.github/workflows/build.yml

@@ -13,25 +13,13 @@ jobs:
     runs-on: ${{matrix.os}}
     timeout-minutes: 40
     steps:
-      - name: Checkout the repo
+      - uses: actions/checkout@v3.0.0
-        uses: actions/checkout@v2
+      - uses: actions/setup-java@v3.0.0
-      - name: Set up JDK 11
-        uses: DeLaGuardo/setup-graalvm@4.0
         with:
-          graalvm: 21.2.0
+          java-version: 11
-          java: java11
+          distribution: liberica
-          arch: amd64
-      - name: Cache gradle
-        uses: actions/cache@v2
-        with:
-          path: |
-            ~/.gradle/caches
-            ~/.gradle/wrapper
-          key: ${{ runner.os }}-gradle-${{ hashFiles('*.gradle.kts') }}
-          restore-keys: |
-            ${{ runner.os }}-gradle-
       - name: Cache konan
-        uses: actions/cache@v2
+        uses: actions/cache@v3.0.1
         with:
           path: ~/.konan
           key: ${{ runner.os }}-gradle-${{ hashFiles('*.gradle.kts') }}
@@ -39,5 +27,6 @@ jobs:
             ${{ runner.os }}-gradle-
       - name: Gradle Wrapper Validation
         uses: gradle/wrapper-validation-action@v1.0.4
-      - name: Build
+      - uses: gradle/gradle-build-action@v2.1.5
-        run: ./gradlew build --build-cache --no-daemon --stacktrace
+        with:
+          arguments: build

.github/workflows/pages.yml

@@ -1,28 +1,31 @@
 name: Dokka publication
 
 on:
-  push:
+  workflow_dispatch:
-    branches: [ master ]
+  release:
+    types: [ created ]
 
 jobs:
   build:
     runs-on: ubuntu-20.04
     timeout-minutes: 40
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3.0.0
-      - uses: DeLaGuardo/setup-graalvm@4.0
+      - uses: actions/setup-java@v3.0.0
         with:
-          graalvm: 21.2.0
+          java-version: 11
-          java: java11
+          distribution: liberica
-          arch: amd64
+      - name: Cache konan
-      - uses: actions/cache@v2
+        uses: actions/cache@v3.0.1
         with:
-          path: ~/.gradle/caches
+          path: ~/.konan
           key: ${{ runner.os }}-gradle-${{ hashFiles('*.gradle.kts') }}
           restore-keys: |
             ${{ runner.os }}-gradle-
-      - run: ./gradlew dokkaHtmlMultiModule --build-cache --no-daemon --no-parallel --stacktrace
+      - uses: gradle/gradle-build-action@v2.1.5
-      - uses: JamesIves/github-pages-deploy-action@4.1.0
+        with:
+          arguments: dokkaHtmlMultiModule --no-parallel
+      - uses: JamesIves/github-pages-deploy-action@v4.3.0
         with:
           branch: gh-pages
           folder: build/dokka/htmlMultiModule

.github/workflows/publish.yml

@@ -14,42 +14,38 @@ jobs:
         os: [ macOS-latest, windows-latest ]
     runs-on: ${{matrix.os}}
     steps:
-      - name: Checkout the repo
+      - uses: actions/checkout@v3.0.0
-        uses: actions/checkout@v2
+      - uses: actions/setup-java@v3.0.0
-      - name: Set up JDK 11
-        uses: DeLaGuardo/setup-graalvm@4.0
         with:
-          graalvm: 21.2.0
+          java-version: 11
-          java: java11
+          distribution: liberica
-          arch: amd64
-      - name: Cache gradle
-        uses: actions/cache@v2
-        with:
-          path: |
-            ~/.gradle/caches
-            ~/.gradle/wrapper
-          key: ${{ runner.os }}-gradle-${{ hashFiles('*.gradle.kts') }}
-          restore-keys: |
-            ${{ runner.os }}-gradle-
       - name: Cache konan
-        uses: actions/cache@v2
+        uses: actions/cache@v3.0.1
         with:
           path: ~/.konan
           key: ${{ runner.os }}-gradle-${{ hashFiles('*.gradle.kts') }}
           restore-keys: |
             ${{ runner.os }}-gradle-
-      - name: Gradle Wrapper Validation
+      - uses: gradle/wrapper-validation-action@v1.0.4
-        uses: gradle/wrapper-validation-action@v1.0.4
       - name: Publish Windows Artifacts
         if: matrix.os == 'windows-latest'
-        shell: cmd
+        uses: gradle/gradle-build-action@v2.1.5
-        run: >
+        with:
-          ./gradlew release --no-daemon --build-cache -Ppublishing.enabled=true
+          arguments: |
+            releaseAll
+            -Ppublishing.enabled=true
+            -Ppublishing.sonatype=false
             -Ppublishing.space.user=${{ secrets.SPACE_APP_ID }}
             -Ppublishing.space.token=${{ secrets.SPACE_APP_SECRET }}
       - name: Publish Mac Artifacts
         if: matrix.os == 'macOS-latest'
-        run: >
+        uses: gradle/gradle-build-action@v2.1.5
-          ./gradlew release --no-daemon --build-cache -Ppublishing.enabled=true -Ppublishing.platform=macosX64
+        with:
+          arguments: |
+            releaseMacosX64
+            releaseIosArm64
+            releaseIosX64
+            -Ppublishing.enabled=true
+            -Ppublishing.sonatype=false            
             -Ppublishing.space.user=${{ secrets.SPACE_APP_ID }}
             -Ppublishing.space.token=${{ secrets.SPACE_APP_SECRET }}

.gitignore

@@ -19,3 +19,4 @@ out/
 
 !/.idea/copyright/
 !/.idea/scopes/
+/kotlin-js-store/yarn.lock

CHANGELOG.md

@@ -2,6 +2,21 @@
 
 ## [Unreleased]
 ### Added
+
+### Changed
+- Kotlin 1.7
+- `LazyStructure` `deffered` -> `async` to comply with coroutines code style
+
+### Deprecated
+
+### Removed
+
+### Fixed
+
+### Security
+
+## [0.3.0]
+### Added
 - `ScaleOperations` interface
 - `Field` extends `ScaleOperations`
 - Basic integration API
@@ -19,6 +34,12 @@
 - Complex power
 - Separate methods for UInt, Int and Number powers. NaN safety.
 - Tensorflow prototype
+- `ValueAndErrorField`
+- MST compilation to WASM: #286
+- Jafama integration: #176
+- `contentEquals` with tolerance: #364
+- Compilation to TeX for MST: #254
+
 
 ### Changed
 - Exponential operations merged with hyperbolic functions
@@ -48,10 +69,15 @@
 - Operations -> Ops
 - Default Buffer and ND algebras are now Ops and lack neutral elements (0, 1) as well as algebra-level shapes.
 - Tensor algebra takes read-only structures as input and inherits AlgebraND
+- `UnivariateDistribution` renamed to `Distribution1D`
+- Rework of histograms.
+- `UnivariateFunction` -> `Function1D`, `MultivariateFunction` -> `FunctionND`
+
 
 ### Deprecated
 - Specialized `DoubleBufferAlgebra`
 
+
 ### Removed
 - Nearest in Domain. To be implemented in geometry package.
 - Number multiplication and division in main Algebra chain
@@ -62,10 +88,12 @@
 - Second generic from DifferentiableExpression
 - Algebra elements are completely removed. Use algebra contexts instead.
 
+
 ### Fixed
 - Ring inherits RingOperations, not GroupOperations
 - Univariate histogram filling
 
+
 ### Security
 
 ## [0.2.0]
@@ -88,6 +116,7 @@
 - New `MatrixFeature` interfaces for matrix decompositions
 - Basic Quaternion vector support in `kmath-complex`.
 
+
 ### Changed
 - Package changed from `scientifik` to `space.kscience`
 - Gradle version: 6.6 -> 6.8.2
@@ -112,7 +141,6 @@
 - `symbol` method in `Algebra` renamed to `bindSymbol` to avoid ambiguity
 - Add `out` projection to `Buffer` generic
 
-### Deprecated
 
 ### Removed
 - `kmath-koma` module because it doesn't support Kotlin 1.4.
@@ -122,13 +150,11 @@
 - `Real` class
 - StructureND identity and equals
 
+
 ### Fixed
 - `symbol` method in `MstExtendedField` (https://github.com/mipt-npm/kmath/pull/140)
 
-### Security
-
 ## [0.1.4]
-
 ### Added
 - Functional Expressions API
 - Mathematical Syntax Tree, its interpreter and API
@@ -146,6 +172,7 @@
 - Full hyperbolic functions support and default implementations within `ExtendedField`
 - Norm support for `Complex`
 
+
 ### Changed
 - `readAsMemory` now has `throws IOException` in JVM signature.
 - Several functions taking functional types were made `inline`.
@@ -157,6 +184,7 @@
 - Gradle version: 6.3 -> 6.6
 - Moved probability distributions to commons-rng and to `kmath-prob`
 
+
 ### Fixed
 - Missing copy method in Memory implementation on JS (https://github.com/mipt-npm/kmath/pull/106)
 - D3.dim value in `kmath-dimensions`

README.md

@@ -52,21 +52,18 @@ module definitions below. The module stability could have the following levels:
 
 ## Modules
 
-<hr/>
 
-* ### [benchmarks](benchmarks)
+### [benchmarks](benchmarks)
 > 
 >
 > **Maturity**: EXPERIMENTAL
-<hr/>
 
-* ### [examples](examples)
+### [examples](examples)
 > 
 >
 > **Maturity**: EXPERIMENTAL
-<hr/>
 
-* ### [kmath-ast](kmath-ast)
+### [kmath-ast](kmath-ast)
 > 
 >
 > **Maturity**: EXPERIMENTAL
@@ -77,15 +74,13 @@ module definitions below. The module stability could have the following levels:
 > - [mst-js-codegen](kmath-ast/src/jsMain/kotlin/space/kscience/kmath/estree/estree.kt) : Dynamic MST to JS compiler
 > - [rendering](kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/MathRenderer.kt) : Extendable MST rendering
 
-<hr/>
 
-* ### [kmath-commons](kmath-commons)
+### [kmath-commons](kmath-commons)
 > 
 >
 > **Maturity**: EXPERIMENTAL
-<hr/>
 
-* ### [kmath-complex](kmath-complex)
+### [kmath-complex](kmath-complex)
 > Complex numbers and quaternions.
 >
 > **Maturity**: PROTOTYPE
@@ -94,9 +89,8 @@ module definitions below. The module stability could have the following levels:
 > - [complex](kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt) : Complex Numbers
 > - [quaternion](kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt) : Quaternions
 
-<hr/>
 
-* ### [kmath-core](kmath-core)
+### [kmath-core](kmath-core)
 > Core classes, algebra definitions, basic linear algebra
 >
 > **Maturity**: DEVELOPMENT
@@ -112,21 +106,18 @@ performance calculations to code generation.
 > - [domains](kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains) : Domains
 > - [autodiff](kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt) : Automatic differentiation
 
-<hr/>
 
-* ### [kmath-coroutines](kmath-coroutines)
+### [kmath-coroutines](kmath-coroutines)
 > 
 >
 > **Maturity**: EXPERIMENTAL
-<hr/>
 
-* ### [kmath-dimensions](kmath-dimensions)
+### [kmath-dimensions](kmath-dimensions)
 > 
 >
 > **Maturity**: PROTOTYPE
-<hr/>
 
-* ### [kmath-ejml](kmath-ejml)
+### [kmath-ejml](kmath-ejml)
 > 
 >
 > **Maturity**: PROTOTYPE
@@ -136,9 +127,8 @@ performance calculations to code generation.
 > - [ejml-matrix](kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/EjmlMatrix.kt) : Matrix implementation.
 > - [ejml-linear-space](kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/EjmlLinearSpace.kt) : LinearSpace implementations.
 
-<hr/>
 
-* ### [kmath-for-real](kmath-for-real)
+### [kmath-for-real](kmath-for-real)
 > Extension module that should be used to achieve numpy-like behavior.
 All operations are specialized to work with `Double` numbers without declaring algebraic contexts.
 One can still use generic algebras though.
@@ -150,9 +140,8 @@ One can still use generic algebras though.
 > - [DoubleMatrix](kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/DoubleMatrix.kt) : Numpy-like operations for 2d real structures
 > - [grids](kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/structures/grids.kt) : Uniform grid generators
 
-<hr/>
 
-* ### [kmath-functions](kmath-functions)
+### [kmath-functions](kmath-functions)
 > 
 >
 > **Maturity**: EXPERIMENTAL
@@ -164,21 +153,18 @@ One can still use generic algebras though.
 > - [spline interpolation](kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt) : Cubic spline XY interpolator.
 > - [integration](kmath-functions/#) : Univariate and multivariate quadratures
 
-<hr/>
 
-* ### [kmath-geometry](kmath-geometry)
+### [kmath-geometry](kmath-geometry)
 > 
 >
 > **Maturity**: PROTOTYPE
-<hr/>
 
-* ### [kmath-histograms](kmath-histograms)
+### [kmath-histograms](kmath-histograms)
 > 
 >
 > **Maturity**: PROTOTYPE
-<hr/>
 
-* ### [kmath-jafama](kmath-jafama)
+### [kmath-jafama](kmath-jafama)
 > 
 >
 > **Maturity**: PROTOTYPE
@@ -186,15 +172,13 @@ One can still use generic algebras though.
 > **Features:**
 > - [jafama-double](kmath-jafama/src/main/kotlin/space/kscience/kmath/jafama/) : Double ExtendedField implementations based on Jafama
 
-<hr/>
 
-* ### [kmath-jupyter](kmath-jupyter)
+### [kmath-jupyter](kmath-jupyter)
 > 
 >
 > **Maturity**: PROTOTYPE
-<hr/>
 
-* ### [kmath-kotlingrad](kmath-kotlingrad)
+### [kmath-kotlingrad](kmath-kotlingrad)
 > 
 >
 > **Maturity**: EXPERIMENTAL
@@ -203,21 +187,18 @@ One can still use generic algebras though.
 > - [differentiable-mst-expression](kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/KotlingradExpression.kt) : MST based DifferentiableExpression.
 > - [scalars-adapters](kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/scalarsAdapters.kt) : Conversions between Kotlin∇'s SFun and MST
 
-<hr/>
 
-* ### [kmath-memory](kmath-memory)
+### [kmath-memory](kmath-memory)
 > An API and basic implementation for arranging objects in a continuous memory block.
 >
 > **Maturity**: DEVELOPMENT
-<hr/>
 
-* ### [kmath-multik](kmath-multik)
+### [kmath-multik](kmath-multik)
 > 
 >
 > **Maturity**: PROTOTYPE
-<hr/>
 
-* ### [kmath-nd4j](kmath-nd4j)
+### [kmath-nd4j](kmath-nd4j)
 > 
 >
 > **Maturity**: EXPERIMENTAL
@@ -227,27 +208,28 @@ One can still use generic algebras though.
 > - [nd4jarrayrings](kmath-nd4j/#) : Rings over Nd4jArrayStructure of Int and Long
 > - [nd4jarrayfields](kmath-nd4j/#) : Fields over Nd4jArrayStructure of Float and Double
 
-<hr/>
 
-* ### [kmath-optimization](kmath-optimization)
+### [kmath-optimization](kmath-optimization)
 > 
 >
 > **Maturity**: EXPERIMENTAL
-<hr/>
 
-* ### [kmath-stat](kmath-stat)
+### [kmath-stat](kmath-stat)
 > 
 >
 > **Maturity**: EXPERIMENTAL
-<hr/>
 
-* ### [kmath-symja](kmath-symja)
+### [kmath-symja](kmath-symja)
 > 
 >
 > **Maturity**: PROTOTYPE
-<hr/>
 
-* ### [kmath-tensors](kmath-tensors)
+### [kmath-tensorflow](kmath-tensorflow)
+> 
+>
+> **Maturity**: PROTOTYPE
+
+### [kmath-tensors](kmath-tensors)
 > 
 >
 > **Maturity**: PROTOTYPE
@@ -257,13 +239,11 @@ One can still use generic algebras though.
 > - [tensor algebra with broadcasting](kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BroadcastDoubleTensorAlgebra.kt) : Basic linear algebra operations implemented with broadcasting.
 > - [linear algebra operations](kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt) : Advanced linear algebra operations like LU decomposition, SVD, etc.
 
