Merge branch 'dev' into nd4j

# Conflicts:
#	CHANGELOG.md
#	settings.gradle.kts

.space.kts

@@ -1 +1,3 @@
-job("Build") { gradlew("openjdk:11", "build") }
+job("Build") {
+    gradlew("openjdk:11", "build")
+}

CHANGELOG.md

@@ -7,16 +7,23 @@
 - Better trigonometric and hyperbolic functions for `AutoDiffField` (https://github.com/mipt-npm/kmath/pull/140).
 - Automatic README generation for features (#139)
 - Native support for `memory`, `core` and `dimensions`
-- ND4J support module submitting `NDStructure` and `NDAlgebra` over `INDArray`.
 - `kmath-ejml` to supply EJML SimpleMatrix wrapper (https://github.com/mipt-npm/kmath/pull/136).
+- A separate `Symbol` entity, which is used for global unbound symbol.
+- A `Symbol` indexing scope.
+- Basic optimization API for Commons-math.
+- Chi squared optimization for array-like data in CM
+- `Fitting` utility object in prob/stat
+- ND4J support module submitting `NDStructure` and `NDAlgebra` over `INDArray`.
 
 ### Changed
 - Package changed from `scientifik` to `kscience.kmath`.
-- Gradle version: 6.6 -> 6.6.1
+- Gradle version: 6.6 -> 6.7
 - Minor exceptions refactor (throwing `IllegalArgumentException` by argument checks instead of `IllegalStateException`)
 - `Polynomial` secondary constructor made function.
 - Kotlin version: 1.3.72 -> 1.4.20-M1
 - `kmath-ast` doesn't depend on heavy `kotlin-reflect` library.
+- Full autodiff refactoring based on `Symbol`
+- `kmath-prob` renamed to `kmath-stat`
 
 ### Deprecated
 

README.md

@@ -54,8 +54,6 @@ can be used for a wide variety of purposes from high performance calculations to
                            library in Kotlin code and maybe rewrite some parts to better suit the Kotlin programming paradigm, however there is no fixed roadmap for that. Feel free
                            to submit a feature request if you want something to be done first.
                            
-* **EJML wrapper** Provides EJML `SimpleMatrix` wrapper consistent with the core matrix structures.
-
 ## Planned features
 
 * **Messaging** A mathematical notation to support multi-language and multi-node communication for mathematical tasks.
@@ -101,7 +99,7 @@ can be used for a wide variety of purposes from high performance calculations to
 > - [buffers](kmath-core/src/commonMain/kotlin/kscience/kmath/structures/Buffers.kt) : One-dimensional structure
 > - [expressions](kmath-core/src/commonMain/kotlin/kscience/kmath/expressions) : Functional Expressions
 > - [domains](kmath-core/src/commonMain/kotlin/kscience/kmath/domains) : Domains
-> - [autodif](kmath-core/src/commonMain/kotlin/kscience/kmath/misc/AutoDiff.kt) : Automatic differentiation
+> - [autodif](kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt) : Automatic differentiation
 
 <hr/>
 
@@ -117,6 +115,12 @@ can be used for a wide variety of purposes from high performance calculations to
 > **Maturity**: EXPERIMENTAL
 <hr/>
 
+* ### [kmath-ejml](kmath-ejml)
+> 
+>
+> **Maturity**: EXPERIMENTAL
+<hr/>
+
 * ### [kmath-for-real](kmath-for-real)
 > 
 >
@@ -147,7 +151,7 @@ can be used for a wide variety of purposes from high performance calculations to
 > **Maturity**: EXPERIMENTAL
 <hr/>
 
-* ### [kmath-prob](kmath-prob)
+* ### [kmath-stat](kmath-stat)
 > 
 >
 > **Maturity**: EXPERIMENTAL
@@ -178,8 +182,8 @@ repositories{
 }
 
