() {
         val x = Variable(PI / 6)
         val y = deriv { cos(x) }
-        assertApprox(kotlin.math.sqrt(3.0) / 2, y.x) //     y =  cos(PI/6) = sqrt(3)/2
+        assertApprox(kotlin.math.sqrt(3.0) / 2, y.value) //     y =  cos(PI/6) = sqrt(3)/2
         assertApprox(-0.5, y.deriv(x))          // dy/dx = -sin(PI/6) = -0.5
     }
 
+    @Test
+    fun testDivGrad() {
+        val x = Variable(1.0)
+        val y = Variable(2.0)
+        val res = deriv { x * x + y * y }
+        assertEquals(6.0, res.div())
+        assertTrue(res.grad(x, y).contentEquals(doubleArrayOf(2.0, 4.0).asBuffer()))
+    }
+
     private fun assertApprox(a: Double, b: Double) {
         if ((a - b) > 1e-10) assertEquals(a, b)
     }