-<hr/>
 
-* ### [kmath-viktor](kmath-viktor)
+### [kmath-viktor](kmath-viktor)
 > 
 >
 > **Maturity**: DEVELOPMENT
-<hr/>
 
 
 ## Multi-platform support
@@ -302,8 +282,8 @@ repositories {
 }
 
 dependencies {
-    api("space.kscience:kmath-core:0.3.0-dev-17")
+    api("space.kscience:kmath-core:$version")
-    // api("space.kscience:kmath-core-jvm:0.3.0-dev-17") for jvm-specific version
+    // api("space.kscience:kmath-core-jvm:$version") for jvm-specific version
 }
 ```
 

benchmarks/README.md

@@ -0,0 +1,4 @@
+# Module benchmarks
+
+
+

benchmarks/build.gradle.kts

@@ -52,6 +52,8 @@ kotlin {
                 implementation(project(":kmath-viktor"))
                 implementation(project(":kmath-jafama"))
                 implementation(project(":kmath-multik"))
+                implementation(projects.kmath.kmathTensorflow)
+                implementation("org.tensorflow:tensorflow-core-platform:0.4.0")
                 implementation("org.nd4j:nd4j-native:1.0.0-M1")
                 //    uncomment if your system supports AVX2
                 //    val os = System.getProperty("os.name")
@@ -122,6 +124,11 @@ benchmark {
         include("JafamaBenchmark")
     }
 
+    configurations.register("tensorAlgebra") {
+        commonConfiguration()
+        include("TensorAlgebraBenchmark")
+    }
+
     configurations.register("viktor") {
         commonConfiguration()
         include("ViktorBenchmark")
@@ -148,7 +155,7 @@ kotlin.sourceSets.all {
     }
 }
 
-tasks.withType<org.jetbrains.kotlin.gradle.tasks.KotlinCompile> {
+tasks.withType<org.jetbrains.kotlin.gradle.dsl.KotlinJvmCompile> {
     kotlinOptions {
         jvmTarget = "11"
         freeCompilerArgs = freeCompilerArgs + "-Xjvm-default=all" + "-Xlambdas=indy"

benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/DotBenchmark.kt

@@ -15,7 +15,11 @@ import space.kscience.kmath.linear.invoke
 import space.kscience.kmath.linear.linearSpace
 import space.kscience.kmath.multik.multikAlgebra
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.tensorflow.produceWithTF
+import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.tensorAlgebra
 import kotlin.random.Random
 
 @State(Scope.Benchmark)
@@ -39,6 +43,16 @@ internal class DotBenchmark {
         val ejmlMatrix2 = EjmlLinearSpaceDDRM { matrix2.toEjml() }
     }
 
+
+    @Benchmark
+    fun tfDot(blackhole: Blackhole) {
+        blackhole.consume(
+            DoubleField.produceWithTF {
+                matrix1 dot matrix1
+            }
+        )
+    }
+
     @Benchmark
     fun cmDotWithConversion(blackhole: Blackhole) = CMLinearSpace {
         blackhole.consume(matrix1 dot matrix2)
@@ -59,13 +73,13 @@ internal class DotBenchmark {
         blackhole.consume(matrix1 dot matrix2)
     }
 
-//    @Benchmark
+    @Benchmark
-//    fun tensorDot(blackhole: Blackhole) = with(Double.tensorAlgebra) {
+    fun tensorDot(blackhole: Blackhole) = with(DoubleField.tensorAlgebra) {
-//        blackhole.consume(matrix1 dot matrix2)
+        blackhole.consume(matrix1 dot matrix2)
-//    }
+    }
 
     @Benchmark
-    fun multikDot(blackhole: Blackhole) = with(Double.multikAlgebra) {
+    fun multikDot(blackhole: Blackhole) = with(DoubleField.multikAlgebra) {
         blackhole.consume(matrix1 dot matrix2)
     }
 
@@ -78,4 +92,9 @@ internal class DotBenchmark {
     fun doubleDot(blackhole: Blackhole) = with(DoubleField.linearSpace) {
         blackhole.consume(matrix1 dot matrix2)
     }
+
+    @Benchmark
+    fun doubleTensorDot(blackhole: Blackhole) = DoubleTensorAlgebra.invoke {
+        blackhole.consume(matrix1 dot matrix2)
+    }
 }

benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/TensorAlgebraBenchmark.kt

@@ -0,0 +1,37 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.benchmarks
+
+import kotlinx.benchmark.Benchmark
+import kotlinx.benchmark.Blackhole
+import kotlinx.benchmark.Scope
+import kotlinx.benchmark.State
+import space.kscience.kmath.linear.linearSpace
+import space.kscience.kmath.linear.matrix
+import space.kscience.kmath.linear.symmetric
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.tensors.core.tensorAlgebra
+import kotlin.random.Random
+
+@State(Scope.Benchmark)
+internal class TensorAlgebraBenchmark {
+    companion object {
+        private val random = Random(12224)
+        private const val dim = 30
+
+        private val matrix = DoubleField.linearSpace.matrix(dim, dim).symmetric { _, _ -> random.nextDouble() }
+    }
+
+    @Benchmark
+    fun tensorSymEigSvd(blackhole: Blackhole) = with(Double.tensorAlgebra) {
+        blackhole.consume(matrix.symEigSvd(1e-10))
+    }
+
+    @Benchmark
+    fun tensorSymEigJacobi(blackhole: Blackhole) = with(Double.tensorAlgebra) {
+        blackhole.consume(matrix.symEigJacobi(50, 1e-10))
+    }
+}

build.gradle.kts

@@ -1,16 +1,17 @@
 plugins {
     id("ru.mipt.npm.gradle.project")
-    id("org.jetbrains.kotlinx.kover") version "0.5.0-RC"
+    id("org.jetbrains.kotlinx.kover") version "0.5.0"
 }
 
 allprojects {
     repositories {
+        maven("https://repo.kotlin.link")
         maven("https://oss.sonatype.org/content/repositories/snapshots")
         mavenCentral()
     }
 
     group = "space.kscience"
-    version = "0.3.0-dev-17"
+    version = "0.3.1-dev-1"
 }
 
 subprojects {
@@ -50,12 +51,24 @@ subprojects {
             }
         }
     }
+
+    plugins.withId("org.jetbrains.kotlin.multiplatform") {
+        configure<org.jetbrains.kotlin.gradle.dsl.KotlinMultiplatformExtension> {
+            sourceSets {
+                val commonTest by getting {
+                    dependencies {
+                        implementation(projects.testUtils)
+                    }
+                }
+            }
+        }
+    }
 }
 
 readme.readmeTemplate = file("docs/templates/README-TEMPLATE.md")
 
 ksciencePublish {
-    github("kmath")
+    github("kmath", addToRelease = false)
     space()
     sonatype()
 }

buildSrc/build.gradle.kts

@@ -1,4 +1,5 @@
 plugins {
+    kotlin("jvm") version "1.7.0"
     `kotlin-dsl`
     `version-catalog`
     alias(npmlibs.plugins.kotlin.plugin.serialization)
@@ -7,17 +8,19 @@ plugins {
 java.targetCompatibility = JavaVersion.VERSION_11
 
 repositories {
+    mavenLocal()
     maven("https://repo.kotlin.link")
     mavenCentral()
     gradlePluginPortal()
 }
 
-val toolsVersion: String by extra
+val toolsVersion = npmlibs.versions.tools.get()
 val kotlinVersion = npmlibs.versions.kotlin.asProvider().get()
-val benchmarksVersion = "0.4.2"
+val benchmarksVersion = npmlibs.versions.kotlinx.benchmark.get()
 
 dependencies {
     api("ru.mipt.npm:gradle-tools:$toolsVersion")
+    api(npmlibs.atomicfu.gradle)
     //plugins form benchmarks
     api("org.jetbrains.kotlinx:kotlinx-benchmark-plugin:$benchmarksVersion")
     api("org.jetbrains.kotlin:kotlin-allopen:$kotlinVersion")

buildSrc/gradle.properties

@@ -1,14 +0,0 @@
-#
-# Copyright 2018-2021 KMath contributors.
-# Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
-#
-
-kotlin.code.style=official
-kotlin.mpp.stability.nowarn=true
-
-kotlin.jupyter.add.scanner=false
-
-org.gradle.configureondemand=true
-org.gradle.parallel=true
-
-toolsVersion=0.10.9-kotlin-1.6.10

buildSrc/settings.gradle.kts

@@ -3,17 +3,26 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
-
 enableFeaturePreview("TYPESAFE_PROJECT_ACCESSORS")
-enableFeaturePreview("VERSION_CATALOGS")
 
 dependencyResolutionManagement {
+    val projectProperties = java.util.Properties()
+    file("../gradle.properties").inputStream().use {
+        projectProperties.load(it)
+    }
 
-    val toolsVersion: String by extra
+    projectProperties.forEach { key, value ->
+        extra.set(key.toString(), value)
+    }
+
+
+    val toolsVersion: String = projectProperties["toolsVersion"].toString()
 
     repositories {
+        mavenLocal()
         maven("https://repo.kotlin.link")
         mavenCentral()
+        gradlePluginPortal()
     }
 
     versionCatalogs {

buildSrc/src/main/kotlin/space/kscience/kmath/ejml/codegen/ejmlCodegen.kt

@@ -319,7 +319,9 @@ public object EjmlLinearSpace${ops} : EjmlLinearSpace<${type}, ${kmathAlgebra},
     }
 
             else -> null
-        }?.let(type::cast)
+        }?.let{
+            type.cast(it)
+        }
     }
 
     /**

docs/templates/README-TEMPLATE.md

@@ -52,7 +52,7 @@ module definitions below. The module stability could have the following levels:
 
 ## Modules
 
-$modules
+${modules}
 
 ## Multi-platform support
 

examples/README.md

@@ -0,0 +1,4 @@
+# Module examples
+
+
+

examples/build.gradle.kts

@@ -58,7 +58,7 @@ kotlin.sourceSets.all {
     }
 }
 
-tasks.withType<org.jetbrains.kotlin.gradle.tasks.KotlinCompile> {
+tasks.withType<org.jetbrains.kotlin.gradle.dsl.KotlinJvmCompile> {
     kotlinOptions {
         jvmTarget = "11"
         freeCompilerArgs = freeCompilerArgs + "-Xjvm-default=all" + "-Xopt-in=kotlin.RequiresOptIn" + "-Xlambdas=indy"

examples/src/main/kotlin/space/kscience/kmath/functions/integrate.kt

@@ -13,7 +13,7 @@ import kotlin.math.pow
 
 fun main() {
     //Define a function
-    val function: UnivariateFunction<Double> = { x -> 3 * x.pow(2) + 2 * x + 1 }
+    val function: Function1D<Double> = { x -> 3 * x.pow(2) + 2 * x + 1 }
 
     //get the result of the integration
     val result = DoubleField.gaussIntegrator.integrate(0.0..10.0, function = function)

examples/src/main/kotlin/space/kscience/kmath/functions/interpolateSquare.kt

@@ -5,8 +5,8 @@
 
 package space.kscience.kmath.functions
 
-import space.kscience.kmath.interpolation.SplineInterpolator
 import space.kscience.kmath.interpolation.interpolatePolynomials
+import space.kscience.kmath.interpolation.splineInterpolator
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.real.map
 import space.kscience.kmath.real.step
@@ -18,7 +18,7 @@ import space.kscience.plotly.scatter
 
 @OptIn(UnstablePlotlyAPI::class)
 fun main() {
-    val function: UnivariateFunction<Double> = { x ->
+    val function: Function1D<Double> = { x ->
         if (x in 30.0..50.0) {
             1.0
         } else {
@@ -28,7 +28,7 @@ fun main() {
     val xs = 0.0..100.0 step 0.5
     val ys = xs.map(function)
 
-    val polynomial: PiecewisePolynomial<Double> = SplineInterpolator.double.interpolatePolynomials(xs, ys)
+    val polynomial: PiecewisePolynomial<Double> = DoubleField.splineInterpolator.interpolatePolynomials(xs, ys)
 
     val polyFunction = polynomial.asFunction(DoubleField, 0.0)
 

gradle.properties

@@ -2,14 +2,14 @@
 # Copyright 2018-2021 KMath contributors.
 # Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
 #
-
 kotlin.code.style=official
-kotlin.mpp.stability.nowarn=true
-
 kotlin.jupyter.add.scanner=false
+kotlin.mpp.stability.nowarn=true
+kotlin.native.ignoreDisabledTargets=true
+//kotlin.incremental.js.ir=true
 
 org.gradle.configureondemand=true
 org.gradle.parallel=true
-org.gradle.jvmargs=-XX:MaxMetaspaceSize=1G
+org.gradle.jvmargs=-Xmx4096m
 
-toolsVersion=0.11.1-kotlin-1.6.10
+toolsVersion=0.11.7-kotlin-1.7.0

gradle/wrapper/gradle-wrapper.properties

@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-7.3.3-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-7.4.2-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists

kmath-ast/README.md

@@ -1,6 +1,6 @@
 # Module kmath-ast
 
-Performance and visualization extensions to MST API.
+Extensions to MST API: transformations, dynamic compilation and visualization.
 
  - [expression-language](src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt) : Expression language and its parser
  - [mst-jvm-codegen](src/jvmMain/kotlin/space/kscience/kmath/asm/asm.kt) : Dynamic MST to JVM bytecode compiler
@@ -10,17 +10,17 @@ Performance and visualization extensions to MST API.
 
 ## Artifact:
 
-The Maven coordinates of this project are `space.kscience:kmath-ast:0.3.0-dev-17`.
+The Maven coordinates of this project are `space.kscience:kmath-ast:0.3.0`.
 
-**Gradle:**
+**Gradle Groovy:**
-```gradle
+```groovy
 repositories {
     maven { url 'https://repo.kotlin.link' }
     mavenCentral()
 }
 
 dependencies {
-    implementation 'space.kscience:kmath-ast:0.3.0-dev-17'
+    implementation 'space.kscience:kmath-ast:0.3.0'
 }
 ```
 **Gradle Kotlin DSL:**
@@ -31,10 +31,30 @@ repositories {
 }
 
 dependencies {
-    implementation("space.kscience:kmath-ast:0.3.0-dev-17")
+    implementation("space.kscience:kmath-ast:0.3.0")
 }
 ```
 
+## Parsing expressions
+
+In this module there is a parser from human-readable strings like `"x^3-x+3"` (in the more specific [grammar](reference/ArithmeticsEvaluator.g4)) to MST instances.
+
+Supported literals:
+1. Constants and variables (consist of latin letters, digits and underscores, can't start with digit): `x`, `_Abc2`.
+2. Numbers: `123`, `1.02`, `1e10`, `1e-10`, `1.0e+3`—all parsed either as `kotlin.Long` or `kotlin.Double`.
+
+Supported binary operators (from the highest precedence to the lowest one):
+1. `^`
+2. `*`, `/`
+3. `+`, `-`
+
+Supported unary operator:
+1. `-`, e. g. `-x`
+
+Arbitrary unary and binary functions are also supported: names consist of latin letters, digits and underscores, can't start with digit. Examples:
+1. `sin(x)`
+2. `add(x, y)`
+
 ## Dynamic expression code generation
 
 ### On JVM
@@ -42,48 +62,66 @@ dependencies {
 `kmath-ast` JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds a
 special implementation of `Expression<T>` with implemented `invoke` function.
 
-For example, the following builder:
+For example, the following code:
 