 dependencies{
-    api("kscience.kmath:kmath-core:0.2.0-dev-1")
+    api("kscience.kmath:kmath-core:0.2.0-dev-2")
-    //api("kscience.kmath:kmath-core-jvm:0.2.0-dev-1") for jvm-specific version
+    //api("kscience.kmath:kmath-core-jvm:0.2.0-dev-2") for jvm-specific version
 }
 ```
 
@@ -197,4 +201,4 @@ with the same artifact names.
 
 ## Contributing
 
-The project requires a lot of additional work. Please feel free to contribute in any way and propose new features.
+The project requires a lot of additional work. The most important thing we need is a feedback about what features are required the most. Feel free to open feature issues with requests. We are also welcome to code contributions, especially in issues marked as [waiting for a hero](https://github.com/mipt-npm/kmath/labels/waiting%20for%20a%20hero).

build.gradle.kts

@@ -2,7 +2,7 @@ plugins {
     id("ru.mipt.npm.project")
 }
 
-val kmathVersion: String by extra("0.2.0-dev-2")
+val kmathVersion: String by extra("0.2.0-dev-3")
 val bintrayRepo: String by extra("kscience")
 val githubProject: String by extra("kmath")
 
@@ -26,3 +26,7 @@ subprojects {
 readme {
     readmeTemplate = file("docs/templates/README-TEMPLATE.md")
 }
+
+apiValidation{
+    validationDisabled = true
+}

docs/templates/README-TEMPLATE.md

@@ -107,4 +107,4 @@ with the same artifact names.
 
 ## Contributing
 
-The project requires a lot of additional work. Please feel free to contribute in any way and propose new features.
+The project requires a lot of additional work. The most important thing we need is a feedback about what features are required the most. Feel free to open feature issues with requests. We are also welcome to code contributions, especially in issues marked as [waiting for a hero](https://github.com/mipt-npm/kmath/labels/waiting%20for%20a%20hero).

examples/build.gradle.kts

@@ -23,7 +23,7 @@ dependencies {
     implementation(project(":kmath-core"))
     implementation(project(":kmath-coroutines"))
     implementation(project(":kmath-commons"))
-    implementation(project(":kmath-prob"))
+    implementation(project(":kmath-stat"))
     implementation(project(":kmath-viktor"))
     implementation(project(":kmath-dimensions"))
     implementation(project(":kmath-ejml"))

examples/src/main/kotlin/kscience/kmath/commons/prob/DistributionBenchmark.kt

@@ -4,7 +4,7 @@ import kotlinx.coroutines.Dispatchers
 import kotlinx.coroutines.async
 import kotlinx.coroutines.runBlocking
 import kscience.kmath.chains.BlockingRealChain
-import kscience.kmath.prob.*
+import kscience.kmath.stat.*
 import org.apache.commons.rng.sampling.distribution.ZigguratNormalizedGaussianSampler
 import org.apache.commons.rng.simple.RandomSource
 import java.time.Duration

examples/src/main/kotlin/kscience/kmath/commons/prob/DistributionDemo.kt

@@ -3,9 +3,9 @@ package kscience.kmath.commons.prob
 import kotlinx.coroutines.runBlocking
 import kscience.kmath.chains.Chain
 import kscience.kmath.chains.collectWithState
-import kscience.kmath.prob.Distribution
+import kscience.kmath.stat.Distribution
-import kscience.kmath.prob.RandomGenerator
+import kscience.kmath.stat.RandomGenerator
-import kscience.kmath.prob.normal
+import kscience.kmath.stat.normal
 
 private data class AveragingChainState(var num: Int = 0, var value: Double = 0.0)
 

examples/src/main/kotlin/kscience/kmath/operations/ComplexDemo.kt

@@ -6,8 +6,8 @@ import kscience.kmath.structures.complex
 
 fun main() {
     // 2d element
-    val element = NDElement.complex(2, 2) { index: IntArray ->
+    val element = NDElement.complex(2, 2) { (i,j) ->
-        Complex(index[0].toDouble() - index[1].toDouble(), index[0].toDouble() + index[1].toDouble())
+        Complex(i.toDouble() - j.toDouble(), i.toDouble() + j.toDouble())
     }
     println(element)
 

gradle/wrapper/gradle-wrapper.properties

@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-6.6.1-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-6.7-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists

kmath-ast/build.gradle.kts

@@ -11,9 +11,9 @@ kotlin.sourceSets {
 
     jvmMain {
         dependencies {
+            api("com.github.h0tk3y.betterParse:better-parse:0.4.0")
             implementation("org.ow2.asm:asm:8.0.1")
             implementation("org.ow2.asm:asm-commons:8.0.1")
-            implementation("com.github.h0tk3y.betterParse:better-parse:0.4.0")
         }
     }
 }

kmath-ast/src/commonMain/kotlin/kscience/kmath/ast/MstExpression.kt

@@ -14,8 +14,8 @@ import kotlin.contracts.contract
  * @author Alexander Nozik
  */
 public class MstExpression<T>(public val algebra: Algebra<T>, public val mst: MST) : Expression<T> {
-    private inner class InnerAlgebra(val arguments: Map<String, T>) : NumericAlgebra<T> {
+    private inner class InnerAlgebra(val arguments: Map<Symbol, T>) : NumericAlgebra<T> {
-        override fun symbol(value: String): T = arguments[value] ?: algebra.symbol(value)
+        override fun symbol(value: String): T = arguments[StringSymbol(value)] ?: algebra.symbol(value)
         override fun unaryOperation(operation: String, arg: T): T = algebra.unaryOperation(operation, arg)
 
         override fun binaryOperation(operation: String, left: T, right: T): T =
@@ -27,7 +27,7 @@ public class MstExpression<T>(public val algebra: Algebra<T>, public val mst: MS
             error("Numeric nodes are not supported by $this")
     }
 
-    override operator fun invoke(arguments: Map<String, T>): T = InnerAlgebra(arguments).evaluate(mst)
+    override operator fun invoke(arguments: Map<Symbol, T>): T = InnerAlgebra(arguments).evaluate(mst)
 }
 
 /**
@@ -37,7 +37,7 @@ public class MstExpression<T>(public val algebra: Algebra<T>, public val mst: MS
  */
 public inline fun <reified T : Any, A : Algebra<T>, E : Algebra<MST>> A.mst(
     mstAlgebra: E,
-    block: E.() -> MST
+    block: E.() -> MST,
 ): MstExpression<T> = MstExpression(this, mstAlgebra.block())
 
 /**
@@ -116,7 +116,7 @@ public inline fun <reified T : Any, A : Field<T>> FunctionalExpressionField<T, A
  * @author Iaroslav Postovalov
  */
 public inline fun <reified T : Any, A : ExtendedField<T>> FunctionalExpressionExtendedField<T, A>.mstInExtendedField(
-    block: MstExtendedField.() -> MST
+    block: MstExtendedField.() -> MST,
 ): MstExpression<T> {
     contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
     return algebra.mstInExtendedField(block)

kmath-ast/src/jvmMain/kotlin/kscience/kmath/asm/internal/AsmBuilder.kt

@@ -25,7 +25,7 @@ internal class AsmBuilder<T> internal constructor(
     private val classOfT: Class<*>,
     private val algebra: Algebra<T>,
     private val className: String,
-    private val invokeLabel0Visitor: AsmBuilder<T>.() -> Unit
+    private val invokeLabel0Visitor: AsmBuilder<T>.() -> Unit,
 ) {
     /**
      * Internal classloader of [AsmBuilder] with alias to define class from byte array.
@@ -379,22 +379,14 @@ internal class AsmBuilder<T> internal constructor(
      * Loads a variable [name] from arguments [Map] parameter of [Expression.invoke]. The [defaultValue] may be
      * provided.
      */
-    internal fun loadVariable(name: String, defaultValue: T? = null): Unit = invokeMethodVisitor.run {
+    internal fun loadVariable(name: String): Unit = invokeMethodVisitor.run {
         load(invokeArgumentsVar, MAP_TYPE)
         aconst(name)
 
-        if (defaultValue != null)
-            loadTConstant(defaultValue)
-
         invokestatic(
             MAP_INTRINSICS_TYPE.internalName,
             "getOrFail",
-
+            Type.getMethodDescriptor(OBJECT_TYPE, MAP_TYPE, STRING_TYPE),
-            Type.getMethodDescriptor(
-                OBJECT_TYPE,
-                MAP_TYPE,
-                OBJECT_TYPE,
-                *OBJECT_TYPE.wrapToArrayIf { defaultValue != null }),
             false
         )
 
@@ -429,7 +421,7 @@ internal class AsmBuilder<T> internal constructor(
         method: String,
         descriptor: String,
         expectedArity: Int,
-        opcode: Int = INVOKEINTERFACE
+        opcode: Int = INVOKEINTERFACE,
     ) {
         run loop@{
             repeat(expectedArity) {

kmath-ast/src/jvmMain/kotlin/kscience/kmath/asm/internal/mapIntrinsics.kt

@@ -2,11 +2,12 @@
 
 package kscience.kmath.asm.internal
 
+import kscience.kmath.expressions.StringSymbol
+import kscience.kmath.expressions.Symbol
+
 /**
- * Gets value with given [key] or throws [IllegalStateException] whenever it is not present.
+ * Gets value with given [key] or throws [NoSuchElementException] whenever it is not present.
  *
  * @author Iaroslav Postovalov
  */
-@JvmOverloads
+internal fun <V> Map<Symbol, V>.getOrFail(key: String): V = getValue(StringSymbol(key))
-internal fun <K, V> Map<K, V>.getOrFail(key: K, default: V? = null): V =
-    this[key] ?: default ?: error("Parameter not found: $key")

kmath-ast/src/jvmTest/kotlin/kscience/kmath/asm/TestAsmAlgebras.kt

@@ -1,6 +1,5 @@
-package scietifik.kmath.asm
+package kscience.kmath.asm
 
-import kscience.kmath.asm.compile
 import kscience.kmath.ast.mstInField
 import kscience.kmath.ast.mstInRing
 import kscience.kmath.ast.mstInSpace
@@ -11,6 +10,7 @@ import kotlin.test.Test
 import kotlin.test.assertEquals
 
 internal class TestAsmAlgebras {
+
     @Test
     fun space() {
         val res1 = ByteRing.mstInSpace {

kmath-ast/src/jvmTest/kotlin/kscience/kmath/asm/TestAsmExpressions.kt

@@ -1,4 +1,4 @@
-package scietifik.kmath.asm
+package kscience.kmath.asm
 
 import kscience.kmath.asm.compile
 import kscience.kmath.ast.mstInField

kmath-ast/src/jvmTest/kotlin/kscience/kmath/asm/TestAsmSpecialization.kt

@@ -1,4 +1,4 @@
-package scietifik.kmath.asm
+package kscience.kmath.asm
 
 import kscience.kmath.asm.compile
 import kscience.kmath.ast.mstInField

kmath-ast/src/jvmTest/kotlin/kscience/kmath/asm/TestAsmVariables.kt

@@ -1,4 +1,4 @@
-package scietifik.kmath.asm
+package kscience.kmath.asm
 
 import kscience.kmath.ast.mstInRing
 import kscience.kmath.expressions.invoke

kmath-ast/src/jvmTest/kotlin/kscience/kmath/ast/AsmTest.kt

@@ -1,4 +1,4 @@
-package scietifik.kmath.ast
+package kscience.kmath.ast
 
 import kscience.kmath.asm.compile
 import kscience.kmath.asm.expression

kmath-ast/src/jvmTest/kotlin/kscience/kmath/ast/ParserPrecedenceTest.kt

@@ -1,4 +1,4 @@
-package scietifik.kmath.ast
+package kscience.kmath.ast
 
 import kscience.kmath.ast.evaluate
 import kscience.kmath.ast.parseMath

kmath-ast/src/jvmTest/kotlin/kscience/kmath/ast/ParserTest.kt

@@ -1,4 +1,4 @@
-package scietifik.kmath.ast
+package kscience.kmath.ast
 
 import kscience.kmath.ast.evaluate
 import kscience.kmath.ast.mstInField

kmath-commons/build.gradle.kts

@@ -6,7 +6,7 @@ description = "Commons math binding for kmath"
 dependencies {
     api(project(":kmath-core"))
     api(project(":kmath-coroutines"))
-    api(project(":kmath-prob"))
+    api(project(":kmath-stat"))
-//    api(project(":kmath-functions"))
+    api(project(":kmath-functions"))
     api("org.apache.commons:commons-math3:3.6.1")
 }

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

@@ -0,0 +1,115 @@
+package kscience.kmath.commons.expressions
+
+import kscience.kmath.expressions.*
+import kscience.kmath.operations.ExtendedField
+import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
+
+/**
+ * A field over commons-math [DerivativeStructure].
+ *
+ * @property order The derivation order.
+ * @property bindings The map of bindings values. All bindings are considered free parameters
+ */
+public class DerivativeStructureField(
+    public val order: Int,
+    private val 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) }
+
+    /**
+     * 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 {
+        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()
+    }
+
+    /**
+     * Identity-based symbol bindings map
+     */
+    private val variables: Map<String, DerivativeStructureSymbol> = bindings.entries.associate { (key, value) ->
+        key.identity to DerivativeStructureSymbol(key, value)
+    }
+
+    override fun const(value: Double): DerivativeStructure = DerivativeStructure(bindings.size, 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())
+
+    public fun DerivativeStructure.derivative(parameter: Symbol, order: Int = 1): Double {
+        return derivative(mapOf(parameter to order))
+    }
+
+    public fun DerivativeStructure.derivative(orders: Map<Symbol, Int>): Double {
+        return getPartialDerivative(*bindings.keys.map { orders[it] ?: 0 }.toIntArray())
+    }
+
+    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) {
+        is Double -> a.multiply(k)
+        is Int -> a.multiply(k)
+        else -> a.multiply(k.toDouble())
+    }
+
+    public override fun multiply(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.multiply(b)
+    public override fun divide(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.divide(b)
+    public override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
+    public override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
+    public override fun tan(arg: DerivativeStructure): DerivativeStructure = arg.tan()
+    public override fun asin(arg: DerivativeStructure): DerivativeStructure = arg.asin()
+    public override fun acos(arg: DerivativeStructure): DerivativeStructure = arg.acos()
+    public override fun atan(arg: DerivativeStructure): DerivativeStructure = arg.atan()
+    public override fun sinh(arg: DerivativeStructure): DerivativeStructure = arg.sinh()
+    public override fun cosh(arg: DerivativeStructure): DerivativeStructure = arg.cosh()
+    public override fun tanh(arg: DerivativeStructure): DerivativeStructure = arg.tanh()
+    public override fun asinh(arg: DerivativeStructure): DerivativeStructure = arg.asinh()
+    public override fun acosh(arg: DerivativeStructure): DerivativeStructure = arg.acosh()
+    public override fun atanh(arg: DerivativeStructure): DerivativeStructure = arg.atanh()
+
