.space.kts

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

CHANGELOG.md

@@ -8,6 +8,11 @@
 - Automatic README generation for features (#139)
 - Native support for `memory`, `core` and `dimensions`
 - `kmath-ejml` to supply EJML SimpleMatrix wrapper.
+- 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
 
 ### Changed
 - Package changed from `scientifik` to `kscience.kmath`.
@@ -16,6 +21,8 @@
 - `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

@@ -53,9 +53,7 @@ can be used for a wide variety of purposes from high performance calculations to
 * **Commons-math wrapper** It is planned to gradually wrap most parts of [Apache commons-math](http://commons.apache.org/proper/commons-math/)
                            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:${kmathVersion}")
-    //api("scientifik:kmath-core:${kmathVersion}") for 0.1.3 and earlier
+    api("kscience.kmath:kmath-core:0.2.0-dev-2")
+    //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")
 
@@ -25,3 +25,7 @@ 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.prob.RandomGenerator
-import kscience.kmath.prob.normal
+import kscience.kmath.stat.Distribution
+import kscience.kmath.stat.RandomGenerator
+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 ->
-        Complex(index[0].toDouble() - index[1].toDouble(), index[0].toDouble() + index[1].toDouble())
+    val element = NDElement.complex(2, 2) { (i,j) ->
+        Complex(i.toDouble() - j.toDouble(), i.toDouble() + j.toDouble())
     }
     println(element)
 

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> {
-        override fun symbol(value: String): T = arguments[value] ?: algebra.symbol(value)
+    private inner class InnerAlgebra(val arguments: Map<Symbol, T>) : NumericAlgebra<T> {
+        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,
-                OBJECT_TYPE,
-                *OBJECT_TYPE.wrapToArrayIf { defaultValue != null }),
+            Type.getMethodDescriptor(OBJECT_TYPE, MAP_TYPE, STRING_TYPE),
             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 <K, V> Map<K, V>.getOrFail(key: K, default: V? = null): V =
-    this[key] ?: default ?: error("Parameter not found: $key")
+internal fun <V> Map<Symbol, V>.getOrFail(key: String): V = getValue(StringSymbol(key))

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

@@ -1,6 +1,5 @@
 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-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-functions"))
+    api(project(":kmath-stat"))
+    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) :
-    org.apache.commons.math3.random.RandomGenerator {
+public class CMRandomGeneratorWrapper(
+    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>,
-    block: DerivativeStructureField.() -> R
+    vararg parameters: Pair<Symbol, Double>,
+    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 x by variable
-            val y = variable("y")
+        val res: Double = diff(3, x to 1.0, y to 1.0) {
+            val x = bind(x)//by binding()
+            val y = symbol("y")
             val z = x * (-sin(x * y) + y)
-            z.deriv("x")
+            z.derivative(x)
         }
+        println(res)
     }
 
     @Test
     fun autoDifTest() {
-        val f = DiffExpression {
-            val x by variable
-            val y by variable
+        val f = DerivativeStructureExpression {
+            val x by binding()
+            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(6.0, f.derivative("x")("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))
     }
 }

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 companion object
+    public operator fun invoke(arguments: Map<Symbol, T>): T
 }
 
+/**
+ * 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) :
-    ExpressionAlgebra<T, Expression<T>> {
+public abstract class FunctionalExpressionAlgebra<T, A : Algebra<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> =
-        FunctionalBinaryOperation(algebra, operation, left, right)
+    public override fun binaryOperation(
+        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> =
-        FunctionalUnaryOperation(algebra, operation, arg)
+    public override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> = Expression { arguments ->
+        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> =
-        FunctionalConstProductExpression(algebra, a, k)
+    public override fun multiply(a: Expression<T>, k: Number): Expression<T> = Expression { arguments ->
+        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),
-    Field<Expression<T>> where A : Field<T>, A : NumericAlgebra<T> {
+    FunctionalExpressionRing<T, A>(algebra), Field<Expression<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(), 9.0)
+        assertEquals(expression(x to 1.0), 4.0)
+        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(), Complex(9.0, 0.0))
+        assertEquals(expression(x to Complex(1.0, 0.0)), Complex(4.0, 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 kotlinVersion = "1.4.20-M1"
+    val toolsVersion = "0.6.4-dev-1.4.20-M2"
+    val kotlinVersion = "1.4.20-M2"
 
     plugins {
         id("kotlinx.benchmark") version "0.2.0-dev-20"
@@ -34,11 +34,11 @@ include(
     ":kmath-histograms",
     ":kmath-commons",
     ":kmath-viktor",
-    ":kmath-prob",
+    ":kmath-stat",
     ":kmath-dimensions",
     ":kmath-for-real",
     ":kmath-geometry",
     ":kmath-ast",
-    ":examples",
-    ":kmath-ejml"
+    ":kmath-ejml",
+    ":examples"
 )