 ```kotlin
-import space.kscience.kmath.expressions.Symbol.Companion.x
+import space.kscience.kmath.asm.compileToExpression
-import space.kscience.kmath.expressions.*
+import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.operations.*
-import space.kscience.kmath.asm.*
 
-MstField { x + 2 }.compileToExpression(DoubleField)
+"x^3-x+3".parseMath().compileToExpression(DoubleField)
 ```
 
-... leads to generation of bytecode, which can be decompiled to the following Java class:
+&mldr; leads to generation of bytecode, which can be decompiled to the following Java class:
 
 ```java
-package space.kscience.kmath.asm.generated;
+import java.util.*;
+import kotlin.jvm.functions.*;
+import space.kscience.kmath.asm.internal.*;
+import space.kscience.kmath.complex.*;
+import space.kscience.kmath.expressions.*;
 
-import java.util.Map;
+public final class CompiledExpression_45045_0 implements Expression<Complex> {
-
-import kotlin.jvm.functions.Function2;
-import space.kscience.kmath.asm.internal.MapIntrinsics;
-import space.kscience.kmath.expressions.Expression;
-import space.kscience.kmath.expressions.Symbol;
-
-public final class AsmCompiledExpression_45045_0 implements Expression<Double> {
     private final Object[] constants;
 
-    public final Double invoke(Map<Symbol, ? extends Double> arguments) {
+    public Complex invoke(Map<Symbol, ? extends Complex> arguments) {
-        return (Double) ((Function2) this.constants[0]).invoke((Double) MapIntrinsics.getOrFail(arguments, "x"), 2);
+        Complex var2 = (Complex)MapIntrinsics.getOrFail(arguments, "x");
-    }
+        return (Complex)((Function2)this.constants[0]).invoke(var2, (Complex)this.constants[1]);
-
-    public AsmCompiledExpression_45045_0(Object[] constants) {
-        this.constants = constants;
     }
 }
-
 ```
 
-#### Known issues
+For `LongRing`, `IntRing`, and `DoubleField` specialization is supported for better performance:
 
-- The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class
+```java
-  loading overhead.
+import java.util.*;
-- This API is not supported by non-dynamic JVM implementations (like TeaVM and GraalVM) because of using class loaders.
+import space.kscience.kmath.asm.internal.*;
+import space.kscience.kmath.expressions.*;
+
+public final class CompiledExpression_-386104628_0 implements DoubleExpression {
+    private final SymbolIndexer indexer;
+
+    public SymbolIndexer getIndexer() {
+        return this.indexer;
+    }
+
+    public double invoke(double[] arguments) {
+        double var2 = arguments[0];
+        return Math.pow(var2, 3.0D) - var2 + 3.0D;
+    }
+
+    public final Double invoke(Map<Symbol, ? extends Double> arguments) {
+        double var2 = ((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue();
+        return Math.pow(var2, 3.0D) - var2 + 3.0D;
+    }
+}
+```
+
+Setting JVM system property `space.kscience.kmath.ast.dump.generated.classes` to `1` makes the translator dump class files to program's working directory, so they can be reviewed manually.
+
+#### Limitations
+
+- The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class loading overhead.
+- This API is not supported by non-dynamic JVM implementations like TeaVM or GraalVM Native Image because they may not support class loaders.
 
 ### On JS
 
@@ -121,15 +159,15 @@ MstField { x + 2 }.compileToExpression(DoubleField)
 An example of emitted Wasm IR in the form of WAT:
 
 ```lisp
-(func $executable (param $0 f64) (result f64)
+(func \$executable (param \$0 f64) (result f64)
   (f64.add
-    (local.get $0)
+    (local.get \$0)
     (f64.const 2)
   )
 )
 ```
 
-#### Known issues
+#### Limitations
 
 - ESTree expression compilation uses `eval` which can be unavailable in several environments.
 - WebAssembly isn't supported by old versions of browsers (see https://webassembly.org/roadmap/).
@@ -161,10 +199,7 @@ public fun main() {
 
 Result LaTeX:
 
-<div style="background-color:white;">
+$$\operatorname{exp}\\,\left(\sqrt{x}\right)-\frac{\frac{\operatorname{arcsin}\\,\left(2\\,x\right)}{2\times10^{10}+x^{3}}}{12}+x^{2/3}$$
-
-![](https://latex.codecogs.com/gif.latex?%5Coperatorname{exp}%5C,%5Cleft(%5Csqrt{x}%5Cright)-%5Cfrac{%5Cfrac{%5Coperatorname{arcsin}%5C,%5Cleft(2%5C,x%5Cright)}{2%5Ctimes10^{10}%2Bx^{3}}}{12}+x^{2/3})
-</div>
 
 Result MathML (can be used with MathJax or other renderers):
 

kmath-ast/build.gradle.kts

@@ -24,7 +24,7 @@ kotlin.sourceSets {
 
     commonMain {
         dependencies {
-            api("com.github.h0tk3y.betterParse:better-parse:0.4.2")
+            api("com.github.h0tk3y.betterParse:better-parse:0.4.4")
             api(project(":kmath-core"))
         }
     }
@@ -57,7 +57,7 @@ tasks.dokkaHtml {
 
 if (System.getProperty("space.kscience.kmath.ast.dump.generated.classes") == "1")
     tasks.jvmTest {
-        jvmArgs = (jvmArgs ?: emptyList()) + listOf("-Dspace.kscience.kmath.ast.dump.generated.classes=1")
+        jvmArgs("-Dspace.kscience.kmath.ast.dump.generated.classes=1")
     }
 
 readme {

kmath-ast/docs/README-TEMPLATE.md

@@ -1,11 +1,31 @@
 # Module kmath-ast
 
-Performance and visualization extensions to MST API.
+Extensions to MST API: transformations, dynamic compilation and visualization.
 
 ${features}
 
 ${artifact}
 
+## Parsing expressions
+
+In this module there is a parser from human-readable strings like `"x^3-x+3"` (in the more specific [grammar](reference/ArithmeticsEvaluator.g4)) to MST instances.
+
+Supported literals:
+1. Constants and variables (consist of latin letters, digits and underscores, can't start with digit): `x`, `_Abc2`.
+2. Numbers: `123`, `1.02`, `1e10`, `1e-10`, `1.0e+3`—all parsed either as `kotlin.Long` or `kotlin.Double`.
+
+Supported binary operators (from the highest precedence to the lowest one):
+1. `^`
+2. `*`, `/`
+3. `+`, `-`
+
+Supported unary operator:
+1. `-`, e. g. `-x`
+
+Arbitrary unary and binary functions are also supported: names consist of latin letters, digits and underscores, can't start with digit. Examples:
+1. `sin(x)`
+2. `add(x, y)`
+
 ## Dynamic expression code generation
 
 ### On JVM
@@ -13,48 +33,66 @@ ${artifact}
 `kmath-ast` JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds a
 special implementation of `Expression<T>` with implemented `invoke` function.
 
-For example, the following builder:
+For example, the following code:
 
 ```kotlin
-import space.kscience.kmath.expressions.Symbol.Companion.x
+import space.kscience.kmath.asm.compileToExpression
-import space.kscience.kmath.expressions.*
+import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.operations.*
-import space.kscience.kmath.asm.*
 
-MstField { x + 2 }.compileToExpression(DoubleField)
+"x^3-x+3".parseMath().compileToExpression(DoubleField)
 ```
 
-... leads to generation of bytecode, which can be decompiled to the following Java class:
+&mldr; leads to generation of bytecode, which can be decompiled to the following Java class:
 
 ```java
-package space.kscience.kmath.asm.generated;
+import java.util.*;
+import kotlin.jvm.functions.*;
+import space.kscience.kmath.asm.internal.*;
+import space.kscience.kmath.complex.*;
+import space.kscience.kmath.expressions.*;
 
-import java.util.Map;
+public final class CompiledExpression_45045_0 implements Expression<Complex> {
-
-import kotlin.jvm.functions.Function2;
-import space.kscience.kmath.asm.internal.MapIntrinsics;
-import space.kscience.kmath.expressions.Expression;
-import space.kscience.kmath.expressions.Symbol;
-
-public final class AsmCompiledExpression_45045_0 implements Expression<Double> {
     private final Object[] constants;
 
-    public final Double invoke(Map<Symbol, ? extends Double> arguments) {
+    public Complex invoke(Map<Symbol, ? extends Complex> arguments) {
-        return (Double) ((Function2) this.constants[0]).invoke((Double) MapIntrinsics.getOrFail(arguments, "x"), 2);
+        Complex var2 = (Complex)MapIntrinsics.getOrFail(arguments, "x");
-    }
+        return (Complex)((Function2)this.constants[0]).invoke(var2, (Complex)this.constants[1]);
-
-    public AsmCompiledExpression_45045_0(Object[] constants) {
-        this.constants = constants;
     }
 }
-
 ```
 
-#### Known issues
+For `LongRing`, `IntRing`, and `DoubleField` specialization is supported for better performance:
 
-- The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class
+```java
-  loading overhead.
+import java.util.*;
-- This API is not supported by non-dynamic JVM implementations (like TeaVM and GraalVM) because of using class loaders.
+import space.kscience.kmath.asm.internal.*;
+import space.kscience.kmath.expressions.*;
+
+public final class CompiledExpression_-386104628_0 implements DoubleExpression {
+    private final SymbolIndexer indexer;
+
+    public SymbolIndexer getIndexer() {
+        return this.indexer;
+    }
+
+    public double invoke(double[] arguments) {
+        double var2 = arguments[0];
+        return Math.pow(var2, 3.0D) - var2 + 3.0D;
+    }
+
+    public final Double invoke(Map<Symbol, ? extends Double> arguments) {
+        double var2 = ((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue();
+        return Math.pow(var2, 3.0D) - var2 + 3.0D;
+    }
+}
+```
+
+Setting JVM system property `space.kscience.kmath.ast.dump.generated.classes` to `1` makes the translator dump class files to program's working directory, so they can be reviewed manually.
+
+#### Limitations
+
+- The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class loading overhead.
+- This API is not supported by non-dynamic JVM implementations like TeaVM or GraalVM Native Image because they may not support class loaders.
 
 ### On JS
 
@@ -100,7 +138,7 @@ An example of emitted Wasm IR in the form of WAT:
 )
 ```
 
-#### Known issues
+#### Limitations
 
 - ESTree expression compilation uses `eval` which can be unavailable in several environments.
 - WebAssembly isn't supported by old versions of browsers (see https://webassembly.org/roadmap/).
@@ -132,10 +170,7 @@ public fun main() {
 
 Result LaTeX:
 
-<div style="background-color:white;">
+$$\operatorname{exp}\\,\left(\sqrt{x}\right)-\frac{\frac{\operatorname{arcsin}\\,\left(2\\,x\right)}{2\times10^{10}+x^{3}}}{12}+x^{2/3}$$
-
-![](https://latex.codecogs.com/gif.latex?%5Coperatorname{exp}%5C,%5Cleft(%5Csqrt{x}%5Cright)-%5Cfrac{%5Cfrac{%5Coperatorname{arcsin}%5C,%5Cleft(2%5C,x%5Cright)}{2%5Ctimes10^{10}%2Bx^{3}}}{12}+x^{2/3})
-</div>
 