+    public override fun power(arg: DerivativeStructure, pow: Number): DerivativeStructure = when (pow) {
+        is Double -> arg.pow(pow)
+        is Int -> arg.pow(pow)
+        else -> arg.pow(pow.toDouble())
+    }
+
+    public fun power(arg: DerivativeStructure, pow: DerivativeStructure): DerivativeStructure = arg.pow(pow)
+    public override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
+    public override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
+
+    public override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())
+    public override operator fun DerivativeStructure.minus(b: Number): DerivativeStructure = subtract(b.toDouble())
+    public override operator fun Number.plus(b: DerivativeStructure): DerivativeStructure = b + this
+    public override operator fun Number.minus(b: DerivativeStructure): DerivativeStructure = b - this
+
+    public companion object : AutoDiffProcessor<Double, DerivativeStructure, DerivativeStructureField> {
+        override fun process(function: DerivativeStructureField.() -> DerivativeStructure): DifferentiableExpression<Double> {
+            return DerivativeStructureExpression(function)
+        }
+    }
+}
+
+/**
+ * A constructs that creates a derivative structure with required order on-demand
+ */
+public class DerivativeStructureExpression(
+    public val function: DerivativeStructureField.() -> DerivativeStructure,
+) : DifferentiableExpression<Double> {
+    public override operator fun invoke(arguments: Map<Symbol, Double>): Double =
+        DerivativeStructureField(0, arguments).function().value
+
+    /**
+     * 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) }
+    }
+}

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

@@ -1,131 +0,0 @@
-package kscience.kmath.commons.expressions
-
-import kscience.kmath.expressions.Expression
-import kscience.kmath.expressions.ExpressionAlgebra
-import kscience.kmath.operations.ExtendedField
-import kscience.kmath.operations.Field
-import kscience.kmath.operations.invoke
-import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
-import kotlin.properties.ReadOnlyProperty
-
-/**
- * A field over commons-math [DerivativeStructure].
- *
- * @property order The derivation order.
- * @property parameters The map of free parameters.
- */
-public class DerivativeStructureField(
-    public val order: Int,
-    public val parameters: Map<String, Double>
-) : ExtendedField<DerivativeStructure> {
-    public override val zero: DerivativeStructure by lazy { DerivativeStructure(parameters.size, order) }
-    public override val one: DerivativeStructure by lazy { DerivativeStructure(parameters.size, order, 1.0) }
-
-    private val variables: Map<String, DerivativeStructure> = parameters.mapValues { (key, value) ->
-        DerivativeStructure(parameters.size, order, parameters.keys.indexOf(key), value)
-    }
-
-    public val variable: ReadOnlyProperty<Any?, DerivativeStructure> = ReadOnlyProperty { _, property ->
-        variables[property.name] ?: error("A variable with name ${property.name} does not exist")
-    }
-
-    public fun variable(name: String, default: DerivativeStructure? = null): DerivativeStructure =
-        variables[name] ?: default ?: error("A variable with name $name does not exist")
-
-    public fun Number.const(): DerivativeStructure = DerivativeStructure(order, parameters.size, toDouble())
-
-    public fun DerivativeStructure.deriv(parName: String, order: Int = 1): Double {
-        return deriv(mapOf(parName to order))
-    }
-
-    public fun DerivativeStructure.deriv(orders: Map<String, Int>): Double {
-        return getPartialDerivative(*parameters.keys.map { orders[it] ?: 0 }.toIntArray())
-    }
-
-    public fun DerivativeStructure.deriv(vararg orders: Pair<String, Int>): Double = deriv(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) {
-        is Double -> a.multiply(k)
-        is Int -> a.multiply(k)
-        else -> a.multiply(k.toDouble())
-    }
-
-    public override fun multiply(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.multiply(b)
-    public override fun divide(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.divide(b)
-    public override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
-    public override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
-    public override fun tan(arg: DerivativeStructure): DerivativeStructure = arg.tan()
-    public override fun asin(arg: DerivativeStructure): DerivativeStructure = arg.asin()
-    public override fun acos(arg: DerivativeStructure): DerivativeStructure = arg.acos()
-    public override fun atan(arg: DerivativeStructure): DerivativeStructure = arg.atan()
-    public override fun sinh(arg: DerivativeStructure): DerivativeStructure = arg.sinh()
-    public override fun cosh(arg: DerivativeStructure): DerivativeStructure = arg.cosh()
-    public override fun tanh(arg: DerivativeStructure): DerivativeStructure = arg.tanh()
-    public override fun asinh(arg: DerivativeStructure): DerivativeStructure = arg.asinh()
-    public override fun acosh(arg: DerivativeStructure): DerivativeStructure = arg.acosh()
-    public override fun atanh(arg: DerivativeStructure): DerivativeStructure = arg.atanh()
-
-    public override fun power(arg: DerivativeStructure, pow: Number): DerivativeStructure = when (pow) {
-        is Double -> arg.pow(pow)
-        is Int -> arg.pow(pow)
-        else -> arg.pow(pow.toDouble())
-    }
-
-    public fun power(arg: DerivativeStructure, pow: DerivativeStructure): DerivativeStructure = arg.pow(pow)
-    public override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
-    public override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
-
-    public override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())
-    public override operator fun DerivativeStructure.minus(b: Number): DerivativeStructure = subtract(b.toDouble())
-    public override operator fun Number.plus(b: DerivativeStructure): DerivativeStructure = b + this
-    public override operator fun Number.minus(b: DerivativeStructure): DerivativeStructure = b - this
-}
-
-/**
- * A constructs that creates a derivative structure with required order on-demand
- */
-public class DiffExpression(public val function: DerivativeStructureField.() -> DerivativeStructure) :
-    Expression<Double> {
-    public override operator fun invoke(arguments: Map<String, Double>): Double = DerivativeStructureField(
-        0,
-        arguments
-    ).function().value
-
-    /**
-     * Get the derivative expression with given orders
-     * TODO make result [DiffExpression]
-     */
-    public fun derivative(orders: Map<String, Int>): Expression<Double> = Expression { arguments ->
-        (DerivativeStructureField(orders.values.maxOrNull() ?: 0, arguments)) { function().deriv(orders) }
-    }
-
-    //TODO add gradient and maybe other vector operators
-}
-
-public fun DiffExpression.derivative(vararg orders: Pair<String, Int>): Expression<Double> = derivative(mapOf(*orders))
-public fun DiffExpression.derivative(name: String): Expression<Double> = derivative(name to 1)
-
-/**
- * A context for [DiffExpression] (not to be confused with [DerivativeStructure])
- */
-public object DiffExpressionAlgebra : ExpressionAlgebra<Double, DiffExpression>, Field<DiffExpression> {
-    public override val zero: DiffExpression = DiffExpression { 0.0.const() }
-    public override val one: DiffExpression = DiffExpression { 1.0.const() }
-
-    public override fun variable(name: String, default: Double?): DiffExpression =
-        DiffExpression { variable(name, default?.const()) }
-
-    public override fun const(value: Double): DiffExpression = DiffExpression { value.const() }
-
-    public override fun add(a: DiffExpression, b: DiffExpression): DiffExpression =
-        DiffExpression { a.function(this) + b.function(this) }
-
-    public override fun multiply(a: DiffExpression, k: Number): DiffExpression = DiffExpression { a.function(this) * k }
-
-    public override fun multiply(a: DiffExpression, b: DiffExpression): DiffExpression =
-        DiffExpression { a.function(this) * b.function(this) }
-
-    public override fun divide(a: DiffExpression, b: DiffExpression): DiffExpression =
-        DiffExpression { a.function(this) / b.function(this) }
-}

kmath-commons/src/main/kotlin/kscience/kmath/commons/optimization/CMOptimizationProblem.kt

@@ -0,0 +1,111 @@
+package kscience.kmath.commons.optimization
+
+import kscience.kmath.expressions.*
+import kscience.kmath.stat.OptimizationFeature
+import kscience.kmath.stat.OptimizationProblem
+import kscience.kmath.stat.OptimizationProblemFactory
+import kscience.kmath.stat.OptimizationResult
+import org.apache.commons.math3.optim.*
+import org.apache.commons.math3.optim.nonlinear.scalar.GoalType
+import org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer
+import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction
+import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunctionGradient
+import org.apache.commons.math3.optim.nonlinear.scalar.gradient.NonLinearConjugateGradientOptimizer
+import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.AbstractSimplex
+import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.NelderMeadSimplex
+import org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
+import kotlin.reflect.KClass
+
+public operator fun PointValuePair.component1(): DoubleArray = point
+public operator fun PointValuePair.component2(): Double = value
+
+public class CMOptimizationProblem(
+    override val symbols: List<Symbol>,
+) : OptimizationProblem<Double>, SymbolIndexer, OptimizationFeature {
+    private val optimizationData: HashMap<KClass<out OptimizationData>, OptimizationData> = HashMap()
+    private var optimizatorBuilder: (() -> MultivariateOptimizer)? = null
+    public var convergenceChecker: ConvergenceChecker<PointValuePair> = SimpleValueChecker(DEFAULT_RELATIVE_TOLERANCE,
+        DEFAULT_ABSOLUTE_TOLERANCE, DEFAULT_MAX_ITER)
+
+    public fun addOptimizationData(data: OptimizationData) {
+        optimizationData[data::class] = data
+    }
+
+    init {
+        addOptimizationData(MaxEval.unlimited())
+    }
+
+    public fun exportOptimizationData(): List<OptimizationData> = optimizationData.values.toList()
+
+    public override fun initialGuess(map: Map<Symbol, Double>): Unit {
+        addOptimizationData(InitialGuess(map.toDoubleArray()))
+    }
+
+    public override fun expression(expression: Expression<Double>): Unit {
+        val objectiveFunction = ObjectiveFunction {
+            val args = it.toMap()
+            expression(args)
+        }
+        addOptimizationData(objectiveFunction)
+    }
+
+    public override fun diffExpression(expression: DifferentiableExpression<Double>): Unit {
+        expression(expression)
+        val gradientFunction = ObjectiveFunctionGradient {
+            val args = it.toMap()
+            DoubleArray(symbols.size) { index ->
+                expression.derivative(symbols[index])(args)
+            }
+        }
+        addOptimizationData(gradientFunction)
+        if (optimizatorBuilder == null) {
+            optimizatorBuilder = {
+                NonLinearConjugateGradientOptimizer(
+                    NonLinearConjugateGradientOptimizer.Formula.FLETCHER_REEVES,
+                    convergenceChecker
+                )
+            }
+        }
+    }
+
+    public fun simplex(simplex: AbstractSimplex) {
+        addOptimizationData(simplex)
+        //Set optimization builder to simplex if it is not present
+        if (optimizatorBuilder == null) {
+            optimizatorBuilder = { SimplexOptimizer(convergenceChecker) }
+        }
+    }
+
+    public fun simplexSteps(steps: Map<Symbol, Double>) {
+        simplex(NelderMeadSimplex(steps.toDoubleArray()))
+    }
+
+    public fun goal(goalType: GoalType) {
+        addOptimizationData(goalType)
+    }
+
+    public fun optimizer(block: () -> MultivariateOptimizer) {
+        optimizatorBuilder = block
+    }
+
+    override fun update(result: OptimizationResult<Double>) {
+        initialGuess(result.point)
+    }
+
+    override fun optimize(): OptimizationResult<Double> {
+        val optimizer = optimizatorBuilder?.invoke() ?: error("Optimizer not defined")
+        val (point, value) = optimizer.optimize(*optimizationData.values.toTypedArray())
+        return OptimizationResult(point.toMap(), value, setOf(this))
+    }
+
+    public companion object : OptimizationProblemFactory<Double, CMOptimizationProblem> {
+        public const val DEFAULT_RELATIVE_TOLERANCE: Double = 1e-4
+        public const val DEFAULT_ABSOLUTE_TOLERANCE: Double = 1e-4
+        public const val DEFAULT_MAX_ITER: Int = 1000
+
+        override fun build(symbols: List<Symbol>): CMOptimizationProblem = CMOptimizationProblem(symbols)
+    }
+}
+
+public fun CMOptimizationProblem.initialGuess(vararg pairs: Pair<Symbol, Double>): Unit = initialGuess(pairs.toMap())
+public fun CMOptimizationProblem.simplexSteps(vararg pairs: Pair<Symbol, Double>): Unit = simplexSteps(pairs.toMap())

kmath-commons/src/main/kotlin/kscience/kmath/commons/optimization/cmFit.kt

@@ -0,0 +1,70 @@
+package kscience.kmath.commons.optimization
+
+import kscience.kmath.commons.expressions.DerivativeStructureField
+import kscience.kmath.expressions.DifferentiableExpression
+import kscience.kmath.expressions.Expression
+import kscience.kmath.expressions.Symbol
+import kscience.kmath.stat.Fitting
+import kscience.kmath.stat.OptimizationResult
+import kscience.kmath.stat.optimizeWith
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.asBuffer
+import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
+import org.apache.commons.math3.optim.nonlinear.scalar.GoalType
+
+
+/**
+ * Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic differentiation
+ */
+public fun Fitting.chiSquared(
+    x: Buffer<Double>,
+    y: Buffer<Double>,
+    yErr: Buffer<Double>,
+    model: DerivativeStructureField.(x: DerivativeStructure) -> DerivativeStructure,