 Result MathML (can be used with MathJax or other renderers):
 

kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/TypedMst.kt

@@ -0,0 +1,177 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.ast
+
+import space.kscience.kmath.expressions.Expression
+import space.kscience.kmath.expressions.Symbol
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.Algebra
+import space.kscience.kmath.operations.NumericAlgebra
+
+/**
+ * MST form where all values belong to the type [T]. It is optimal for constant folding, dynamic compilation, etc.
+ *
+ * @param T the type.
+ */
+@UnstableKMathAPI
+public sealed interface TypedMst<T> {
+    /**
+     * A node containing a unary operation.
+     *
+     * @param T the type.
+     * @property operation The identifier of operation.
+     * @property function The function implementing this operation.
+     * @property value The argument of this operation.
+     */
+    public class Unary<T>(public val operation: String, public val function: (T) -> T, public val value: TypedMst<T>) :
+        TypedMst<T> {
+        override fun equals(other: Any?): Boolean {
+            if (this === other) return true
+            if (other == null || this::class != other::class) return false
+            other as Unary<*>
+            if (operation != other.operation) return false
+            if (value != other.value) return false
+            return true
+        }
+
+        override fun hashCode(): Int {
+            var result = operation.hashCode()
+            result = 31 * result + value.hashCode()
+            return result
+        }
+
+        override fun toString(): String = "Unary(operation=$operation, value=$value)"
+    }
+
+    /**
+     * A node containing binary operation.
+     *
+     * @param T the type.
+     * @property operation The identifier of operation.
+     * @property function The binary function implementing this operation.
+     * @property left The left operand.
+     * @property right The right operand.
+     */
+    public class Binary<T>(
+        public val operation: String,
+        public val function: Function<T>,
+        public val left: TypedMst<T>,
+        public val right: TypedMst<T>,
+    ) : TypedMst<T> {
+        override fun equals(other: Any?): Boolean {
+            if (this === other) return true
+            if (other == null || this::class != other::class) return false
+
+            other as Binary<*>
+
+            if (operation != other.operation) return false
+            if (left != other.left) return false
+            if (right != other.right) return false
+
+            return true
+        }
+
+        override fun hashCode(): Int {
+            var result = operation.hashCode()
+            result = 31 * result + left.hashCode()
+            result = 31 * result + right.hashCode()
+            return result
+        }
+
+        override fun toString(): String = "Binary(operation=$operation, left=$left, right=$right)"
+    }
+
+    /**
+     * The non-numeric constant value.
+     *
+     * @param T the type.
+     * @property value The held value.
+     * @property number The number this value corresponds.
+     */
+    public class Constant<T>(public val value: T, public val number: Number?) : TypedMst<T> {
+        override fun equals(other: Any?): Boolean {
+            if (this === other) return true
+            if (other == null || this::class != other::class) return false
+            other as Constant<*>
+            if (value != other.value) return false
+            if (number != other.number) return false
+            return true
+        }
+
+        override fun hashCode(): Int {
+            var result = value?.hashCode() ?: 0
+            result = 31 * result + (number?.hashCode() ?: 0)
+            return result
+        }
+
+        override fun toString(): String = "Constant(value=$value, number=$number)"
+    }
+
+    /**
+     * The node containing a variable
+     *
+     * @param T the type.
+     * @property symbol The symbol of the variable.
+     */
+    public class Variable<T>(public val symbol: Symbol) : TypedMst<T> {
+        override fun equals(other: Any?): Boolean {
+            if (this === other) return true
+            if (other == null || this::class != other::class) return false
+            other as Variable<*>
+            if (symbol != other.symbol) return false
+            return true
+        }
+
+        override fun hashCode(): Int = symbol.hashCode()
+        override fun toString(): String = "Variable(symbol=$symbol)"
+    }
+}
+
+/**
+ * Interprets the [TypedMst] node with this [Algebra] and [arguments].
+ */
+@UnstableKMathAPI
+public fun <T> TypedMst<T>.interpret(algebra: Algebra<T>, arguments: Map<Symbol, T>): T = when (this) {
+    is TypedMst.Unary -> algebra.unaryOperation(operation, interpret(algebra, arguments))
+
+    is TypedMst.Binary -> when {
+        algebra is NumericAlgebra && left is TypedMst.Constant && left.number != null ->
+            algebra.leftSideNumberOperation(operation, left.number, right.interpret(algebra, arguments))
+
+        algebra is NumericAlgebra && right is TypedMst.Constant && right.number != null ->
+            algebra.rightSideNumberOperation(operation, left.interpret(algebra, arguments), right.number)
+
+        else -> algebra.binaryOperation(
+            operation,
+            left.interpret(algebra, arguments),
+            right.interpret(algebra, arguments),
+        )
+    }
+
+    is TypedMst.Constant -> value
+    is TypedMst.Variable -> arguments.getValue(symbol)
+}
+
+/**
+ * Interprets the [TypedMst] node with this [Algebra] and optional [arguments].
+ */
+@UnstableKMathAPI
+public fun <T> TypedMst<T>.interpret(algebra: Algebra<T>, vararg arguments: Pair<Symbol, T>): T = interpret(
+    algebra,
+    when (arguments.size) {
+        0 -> emptyMap()
+        1 -> mapOf(arguments[0])
+        else -> hashMapOf(*arguments)
+    },
+)
+
+/**
+ * Interpret this [TypedMst] node as expression.
+ */
+@UnstableKMathAPI
+public fun <T : Any> TypedMst<T>.toExpression(algebra: Algebra<T>): Expression<T> = Expression { arguments ->
+    interpret(algebra, arguments)
+}

kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/evaluateConstants.kt

@@ -0,0 +1,93 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.ast
+
+import space.kscience.kmath.expressions.MST
+import space.kscience.kmath.expressions.Symbol
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.Algebra
+import space.kscience.kmath.operations.NumericAlgebra
+import space.kscience.kmath.operations.bindSymbolOrNull
+
+/**
+ * Evaluates constants in given [MST] for given [algebra] at the same time with converting to [TypedMst].
+ */
+@UnstableKMathAPI
+public fun <T> MST.evaluateConstants(algebra: Algebra<T>): TypedMst<T> = when (this) {
+    is MST.Numeric -> TypedMst.Constant(
+        (algebra as? NumericAlgebra<T>)?.number(value) ?: error("Numeric nodes are not supported by $algebra"),
+        value,
+    )
+
+    is MST.Unary -> when (val arg = value.evaluateConstants(algebra)) {
+        is TypedMst.Constant<T> -> {
+            val value = algebra.unaryOperation(
+                operation,
+                arg.value,
+            )
+
+            TypedMst.Constant(value, if (value is Number) value else null)
+        }
+
+        else -> TypedMst.Unary(operation, algebra.unaryOperationFunction(operation), arg)
+    }
+
+    is MST.Binary -> {
+        val left = left.evaluateConstants(algebra)
+        val right = right.evaluateConstants(algebra)
+
+        when {
+            left is TypedMst.Constant<T> && right is TypedMst.Constant<T> -> {
+                val value = when {
+                    algebra is NumericAlgebra && left.number != null -> algebra.leftSideNumberOperation(
+                        operation,
+                        left.number,
+                        right.value,
+                    )
+
+                    algebra is NumericAlgebra && right.number != null -> algebra.rightSideNumberOperation(
+                        operation,
+                        left.value,
+                        right.number,
+                    )
+
+                    else -> algebra.binaryOperation(
+                        operation,
+                        left.value,
+                        right.value,
+                    )
+                }
+
+                TypedMst.Constant(value, if (value is Number) value else null)
+            }
+
+            algebra is NumericAlgebra && left is TypedMst.Constant && left.number != null -> TypedMst.Binary(
+                operation,
+                algebra.leftSideNumberOperationFunction(operation),
+                left,
+                right,
+            )
+
+            algebra is NumericAlgebra && right is TypedMst.Constant && right.number != null -> TypedMst.Binary(
+                operation,
+                algebra.rightSideNumberOperationFunction(operation),
+                left,
+                right,
+            )
+
+            else -> TypedMst.Binary(operation, algebra.binaryOperationFunction(operation), left, right)
+        }
+    }
+
+    is Symbol -> {
+        val boundSymbol = algebra.bindSymbolOrNull(this)
+
+        if (boundSymbol != null)
+            TypedMst.Constant(boundSymbol, if (boundSymbol is Number) boundSymbol else null)
+        else
+            TypedMst.Variable(this)
+    }
+}

kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/TestFolding.kt

@@ -0,0 +1,52 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.ast
+
+import space.kscience.kmath.operations.ByteRing
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.IntRing
+import space.kscience.kmath.operations.pi
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.fail
+
+internal class TestFolding {
+    @Test
+    fun foldUnary() = assertEquals(
+        -1,
+        ("-(1)".parseMath().evaluateConstants(IntRing) as? TypedMst.Constant<Int> ?: fail()).value,
+    )
+
+    @Test
+    fun foldDeepUnary() = assertEquals(
+        1,
+        ("-(-(1))".parseMath().evaluateConstants(IntRing) as? TypedMst.Constant<Int> ?: fail()).value,
+    )
+
+    @Test
+    fun foldBinary() = assertEquals(
+        2,
+        ("1*2".parseMath().evaluateConstants(IntRing) as? TypedMst.Constant<Int> ?: fail()).value,
+    )
+
+    @Test
+    fun foldDeepBinary() = assertEquals(
+        10,
+        ("1*2*5".parseMath().evaluateConstants(IntRing) as? TypedMst.Constant<Int> ?: fail()).value,
+    )
+
+    @Test
+    fun foldSymbol() = assertEquals(
+        DoubleField.pi,
+        ("pi".parseMath().evaluateConstants(DoubleField) as? TypedMst.Constant<Double> ?: fail()).value,
+    )
+
+    @Test
+    fun foldNumeric() = assertEquals(
+        42.toByte(),
+        ("42".parseMath().evaluateConstants(ByteRing) as? TypedMst.Constant<Byte> ?: fail()).value,
+    )
+}

kmath-ast/src/jsMain/kotlin/space/kscience/kmath/estree/estree.kt

@@ -5,87 +5,48 @@
 
 package space.kscience.kmath.estree
 
+import space.kscience.kmath.ast.TypedMst
+import space.kscience.kmath.ast.evaluateConstants
 import space.kscience.kmath.estree.internal.ESTreeBuilder
 import space.kscience.kmath.expressions.Expression
 import space.kscience.kmath.expressions.MST
-import space.kscience.kmath.expressions.MST.*
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.expressions.invoke
 import space.kscience.kmath.internal.estree.BaseExpression
+import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.Algebra
-import space.kscience.kmath.operations.NumericAlgebra
-import space.kscience.kmath.operations.bindSymbolOrNull
-
-@PublishedApi
-internal fun <T> MST.compileWith(algebra: Algebra<T>): Expression<T> {
-    fun ESTreeBuilder<T>.visit(node: MST): BaseExpression = when (node) {
-        is Symbol -> {
-            val symbol = algebra.bindSymbolOrNull(node)
-
-            if (symbol != null)
-                constant(symbol)
-            else
-                variable(node.identity)
-        }
-
-        is Numeric -> constant(
-            (algebra as? NumericAlgebra<T>)?.number(node.value) ?: error("Numeric nodes are not supported by $this")
-        )
-
-        is Unary -> when {
-            algebra is NumericAlgebra && node.value is Numeric -> constant(
-                algebra.unaryOperationFunction(node.operation)(algebra.number((node.value as Numeric).value))
-            )
-
-            else -> call(algebra.unaryOperationFunction(node.operation), visit(node.value))
-        }
-
-        is Binary -> when {
-            algebra is NumericAlgebra && node.left is Numeric && node.right is Numeric -> constant(
-                algebra.binaryOperationFunction(node.operation).invoke(
-                    algebra.number((node.left as Numeric).value),
-                    algebra.number((node.right as Numeric).value)
-                )
-            )
-
-            algebra is NumericAlgebra && node.left is Numeric -> call(
-                algebra.leftSideNumberOperationFunction(node.operation),
-                visit(node.left),
-                visit(node.right),
-            )
-
-            algebra is NumericAlgebra && node.right is Numeric -> call(
-                algebra.rightSideNumberOperationFunction(node.operation),
-                visit(node.left),
-                visit(node.right),
-            )
-
-            else -> call(
-                algebra.binaryOperationFunction(node.operation),
-                visit(node.left),
-                visit(node.right),
-            )
-        }
-    }
-
-    return ESTreeBuilder<T> { visit(this@compileWith) }.instance
-}
 
 /**
  * Create a compiled expression with given [MST] and given [algebra].
  */
-public fun <T : Any> MST.compileToExpression(algebra: Algebra<T>): Expression<T> = compileWith(algebra)
+@OptIn(UnstableKMathAPI::class)
+public fun <T : Any> MST.compileToExpression(algebra: Algebra<T>): Expression<T> {
+    val typed = evaluateConstants(algebra)
+    if (typed is TypedMst.Constant<T>) return Expression { typed.value }
 
+    fun ESTreeBuilder<T>.visit(node: TypedMst<T>): BaseExpression = when (node) {
+        is TypedMst.Constant -> constant(node.value)
+        is TypedMst.Variable -> variable(node.symbol)
+        is TypedMst.Unary -> call(node.function, visit(node.value))
+
+        is TypedMst.Binary -> call(
+            node.function,
+            visit(node.left),
+            visit(node.right),
+        )
+    }
+
+    return ESTreeBuilder { visit(typed) }.instance
+}
 
 /**
  * Compile given MST to expression and evaluate it against [arguments]
  */
-public inline fun <reified T : Any> MST.compile(algebra: Algebra<T>, arguments: Map<Symbol, T>): T =
+public fun <T : Any> MST.compile(algebra: Algebra<T>, arguments: Map<Symbol, T>): T =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
-
 
 /**
  * Compile given MST to expression and evaluate it against [arguments]
  */
-public inline fun <reified T : Any> MST.compile(algebra: Algebra<T>, vararg arguments: Pair<Symbol, T>): T =
+public fun <T : Any> MST.compile(algebra: Algebra<T>, vararg arguments: Pair<Symbol, T>): T =
-    compileToExpression(algebra).invoke(*arguments)
+    compileToExpression(algebra)(*arguments)

kmath-ast/src/jsMain/kotlin/space/kscience/kmath/estree/internal/ESTreeBuilder.kt

@@ -22,28 +22,20 @@ internal class ESTreeBuilder<T>(val bodyCallback: ESTreeBuilder<T>.() -> BaseExp
         }
     }
 
+    @Suppress("UNUSED_VARIABLE")
     val instance: Expression<T> by lazy {
         val node = Program(
             sourceType = "script",
-            VariableDeclaration(
+            ReturnStatement(bodyCallback())
-                kind = "var",
-                VariableDeclarator(
-                    id = Identifier("executable"),
-                    init = FunctionExpression(
-                        params = arrayOf(Identifier("constants"), Identifier("arguments")),
-                        body = BlockStatement(ReturnStatement(bodyCallback())),
-                    ),
-                ),
-            ),
         )
 
-        eval(generate(node))
+        val code = generate(node)
-        GeneratedExpression(js("executable"), constants.toTypedArray())
+        GeneratedExpression(js("new Function('constants', 'arguments_0', code)"), constants.toTypedArray())
     }
 
     private val constants = mutableListOf<Any>()
 
-    fun constant(value: Any?) = when {
+    fun constant(value: Any?): BaseExpression = when {
         value == null || jsTypeOf(value) == "number" || jsTypeOf(value) == "string" || jsTypeOf(value) == "boolean" ->
             SimpleLiteral(value)
 
@@ -61,7 +53,8 @@ internal class ESTreeBuilder<T>(val bodyCallback: ESTreeBuilder<T>.() -> BaseExp
         }
     }
 
-    fun variable(name: String): BaseExpression = call(getOrFail, Identifier("arguments"), SimpleLiteral(name))
+    fun variable(name: Symbol): BaseExpression =
+        call(getOrFail, Identifier("arguments_0"), SimpleLiteral(name.identity))
 
     fun call(function: Function<T>, vararg args: BaseExpression): BaseExpression = SimpleCallExpression(
         optional = false,

kmath-ast/src/jsMain/kotlin/space/kscience/kmath/internal/estree/estree.extensions.kt

@@ -3,6 +3,8 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+@file:Suppress("unused")
+
 package space.kscience.kmath.internal.estree
 
 internal fun Program(sourceType: String, vararg body: dynamic) = object : Program {
@@ -28,9 +30,10 @@ internal fun Identifier(name: String) = object : Identifier {
     override var name = name
 }
 