+): DifferentiableExpression<Double> = chiSquared(DerivativeStructureField, x, y, yErr, model)
+
+/**
+ * Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic differentiation
+ */
+public fun Fitting.chiSquared(
+    x: Iterable<Double>,
+    y: Iterable<Double>,
+    yErr: Iterable<Double>,
+    model: DerivativeStructureField.(x: DerivativeStructure) -> DerivativeStructure,
+): DifferentiableExpression<Double> = chiSquared(
+    DerivativeStructureField,
+    x.toList().asBuffer(),
+    y.toList().asBuffer(),
+    yErr.toList().asBuffer(),
+    model
+)
+
+
+/**
+ * Optimize expression without derivatives
+ */
+public fun Expression<Double>.optimize(
+    vararg symbols: Symbol,
+    configuration: CMOptimizationProblem.() -> Unit,
+): OptimizationResult<Double> = optimizeWith(CMOptimizationProblem, symbols = symbols, configuration)
+
+
+/**
+ * Optimize differentiable expression
+ */
+public fun DifferentiableExpression<Double>.optimize(
+    vararg symbols: Symbol,
+    configuration: CMOptimizationProblem.() -> Unit,
+): OptimizationResult<Double> = optimizeWith(CMOptimizationProblem, symbols = symbols, configuration)
+
+public fun DifferentiableExpression<Double>.minimize(
+    vararg startPoint: Pair<Symbol, Double>,
+    configuration: CMOptimizationProblem.() -> Unit = {},
+): OptimizationResult<Double> {
+    require(startPoint.isNotEmpty()) { "Must provide a list of symbols for optimization" }
+    val problem = CMOptimizationProblem(startPoint.map { it.first }).apply(configuration)
+    problem.diffExpression(this)
+    problem.initialGuess(startPoint.toMap())
+    problem.goal(GoalType.MINIMIZE)
+    return problem.optimize()
+}

kmath-commons/src/main/kotlin/kscience/kmath/commons/random/CMRandomGeneratorWrapper.kt

@@ -1,9 +1,10 @@
 package kscience.kmath.commons.random
 
-import kscience.kmath.prob.RandomGenerator
+import kscience.kmath.stat.RandomGenerator
 
-public class CMRandomGeneratorWrapper(public val factory: (IntArray) -> RandomGenerator) :
+public class CMRandomGeneratorWrapper(
-    org.apache.commons.math3.random.RandomGenerator {
+    public val factory: (IntArray) -> RandomGenerator,
+) : org.apache.commons.math3.random.RandomGenerator {
     private var generator: RandomGenerator = factory(intArrayOf())
 
     public override fun nextBoolean(): Boolean = generator.nextBoolean()

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

@@ -1,6 +1,6 @@
 package kscience.kmath.commons.expressions
 
-import kscience.kmath.expressions.invoke
+import kscience.kmath.expressions.*
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 import kotlin.test.Test
@@ -8,33 +8,37 @@ import kotlin.test.assertEquals
 
 internal inline fun <R> diff(
     order: Int,
-    vararg parameters: Pair<String, Double>,
+    vararg parameters: Pair<Symbol, Double>,
-    block: DerivativeStructureField.() -> R
+    block: DerivativeStructureField.() -> R,
 ): R {
     contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
     return DerivativeStructureField(order, mapOf(*parameters)).run(block)
 }
 
 internal class AutoDiffTest {
+    private val x by symbol
+    private val y by symbol
+
     @Test
     fun derivativeStructureFieldTest() {
-        val res = diff(3, "x" to 1.0, "y" to 1.0) {
+        val res: Double = diff(3, x to 1.0, y to 1.0) {
-            val x by variable
+            val x = bind(x)//by binding()
-            val y = variable("y")
+            val y = symbol("y")
             val z = x * (-sin(x * y) + y)
-            z.deriv("x")
+            z.derivative(x)
         }
+        println(res)
     }
 
     @Test
     fun autoDifTest() {
-        val f = DiffExpression {
+        val f = DerivativeStructureExpression {
-            val x by variable
+            val x by binding()
-            val y by variable
+            val y by binding()
             x.pow(2) + 2 * x * y + y.pow(2) + 1
         }
 
-        assertEquals(10.0, f("x" to 1.0, "y" to 2.0))
+        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(6.0, f.derivative(x)(x to 1.0, y to 2.0))
     }
 }

kmath-commons/src/test/kotlin/kscience/kmath/commons/optimization/OptimizeTest.kt

@@ -0,0 +1,66 @@
+package kscience.kmath.commons.optimization
+
+import kscience.kmath.commons.expressions.DerivativeStructureExpression
+import kscience.kmath.expressions.symbol
+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
+
+internal class OptimizeTest {
+    val x by symbol
+    val y by symbol
+
+    val normal = DerivativeStructureExpression {
+        exp(-bind(x).pow(2) / 2) + exp(-bind(y).pow(2) / 2)
+    }
+
+    @Test
+    fun testGradientOptimization() {
+        val result = normal.optimize(x, y) {
+            initialGuess(x to 1.0, y to 1.0)
+            //no need to select optimizer. Gradient optimizer is used by default because gradients are provided by function
+        }
+        println(result.point)
+        println(result.value)
+    }
+
+    @Test
+    fun testSimplexOptimization() {
+        val result = normal.optimize(x, y) {
+            initialGuess(x to 1.0, y to 1.0)
+            simplexSteps(x to 2.0, y to 0.5)
+            //this sets simplex optimizer
+        }
+        println(result.point)
+        println(result.value)
+    }
+
+    @Test
+    fun testCmFit() {
+        val a by symbol
+        val b by symbol
+        val c by symbol
+
+        val sigma = 1.0
+        val generator = Distribution.normal(0.0, sigma)
+        val chain = generator.sample(RandomGenerator.default(112667))
+        val x = (1..100).map { it.toDouble() }
+        val y = x.map { it ->
+            it.pow(2) + it + 1 + chain.nextDouble()
+        }
+        val yErr = x.map { sigma }
+        val chi2 = Fitting.chiSquared(x.asBuffer(), y.asBuffer(), yErr.asBuffer()) { x ->
+            val cWithDefault = bindOrNull(c) ?: one
+            bind(a) * x.pow(2) + bind(b) * x + cWithDefault
+        }
+
+        val result = chi2.minimize(a to 1.5, b to 0.9, c to 1.0)
+        println(result)
+        println("Chi2/dof = ${result.value / (x.size - 3)}")
+    }
+
+}

kmath-core/README.md

@@ -7,12 +7,12 @@ The core features of KMath:
  - [buffers](src/commonMain/kotlin/kscience/kmath/structures/Buffers.kt) : One-dimensional structure
  - [expressions](src/commonMain/kotlin/kscience/kmath/expressions) : Functional Expressions
  - [domains](src/commonMain/kotlin/kscience/kmath/domains) : Domains
- - [autodif](src/commonMain/kotlin/kscience/kmath/misc/AutoDiff.kt) : Automatic differentiation
+ - [autodif](src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt) : Automatic differentiation
 
 
 > #### Artifact:
 >
-> This module artifact: `kscience.kmath:kmath-core:0.2.0-dev-1`.
+> This module artifact: `kscience.kmath:kmath-core:0.2.0-dev-2`.
 >
 > Bintray release version:        [ ![Download](https://api.bintray.com/packages/mipt-npm/kscience/kmath-core/images/download.svg) ](https://bintray.com/mipt-npm/kscience/kmath-core/_latestVersion)
 >
@@ -22,25 +22,28 @@ The core features of KMath:
 >
 > ```gradle
 > repositories {
+>     maven { url "https://dl.bintray.com/kotlin/kotlin-eap" }
 >     maven { url 'https://dl.bintray.com/mipt-npm/kscience' }
 >     maven { url 'https://dl.bintray.com/mipt-npm/dev' }
 >     maven { url 'https://dl.bintray.com/hotkeytlt/maven' }
+
 > }
 > 
 > dependencies {
->     implementation 'kscience.kmath:kmath-core:0.2.0-dev-1'
+>     implementation 'kscience.kmath:kmath-core:0.2.0-dev-2'
 > }
 > ```
 > **Gradle Kotlin DSL:**
 >
 > ```kotlin
 > repositories {
+>     maven("https://dl.bintray.com/kotlin/kotlin-eap")
 >     maven("https://dl.bintray.com/mipt-npm/kscience")
 >     maven("https://dl.bintray.com/mipt-npm/dev")
 >     maven("https://dl.bintray.com/hotkeytlt/maven")
 > }
 > 
 > dependencies {
->     implementation("kscience.kmath:kmath-core:0.2.0-dev-1")
+>     implementation("kscience.kmath:kmath-core:0.2.0-dev-2")
 > }
 > ```

kmath-core/build.gradle.kts

@@ -41,6 +41,6 @@ readme {
     feature(
         id = "autodif",
         description = "Automatic differentiation",
-        ref = "src/commonMain/kotlin/kscience/kmath/misc/AutoDiff.kt"
+        ref = "src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt"
     )
 }

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

@@ -0,0 +1,39 @@
+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 <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(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(name: String): Expression<T> =
+    derivative(StringSymbol(name) to 1)
+
+/**
+ * A [DifferentiableExpression] that defines only first derivatives
+ */
+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
+        return derivativeOrNull(dSymbol)
+    }
+}
+
+/**
+ * A factory that converts an expression in autodiff variables to a [DifferentiableExpression]
+ */
+public interface AutoDiffProcessor<T : Any, I : Any, A : ExpressionAlgebra<T, I>> {
+    public fun process(function: A.() -> I): DifferentiableExpression<T>
+}

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

@@ -1,6 +1,25 @@
 package kscience.kmath.expressions
 
 import kscience.kmath.operations.Algebra
+import kotlin.jvm.JvmName
+import kotlin.properties.ReadOnlyProperty
+
+/**
+ * A marker interface for a symbol. A symbol mus have an identity
+ */
+public interface Symbol {
+    /**
+     * Identity object for the symbol. Two symbols with the same identity are considered to be the same symbol.
+     */
+    public val identity: String
+}
+
+/**
+ * A [Symbol] with a [String] identity
+ */
+public inline class StringSymbol(override val identity: String) : Symbol {
+    override fun toString(): String = identity
+}
 
 /**
  * An elementary function that could be invoked on a map of arguments
@@ -12,30 +31,69 @@ public fun interface Expression<T> {
      * @param arguments the map of arguments.
      * @return the value.
      */
-    public operator fun invoke(arguments: Map<String, T>): T
+    public operator fun invoke(arguments: Map<Symbol, T>): T
-
-    public companion object
 }
 
+/**
+ * Invoke an expression without parameters
+ */
+public operator fun <T> Expression<T>.invoke(): T = invoke(emptyMap())
+//This method exists to avoid resolution ambiguity of vararg methods
+
 /**
  * Calls this expression from arguments.
  *
  * @param pairs the pair of arguments' names to values.
  * @return the value.
  */
-public operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
+@JvmName("callBySymbol")
+public operator fun <T> Expression<T>.invoke(vararg pairs: Pair<Symbol, T>): T = invoke(mapOf(*pairs))
+
+@JvmName("callByString")
+public operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T =
+    invoke(mapOf(*pairs).mapKeys { StringSymbol(it.key) })
+
 
 /**
  * A context for expression construction
+ *
+ * @param T type of the constants for the expression
+ * @param E type of the actual expression state
  */
-public interface ExpressionAlgebra<T, E> : Algebra<E> {
+public interface ExpressionAlgebra<in T, E> : Algebra<E> {
+
     /**
-     * Introduce a variable into expression context
+     * Bind a given [Symbol] to this context variable and produce context-specific object. Return null if symbol could not be bound in current context.
      */
-    public fun variable(name: String, default: T? = null): E
+    public fun bindOrNull(symbol: Symbol): E?
+
+    /**
+     * Bind a string to a context using [StringSymbol]
+     */
+    override fun symbol(value: String): E = bind(StringSymbol(value))
 
     /**
      * A constant expression which does not depend on arguments
      */
     public fun const(value: T): E
 }
+
+/**
+ * Bind a given [Symbol] to this context variable and produce context-specific object.
+ */
+public fun <T, E> ExpressionAlgebra<T, E>.bind(symbol: Symbol): E =
+    bindOrNull(symbol) ?: error("Symbol $symbol could not be bound to $this")
+
+/**
+ * A delegate to create a symbol with a string identity in this scope
+ */
+public val symbol: ReadOnlyProperty<Any?, StringSymbol> =    ReadOnlyProperty { thisRef, property ->
+    StringSymbol(property.name)
+}
+
+/**
+ * Bind a symbol by name inside the [ExpressionAlgebra]
+ */
+public fun <T, E> ExpressionAlgebra<T, E>.binding(): ReadOnlyProperty<Any?, E> = ReadOnlyProperty { _, property ->
+    bind(StringSymbol(property.name)) ?: error("A variable with name ${property.name} does not exist")
+}

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

@@ -2,67 +2,43 @@ package kscience.kmath.expressions
 
 import kscience.kmath.operations.*
 
-internal class FunctionalUnaryOperation<T>(val context: Algebra<T>, val name: String, private val expr: Expression<T>) :
-    Expression<T> {
-    override operator fun invoke(arguments: Map<String, T>): T =
-        context.unaryOperation(name, expr.invoke(arguments))
-}
-
-internal class FunctionalBinaryOperation<T>(
-    val context: Algebra<T>,
-    val name: String,
-    val first: Expression<T>,
-    val second: Expression<T>
-) : Expression<T> {
-    override operator fun invoke(arguments: Map<String, T>): T =
-        context.binaryOperation(name, first.invoke(arguments), second.invoke(arguments))
-}
-
-internal class FunctionalVariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
-    override operator fun invoke(arguments: Map<String, T>): T =
-        arguments[name] ?: default ?: error("Parameter not found: $name")
-}
-
-internal class FunctionalConstantExpression<T>(val value: T) : Expression<T> {
-    override operator fun invoke(arguments: Map<String, T>): T = value
-}
-
-internal class FunctionalConstProductExpression<T>(
-    val context: Space<T>,
-    private val expr: Expression<T>,
-    val const: Number
-) : Expression<T> {
-    override operator fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
-}
-
 /**
  * A context class for [Expression] construction.
  *
  * @param algebra The algebra to provide for Expressions built.
  */
-public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(public val algebra: A) :