-internal fun FunctionExpression(params: Array<dynamic>, body: BlockStatement) = object : FunctionExpression {
+internal fun FunctionExpression(id: Identifier?, params: Array<dynamic>, body: BlockStatement) = object : FunctionExpression {
     override var params = params
     override var type = "FunctionExpression"
+    override var id: Identifier? = id
     override var body = body
 }
 

kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/internal/WasmBuilder.kt

@@ -5,8 +5,8 @@
 
 package space.kscience.kmath.wasm.internal
 
+import space.kscience.kmath.ast.TypedMst
 import space.kscience.kmath.expressions.*
-import space.kscience.kmath.expressions.MST.*
 import space.kscience.kmath.internal.binaryen.*
 import space.kscience.kmath.internal.webassembly.Instance
 import space.kscience.kmath.misc.UnstableKMathAPI
@@ -16,11 +16,12 @@ import space.kscience.kmath.internal.webassembly.Module as WasmModule
 
 private val spreader = eval("(obj, args) => obj(...args)")
 
+@OptIn(UnstableKMathAPI::class)
 @Suppress("UnsafeCastFromDynamic")
 internal sealed class WasmBuilder<T : Number, out E : Expression<T>>(
     protected val binaryenType: Type,
     protected val algebra: Algebra<T>,
-    protected val target: MST,
+    protected val target: TypedMst<T>,
 ) {
     protected val keys: MutableList<Symbol> = mutableListOf()
     protected lateinit var ctx: BinaryenModule
@@ -51,59 +52,41 @@ internal sealed class WasmBuilder<T : Number, out E : Expression<T>>(
         Instance(c, js("{}")).exports.executable
     }
 
-    protected open fun visitSymbol(node: Symbol): ExpressionRef {
+    protected abstract fun visitNumber(number: Number): ExpressionRef
-        algebra.bindSymbolOrNull(node)?.let { return visitNumeric(Numeric(it)) }
 
-        var idx = keys.indexOf(node)
+    protected open fun visitVariable(node: TypedMst.Variable<T>): ExpressionRef {
+        var idx = keys.indexOf(node.symbol)
 
         if (idx == -1) {
-            keys += node
+            keys += node.symbol
             idx = keys.lastIndex
         }
 
         return ctx.local.get(idx, binaryenType)
     }
 
-    protected abstract fun visitNumeric(node: Numeric): ExpressionRef
+    protected open fun visitUnary(node: TypedMst.Unary<T>): ExpressionRef =
-
-    protected open fun visitUnary(node: Unary): ExpressionRef =
         error("Unary operation ${node.operation} not defined in $this")
 
-    protected open fun visitBinary(mst: Binary): ExpressionRef =
+    protected open fun visitBinary(mst: TypedMst.Binary<T>): ExpressionRef =
         error("Binary operation ${mst.operation} not defined in $this")
 
-    protected open fun createModule(): BinaryenModule = js("new \$module\$binaryen.Module()")
+    protected open fun createModule(): BinaryenModule = space.kscience.kmath.internal.binaryen.Module()
 
-    protected fun visit(node: MST): ExpressionRef = when (node) {
+    protected fun visit(node: TypedMst<T>): ExpressionRef = when (node) {
-        is Symbol -> visitSymbol(node)
+        is TypedMst.Constant -> visitNumber(
-        is Numeric -> visitNumeric(node)
+            node.number ?: error("Object constants are not supported by pritimive ASM builder"),
-
-        is Unary -> when {
-            algebra is NumericAlgebra && node.value is Numeric -> visitNumeric(
-                Numeric(algebra.unaryOperationFunction(node.operation)(algebra.number((node.value as Numeric).value)))
         )
 
-            else -> visitUnary(node)
+        is TypedMst.Variable -> visitVariable(node)
-        }
+        is TypedMst.Unary -> visitUnary(node)
-
+        is TypedMst.Binary -> visitBinary(node)
-        is Binary -> when {
-            algebra is NumericAlgebra && node.left is Numeric && node.right is Numeric -> visitNumeric(
-                Numeric(
-                    algebra.binaryOperationFunction(node.operation)
-                        .invoke(
-                            algebra.number((node.left as Numeric).value),
-                            algebra.number((node.right as Numeric).value)
-                        )
-                )
-            )
-
-            else -> visitBinary(node)
-        }
     }
 }
 
 @UnstableKMathAPI
-internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double, DoubleExpression>(f64, DoubleField, target) {
+internal class DoubleWasmBuilder(target: TypedMst<Double>) :
+    WasmBuilder<Double, DoubleExpression>(f64, DoubleField, target) {
     override val instance by lazy {
         object : DoubleExpression {
             override val indexer = SimpleSymbolIndexer(keys)
@@ -114,9 +97,9 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double, DoubleExpres
 
     override fun createModule() = readBinary(f64StandardFunctions)
 
-    override fun visitNumeric(node: Numeric) = ctx.f64.const(node.value.toDouble())
+    override fun visitNumber(number: Number) = ctx.f64.const(number.toDouble())
 
-    override fun visitUnary(node: Unary): ExpressionRef = when (node.operation) {
+    override fun visitUnary(node: TypedMst.Unary<Double>): ExpressionRef = when (node.operation) {
         GroupOps.MINUS_OPERATION -> ctx.f64.neg(visit(node.value))
         GroupOps.PLUS_OPERATION -> visit(node.value)
         PowerOperations.SQRT_OPERATION -> ctx.f64.sqrt(visit(node.value))
@@ -137,7 +120,7 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double, DoubleExpres
         else -> super.visitUnary(node)
     }
 
-    override fun visitBinary(mst: Binary): ExpressionRef = when (mst.operation) {
+    override fun visitBinary(mst: TypedMst.Binary<Double>): ExpressionRef = when (mst.operation) {
         GroupOps.PLUS_OPERATION -> ctx.f64.add(visit(mst.left), visit(mst.right))
         GroupOps.MINUS_OPERATION -> ctx.f64.sub(visit(mst.left), visit(mst.right))
         RingOps.TIMES_OPERATION -> ctx.f64.mul(visit(mst.left), visit(mst.right))
@@ -148,7 +131,7 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double, DoubleExpres
 }
 
 @UnstableKMathAPI
-internal class IntWasmBuilder(target: MST) : WasmBuilder<Int, IntExpression>(i32, IntRing, target) {
+internal class IntWasmBuilder(target: TypedMst<Int>) : WasmBuilder<Int, IntExpression>(i32, IntRing, target) {
     override val instance by lazy {
         object : IntExpression {
             override val indexer = SimpleSymbolIndexer(keys)
@@ -157,15 +140,15 @@ internal class IntWasmBuilder(target: MST) : WasmBuilder<Int, IntExpression>(i32
         }
     }
 
-    override fun visitNumeric(node: Numeric) = ctx.i32.const(node.value.toInt())
+    override fun visitNumber(number: Number) = ctx.i32.const(number.toInt())
 
-    override fun visitUnary(node: Unary): ExpressionRef = when (node.operation) {
+    override fun visitUnary(node: TypedMst.Unary<Int>): ExpressionRef = when (node.operation) {
         GroupOps.MINUS_OPERATION -> ctx.i32.sub(ctx.i32.const(0), visit(node.value))
         GroupOps.PLUS_OPERATION -> visit(node.value)
         else -> super.visitUnary(node)
     }
 
-    override fun visitBinary(mst: Binary): ExpressionRef = when (mst.operation) {
+    override fun visitBinary(mst: TypedMst.Binary<Int>): ExpressionRef = when (mst.operation) {
         GroupOps.PLUS_OPERATION -> ctx.i32.add(visit(mst.left), visit(mst.right))
         GroupOps.MINUS_OPERATION -> ctx.i32.sub(visit(mst.left), visit(mst.right))
         RingOps.TIMES_OPERATION -> ctx.i32.mul(visit(mst.left), visit(mst.right))

kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/wasm.kt

@@ -7,7 +7,8 @@
 
 package space.kscience.kmath.wasm
 
-import space.kscience.kmath.estree.compileWith
+import space.kscience.kmath.ast.TypedMst
+import space.kscience.kmath.ast.evaluateConstants
 import space.kscience.kmath.expressions.*
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.DoubleField
@@ -21,8 +22,16 @@ import space.kscience.kmath.wasm.internal.IntWasmBuilder
  * @author Iaroslav Postovalov
  */
 @UnstableKMathAPI
-public fun MST.compileToExpression(algebra: IntRing): IntExpression = IntWasmBuilder(this).instance
+public fun MST.compileToExpression(algebra: IntRing): IntExpression {
+    val typed = evaluateConstants(algebra)
 
+    return if (typed is TypedMst.Constant) object : IntExpression {
+        override val indexer = SimpleSymbolIndexer(emptyList())
+
+        override fun invoke(arguments: IntArray): Int = typed.value
+    } else
+        IntWasmBuilder(typed).instance
+}
 
 /**
  * Compile given MST to expression and evaluate it against [arguments].
@@ -31,7 +40,7 @@ public fun MST.compileToExpression(algebra: IntRing): IntExpression = IntWasmBui
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: IntRing, arguments: Map<Symbol, Int>): Int =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
 
 
 /**
@@ -49,7 +58,16 @@ public fun MST.compile(algebra: IntRing, vararg arguments: Pair<Symbol, Int>): I
  * @author Iaroslav Postovalov
  */
 @UnstableKMathAPI
-public fun MST.compileToExpression(algebra: DoubleField): Expression<Double> = DoubleWasmBuilder(this).instance
+public fun MST.compileToExpression(algebra: DoubleField): Expression<Double> {
+    val typed = evaluateConstants(algebra)
+
+    return if (typed is TypedMst.Constant) object : DoubleExpression {
+        override val indexer = SimpleSymbolIndexer(emptyList())
+
+        override fun invoke(arguments: DoubleArray): Double = typed.value
+    } else
+        DoubleWasmBuilder(typed).instance
+}
 
 
 /**
@@ -59,7 +77,7 @@ public fun MST.compileToExpression(algebra: DoubleField): Expression<Double> = D
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: DoubleField, arguments: Map<Symbol, Double>): Double =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
 
 
 /**
@@ -69,4 +87,4 @@ public fun MST.compile(algebra: DoubleField, arguments: Map<Symbol, Double>): Do
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: DoubleField, vararg arguments: Pair<Symbol, Double>): Double =
-    compileToExpression(algebra).invoke(*arguments)
+    compileToExpression(algebra)(*arguments)

kmath-ast/src/jvmMain/kotlin/space/kscience/kmath/asm/asm.kt

@@ -8,10 +8,14 @@
 package space.kscience.kmath.asm
 
 import space.kscience.kmath.asm.internal.*
+import space.kscience.kmath.ast.TypedMst
+import space.kscience.kmath.ast.evaluateConstants
 import space.kscience.kmath.expressions.*
-import space.kscience.kmath.expressions.MST.*
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.*
+import space.kscience.kmath.operations.Algebra
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.IntRing
+import space.kscience.kmath.operations.LongRing
 
 /**
  * Compiles given MST to an Expression using AST compiler.
@@ -21,102 +25,64 @@ import space.kscience.kmath.operations.*
  * @return the compiled expression.
  * @author Alexander Nozik
  */
+@OptIn(UnstableKMathAPI::class)
 @PublishedApi
 internal fun <T : Any> MST.compileWith(type: Class<T>, algebra: Algebra<T>): Expression<T> {
-    fun GenericAsmBuilder<T>.variablesVisitor(node: MST): Unit = when (node) {
+    val typed = evaluateConstants(algebra)
-        is Symbol -> prepareVariable(node.identity)
+    if (typed is TypedMst.Constant<T>) return Expression { typed.value }
-        is Unary -> variablesVisitor(node.value)
 
-        is Binary -> {
+    fun GenericAsmBuilder<T>.variablesVisitor(node: TypedMst<T>): Unit = when (node) {
+        is TypedMst.Unary -> variablesVisitor(node.value)
+
+        is TypedMst.Binary -> {
             variablesVisitor(node.left)
             variablesVisitor(node.right)
         }
 
-        else -> Unit
+        is TypedMst.Variable -> prepareVariable(node.symbol)
+        is TypedMst.Constant -> Unit
     }
 
-    fun GenericAsmBuilder<T>.expressionVisitor(node: MST): Unit = when (node) {
+    fun GenericAsmBuilder<T>.expressionVisitor(node: TypedMst<T>): Unit = when (node) {
-        is Symbol -> {
+        is TypedMst.Constant -> if (node.number != null)
-            val symbol = algebra.bindSymbolOrNull(node)
+            loadNumberConstant(node.number)
-
-            if (symbol != null)
-                loadObjectConstant(symbol as Any)
         else
-                loadVariable(node.identity)
+            loadObjectConstant(node.value)
-        }
 
-        is Numeric -> if (algebra is NumericAlgebra) {
+        is TypedMst.Variable -> loadVariable(node.symbol)
-            if (Number::class.java.isAssignableFrom(type))
+        is TypedMst.Unary -> buildCall(node.function) { expressionVisitor(node.value) }
-                loadNumberConstant(algebra.number(node.value) as Number)
-            else
-                loadObjectConstant(algebra.number(node.value))
-        } else
-            error("Numeric nodes are not supported by $this")
 
-        is Unary -> when {
+        is TypedMst.Binary -> buildCall(node.function) {
-            algebra is NumericAlgebra && node.value is Numeric -> loadObjectConstant(
-                algebra.unaryOperationFunction(node.operation)(algebra.number((node.value as Numeric).value)),
-            )
-
-            else -> buildCall(algebra.unaryOperationFunction(node.operation)) { expressionVisitor(node.value) }
-        }
-
-        is Binary -> when {
-            algebra is NumericAlgebra && node.left is Numeric && node.right is Numeric -> loadObjectConstant(
-                algebra.binaryOperationFunction(node.operation).invoke(
-                    algebra.number((node.left as Numeric).value),
-                    algebra.number((node.right as Numeric).value),
-                )
-            )
-
-            algebra is NumericAlgebra && node.left is Numeric -> buildCall(
-                algebra.leftSideNumberOperationFunction(node.operation),
-            ) {
             expressionVisitor(node.left)
             expressionVisitor(node.right)
         }
-
-            algebra is NumericAlgebra && node.right is Numeric -> buildCall(
-                algebra.rightSideNumberOperationFunction(node.operation),
-            ) {
-                expressionVisitor(node.left)
-                expressionVisitor(node.right)
-            }
-
-            else -> buildCall(algebra.binaryOperationFunction(node.operation)) {
-                expressionVisitor(node.left)
-                expressionVisitor(node.right)
-            }
-        }
     }
 
     return GenericAsmBuilder<T>(
         type,
-        buildName(this),
+        buildName("${typed.hashCode()}_${type.simpleName}"),
-        { variablesVisitor(this@compileWith) },
+        { variablesVisitor(typed) },
-        { expressionVisitor(this@compileWith) },
+        { expressionVisitor(typed) },
     ).instance
 }
 
-
 /**
  * Create a compiled expression with given [MST] and given [algebra].
  */
 public inline fun <reified T : Any> MST.compileToExpression(algebra: Algebra<T>): Expression<T> =
     compileWith(T::class.java, algebra)
 