+public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(
-    ExpressionAlgebra<T, Expression<T>> {
+    public val algebra: A,
+) : ExpressionAlgebra<T, Expression<T>> {
     /**
      * Builds an Expression of constant expression which does not depend on arguments.
      */
-    public override fun const(value: T): Expression<T> = FunctionalConstantExpression(value)
+    public override fun const(value: T): Expression<T> = Expression { value }
 
     /**
      * Builds an Expression to access a variable.
      */
-    public override fun variable(name: String, default: T?): Expression<T> = FunctionalVariableExpression(name, default)
+    public override fun bindOrNull(symbol: Symbol): Expression<T>? = Expression { arguments ->
+        arguments[symbol] ?: error("Argument not found: $symbol")
+    }
 
     /**
      * Builds an Expression of dynamic call of binary operation [operation] on [left] and [right].
      */
-    public override fun binaryOperation(operation: String, left: Expression<T>, right: Expression<T>): Expression<T> =
+    public override fun binaryOperation(
-        FunctionalBinaryOperation(algebra, operation, left, right)
+        operation: String,
+        left: Expression<T>,
+        right: Expression<T>,
+    ): Expression<T> = Expression { arguments ->
+        algebra.binaryOperation(operation, left.invoke(arguments), right.invoke(arguments))
+    }
 
     /**
      * Builds an Expression of dynamic call of unary operation with name [operation] on [arg].
      */
-    public override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> =
+    public override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> = Expression { arguments ->
-        FunctionalUnaryOperation(algebra, operation, arg)
+        algebra.unaryOperation(operation, arg.invoke(arguments))
+    }
 }
 
 /**
@@ -81,8 +57,9 @@ public open class FunctionalExpressionSpace<T, A : Space<T>>(algebra: A) :
     /**
      * Builds an Expression of multiplication of expression by number.
      */
-    public override fun multiply(a: Expression<T>, k: Number): Expression<T> =
+    public override fun multiply(a: Expression<T>, k: Number): Expression<T> = Expression { arguments ->
-        FunctionalConstProductExpression(algebra, a, k)
+        algebra.multiply(a.invoke(arguments), k)
+    }
 
     public operator fun Expression<T>.plus(arg: T): Expression<T> = this + const(arg)
     public operator fun Expression<T>.minus(arg: T): Expression<T> = this - const(arg)
@@ -118,8 +95,8 @@ public open class FunctionalExpressionRing<T, A>(algebra: A) : FunctionalExpress
 }
 
 public open class FunctionalExpressionField<T, A>(algebra: A) :
-    FunctionalExpressionRing<T, A>(algebra),
+    FunctionalExpressionRing<T, A>(algebra), Field<Expression<T>>
-    Field<Expression<T>> where A : Field<T>, A : NumericAlgebra<T> {
+        where A : Field<T>, A : NumericAlgebra<T> {
     /**
      * Builds an Expression of division an expression by another one.
      */

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

@@ -0,0 +1,395 @@
+package kscience.kmath.expressions
+
+import kscience.kmath.linear.Point
+import kscience.kmath.operations.*
+import kscience.kmath.structures.asBuffer
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+
+/*
+ * Implementation of backward-mode automatic differentiation.
+ * Initial gist by Roman Elizarov: https://gist.github.com/elizarov/1ad3a8583e88cb6ea7a0ad09bb591d3d
+ */
+
+
+public open class AutoDiffValue<out T>(public val value: T)
+
+/**
+ * Represents result of [simpleAutoDiff] call.
+ *
+ * @param T the non-nullable type of value.
+ * @param value the value of result.
+ * @property simpleAutoDiff The mapping of differentiated variables to their derivatives.
+ * @property context The field over [T].
+ */
+public class DerivationResult<T : Any>(
+    public val value: T,
+    private val derivativeValues: Map<String, T>,
+    public val context: Field<T>,
+) {
+    /**
+     * Returns derivative of [variable] or returns [Ring.zero] in [context].
+     */
+    public fun derivative(variable: Symbol): T = derivativeValues[variable.identity] ?: context.zero
+
+    /**
+     * Computes the divergence.
+     */
+    public fun div(): T = context { sum(derivativeValues.values) }
+}
+
+/**
+ * Computes the gradient for variables in given order.
+ */
+public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T> {
+    check(variables.isNotEmpty()) { "Variable order is not provided for gradient construction" }
+    return variables.map(::derivative).asBuffer()
+}
+
+/**
+ * Runs differentiation and establishes [SimpleAutoDiffField] context inside the block of code.
+ *
+ * The partial derivatives are placed in argument `d` variable
+ *
+ * Example:
+ * ```
+ * val x by symbol // define variable(s) and their values
+ * val y = RealField.withAutoDiff() { sqr(x) + 5 * x + 3 } // write formulate in deriv context
+ * assertEquals(17.0, y.x) // the value of result (y)
+ * assertEquals(9.0, x.d)  // dy/dx
+ * ```
+ *
+ * @param body the action in [SimpleAutoDiffField] context returning [AutoDiffVariable] to differentiate with respect to.
+ * @return the result of differentiation.
+ */
+public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
+    bindings: Map<Symbol, T>,
+    body: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
+): DerivationResult<T> {
+    contract { callsInPlace(body, InvocationKind.EXACTLY_ONCE) }
+
+    return SimpleAutoDiffField(this, bindings).derivate(body)
+}
+
+public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
+    vararg bindings: Pair<Symbol, T>,
+    body: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
+): DerivationResult<T> = simpleAutoDiff(bindings.toMap(), body)
+
+/**
+ * Represents field in context of which functions can be derived.
+ */
+public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
+    public val context: F,
+    bindings: Map<Symbol, T>,
+) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>> {
+
+    // 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<AutoDiffValue<T>, T> = hashMapOf()
+
+    /**
+     * Differentiable variable with value and derivative of differentiation ([simpleAutoDiff]) result
+     * with respect to this variable.
+     *
+     * @param T the non-nullable type of value.
+     * @property value The value of this variable.
+     */
+    private class AutoDiffVariableWithDerivative<T : Any>(
+        override val identity: String,
+        value: T,
+        var d: T,
+    ) : AutoDiffValue<T>(value), Symbol {
+        override fun toString(): String = identity
+        override fun equals(other: Any?): Boolean = this.identity == (other as? Symbol)?.identity
+        override fun hashCode(): Int = identity.hashCode()
+    }
+
+    private val bindings: Map<String, AutoDiffVariableWithDerivative<T>> = bindings.entries.associate {
+        it.key.identity to AutoDiffVariableWithDerivative(it.key.identity, it.value, context.zero)
+    }
+
+    override fun bindOrNull(symbol: Symbol): AutoDiffValue<T>? = bindings[symbol.identity]
+
+    private fun getDerivative(variable: AutoDiffValue<T>): T =
+        (variable as? AutoDiffVariableWithDerivative)?.d ?: derivatives[variable] ?: context.zero
+
+    private fun setDerivative(variable: AutoDiffValue<T>, value: T) {
+        if (variable is AutoDiffVariableWithDerivative) variable.d = value else derivatives[variable] = value
+    }
+
+
+    @Suppress("UNCHECKED_CAST")
+    private fun runBackwardPass() {
+        while (sp > 0) {
+            val value = stack[--sp]
+            val block = stack[--sp] as F.(Any?) -> Unit
+            context.block(value)
+        }
+    }
+
+    override val zero: AutoDiffValue<T> get() = const(context.zero)
+    override val one: AutoDiffValue<T> get() = const(context.one)
+
+    override fun const(value: T): AutoDiffValue<T> = AutoDiffValue(value)
+
+    /**
+     * A variable accessing inner state of derivatives.
+     * Use this value in inner builders to avoid creating additional derivative bindings.
+     */
+    public var AutoDiffValue<T>.d: T
+        get() = getDerivative(this)
+        set(value) = setDerivative(this, value)
+
+    public inline fun const(block: F.() -> T): AutoDiffValue<T> = const(context.block())
+
+    /**
+     * Performs update of derivative after the rest of the formula in the back-pass.
+     *
+     * For example, implementation of `sin` function is:
+     *
+     * ```
+     * fun AD.sin(x: Variable): Variable = derive(Variable(sin(x.x)) { z -> // call derive with function result
+     *     x.d += z.d * cos(x.x) // update derivative using chain rule and derivative of the function
+     * }
+     * ```
+     */
+    @Suppress("UNCHECKED_CAST")
+    public fun <R> derive(value: R, block: F.(R) -> Unit): R {
+        // save block to stack for backward pass
+        if (sp >= stack.size) stack = stack.copyOf(stack.size * 2)
+        stack[sp++] = block
+        stack[sp++] = value
+        return value
+    }
+
+
+    internal fun derivate(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T> {
+        val result = function()
+        result.d = context.one // computing derivative w.r.t result
+        runBackwardPass()
+        return DerivationResult(result.value, bindings.mapValues { it.value.d }, context)
+    }
+
+    // Overloads for Double constants
+
+    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 AutoDiffValue<T>.plus(b: Number): AutoDiffValue<T> = b.plus(this)
+
+    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 AutoDiffValue<T>.minus(b: Number): AutoDiffValue<T> =
+        derive(const { this@minus.value - one * b.toDouble() }) { z -> this@minus.d += z.d }
+
+
+    // Basic math (+, -, *, /)
+
+    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: 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: 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: AutoDiffValue<T>, k: Number): AutoDiffValue<T> =
+        derive(const { k.toDouble() * a.value }) { z ->
+            a.d += z.d * k.toDouble()
+        }
+}
+
+/**
+ * A constructs that creates a derivative structure with required order on-demand
+ */
+public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
+    public val field: F,
+    public val function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
+) : FirstDerivativeExpression<T>() {
+    public override operator fun invoke(arguments: Map<Symbol, T>): T {
+        //val bindings = arguments.entries.map { it.key.bind(it.value) }
+        return SimpleAutoDiffField(field, arguments).function().value
+    }
+
+    override fun derivativeOrNull(symbol: Symbol): Expression<T> = Expression { arguments ->
+        //val bindings = arguments.entries.map { it.key.bind(it.value) }
+        val derivationResult = SimpleAutoDiffField(field, arguments).derivate(function)
+        derivationResult.derivative(symbol)
+    }
+}
+
+/**
+ * Generate [AutoDiffProcessor] for [SimpleAutoDiffExpression]
+ */
+public fun <T : Any, F : Field<T>> simpleAutoDiff(field: F): AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>> {
+    return object : AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>> {
+        override fun process(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DifferentiableExpression<T> {
+            return SimpleAutoDiffExpression(field, function)
+        }
+    }
+}
+
+// Extensions for differentiation of various basic mathematical functions
+
+// x ^ 2
+public fun <T : Any, F : Field<T>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<T, F>.pow(
+    x: AutoDiffValue<T>,
+    y: Double,
+): 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>> SimpleAutoDiffField<T, F>.pow(
+    x: AutoDiffValue<T>,
+    y: Int,
+): AutoDiffValue<T> = pow(x, y.toDouble())
+
+// exp(x)
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<T, F>.pow(
+    x: AutoDiffValue<T>,
+    y: AutoDiffValue<T>,
+): AutoDiffValue<T> =
+    exp(y * ln(x))
+
+// sin(x)
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<T, F>.sinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+    derive(const { sinh(x.value) }) { z -> x.d += z.d * cosh(x.value) }
+
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.cosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+    derive(const { cosh(x.value) }) { z -> x.d += z.d * sinh(x.value) }
+
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.tanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+    derive(const { tanh(x.value) }) { z ->
+        val c = cosh(x.value)
+        x.d += z.d / (c * c)
+    }
+
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<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>> SimpleAutoDiffField<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>> SimpleAutoDiffField<T, F>.atanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+    derive(const { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) }
+
+public class SimpleAutoDiffExtendedField<T : Any, F : ExtendedField<T>>(
+    context: F,
+    bindings: Map<Symbol, T>,
+) : ExtendedField<AutoDiffValue<T>>, SimpleAutoDiffField<T, F>(context, bindings) {
+    // x ^ 2
+    public fun sqr(x: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sqr(x)
+
+    // x ^ 1/2
+    public override fun sqrt(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sqrt(arg)
+
+    // x ^ y (const)
+    public override fun power(arg: AutoDiffValue<T>, pow: Number): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).pow(arg, pow.toDouble())
+
+    // exp(x)
+    public override fun exp(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).exp(arg)
+
+    // ln(x)
+    public override fun ln(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).ln(arg)
+
+    // x ^ y (any)
+    public fun pow(
+        x: AutoDiffValue<T>,
+        y: AutoDiffValue<T>,
+    ): AutoDiffValue<T> = exp(y * ln(x))
+
+    // sin(x)
+    public override fun sin(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sin(arg)
+
+    // cos(x)