-
 /**
  * Compile given MST to expression and evaluate it against [arguments]
  */
 public inline fun <reified T : Any> MST.compile(algebra: Algebra<T>, arguments: Map<Symbol, T>): T =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
 
 /**
  * Compile given MST to expression and evaluate it against [arguments]
  */
 public inline fun <reified T : Any> MST.compile(algebra: Algebra<T>, vararg arguments: Pair<Symbol, T>): T =
-    compileToExpression(algebra).invoke(*arguments)
+    compileToExpression(algebra)(*arguments)
 
 
 /**
@@ -125,7 +91,16 @@ public inline fun <reified T : Any> MST.compile(algebra: Algebra<T>, vararg argu
  * @author Iaroslav Postovalov
  */
 @UnstableKMathAPI
-public fun MST.compileToExpression(algebra: IntRing): IntExpression = IntAsmBuilder(this).instance
+public fun MST.compileToExpression(algebra: IntRing): IntExpression  {
+    val typed = evaluateConstants(algebra)
+
+    return if (typed is TypedMst.Constant) object : IntExpression {
+        override val indexer = SimpleSymbolIndexer(emptyList())
+
+        override fun invoke(arguments: IntArray): Int = typed.value
+    } else
+        IntAsmBuilder(typed).instance
+}
 
 /**
  * Compile given MST to expression and evaluate it against [arguments].
@@ -134,7 +109,7 @@ public fun MST.compileToExpression(algebra: IntRing): IntExpression = IntAsmBuil
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: IntRing, arguments: Map<Symbol, Int>): Int =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
 
 /**
  * Compile given MST to expression and evaluate it against [arguments].
@@ -152,8 +127,16 @@ public fun MST.compile(algebra: IntRing, vararg arguments: Pair<Symbol, Int>): I
  * @author Iaroslav Postovalov
  */
 @UnstableKMathAPI
-public fun MST.compileToExpression(algebra: LongRing): LongExpression = LongAsmBuilder(this).instance
+public fun MST.compileToExpression(algebra: LongRing): LongExpression {
+    val typed = evaluateConstants(algebra)
 
+    return if (typed is TypedMst.Constant<Long>) object : LongExpression {
+        override val indexer = SimpleSymbolIndexer(emptyList())
+
+        override fun invoke(arguments: LongArray): Long = typed.value
+    } else
+        LongAsmBuilder(typed).instance
+}
 
 /**
  * Compile given MST to expression and evaluate it against [arguments].
@@ -162,7 +145,7 @@ public fun MST.compileToExpression(algebra: LongRing): LongExpression = LongAsmB
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: LongRing, arguments: Map<Symbol, Long>): Long =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
 
 
 /**
@@ -181,7 +164,17 @@ public fun MST.compile(algebra: LongRing, vararg arguments: Pair<Symbol, Long>):
  * @author Iaroslav Postovalov
  */
 @UnstableKMathAPI
-public fun MST.compileToExpression(algebra: DoubleField): DoubleExpression = DoubleAsmBuilder(this).instance
+public fun MST.compileToExpression(algebra: DoubleField): DoubleExpression {
+    val typed = evaluateConstants(algebra)
+
+    return if (typed is TypedMst.Constant) object : DoubleExpression {
+        override val indexer = SimpleSymbolIndexer(emptyList())
+
+        override fun invoke(arguments: DoubleArray): Double = typed.value
+    } else
+        DoubleAsmBuilder(typed).instance
+}
+
 
 /**
  * Compile given MST to expression and evaluate it against [arguments].
@@ -190,7 +183,7 @@ public fun MST.compileToExpression(algebra: DoubleField): DoubleExpression = Dou
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: DoubleField, arguments: Map<Symbol, Double>): Double =
-    compileToExpression(algebra).invoke(arguments)
+    compileToExpression(algebra)(arguments)
 
 /**
  * Compile given MST to expression and evaluate it against [arguments].
@@ -199,4 +192,4 @@ public fun MST.compile(algebra: DoubleField, arguments: Map<Symbol, Double>): Do
  */
 @UnstableKMathAPI
 public fun MST.compile(algebra: DoubleField, vararg arguments: Pair<Symbol, Double>): Double =
-    compileToExpression(algebra).invoke(*arguments)
+    compileToExpression(algebra)(*arguments)

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

@@ -49,5 +49,7 @@ internal abstract class AsmBuilder {
          * ASM Type for [space.kscience.kmath.expressions.Symbol].
          */
         val SYMBOL_TYPE: Type = getObjectType("space/kscience/kmath/expressions/Symbol")
+
+        const val ARGUMENTS_NAME = "args"
     }
 }

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

@@ -56,7 +56,7 @@ internal class GenericAsmBuilder<T>(
     /**
      * Local variables indices are indices of symbols in this list.
      */
-    private val argumentsLocals = mutableListOf<String>()
+    private val argumentsLocals = mutableListOf<Symbol>()
 
     /**
      * Subclasses, loads and instantiates [Expression] for given parameters.
@@ -253,10 +253,10 @@ internal class GenericAsmBuilder<T>(
      * Stores value variable [name] into a local. Should be called within [variablesPrepareCallback] before using
      * [loadVariable].
      */
-    fun prepareVariable(name: String): Unit = invokeMethodVisitor.run {
+    fun prepareVariable(name: Symbol): Unit = invokeMethodVisitor.run {
         if (name in argumentsLocals) return@run
         load(1, MAP_TYPE)
-        aconst(name)
+        aconst(name.identity)
 
         invokestatic(
             MAP_INTRINSICS_TYPE.internalName,
@@ -280,7 +280,7 @@ internal class GenericAsmBuilder<T>(
      * Loads a variable [name] from arguments [Map] parameter of [Expression.invoke]. The variable should be stored
      * with [prepareVariable] first.
      */
-    fun loadVariable(name: String): Unit = invokeMethodVisitor.load(2 + argumentsLocals.indexOf(name), tType)
+    fun loadVariable(name: Symbol): Unit = invokeMethodVisitor.load(2 + argumentsLocals.indexOf(name), tType)
 
     inline fun buildCall(function: Function<T>, parameters: GenericAsmBuilder<T>.() -> Unit) {
         contract { callsInPlace(parameters, InvocationKind.EXACTLY_ONCE) }

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

@@ -11,6 +11,7 @@ import org.objectweb.asm.Opcodes.*
 import org.objectweb.asm.Type
 import org.objectweb.asm.Type.*
 import org.objectweb.asm.commons.InstructionAdapter
+import space.kscience.kmath.ast.TypedMst
 import space.kscience.kmath.expressions.*
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
@@ -25,9 +26,9 @@ internal sealed class PrimitiveAsmBuilder<T : Number, out E : Expression<T>>(
     classOfT: Class<*>,
     protected val classOfTPrimitive: Class<*>,
     expressionParent: Class<E>,
-    protected val target: MST,
+    protected val target: TypedMst<T>,
 ) : AsmBuilder() {
-    private val className: String = buildName(target)
+    private val className: String = buildName("${target.hashCode()}_${classOfT.simpleName}")
 
     /**
      * ASM type for [tType].
@@ -329,63 +330,39 @@ internal sealed class PrimitiveAsmBuilder<T : Number, out E : Expression<T>>(
     }
 
     private fun visitVariables(
-        node: MST,
+        node: TypedMst<T>,
         arrayMode: Boolean,
         alreadyLoaded: MutableList<Symbol> = mutableListOf()
     ): Unit = when (node) {
-        is Symbol -> when (node) {
+        is TypedMst.Variable -> if (node.symbol !in alreadyLoaded) {
-            !in alreadyLoaded -> {
+            alreadyLoaded += node.symbol
-                alreadyLoaded += node
+            prepareVariable(node.symbol, arrayMode)
-                prepareVariable(node, arrayMode)
+        } else Unit
-            }
-            else -> {
-            }
-        }
 
-        is MST.Unary -> visitVariables(node.value, arrayMode, alreadyLoaded)
+        is TypedMst.Unary -> visitVariables(node.value, arrayMode, alreadyLoaded)
 
-        is MST.Binary -> {
+        is TypedMst.Binary -> {
             visitVariables(node.left, arrayMode, alreadyLoaded)
             visitVariables(node.right, arrayMode, alreadyLoaded)
         }
 
-        else -> Unit
+        is TypedMst.Constant -> Unit
     }
 
-    private fun visitExpression(node: MST): Unit = when (node) {
+    private fun visitExpression(node: TypedMst<T>): Unit = when (node) {
-        is Symbol -> {
+        is TypedMst.Variable -> loadVariable(node.symbol)
-            val symbol = algebra.bindSymbolOrNull(node)
 
-            if (symbol != null)
+        is TypedMst.Constant -> loadNumberConstant(
-                loadNumberConstant(symbol)
+            node.number ?: error("Object constants are not supported by pritimive ASM builder"),
-            else
-                loadVariable(node)
-        }
-
-        is MST.Numeric -> loadNumberConstant(algebra.number(node.value))
-
-        is MST.Unary -> if (node.value is MST.Numeric)
-            loadNumberConstant(
-                algebra.unaryOperationFunction(node.operation)(algebra.number((node.value as MST.Numeric).value)),
-            )
-        else
-            visitUnary(node)
-
-        is MST.Binary -> when {
-            node.left is MST.Numeric && node.right is MST.Numeric -> loadNumberConstant(
-                algebra.binaryOperationFunction(node.operation)(
-                    algebra.number((node.left as MST.Numeric).value),
-                    algebra.number((node.right as MST.Numeric).value),
-                ),
         )
 
-            else -> visitBinary(node)
+        is TypedMst.Unary -> visitUnary(node)
-        }
+        is TypedMst.Binary -> visitBinary(node)
     }
 
-    protected open fun visitUnary(node: MST.Unary) = visitExpression(node.value)
+    protected open fun visitUnary(node: TypedMst.Unary<T>) = visitExpression(node.value)
 
-    protected open fun visitBinary(node: MST.Binary) {
+    protected open fun visitBinary(node: TypedMst.Binary<T>) {
         visitExpression(node.left)
         visitExpression(node.right)
     }
@@ -404,14 +381,13 @@ internal sealed class PrimitiveAsmBuilder<T : Number, out E : Expression<T>>(
 }
 
 @UnstableKMathAPI
-internal class DoubleAsmBuilder(target: MST) : PrimitiveAsmBuilder<Double, DoubleExpression>(
+internal class DoubleAsmBuilder(target: TypedMst<Double>) : PrimitiveAsmBuilder<Double, DoubleExpression>(
     DoubleField,
     java.lang.Double::class.java,
     java.lang.Double.TYPE,
     DoubleExpression::class.java,
     target,
 ) {
-
     private fun buildUnaryJavaMathCall(name: String) = invokeMethodVisitor.invokestatic(
         MATH_TYPE.internalName,
         name,
@@ -434,7 +410,7 @@ internal class DoubleAsmBuilder(target: MST) : PrimitiveAsmBuilder<Double, Doubl
         false,
     )
 
-    override fun visitUnary(node: MST.Unary) {
+    override fun visitUnary(node: TypedMst.Unary<Double>) {
         super.visitUnary(node)
 
         when (node.operation) {
@@ -459,7 +435,7 @@ internal class DoubleAsmBuilder(target: MST) : PrimitiveAsmBuilder<Double, Doubl
         }
     }
 
-    override fun visitBinary(node: MST.Binary) {
+    override fun visitBinary(node: TypedMst.Binary<Double>) {
         super.visitBinary(node)
 
         when (node.operation) {
@@ -479,7 +455,7 @@ internal class DoubleAsmBuilder(target: MST) : PrimitiveAsmBuilder<Double, Doubl
 }
 
 @UnstableKMathAPI
-internal class IntAsmBuilder(target: MST) :
+internal class IntAsmBuilder(target: TypedMst<Int>) :
     PrimitiveAsmBuilder<Int, IntExpression>(
         IntRing,
         Integer::class.java,
@@ -487,7 +463,7 @@ internal class IntAsmBuilder(target: MST) :
         IntExpression::class.java,
         target
     ) {
-    override fun visitUnary(node: MST.Unary) {
+    override fun visitUnary(node: TypedMst.Unary<Int>) {
         super.visitUnary(node)
 
         when (node.operation) {
@@ -497,7 +473,7 @@ internal class IntAsmBuilder(target: MST) :
         }
     }
 
-    override fun visitBinary(node: MST.Binary) {
+    override fun visitBinary(node: TypedMst.Binary<Int>) {
         super.visitBinary(node)
 
         when (node.operation) {
@@ -510,14 +486,14 @@ internal class IntAsmBuilder(target: MST) :
 }
 
 @UnstableKMathAPI
-internal class LongAsmBuilder(target: MST) : PrimitiveAsmBuilder<Long, LongExpression>(
+internal class LongAsmBuilder(target: TypedMst<Long>) : PrimitiveAsmBuilder<Long, LongExpression>(
     LongRing,
     java.lang.Long::class.java,
     java.lang.Long.TYPE,
     LongExpression::class.java,
     target,
 ) {
-    override fun visitUnary(node: MST.Unary) {
+    override fun visitUnary(node: TypedMst.Unary<Long>) {
         super.visitUnary(node)
 
         when (node.operation) {
@@ -527,7 +503,7 @@ internal class LongAsmBuilder(target: MST) : PrimitiveAsmBuilder<Long, LongExpre
         }
     }
 
-    override fun visitBinary(node: MST.Binary) {
+    override fun visitBinary(node: TypedMst.Binary<Long>) {
         super.visitBinary(node)
 
         when (node.operation) {

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

@@ -55,15 +55,15 @@ internal inline fun MethodVisitor.instructionAdapter(block: InstructionAdapter.(
 internal fun MethodVisitor.label(): Label = Label().also(::visitLabel)
 
 /**
- * Creates a class name for [Expression] subclassed to implement [mst] provided.
+ * Creates a class name for [Expression] based with appending [marker] to reduce collisions.
  *
  * These methods help to avoid collisions of class name to prevent loading several classes with the same name. If there
  * is a colliding class, change [collision] parameter or leave it `0` to check existing classes recursively.
  *
  * @author Iaroslav Postovalov
  */
-internal tailrec fun buildName(mst: MST, collision: Int = 0): String {
+internal tailrec fun buildName(marker: String, collision: Int = 0): String {
-    val name = "space.kscience.kmath.asm.generated.CompiledExpression_${mst.hashCode()}_$collision"
+    val name = "space.kscience.kmath.asm.generated.CompiledExpression_${marker}_$collision"
 
     try {
         Class.forName(name)
@@ -71,7 +71,7 @@ internal tailrec fun buildName(mst: MST, collision: Int = 0): String {
         return name
     }
 
-    return buildName(mst, collision + 1)
+    return buildName(marker, collision + 1)
 }
 
 @Suppress("FunctionName")

kmath-commons/README.md

@@ -0,0 +1,32 @@
+# Module kmath-commons
+
+Commons math binding for kmath
+
+## Usage
+
+## Artifact:
+
+The Maven coordinates of this project are `space.kscience:kmath-commons:0.3.0`.
+
+**Gradle Groovy:**
+```groovy
+repositories {
+    maven { url 'https://repo.kotlin.link' }
+    mavenCentral()
+}
+
+dependencies {
+    implementation 'space.kscience:kmath-commons:0.3.0'
+}
+```
+**Gradle Kotlin DSL:**
+```kotlin
+repositories {
+    maven("https://repo.kotlin.link")
+    mavenCentral()
+}
+
+dependencies {
+    implementation("space.kscience:kmath-commons:0.3.0")
+}
+```

kmath-complex/README.md

@@ -8,17 +8,17 @@ Complex and hypercomplex number systems in KMath.
 
 ## Artifact:
 
-The Maven coordinates of this project are `space.kscience:kmath-complex:0.3.0-dev-17`.
+The Maven coordinates of this project are `space.kscience:kmath-complex:0.3.0`.
 
-**Gradle:**
+**Gradle Groovy:**
-```gradle
+```groovy
 repositories {
     maven { url 'https://repo.kotlin.link' }
     mavenCentral()
 }
 
 dependencies {
-    implementation 'space.kscience:kmath-complex:0.3.0-dev-17'
+    implementation 'space.kscience:kmath-complex:0.3.0'
 }
 ```
 **Gradle Kotlin DSL:**
@@ -29,6 +29,6 @@ repositories {
 }
 
 dependencies {
-    implementation("space.kscience:kmath-complex:0.3.0-dev-17")
+    implementation("space.kscience:kmath-complex:0.3.0")
 }
 ```

kmath-complex/build.gradle.kts

@@ -19,13 +19,15 @@ readme {
 
     feature(
         id = "complex",
-        description = "Complex Numbers",
         ref = "src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt"
-    )
+    ){
+        "Complex numbers operations"
+    }
 
     feature(
         id = "quaternion",
-        description = "Quaternions",
         ref = "src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt"
-    )
+    ){
+        "Quaternions and their composition"
+    }
 }

kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Quaternion.kt

@@ -16,52 +16,132 @@ import space.kscience.kmath.structures.MutableBuffer
 import space.kscience.kmath.structures.MutableMemoryBuffer
 import kotlin.math.*
 
+/**
+ * Represents `double`-based quaternion.
+ *
+ * @property w The first component.
+ * @property x The second component.
+ * @property y The third component.
+ * @property z The fourth component.
+ */
+public class Quaternion(
+    public val w: Double,
+    public val x: Double,
+    public val y: Double,
+    public val z: Double,
+) : Buffer<Double> {
+    init {
+        require(!w.isNaN()) { "w-component of quaternion is not-a-number" }
+        require(!x.isNaN()) { "x-component of quaternion is not-a-number" }
+        require(!y.isNaN()) { "y-component of quaternion is not-a-number" }
+        require(!z.isNaN()) { "z-component of quaternion is not-a-number" }
+    }
+
+    /**
+     * Returns a string representation of this quaternion.
+     */
+    override fun toString(): String = "($w + $x * i + $y * j + $z * k)"
+
+    override val size: Int get() = 4
+
+    override fun get(index: Int): Double = when (index) {
+        0 -> w
+        1 -> x
+        2 -> y
+        3 -> z
+        else -> error("Index $index out of bounds [0,3]")
+    }
+
+    override fun iterator(): Iterator<Double> = listOf(w, x, y, z).iterator()
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other == null || this::class != other::class) return false
+
+        other as Quaternion
+
+        if (w != other.w) return false
+        if (x != other.x) return false
+        if (y != other.y) return false
+        if (z != other.z) return false
+
+        return true
+    }
+
+    override fun hashCode(): Int {
+        var result = w.hashCode()
+        result = 31 * result + x.hashCode()
+        result = 31 * result + y.hashCode()
+        result = 31 * result + z.hashCode()
+        return result
+    }
+
+    public companion object : MemorySpec<Quaternion> {
+        override val objectSize: Int get() = 32
+
+        override fun MemoryReader.read(offset: Int): Quaternion = Quaternion(
+            readDouble(offset),
+            readDouble(offset + 8),
+            readDouble(offset + 16),
+            readDouble(offset + 24)
+        )
+
+        override fun MemoryWriter.write(offset: Int, value: Quaternion) {
+            writeDouble(offset, value.w)
+            writeDouble(offset + 8, value.x)
+            writeDouble(offset + 16, value.y)
+            writeDouble(offset + 24, value.z)
+        }
+    }
+}
+
+public fun Quaternion(w: Number, x: Number = 0.0, y: Number = 0.0, z: Number = 0.0): Quaternion = Quaternion(
+    w.toDouble(),
+    x.toDouble(),
+    y.toDouble(),
+    z.toDouble(),
+)
+
 /**
  * This quaternion's conjugate.
  */
 public val Quaternion.conjugate: Quaternion
-    get() = QuaternionField { z - x * i - y * j - z * k }
+    get() = Quaternion(w, -x, -y, -z)
 
 /**
  * This quaternion's reciprocal.
  */
 public val Quaternion.reciprocal: Quaternion
     get() {
-        QuaternionField {
+        val norm2 = (w * w + x * x + y * y + z * z)
-            val n = norm(this@reciprocal)
+        return Quaternion(w / norm2, -x / norm2, -y / norm2, -z / norm2)
-            return conjugate / (n * n)
-        }
     }
 
-/**
+public fun Quaternion.normalized(): Quaternion = with(QuaternionField){ this@normalized / norm(this@normalized) }
- * Absolute value of the quaternion.
- */
-public val Quaternion.r: Double
-    get() = sqrt(w * w + x * x + y * y + z * z)
 
 /**
  * A field of [Quaternion].
  */
 @OptIn(UnstableKMathAPI::class)
-public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>, PowerOperations<Quaternion>,
+public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Double>, PowerOperations<Quaternion>,
     ExponentialOperations<Quaternion>, NumbersAddOps<Quaternion>, ScaleOperations<Quaternion> {
-    override val zero: Quaternion = 0.toQuaternion()
+    override val zero: Quaternion = Quaternion(0.0)
-    override val one: Quaternion = 1.toQuaternion()
+    override val one: Quaternion = Quaternion(1.0)
 
     /**
      * The `i` quaternion unit.
      */
-    public val i: Quaternion = Quaternion(0, 1)
+    public val i: Quaternion = Quaternion(0.0, 1.0, 0.0, 0.0)
 
     /**
      * The `j` quaternion unit.
      */
-    public val j: Quaternion = Quaternion(0, 0, 1)
+    public val j: Quaternion = Quaternion(0.0, 0.0, 1.0, 0.0)
 
     /**
      * The `k` quaternion unit.
      */
-    public val k: Quaternion = Quaternion(0, 0, 0, 1)
+    public val k: Quaternion = Quaternion(0.0, 0.0, 0.0, 1.0)
 
     override fun add(left: Quaternion, right: Quaternion): Quaternion =
         Quaternion(left.w + right.w, left.x + right.x, left.y + right.y, left.z + right.z)
@@ -133,7 +213,7 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
 
     override fun exp(arg: Quaternion): Quaternion {
         val un = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
-        if (un == 0.0) return exp(arg.w).toQuaternion()
+        if (un == 0.0) return Quaternion(exp(arg.w))
         val n1 = sqrt(un)
         val ea = exp(arg.w)
         val n2 = ea * sin(n1) / n1
@@ -158,7 +238,8 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
         return Quaternion(ln(n), th * arg.x, th * arg.y, th * arg.z)
     }
 
-    override operator fun Number.plus(other: Quaternion): Quaternion = Quaternion(toDouble() + other.w, other.x, other.y, other.z)
+    override operator fun Number.plus(other: Quaternion): Quaternion =
+        Quaternion(toDouble() + other.w, other.x, other.y, other.z)
 
     override operator fun Number.minus(other: Quaternion): Quaternion =
         Quaternion(toDouble() - other.w, -other.x, -other.y, -other.z)
@@ -170,7 +251,12 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
         Quaternion(toDouble() * arg.w, toDouble() * arg.x, toDouble() * arg.y, toDouble() * arg.z)
 
     override fun Quaternion.unaryMinus(): Quaternion = Quaternion(-w, -x, -y, -z)
-    override fun norm(arg: Quaternion): Quaternion = sqrt(arg.conjugate * arg)
+    override fun norm(arg: Quaternion): Double = sqrt(
+        arg.w.pow(2) +
+                arg.x.pow(2) +
+                arg.y.pow(2) +
+                arg.z.pow(2)
+    )
 
     override fun bindSymbolOrNull(value: String): Quaternion? = when (value) {
         "i" -> i
@@ -179,7 +265,7 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
         else -> null
     }
 
-    override fun number(value: Number): Quaternion = value.toQuaternion()
+    override fun number(value: Number): Quaternion = Quaternion(value)
 
     override fun sinh(arg: Quaternion): Quaternion = (exp(arg) - exp(-arg)) / 2.0
     override fun cosh(arg: Quaternion): Quaternion = (exp(arg) + exp(-arg)) / 2.0
@@ -189,76 +275,6 @@ public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>,
     override fun atanh(arg: Quaternion): Quaternion = (ln(arg + one) - ln(one - arg)) / 2.0
 }
 
-/**
- * Represents `double`-based quaternion.
- *
- * @property w The first component.
- * @property x The second component.
- * @property y The third component.
- * @property z The fourth component.
- */
-@OptIn(UnstableKMathAPI::class)
-public data class Quaternion(
-    val w: Double, val x: Double, val y: Double, val z: Double,
-) {
-    public constructor(w: Number, x: Number, y: Number, z: Number) : this(
-        w.toDouble(),
-        x.toDouble(),
-        y.toDouble(),
-        z.toDouble(),
-    )
-
-    public constructor(w: Number, x: Number, y: Number) : this(w.toDouble(), x.toDouble(), y.toDouble(), 0.0)
-    public constructor(w: Number, x: Number) : this(w.toDouble(), x.toDouble(), 0.0, 0.0)
-    public constructor(w: Number) : this(w.toDouble(), 0.0, 0.0, 0.0)
-    public constructor(wx: Complex, yz: Complex) : this(wx.re, wx.im, yz.re, yz.im)
-    public constructor(wx: Complex) : this(wx.re, wx.im, 0, 0)
-
-    init {
-        require(!w.isNaN()) { "w-component of quaternion is not-a-number" }
-        require(!x.isNaN()) { "x-component of quaternion is not-a-number" }
-        require(!y.isNaN()) { "x-component of quaternion is not-a-number" }
-        require(!z.isNaN()) { "x-component of quaternion is not-a-number" }
-    }
-
-    /**
-     * Returns a string representation of this quaternion.
-     */
-    override fun toString(): String = "($w + $x * i + $y * j + $z * k)"
-
-    public companion object : MemorySpec<Quaternion> {
-        override val objectSize: Int
-            get() = 32
-
-        override fun MemoryReader.read(offset: Int): Quaternion =
-            Quaternion(readDouble(offset), readDouble(offset + 8), readDouble(offset + 16), readDouble(offset + 24))
-
-        override fun MemoryWriter.write(offset: Int, value: Quaternion) {
-            writeDouble(offset, value.w)
-            writeDouble(offset + 8, value.x)
-            writeDouble(offset + 16, value.y)
-            writeDouble(offset + 24, value.z)
-        }
-    }
-}
-
-/**
- * Creates a quaternion with real part equal to this real.
- *
- * @receiver the real part.
- * @return a new quaternion.
- */
-public fun Number.toQuaternion(): Quaternion = Quaternion(this)
-
-/**
- * Creates a quaternion with `w`-component equal to `re`-component of given complex and `x`-component equal to
- * `im`-component of given complex.
- *
- * @receiver the complex number.
- * @return a new quaternion.
- */
-public fun Complex.toQuaternion(): Quaternion = Quaternion(this)
-
 /**
  * Creates a new buffer of quaternions with the specified [size], where each element is calculated by calling the
  * specified [init] function.

kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/QuaternionTest.kt

@@ -6,10 +6,23 @@
 package space.kscience.kmath.complex
 
 import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.testutils.assertBufferEquals
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
-internal class QuaternionFieldTest {
+internal class QuaternionTest {
+
+    @Test
+    fun testNorm() {
+        assertEquals(2.0, QuaternionField.norm(Quaternion(1.0, 1.0, 1.0, 1.0)))
+    }
+
+    @Test
+    fun testInverse() = QuaternionField {
+        val q = Quaternion(1.0, 2.0, -3.0, 4.0)
+        assertBufferEquals(one, q * q.reciprocal, 1e-4)
+    }
+
     @Test
     fun testAddition() {
         assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(16, 16) + Quaternion(26, 26) })

kmath-core/README.md

@@ -15,17 +15,17 @@ performance calculations to code generation.
 
 ## Artifact:
 
-The Maven coordinates of this project are `space.kscience:kmath-core:0.3.0-dev-17`.
+The Maven coordinates of this project are `space.kscience:kmath-core:0.3.0`.
 