+    public override fun cos(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).cos(arg)
+
+    public override fun tan(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).tan(arg)
+
+    public override fun asin(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).asin(arg)
+
+    public override fun acos(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).acos(arg)
+
+    public override fun atan(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).atan(arg)
+
+    public override fun sinh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sinh(arg)
+
+    public override fun cosh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).cosh(arg)
+
+    public override fun tanh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).tanh(arg)
+
+    public override fun asinh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).asinh(arg)
+
+    public override fun acosh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).acosh(arg)
+
+    public override fun atanh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).atanh(arg)
+}

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

@@ -0,0 +1,61 @@
+package kscience.kmath.expressions
+
+import kscience.kmath.linear.Point
+import kscience.kmath.structures.BufferFactory
+import kscience.kmath.structures.Structure2D
+
+/**
+ * An environment to easy transform indexed variables to symbols and back.
+ * TODO requires multi-receivers to be beutiful
+ */
+public interface SymbolIndexer {
+    public val symbols: List<Symbol>
+    public fun indexOf(symbol: Symbol): Int = symbols.indexOf(symbol)
+
+    public operator fun <T> List<T>.get(symbol: Symbol): T {
+        require(size == symbols.size) { "The input list size for indexer should be ${symbols.size} but $size found" }
+        return get(this@SymbolIndexer.indexOf(symbol))
+    }
+
+    public operator fun <T> Array<T>.get(symbol: Symbol): T {
+        require(size == symbols.size) { "The input array size for indexer should be ${symbols.size} but $size found" }
+        return get(this@SymbolIndexer.indexOf(symbol))
+    }
+
+    public operator fun DoubleArray.get(symbol: Symbol): Double {
+        require(size == symbols.size) { "The input array size for indexer should be ${symbols.size} but $size found" }
+        return get(this@SymbolIndexer.indexOf(symbol))
+    }
+
+    public operator fun <T> Point<T>.get(symbol: Symbol): T {
+        require(size == symbols.size) { "The input buffer size for indexer should be ${symbols.size} but $size found" }
+        return get(this@SymbolIndexer.indexOf(symbol))
+    }
+
+    public fun DoubleArray.toMap(): Map<Symbol, Double> {
+        require(size == symbols.size) { "The input array size for indexer should be ${symbols.size} but $size found" }
+        return symbols.indices.associate { symbols[it] to get(it) }
+    }
+
+    public operator fun <T> Structure2D<T>.get(rowSymbol: Symbol, columnSymbol: Symbol): T =
+        get(indexOf(rowSymbol), indexOf(columnSymbol))
+
+
+    public fun <T> Map<Symbol, T>.toList(): List<T> = symbols.map { getValue(it) }
+
+    public fun <T> Map<Symbol, T>.toPoint(bufferFactory: BufferFactory<T>): Point<T> =
+        bufferFactory(symbols.size) { getValue(symbols[it]) }
+
+    public fun Map<Symbol, Double>.toDoubleArray(): DoubleArray = DoubleArray(symbols.size) { getValue(symbols[it]) }
+}
+
+public inline class SimpleSymbolIndexer(override val symbols: List<Symbol>) : SymbolIndexer
+
+/**
+ * Execute the block with symbol indexer based on given symbol order
+ */
+public inline fun <R> withSymbols(vararg symbols: Symbol, block: SymbolIndexer.() -> R): R =
+    with(SimpleSymbolIndexer(symbols.toList()), block)
+
+public inline fun <R> withSymbols(symbols: Collection<Symbol>, block: SymbolIndexer.() -> R): R =
+    with(SimpleSymbolIndexer(symbols.toList()), block)

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

@@ -7,6 +7,7 @@ import kscience.kmath.operations.Space
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
+
 /**
  * Creates a functional expression with this [Space].
  */

kmath-core/src/commonMain/kotlin/kscience/kmath/misc/AutoDiff.kt

@@ -1,266 +0,0 @@
-package kscience.kmath.misc
-
-import kscience.kmath.linear.Point
-import kscience.kmath.operations.*
-import kscience.kmath.structures.asBuffer
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-
-/*
- * Implementation of backward-mode automatic differentiation.
- * Initial gist by Roman Elizarov: https://gist.github.com/elizarov/1ad3a8583e88cb6ea7a0ad09bb591d3d
- */
-
-/**
- * Differentiable variable with value and derivative of differentiation ([deriv]) result
- * with respect to this variable.
- *
- * @param T the non-nullable type of value.
- * @property value The value of this variable.
- */
-public open class Variable<T : Any>(public val value: T)
-
-/**
- * Represents result of [deriv] call.
- *
- * @param T the non-nullable type of value.
- * @param value the value of result.
- * @property deriv The mapping of differentiated variables to their derivatives.
- * @property context The field over [T].
- */
-public class DerivationResult<T : Any>(
-    value: T,
-    public val deriv: Map<Variable<T>, T>,
-    public val context: Field<T>
-) : Variable<T>(value) {
-    /**
-     * Returns derivative of [variable] or returns [Ring.zero] in [context].
-     */
-    public fun deriv(variable: Variable<T>): T = deriv[variable] ?: context.zero
-
-    /**
-     * Computes the divergence.
-     */
-    public fun div(): T = context { sum(deriv.values) }
-
-    /**
-     * Computes the gradient for variables in given order.
-     */
-    public fun grad(vararg variables: Variable<T>): Point<T> {
-        check(variables.isNotEmpty()) { "Variable order is not provided for gradient construction" }
-        return variables.map(::deriv).asBuffer()
-    }
-}
-
-/**
- * Runs differentiation and establishes [AutoDiffField] context inside the block of code.
- *
- * The partial derivatives are placed in argument `d` variable
- *
- * Example:
- * ```
- * val x = Variable(2) // define variable(s) and their values
- * val y = deriv { sqr(x) + 5 * x + 3 } // write formulate in deriv context
- * assertEquals(17.0, y.x) // the value of result (y)
- * assertEquals(9.0, x.d)  // dy/dx
- * ```
- *
- * @param body the action in [AutoDiffField] context returning [Variable] to differentiate with respect to.
- * @return the result of differentiation.
- */
-public inline fun <T : Any, F : Field<T>> F.deriv(body: AutoDiffField<T, F>.() -> Variable<T>): DerivationResult<T> {
-    contract { callsInPlace(body, InvocationKind.EXACTLY_ONCE) }
-
-    return (AutoDiffContext(this)) {
-        val result = body()
-        result.d = context.one // computing derivative w.r.t result
-        runBackwardPass()
-        DerivationResult(result.value, derivatives, this@deriv)
-    }
-}
-
-/**
- * Represents field in context of which functions can be derived.
- */
-public abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> {
-    public abstract val context: F
-
-    /**
-     * A variable accessing inner state of derivatives.
-     * Use this value in inner builders to avoid creating additional derivative bindings.
-     */
-    public abstract var Variable<T>.d: T
-
-    /**
-     * Performs update of derivative after the rest of the formula in the back-pass.
-     *
-     * For example, implementation of `sin` function is:
-     *
-     * ```
-     * fun AD.sin(x: Variable): Variable = derive(Variable(sin(x.x)) { z -> // call derive with function result
-     *     x.d += z.d * cos(x.x) // update derivative using chain rule and derivative of the function
-     * }
-     * ```
-     */
-    public abstract fun <R> derive(value: R, block: F.(R) -> Unit): R
-
-    /**
-     *
-     */
-    public abstract fun variable(value: T): Variable<T>
-
-    public inline fun variable(block: F.() -> T): Variable<T> = variable(context.block())
-
-    // Overloads for Double constants
-
-    override operator fun Number.plus(b: Variable<T>): Variable<T> =
-        derive(variable { this@plus.toDouble() * one + b.value }) { z ->
-            b.d += z.d
-        }
-
-    override operator fun Variable<T>.plus(b: Number): Variable<T> = b.plus(this)
-
-    override operator fun Number.minus(b: Variable<T>): Variable<T> =
-        derive(variable { this@minus.toDouble() * one - b.value }) { z -> b.d -= z.d }
-
-    override operator fun Variable<T>.minus(b: Number): Variable<T> =
-        derive(variable { this@minus.value - one * b.toDouble() }) { z -> this@minus.d += z.d }
-}
-
-/**
- * Automatic Differentiation context class.
- */
-@PublishedApi
-internal class AutoDiffContext<T : Any, F : Field<T>>(override val context: F) : 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
-    val derivatives: MutableMap<Variable<T>, T> = hashMapOf()
-    override val zero: Variable<T> get() = Variable(context.zero)
-    override val one: Variable<T> get() = Variable(context.one)
-
-    /**
-     * A variable coupled with its derivative. For internal use only
-     */
-    private class VariableWithDeriv<T : Any>(x: T, var d: T) : Variable<T>(x)
-
-    override fun variable(value: T): Variable<T> =
-        VariableWithDeriv(value, context.zero)
-
-    override var Variable<T>.d: T
-        get() = (this as? VariableWithDeriv)?.d ?: derivatives[this] ?: context.zero
-        set(value) = if (this is VariableWithDeriv) d = value else derivatives[this] = value
-
-    @Suppress("UNCHECKED_CAST")
-    override fun <R> derive(value: R, block: F.(R) -> Unit): R {
-        // save block to stack for backward pass
-        if (sp >= stack.size) stack = stack.copyOf(stack.size * 2)
-        stack[sp++] = block
-        stack[sp++] = value
-        return value
-    }
-
-    @Suppress("UNCHECKED_CAST")
-    fun runBackwardPass() {
-        while (sp > 0) {
-            val value = stack[--sp]
-            val block = stack[--sp] as F.(Any?) -> Unit
-            context.block(value)
-        }
-    }
-
-    // Basic math (+, -, *, /)
-
-    override fun add(a: Variable<T>, b: Variable<T>): Variable<T> = derive(variable { a.value + b.value }) { z ->
-        a.d += z.d
-        b.d += z.d
-    }
-
-    override fun multiply(a: Variable<T>, b: Variable<T>): Variable<T> = derive(variable { a.value * b.value }) { z ->
-        a.d += z.d * b.value
-        b.d += z.d * a.value
-    }
-
-    override fun divide(a: Variable<T>, b: Variable<T>): Variable<T> = derive(variable { 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: Variable<T>, k: Number): Variable<T> = derive(variable { k.toDouble() * a.value }) { z ->
-        a.d += z.d * k.toDouble()
-    }
-}
-
-// Extensions for differentiation of various basic mathematical functions
-
-// x ^ 2
-public fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>, y: Double): Variable<T> =
-    derive(variable { 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: Variable<T>, y: Int): Variable<T> =
-    pow(x, y.toDouble())
-
-// exp(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: Variable<T>): Variable<T> =
-    derive(variable { exp(x.value) }) { z -> x.d += z.d * z.value }
-
-// ln(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>, y: Variable<T>): Variable<T> =
-    exp(y * ln(x))
-
-// sin(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { cos(x.value) }) { z -> x.d -= z.d * sin(x.value) }
-
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tan(x: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { sin(x.value) }) { z -> x.d += z.d * cosh(x.value) }
-
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cosh(x: Variable<T>): Variable<T> =
-    derive(variable { cos(x.value) }) { z -> x.d += z.d * sinh(x.value) }
-
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tanh(x: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { 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: Variable<T>): Variable<T> =
-    derive(variable { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) }
-

kmath-core/src/commonMain/kotlin/kscience/kmath/operations/Complex.kt

@@ -195,6 +195,7 @@ public data class Complex(val re: Double, val im: Double) : FieldElement<Complex
     }
 }
 
+
 /**
  * Creates a complex number with real part equal to this real.
  *

kmath-core/src/commonTest/kotlin/kscience/kmath/expressions/ExpressionFieldTest.kt

@@ -6,19 +6,21 @@ import kscience.kmath.operations.RealField
 import kscience.kmath.operations.invoke
 import kotlin.test.Test
 import kotlin.test.assertEquals
+import kotlin.test.assertFails
 
 class ExpressionFieldTest {
+    val x by symbol
     @Test
     fun testExpression() {
         val context = FunctionalExpressionField(RealField)
 
         val expression = context {
-            val x = variable("x", 2.0)
+            val x by binding()
             x * x + 2 * x + one
         }
 
-        assertEquals(expression("x" to 1.0), 4.0)
+        assertEquals(expression(x to 1.0), 4.0)
-        assertEquals(expression(), 9.0)
+        assertFails {  expression()}
     }
 
     @Test
@@ -26,33 +28,33 @@ class ExpressionFieldTest {
         val context = FunctionalExpressionField(ComplexField)
 
         val expression = context {
-            val x = variable("x", Complex(2.0, 0.0))
+            val  x = bind(x)
             x * x + 2 * x + one
         }
 
-        assertEquals(expression("x" to Complex(1.0, 0.0)), Complex(4.0, 0.0))
+        assertEquals(expression(x to Complex(1.0, 0.0)), Complex(4.0, 0.0))
-        assertEquals(expression(), Complex(9.0, 0.0))
+        //assertEquals(expression(), Complex(9.0, 0.0))
     }
 
     @Test
     fun separateContext() {
         fun <T> FunctionalExpressionField<T, *>.expression(): Expression<T> {
-            val x = variable("x")
+            val x by binding()
             return x * x + 2 * x + one
         }
 
         val expression = FunctionalExpressionField(RealField).expression()
-        assertEquals(expression("x" to 1.0), 4.0)
+        assertEquals(expression(x to 1.0), 4.0)
     }
 
     @Test
     fun valueExpression() {
         val expressionBuilder: FunctionalExpressionField<Double, *>.() -> Expression<Double> = {
-            val x = variable("x")
+            val x by binding()
             x * x + 2 * x + one
         }
 
         val expression = FunctionalExpressionField(RealField).expressionBuilder()
-        assertEquals(expression("x" to 1.0), 4.0)
+        assertEquals(expression(x to 1.0), 4.0)
     }
 }

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

@@ -0,0 +1,285 @@
+package kscience.kmath.expressions
+
+import kscience.kmath.operations.RealField
+import kscience.kmath.structures.asBuffer
+import kotlin.math.E
+import kotlin.math.PI
+import kotlin.math.pow
+import kotlin.math.sqrt
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.assertTrue
+
+class SimpleAutoDiffTest {
+
+    fun dx(
+        xBinding: Pair<Symbol, Double>,
+        body: SimpleAutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
+    ): DerivationResult<Double> = RealField.simpleAutoDiff(xBinding) { body(bind(xBinding.first)) }
+
+    fun dxy(
+        xBinding: Pair<Symbol, Double>,
+        yBinding: Pair<Symbol, Double>,
+        body: SimpleAutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>, y: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
+    ): DerivationResult<Double> = RealField.simpleAutoDiff(xBinding, yBinding) {
+        body(bind(xBinding.first), bind(yBinding.first))
+    }
+
+    fun diff(block: SimpleAutoDiffField<Double, RealField>.() -> AutoDiffValue<Double>): SimpleAutoDiffExpression<Double, RealField> {
+        return SimpleAutoDiffExpression(RealField, block)
+    }
+
+    val x by symbol
+    val y by symbol
+    val z by symbol
+
+    @Test
+    fun testPlusX2() {
+        val y = RealField.simpleAutoDiff(x to 3.0) {
+            // diff w.r.t this x at 3
+            val x = bind(x)
+            x + x
+        }
+        assertEquals(6.0, y.value) //    y  = x + x = 6
+        assertEquals(2.0, y.derivative(x)) // dy/dx = 2
+    }
+
+    @Test
+    fun testPlusX2Expr() {
+        val expr = diff {
+            val x = bind(x)
+            x + x
+        }
+        assertEquals(6.0, expr(x to 3.0)) //    y  = x + x = 6
+        assertEquals(2.0, expr.derivative(x)(x to 3.0)) // dy/dx = 2
+    }
+
+
+    @Test
+    fun testPlus() {
+        // two variables
+        val z = RealField.simpleAutoDiff(x to 2.0, y to 3.0) {
+            val x = bind(x)
+            val y = bind(y)
+            x + y
+        }
+        assertEquals(5.0, z.value) //    z  = x + y = 5
+        assertEquals(1.0, z.derivative(x)) // dz/dx = 1
+        assertEquals(1.0, z.derivative(y)) // dz/dy = 1
+    }
+
+    @Test
+    fun testMinus() {
+        // two variables
+        val z = RealField.simpleAutoDiff(x to 7.0, y to 3.0) {
+            val x = bind(x)
+            val y = bind(y)
+
+            x - y
+        }
+        assertEquals(4.0, z.value)  //    z  = x - y = 4
+        assertEquals(1.0, z.derivative(x))  // dz/dx = 1
+        assertEquals(-1.0, z.derivative(y)) // dz/dy = -1
+    }
+
+    @Test
+    fun testMulX2() {
+        val y = dx(x to 3.0) { x ->
+            // diff w.r.t this x at 3
+            x * x
+        }
+        assertEquals(9.0, y.value) //    y  = x * x = 9
+        assertEquals(6.0, y.derivative(x)) // dy/dx = 2 * x = 7
+    }
+
+    @Test
+    fun testSqr() {
+        val y = dx(x to 3.0) { x -> sqr(x) }
+        assertEquals(9.0, y.value) //    y  = x ^ 2 = 9
+        assertEquals(6.0, y.derivative(x)) // dy/dx = 2 * x = 7
+    }
+
+    @Test
+    fun testSqrSqr() {
+        val y = dx(x to 2.0) { x -> sqr(sqr(x)) }
+        assertEquals(16.0, y.value) //     y = x ^ 4   = 16
+        assertEquals(32.0, y.derivative(x)) // dy/dx = 4 * x^3 = 32
+    }
+
+    @Test
+    fun testX3() {
+        val y = dx(x to 2.0) { x ->
+            // diff w.r.t this x at 2
+            x * x * x
+        }
+        assertEquals(8.0, y.value)  //    y  = x * x * x = 8
+        assertEquals(12.0, y.derivative(x)) // dy/dx = 3 * x * x = 12
+    }
+
+    @Test
+    fun testDiv() {
+        val z = dxy(x to 5.0, y to 2.0) { x, y ->
+            x / y
+        }
+        assertEquals(2.5, z.value)   //     z =  x / y   = 2.5
+        assertEquals(0.5, z.derivative(x))   // dz/dx =  1 / y   = 0.5
+        assertEquals(-1.25, z.derivative(y)) // dz/dy = -x / y^2 = -1.25
+    }
+
+    @Test
+    fun testPow3() {
+        val y = dx(x to 2.0) { x ->
+            // diff w.r.t this x at 2
+            pow(x, 3)
+        }
+        assertEquals(8.0, y.value)  //    y  = x ^ 3     = 8
+        assertEquals(12.0, y.derivative(x)) // dy/dx = 3 * x ^ 2 = 12
+    }
+
+    @Test
+    fun testPowFull() {
+        val z = dxy(x to 2.0, y to 3.0) { x, y ->
+            pow(x, y)
+        }
+        assertApprox(8.0, z.value)           //     z = x ^ y = 8
+        assertApprox(12.0, z.derivative(x))          // dz/dx = y * x ^ (y - 1) = 12
+        assertApprox(8.0 * kotlin.math.ln(2.0), z.derivative(y)) // dz/dy = x ^ y * ln(x)
+    }
+
+    @Test
+    fun testFromPaper() {
+        val y = dx(x to 3.0) { x -> 2 * x + x * x * x }
+        assertEquals(33.0, y.value)  //     y = 2 * x + x * x * x = 33
+        assertEquals(29.0, y.derivative(x))  // dy/dx = 2 + 3 * x * x = 29
+    }
+
+    @Test
+    fun testInnerVariable() {
+        val y = dx(x to 1.0) { x ->
+            const(1.0) * x
+        }
+        assertEquals(1.0, y.value)          //     y = x ^ n = 1
+        assertEquals(1.0, y.derivative(x)) // dy/dx = n * x ^ (n - 1) = n - 1
+    }
+
+    @Test
+    fun testLongChain() {
+        val n = 10_000
+        val y = dx(x to 1.0) { x ->
+            var res = const(1.0)
+            for (i in 1..n) res *= x
+            res
+        }
+        assertEquals(1.0, y.value)          //     y = x ^ n = 1
+        assertEquals(n.toDouble(), y.derivative(x)) // dy/dx = n * x ^ (n - 1) = n - 1
+    }
+
+    @Test
+    fun testExample() {
+        val y = dx(x to 2.0) { x -> sqr(x) + 5 * x + 3 }
+        assertEquals(17.0, y.value) // the value of result (y)
+        assertEquals(9.0, y.derivative(x))  // dy/dx
+    }
+
+    @Test
+    fun testSqrt() {
+        val y = dx(x to 16.0) { x -> sqrt(x) }
+        assertEquals(4.0, y.value)     //     y = x ^ 1/2 = 4
+        assertEquals(1.0 / 8, y.derivative(x)) // dy/dx = 1/2 / x ^ 1/4 = 1/8
+    }
+
+    @Test
+    fun testSin() {
+        val y = dx(x to PI / 6.0) { x -> sin(x) }
+        assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5
+        assertApprox(sqrt(3.0) / 2, y.derivative(x)) // dy/dx = cos(pi/6) = sqrt(3)/2
+    }
+
+    @Test
+    fun testCos() {
+        val y = dx(x to PI / 6) { x -> cos(x) }
+        assertApprox(sqrt(3.0) / 2, y.value) //y = cos(pi/6) = sqrt(3)/2
+        assertApprox(-0.5, y.derivative(x)) // dy/dx = -sin(pi/6) = -0.5
+    }
+
+    @Test
+    fun testTan() {
+        val y = dx(x to PI / 6) { x -> tan(x) }
+        assertApprox(1.0 / sqrt(3.0), y.value) // y = tan(pi/6) = 1/sqrt(3)
+        assertApprox(4.0 / 3.0, y.derivative(x)) // dy/dx = sec(pi/6)^2 = 4/3
+    }
+
+    @Test
+    fun testAsin() {
+        val y = dx(x to PI / 6) { x -> asin(x) }
+        assertApprox(kotlin.math.asin(PI / 6.0), y.value) // y = asin(pi/6)
+        assertApprox(6.0 / sqrt(36 - PI * PI), y.derivative(x)) // dy/dx = 6/sqrt(36-pi^2)
+    }
+
+    @Test
+    fun testAcos() {
+        val y = dx(x to PI / 6) { x -> acos(x) }
+        assertApprox(kotlin.math.acos(PI / 6.0), y.value) // y = acos(pi/6)
+        assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.derivative(x)) // dy/dx = -6/sqrt(36-pi^2)
+    }
+
+    @Test
+    fun testAtan() {
+        val y = dx(x to PI / 6) { x -> atan(x) }
+        assertApprox(kotlin.math.atan(PI / 6.0), y.value) // y = atan(pi/6)
+        assertApprox(36.0 / (36.0 + PI * PI), y.derivative(x)) // dy/dx = 36/(36+pi^2)
+    }
+
+    @Test
+    fun testSinh() {
+        val y = dx(x to 0.0) { x -> sinh(x) }
+        assertApprox(kotlin.math.sinh(0.0), y.value) // y = sinh(0)
+        assertApprox(kotlin.math.cosh(0.0), y.derivative(x)) // dy/dx = cosh(0)
+    }
+
+    @Test
+    fun testCosh() {
+        val y = dx(x to 0.0) { x -> cosh(x) }
+        assertApprox(1.0, y.value) //y = cosh(0)
+        assertApprox(0.0, y.derivative(x)) // dy/dx = sinh(0)
+    }
+
+    @Test
+    fun testTanh() {
+        val y = dx(x to 1.0) { x -> tanh(x) }
+        assertApprox((E * E - 1) / (E * E + 1), y.value) // y = tanh(pi/6)
+        assertApprox(1.0 / kotlin.math.cosh(1.0).pow(2), y.derivative(x)) // dy/dx = sech(pi/6)^2
+    }
+
+    @Test
+    fun testAsinh() {
+        val y = dx(x to PI / 6) { x -> asinh(x) }
+        assertApprox(kotlin.math.asinh(PI / 6.0), y.value) // y = asinh(pi/6)
+        assertApprox(6.0 / sqrt(36 + PI * PI), y.derivative(x)) // dy/dx = 6/sqrt(pi^2+36)
+    }
+
+    @Test
+    fun testAcosh() {
+        val y = dx(x to PI / 6) { x -> acosh(x) }
+        assertApprox(kotlin.math.acosh(PI / 6.0), y.value) // y = acosh(pi/6)
+        assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.derivative(x)) // dy/dx = -6/sqrt(36-pi^2)
+    }
+
+    @Test
+    fun testAtanh() {
+        val y = dx(x to PI / 6) { x -> atanh(x) }
+        assertApprox(kotlin.math.atanh(PI / 6.0), y.value) // y = atanh(pi/6)
+        assertApprox(-36.0 / (PI * PI - 36.0), y.derivative(x)) // dy/dx = -36/(pi^2-36)
+    }
+
+    @Test
+    fun testDivGrad() {
+        val res = dxy(x to 1.0, y to 2.0) { x, y -> 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)
+    }
+}

kmath-core/src/commonTest/kotlin/kscience/kmath/misc/AutoDiffTest.kt

@@ -1,261 +0,0 @@
-package kscience.kmath.misc
-
-import kscience.kmath.operations.RealField
-import kscience.kmath.structures.asBuffer
-import kotlin.math.PI
-import kotlin.math.pow
-import kotlin.math.sqrt
-import kotlin.test.Test
-import kotlin.test.assertEquals
-import kotlin.test.assertTrue
-
-class AutoDiffTest {
-    inline fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>): DerivationResult<Double> =
-        RealField.deriv(body)
-
-    @Test
-    fun testPlusX2() {
-        val x = Variable(3.0) // diff w.r.t this x at 3
-        val y = deriv { x + x }
-        assertEquals(6.0, y.value) //    y  = x + x = 6
-        assertEquals(2.0, y.deriv(x)) // dy/dx = 2
-    }
-
-    @Test
-    fun testPlus() {
-        // two variables
-        val x = Variable(2.0)
-        val y = Variable(3.0)
-        val z = deriv { x + y }
-        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
-    }
-
-    @Test
-    fun testMinus() {
-        // two variables
-        val x = Variable(7.0)
-        val y = Variable(3.0)
-        val z = deriv { x - y }
-        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
-    }
-
-    @Test
-    fun testMulX2() {
-        val x = Variable(3.0) // diff w.r.t this x at 3
-        val y = deriv { x * x }
-        assertEquals(9.0, y.value) //    y  = x * x = 9
-        assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
-    }
-
-    @Test
-    fun testSqr() {
-        val x = Variable(3.0)
-        val y = deriv { sqr(x) }
-        assertEquals(9.0, y.value) //    y  = x ^ 2 = 9
-        assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
-    }
-
-    @Test
-    fun testSqrSqr() {
-        val x = Variable(2.0)
-        val y = deriv { sqr(sqr(x)) }
-        assertEquals(16.0, y.value) //     y = x ^ 4   = 16
-        assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32
-    }
-
-    @Test
-    fun testX3() {
-        val x = Variable(2.0) // diff w.r.t this x at 2
-        val y = deriv { x * x * x }
-        assertEquals(8.0, y.value)  //    y  = x * x * x = 8
-        assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12
-    }
-
-    @Test
-    fun testDiv() {
-        val x = Variable(5.0)
-        val y = Variable(2.0)
-        val z = deriv { x / y }
-        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
-    }
-
-    @Test
-    fun testPow3() {
-        val x = Variable(2.0) // diff w.r.t this x at 2
-        val y = deriv { pow(x, 3) }
-        assertEquals(8.0, y.value)  //    y  = x ^ 3     = 8
-        assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12
-    }
-
-    @Test
-    fun testPowFull() {
-        val x = Variable(2.0)
-        val y = Variable(3.0)
-        val z = deriv { pow(x, y) }
-        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)
-    }
-
-    @Test
-    fun testFromPaper() {
-        val x = Variable(3.0)
-        val y = deriv { 2 * x + x * x * x }
-        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
-    }
-
-    @Test
-    fun testInnerVariable() {
-        val x = Variable(1.0)
-        val y = deriv {
-            Variable(1.0) * x
-        }
-        assertEquals(1.0, y.value)          //     y = x ^ n = 1
-        assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
-    }
-
-    @Test
-    fun testLongChain() {
-        val n = 10_000
-        val x = Variable(1.0)
-        val y = deriv {
-            var res = Variable(1.0)
-            for (i in 1..n) res *= x
-            res
-        }
-        assertEquals(1.0, y.value)          //     y = x ^ n = 1
-        assertEquals(n.toDouble(), y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
-    }
-
-    @Test
-    fun testExample() {
-        val x = Variable(2.0)
-        val y = deriv { sqr(x) + 5 * x + 3 }
-        assertEquals(17.0, y.value) // the value of result (y)
-        assertEquals(9.0, y.deriv(x))  // dy/dx
-    }
-
-    @Test
-    fun testSqrt() {
-        val x = Variable(16.0)
-        val y = deriv { sqrt(x) }
-        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
-    }
-
-    @Test
-    fun testSin() {
-        val x = Variable(PI / 6.0)
-        val y = deriv { sin(x) }
-        assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5
-        assertApprox(sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(pi/6) = sqrt(3)/2
-    }
-
-    @Test
-    fun testCos() {
-        val x = Variable(PI / 6)
-        val y = deriv { cos(x) }
-        assertApprox(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 testTan() {
-        val x = Variable(PI / 6)
-        val y = deriv { tan(x) }
-        assertApprox(1.0 / sqrt(3.0), y.value) // y = tan(pi/6) = 1/sqrt(3)
-        assertApprox(4.0 / 3.0, y.deriv(x)) // dy/dx = sec(pi/6)^2 = 4/3
-    }
-
-    @Test
-    fun testAsin() {
-        val x = Variable(PI / 6)
-        val y = deriv { asin(x) }
-        assertApprox(kotlin.math.asin(PI / 6.0), y.value) // y = asin(pi/6)
-        assertApprox(6.0 / sqrt(36 - PI * PI), y.deriv(x)) // dy/dx = 6/sqrt(36-pi^2)
-    }
-
-    @Test
-    fun testAcos() {
-        val x = Variable(PI / 6)
-        val y = deriv { acos(x) }
-        assertApprox(kotlin.math.acos(PI / 6.0), y.value) // y = acos(pi/6)
-        assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.deriv(x)) // dy/dx = -6/sqrt(36-pi^2)
-    }
-
-    @Test
-    fun testAtan() {
-        val x = Variable(PI / 6)
-        val y = deriv { atan(x) }
-        assertApprox(kotlin.math.atan(PI / 6.0), y.value) // y = atan(pi/6)
-        assertApprox(36.0 / (36.0 + PI * PI), y.deriv(x)) // dy/dx = 36/(36+pi^2)
-    }
-
-    @Test
-    fun testSinh() {
-        val x = Variable(0.0)
-        val y = deriv { sinh(x) }
-        assertApprox(kotlin.math.sinh(0.0), y.value) // y = sinh(0)
-        assertApprox(kotlin.math.cosh(0.0), y.deriv(x)) // dy/dx = cosh(0)
-    }
-
-    @Test
-    fun testCosh() {
-        val x = Variable(0.0)
-        val y = deriv { cosh(x) }
-        assertApprox(1.0, y.value) //y = cosh(0)
-        assertApprox(0.0, y.deriv(x)) // dy/dx = sinh(0)
-    }
-
-    @Test
-    fun testTanh() {
-        val x = Variable(PI / 6)
-        val y = deriv { tanh(x) }
-        assertApprox(1.0 / sqrt(3.0), y.value) // y = tanh(pi/6)
-        assertApprox(1.0 / kotlin.math.cosh(PI / 6.0).pow(2), y.deriv(x)) // dy/dx = sech(pi/6)^2
-    }
-
-    @Test
-    fun testAsinh() {
-        val x = Variable(PI / 6)
-        val y = deriv { asinh(x) }
-        assertApprox(kotlin.math.asinh(PI / 6.0), y.value) // y = asinh(pi/6)
-        assertApprox(6.0 / sqrt(36 + PI * PI), y.deriv(x)) // dy/dx = 6/sqrt(pi^2+36)
-    }
-
-    @Test
-    fun testAcosh() {
-        val x = Variable(PI / 6)
-        val y = deriv { acosh(x) }
-        assertApprox(kotlin.math.acosh(PI / 6.0), y.value) // y = acosh(pi/6)
-        assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.deriv(x)) // dy/dx = -6/sqrt(36-pi^2)
-    }
-
-    @Test
-    fun testAtanh() {
-        val x = Variable(PI / 6.0)
-        val y = deriv { atanh(x) }
-        assertApprox(kotlin.math.atanh(PI / 6.0), y.value) // y = atanh(pi/6)
-        assertApprox(-36.0 / (PI * PI - 36.0), y.deriv(x)) // dy/dx = -36/(pi^2-36)
-    }
-
-    @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)
-    }
-}

kmath-functions/src/commonMain/kotlin/kscience/kmath/functions/Polynomial.kt

@@ -8,13 +8,13 @@ import kotlin.contracts.contract
 import kotlin.math.max
 import kotlin.math.pow
 
-// TODO make `inline`, when KT-41771 gets fixed
 /**
  * Polynomial coefficients without fixation on specific context they are applied to
  * @param coefficients constant is the leftmost coefficient
  */
 public inline class Polynomial<T : Any>(public val coefficients: List<T>)
 
+@Suppress("FunctionName")
 public fun <T : Any> Polynomial(vararg coefficients: T): Polynomial<T> = Polynomial(coefficients.toList())
 
 public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { index, acc, d -> acc + d.pow(index) }
@@ -33,14 +33,6 @@ public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring
     res
 }
 
-/**
- * Represent a polynomial as a context-dependent function
- */
-public fun <T : Any, C : Ring<T>> Polynomial<T>.asMathFunction(): MathFunction<T, C, T> =
-    object : MathFunction<T, C, T> {
-        override fun C.invoke(arg: T): T = value(this, arg)
-    }
-
 /**
  * Represent the polynomial as a regular context-less function
  */
@@ -49,7 +41,7 @@ public fun <T : Any, C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T =
 /**
  * An algebra for polynomials
  */
-public class PolynomialSpace<T : Any, C : Ring<T>>(public val ring: C) : Space<Polynomial<T>> {
+public class PolynomialSpace<T : Any, C : Ring<T>>(private val ring: C) : Space<Polynomial<T>> {
     public override val zero: Polynomial<T> = Polynomial(emptyList())
 
     public override fun add(a: Polynomial<T>, b: Polynomial<T>): Polynomial<T> {

kmath-functions/src/commonMain/kotlin/kscience/kmath/functions/functions.kt

@@ -1,34 +0,0 @@
-package kscience.kmath.functions
-
-import kscience.kmath.operations.Algebra
-import kscience.kmath.operations.RealField
-
-// TODO make fun interface when KT-41770 is fixed
-/**
- * A regular function that could be called only inside specific algebra context
- * @param T source type
- * @param C source algebra constraint
- * @param R result type
- */
-public /*fun*/ interface MathFunction<T, C : Algebra<T>, R> {
-    public operator fun C.invoke(arg: T): R
-}
-
-public fun <R> MathFunction<Double, RealField, R>.invoke(arg: Double): R = RealField.invoke(arg)
-
-/**
- * A suspendable function defined in algebraic context
- */
-// TODO make fun interface, when the new JVM IR is enabled
-public interface SuspendableMathFunction<T, C : Algebra<T>, R> {
-    public suspend operator fun C.invoke(arg: T): R
-}
-
-public suspend fun <R> SuspendableMathFunction<Double, RealField, R>.invoke(arg: Double): R = RealField.invoke(arg)
-
-/**
- * A parametric function with parameter
- */
-public fun interface ParametricFunction<T, P, C : Algebra<T>> {
-    public operator fun C.invoke(arg: T, parameter: P): T
-}

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/Distribution.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kscience.kmath.chains.Chain
 import kscience.kmath.chains.collect

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/FactorizedDistribution.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kscience.kmath.chains.Chain
 import kscience.kmath.chains.SimpleChain

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/Fitting.kt

@@ -0,0 +1,59 @@
+package kscience.kmath.stat
+
+import kscience.kmath.expressions.*
+import kscience.kmath.operations.ExtendedField
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.indices
+import kotlin.math.pow
+
+public object Fitting {
+
+    /**
+     * Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic differentiation
+     */
+    public fun <T : Any, I : Any, A> chiSquared(
+        autoDiff: AutoDiffProcessor<T, I, A>,
+        x: Buffer<T>,
+        y: Buffer<T>,
+        yErr: Buffer<T>,
+        model: A.(I) -> I,
+    ): DifferentiableExpression<T> where A : ExtendedField<I>, A : ExpressionAlgebra<T, I> {
+        require(x.size == y.size) { "X and y buffers should be of the same size" }
+        require(y.size == yErr.size) { "Y and yErr buffer should of the same size" }
+        return autoDiff.process {
+            var sum = zero
+            x.indices.forEach {
+                val xValue = const(x[it])
+                val yValue = const(y[it])
+                val yErrValue = const(yErr[it])
+                val modelValue = model(xValue)
+                sum += ((yValue - modelValue) / yErrValue).pow(2)
+            }
+            sum
+        }
+    }
+
+    /**
+     * Generate a chi squared expression from given x-y-sigma model represented by an expression. Does not provide derivatives
+     */
+    public fun chiSquared(
+        x: Buffer<Double>,
+        y: Buffer<Double>,
+        yErr: Buffer<Double>,
+        model: Expression<Double>,
+        xSymbol: Symbol = StringSymbol("x"),
+    ): Expression<Double> {
+        require(x.size == y.size) { "X and y buffers should be of the same size" }
+        require(y.size == yErr.size) { "Y and yErr buffer should of the same size" }
+        return Expression { arguments ->
+            x.indices.sumByDouble {
+                val xValue = x[it]
+                val yValue = y[it]
+                val yErrValue = yErr[it]
+                val modifiedArgs = arguments + (xSymbol to xValue)
+                val modelValue = model(modifiedArgs)
+                ((yValue - modelValue) / yErrValue).pow(2)
+            }
+        }
+    }
+}

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/OptimizationProblem.kt

@@ -0,0 +1,91 @@
+package kscience.kmath.stat
+
+import kscience.kmath.expressions.DifferentiableExpression
+import kscience.kmath.expressions.Expression
+import kscience.kmath.expressions.Symbol
+
+public interface OptimizationFeature
+
+public class OptimizationResult<T>(
+    public val point: Map<Symbol, T>,
+    public val value: T,
+    public val features: Set<OptimizationFeature> = emptySet(),
+) {
+    override fun toString(): String {
+        return "OptimizationResult(point=$point, value=$value)"
+    }
+}
+
+public operator fun <T> OptimizationResult<T>.plus(
+    feature: OptimizationFeature,
+): OptimizationResult<T> = OptimizationResult(point, value, features + feature)
+
+/**
+ * A configuration builder for optimization problem
+ */
+public interface OptimizationProblem<T : Any> {
+    /**
+     * Define the initial guess for the optimization problem
+     */
+    public fun initialGuess(map: Map<Symbol, T>): Unit
+
+    /**
+     * Set an objective function expression
+     */
+    public fun expression(expression: Expression<T>): Unit
+
+    /**
+     * Set a differentiable expression as objective function as function and gradient provider
+     */
+    public fun diffExpression(expression: DifferentiableExpression<T>): Unit
+
+    /**
+     * Update the problem from previous optimization run
+     */
+    public fun update(result: OptimizationResult<T>)
+
+    /**
+     * Make an optimization run
+     */
+    public fun optimize(): OptimizationResult<T>
+}
+
+public interface OptimizationProblemFactory<T : Any, out P : OptimizationProblem<T>> {
+    public fun build(symbols: List<Symbol>): P
+
+}
+
+public operator fun <T : Any, P : OptimizationProblem<T>> OptimizationProblemFactory<T, P>.invoke(
+    symbols: List<Symbol>,
+    block: P.() -> Unit,
+): P = build(symbols).apply(block)
+
+
+/**
+ * Optimize expression without derivatives using specific [OptimizationProblemFactory]
+ */
+public fun <T : Any, F : OptimizationProblem<T>> Expression<T>.optimizeWith(
+    factory: OptimizationProblemFactory<T, F>,
+    vararg symbols: Symbol,
+    configuration: F.() -> Unit,
+): OptimizationResult<T> {
+    require(symbols.isNotEmpty()) { "Must provide a list of symbols for optimization" }
+    val problem = factory(symbols.toList(),configuration)
+    problem.expression(this)
+    return problem.optimize()
+}
+
+/**
+ * Optimize differentiable expression using specific [OptimizationProblemFactory]
+ */
+public fun <T : Any, F : OptimizationProblem<T>>  DifferentiableExpression<T>.optimizeWith(
+    factory: OptimizationProblemFactory<T, F>,
+    vararg symbols: Symbol,
+    configuration: F.() -> Unit,
+): OptimizationResult<T> {
+    require(symbols.isNotEmpty()) { "Must provide a list of symbols for optimization" }
+    val problem = factory(symbols.toList(), configuration)
+    problem.diffExpression(this)
+    return problem.optimize()
+}
+

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/RandomChain.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kscience.kmath.chains.Chain
 

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/RandomGenerator.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kotlin.random.Random
 

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/SamplerAlgebra.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kscience.kmath.chains.Chain
 import kscience.kmath.chains.ConstantChain

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/Statistic.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kotlinx.coroutines.CoroutineDispatcher
 import kotlinx.coroutines.Dispatchers

kmath-stat/src/commonMain/kotlin/kscience/kmath/stat/UniformDistribution.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kscience.kmath.chains.Chain
 import kscience.kmath.chains.SimpleChain

kmath-stat/src/jvmMain/kotlin/kscience/kmath/stat/RandomSourceGenerator.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import org.apache.commons.rng.UniformRandomProvider
 import org.apache.commons.rng.simple.RandomSource

kmath-stat/src/jvmMain/kotlin/kscience/kmath/stat/distributions.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kscience.kmath.chains.BlockingIntChain
 import kscience.kmath.chains.BlockingRealChain

kmath-stat/src/jvmTest/kotlin/kscience/kmath/stat/CommonsDistributionsTest.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kotlinx.coroutines.flow.take
 import kotlinx.coroutines.flow.toList

kmath-stat/src/jvmTest/kotlin/kscience/kmath/stat/SamplerTest.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kotlinx.coroutines.runBlocking
 import kotlin.test.Test

kmath-stat/src/jvmTest/kotlin/kscience/kmath/stat/StatisticTest.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.prob
+package kscience.kmath.stat
 
 import kotlinx.coroutines.flow.drop
 import kotlinx.coroutines.flow.first

settings.gradle.kts

@@ -10,8 +10,8 @@ pluginManagement {
         maven("https://dl.bintray.com/kotlin/kotlin-dev/")
     }
 
-    val toolsVersion = "0.6.1-dev-1.4.20-M1"
+    val toolsVersion = "0.6.4-dev-1.4.20-M2"
-    val kotlinVersion = "1.4.20-M1"
+    val kotlinVersion = "1.4.20-M2"
 
     plugins {
         id("kotlinx.benchmark") version "0.2.0-dev-20"
@@ -34,12 +34,12 @@ include(
     ":kmath-histograms",
     ":kmath-commons",
     ":kmath-viktor",
-    ":kmath-prob",
+    ":kmath-stat",
     ":kmath-nd4j",
     ":kmath-dimensions",
     ":kmath-for-real",
     ":kmath-geometry",
     ":kmath-ast",
-    ":examples",
+    ":kmath-ejml",
-    ":kmath-ejml"
+    ":examples"
 )