-**Gradle:**
+**Gradle Groovy:**
-```gradle
+```groovy
 repositories {
     maven { url 'https://repo.kotlin.link' }
     mavenCentral()
 }
 
 dependencies {
-    implementation 'space.kscience:kmath-core:0.3.0-dev-17'
+    implementation 'space.kscience:kmath-core:0.3.0'
 }
 ```
 **Gradle Kotlin DSL:**
@@ -36,6 +36,6 @@ repositories {
 }
 
 dependencies {
-    implementation("space.kscience:kmath-core:0.3.0-dev-17")
+    implementation("space.kscience:kmath-core:0.3.0")
 }
 ```

kmath-core/build.gradle.kts

@@ -1,8 +1,6 @@
 plugins {
-    kotlin("multiplatform")
+    id("ru.mipt.npm.gradle.mpp")
-    id("ru.mipt.npm.gradle.common")
     id("ru.mipt.npm.gradle.native")
-//    id("com.xcporter.metaview") version "0.0.5"
 }
 
 kotlin.sourceSets {

kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/Domain1D.kt

@@ -0,0 +1,59 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.domains
+
+import space.kscience.kmath.linear.Point
+import space.kscience.kmath.misc.UnstableKMathAPI
+
+@UnstableKMathAPI
+public abstract class Domain1D<T : Comparable<T>>(public val range: ClosedRange<T>) : Domain<T> {
+    override val dimension: Int get() = 1
+
+    public operator fun contains(value: T): Boolean = range.contains(value)
+
+    override operator fun contains(point: Point<T>): Boolean {
+        require(point.size == 0)
+        return contains(point[0])
+    }
+}
+
+@UnstableKMathAPI
+public class DoubleDomain1D(
+    @Suppress("CanBeParameter") public val doubleRange: ClosedFloatingPointRange<Double>,
+) : Domain1D<Double>(doubleRange), DoubleDomain {
+    override fun getLowerBound(num: Int): Double {
+        require(num == 0)
+        return range.start
+    }
+
+    override fun getUpperBound(num: Int): Double {
+        require(num == 0)
+        return range.endInclusive
+    }
+
+    override fun volume(): Double = range.endInclusive - range.start
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other == null || this::class != other::class) return false
+
+        other as DoubleDomain1D
+
+        if (doubleRange != other.doubleRange) return false
+
+        return true
+    }
+
+    override fun hashCode(): Int = doubleRange.hashCode()
+
+    override fun toString(): String = doubleRange.toString()
+
+
+}
+
+@UnstableKMathAPI
+public val Domain1D<Double>.center: Double
+    get() = (range.endInclusive + range.start) / 2

kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/HyperSquareDomain.kt

@@ -7,18 +7,28 @@ package space.kscience.kmath.domains
 import space.kscience.kmath.linear.Point
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.indices
 
 /**
- *
+ * A hyper-square (or hyper-cube) real-space domain. It is formed by a [Buffer] of [lower] boundaries
- * HyperSquareDomain class.
+ * and a [Buffer] of upper boundaries. Upper should be greater or equals than lower.
- *
- * @author Alexander Nozik
  */
 @UnstableKMathAPI
-public class HyperSquareDomain(private val lower: Buffer<Double>, private val upper: Buffer<Double>) : DoubleDomain {
+public class HyperSquareDomain(public val lower: Buffer<Double>, public val upper: Buffer<Double>) : DoubleDomain {
+    init {
+        require(lower.size == upper.size) {
+            "Domain borders size mismatch. Lower borders size is ${lower.size}, but upper borders size is ${upper.size}."
+        }
+        require(lower.indices.all { lower[it] <= upper[it] }) {
+            "Domain borders order mismatch. Lower borders must be less or equals than upper borders."
+        }
+    }
+
     override val dimension: Int get() = lower.size
 
+    public val center: DoubleBuffer get() = DoubleBuffer(dimension) { (lower[it] + upper[it]) / 2.0 }
+
     override operator fun contains(point: Point<Double>): Boolean = point.indices.all { i ->
         point[i] in lower[i]..upper[i]
     }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/UnivariateDomain.kt

@@ -1,33 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-package space.kscience.kmath.domains
-
-import space.kscience.kmath.linear.Point
-import space.kscience.kmath.misc.UnstableKMathAPI
-
-@UnstableKMathAPI
-public class UnivariateDomain(public val range: ClosedFloatingPointRange<Double>) : DoubleDomain {
-    override val dimension: Int get() = 1
-
-    public operator fun contains(d: Double): Boolean = range.contains(d)
-
-    override operator fun contains(point: Point<Double>): Boolean {
-        require(point.size == 0)
-        return contains(point[0])
-    }
-
-    override fun getLowerBound(num: Int): Double {
-        require(num == 0)
-        return range.start
-    }
-
-    override fun getUpperBound(num: Int): Double {
-        require(num == 0)
-        return range.endInclusive
-    }
-
-    override fun volume(): Double = range.endInclusive - range.start
-}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSAlgebra.kt

@@ -0,0 +1,458 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
+ */
+
+package space.kscience.kmath.expressions
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.*
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.MutableBuffer
+import space.kscience.kmath.structures.MutableBufferFactory
+import space.kscience.kmath.structures.asBuffer
+import kotlin.math.max
+import kotlin.math.min
+
+/**
+ * Class representing both the value and the differentials of a function.
+ *
+ * This class is the workhorse of the differentiation package.
+ *
+ * This class is an implementation of the extension to Rall's numbers described in Dan Kalman's paper
+ * [Doubly Recursive Multivariate Automatic Differentiation](http://www1.american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf),
+ * Mathematics Magazine, vol. 75, no. 3, June 2002. Rall's numbers are an extension to the real numbers used
+ * throughout mathematical expressions; they hold the derivative together with the value of a function. Dan Kalman's
+ * derivative structures hold all partial derivatives up to any specified order, with respect to any number of free
+ * parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free
+ * parameter, and real numbers can be seen as derivative structures with zero order derivative and no free parameters.
+ *
+ * Derived from
+ * [Commons Math's `DerivativeStructure`](https://github.com/apache/commons-math/blob/924f6c357465b39beb50e3c916d5eb6662194175/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java).
+ */
+@UnstableKMathAPI
+public interface DS<T, A : Ring<T>> {
+    public val derivativeAlgebra: DSAlgebra<T, A>
+    public val data: Buffer<T>
+}
+
+/**
+ * Get a partial derivative.
+ *
+ * @param orders derivation orders with respect to each variable (if all orders are 0, the value is returned).
+ * @return partial derivative.
+ * @see value
+ */
+@UnstableKMathAPI
+private fun <T, A : Ring<T>> DS<T, A>.getPartialDerivative(vararg orders: Int): T =
+    data[derivativeAlgebra.compiler.getPartialDerivativeIndex(*orders)]
+
+/**
+ * Provide a partial derivative with given symbols. On symbol could me mentioned multiple times
+ */
+@UnstableKMathAPI
+public fun <T, A : Ring<T>> DS<T, A>.derivative(symbols: List<Symbol>): T {
+    require(symbols.size <= derivativeAlgebra.order) { "The order of derivative ${symbols.size} exceeds computed order ${derivativeAlgebra.order}" }
+    val ordersCount: Map<String, Int> = symbols.map { it.identity }.groupBy { it }.mapValues { it.value.size }
+    return getPartialDerivative(*symbols.map { ordersCount[it] ?: 0 }.toIntArray())
+}
+
+/**
+ * Provide a partial derivative with given symbols. On symbol could me mentioned multiple times
+ */
+@UnstableKMathAPI
+public fun <T, A : Ring<T>> DS<T, A>.derivative(vararg symbols: Symbol): T {
+    require(symbols.size <= derivativeAlgebra.order) { "The order of derivative ${symbols.size} exceeds computed order ${derivativeAlgebra.order}" }
+    val ordersCount: Map<String, Int> = symbols.map { it.identity }.groupBy { it }.mapValues { it.value.size }
+    return getPartialDerivative(*symbols.map { ordersCount[it] ?: 0 }.toIntArray())
+}
+
+/**
+ * The value part of the derivative structure.
+ *
+ * @see getPartialDerivative
+ */
+@UnstableKMathAPI
+public val <T, A : Ring<T>> DS<T, A>.value: T get() = data[0]
+
+@UnstableKMathAPI
+public abstract class DSAlgebra<T, A : Ring<T>>(
+    public val algebra: A,
+    public val bufferFactory: MutableBufferFactory<T>,
+    public val order: Int,
+    bindings: Map<Symbol, T>,
+) : ExpressionAlgebra<T, DS<T, A>>, SymbolIndexer {
+
+    /**
+     * Get the compiler for number of free parameters and order.
+     *
+     * @return cached rules set.
+     */
+    @PublishedApi
+    internal val compiler: DSCompiler<T, A> by lazy {
+        // get the cached compilers
+        val cache: Array<Array<DSCompiler<T, A>?>>? = null
+
+        // we need to create more compilers
+        val maxParameters: Int = max(numberOfVariables, cache?.size ?: 0)
+        val maxOrder: Int = max(order, if (cache == null) 0 else cache[0].size)
+        val newCache: Array<Array<DSCompiler<T, A>?>> = Array(maxParameters + 1) { arrayOfNulls(maxOrder + 1) }
+
+        if (cache != null) {
+            // preserve the already created compilers
+            for (i in cache.indices) {
+                cache[i].copyInto(newCache[i], endIndex = cache[i].size)
+            }
+        }
+
+        // create the array in increasing diagonal order
+        for (diag in 0..numberOfVariables + order) {
+            for (o in max(0, diag - numberOfVariables)..min(order, diag)) {
+                val p: Int = diag - o
+                if (newCache[p][o] == null) {
+                    val valueCompiler: DSCompiler<T, A>? = if (p == 0) null else newCache[p - 1][o]!!
+                    val derivativeCompiler: DSCompiler<T, A>? = if (o == 0) null else newCache[p][o - 1]!!
+
+                    newCache[p][o] = DSCompiler(
+                        algebra,
+                        bufferFactory,
+                        p,
+                        o,
+                        valueCompiler,
+                        derivativeCompiler,
+                    )
+                }
+            }
+        }
+
+        return@lazy newCache[numberOfVariables][order]!!
+    }
+
+    private val variables: Map<Symbol, DSSymbol> by lazy {
+        bindings.entries.mapIndexed { index, (key, value) ->
+            key to DSSymbol(
+                index,
+                key,
+                value,
+            )
+        }.toMap()
+    }
+    override val symbols: List<Symbol> = bindings.map { it.key }
+
+    public val numberOfVariables: Int get() = symbols.size
+
+
+    private fun bufferForVariable(index: Int, value: T): Buffer<T> {
+        val buffer = bufferFactory(compiler.size) { algebra.zero }
+        buffer[0] = value
+        if (compiler.order > 0) {
+            // the derivative of the variable with respect to itself is 1.
+
+            val indexOfDerivative = compiler.getPartialDerivativeIndex(*IntArray(numberOfVariables).apply {
+                set(index, 1)
+            })
+
+            buffer[indexOfDerivative] = algebra.one
+        }
+        return buffer
+    }
+
+    @UnstableKMathAPI
+    private inner class DSImpl(
+        override val data: Buffer<T>,
+    ) : DS<T, A> {
+        override val derivativeAlgebra: DSAlgebra<T, A> get() = this@DSAlgebra
+    }
+
+    protected fun DS(data: Buffer<T>): DS<T, A> = DSImpl(data)
+
+
+    /**
+     * Build an instance representing a variable.
+     *
+     * Instances built using this constructor are considered to be the free variables with respect to which
+     * differentials are computed. As such, their differential with respect to themselves is +1.
+     */
+    public fun variable(
+        index: Int,
+        value: T,
+    ): DS<T, A> {
+        require(index < compiler.freeParameters) { "number is too large: $index >= ${compiler.freeParameters}" }
+        return DS(bufferForVariable(index, value))
+    }
+
+    /**
+     * Build an instance from all its derivatives.
+     *
+     * @param derivatives derivatives sorted according to [DSCompiler.getPartialDerivativeIndex].
+     */
+    public fun ofDerivatives(
+        vararg derivatives: T,
+    ): DS<T, A> {
+        require(derivatives.size == compiler.size) { "dimension mismatch: ${derivatives.size} and ${compiler.size}" }
+        val data = derivatives.asBuffer()
+
+        return DS(data)
+    }
+
+    /**
+     * A class implementing both [DS] and [Symbol].
+     */
+    @UnstableKMathAPI
+    public inner class DSSymbol internal constructor(
+        index: Int,
+        symbol: Symbol,
+        value: T,
+    ) : Symbol by symbol, DS<T, A> {
+        override val derivativeAlgebra: DSAlgebra<T, A> get() = this@DSAlgebra
+        override val data: Buffer<T> = bufferForVariable(index, value)
+    }
+
+    public override fun const(value: T): DS<T, A> {
+        val buffer = bufferFactory(compiler.size) { algebra.zero }
+        buffer[0] = value
+
+        return DS(buffer)
+    }
+
+    override fun bindSymbolOrNull(value: String): DSSymbol? = variables[StringSymbol(value)]
+
+    override fun bindSymbol(value: String): DSSymbol =
+        bindSymbolOrNull(value) ?: error("Symbol '$value' is not supported in $this")
+
+    public fun bindSymbolOrNull(symbol: Symbol): DSSymbol? = variables[symbol.identity]
+
+    public fun bindSymbol(symbol: Symbol): DSSymbol =
+        bindSymbolOrNull(symbol.identity) ?: error("Symbol '${symbol}' is not supported in $this")
+
+    public fun DS<T, A>.derivative(symbols: List<Symbol>): T {
+        require(symbols.size <= order) { "The order of derivative ${symbols.size} exceeds computed order $order" }
+        val ordersCount = symbols.groupBy { it }.mapValues { it.value.size }
+        return getPartialDerivative(*variables.keys.map { ordersCount[it] ?: 0 }.toIntArray())
+    }
+
+    public fun DS<T, A>.derivative(vararg symbols: Symbol): T = derivative(symbols.toList())
+
+}
+
+
+/**
+ * A ring over [DS].
+ *
+ * @property order The derivation order.
+ * @param bindings The map of bindings values. All bindings are considered free parameters.
+ */
+@UnstableKMathAPI
+public open class DSRing<T, A>(
+    algebra: A,
+    bufferFactory: MutableBufferFactory<T>,
+    order: Int,
+    bindings: Map<Symbol, T>,
+) : DSAlgebra<T, A>(algebra, bufferFactory, order, bindings),
+    Ring<DS<T, A>>, ScaleOperations<DS<T, A>>,
+    NumericAlgebra<DS<T, A>>,
+    NumbersAddOps<DS<T, A>> where A : Ring<T>, A : NumericAlgebra<T>, A : ScaleOperations<T> {
+
+    override fun bindSymbolOrNull(value: String): DSSymbol? =
+        super<DSAlgebra>.bindSymbolOrNull(value)
+
+    override fun DS<T, A>.unaryMinus(): DS<T, A> = mapData { -it }
+
+    /**
+     * Create a copy of given [Buffer] and modify it according to [block]
+     */
+    protected inline fun DS<T, A>.transformDataBuffer(block: A.(MutableBuffer<T>) -> Unit): DS<T, A> {
+        require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" }
+        val newData = bufferFactory(compiler.size) { data[it] }
+        algebra.block(newData)
+        return DS(newData)
+    }
+
+    protected fun DS<T, A>.mapData(block: A.(T) -> T): DS<T, A> {
+        require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" }
+        val newData: Buffer<T> = data.map(bufferFactory) {
+            algebra.block(it)
+        }
+        return DS(newData)
+    }
+
+    protected fun DS<T, A>.mapDataIndexed(block: (Int, T) -> T): DS<T, A> {
+        require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" }
+        val newData: Buffer<T> = data.mapIndexed(bufferFactory, block)
+        return DS(newData)
+    }
+
+    override val zero: DS<T, A> by lazy {
+        const(algebra.zero)
+    }
+
+    override val one: DS<T, A> by lazy {
+        const(algebra.one)
+    }
+
+    override fun number(value: Number): DS<T, A> = const(algebra.number(value))
+
+    override fun add(left: DS<T, A>, right: DS<T, A>): DS<T, A> = left.transformDataBuffer { result ->
+        require(right.derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" }
+        compiler.add(left.data, 0, right.data, 0, result, 0)
+    }
+
+    override fun scale(a: DS<T, A>, value: Double): DS<T, A> = a.mapData {
+        it.times(value)
+    }
+
+    override fun multiply(
+        left: DS<T, A>,
+        right: DS<T, A>,
+    ): DS<T, A> = left.transformDataBuffer { result ->
+        compiler.multiply(left.data, 0, right.data, 0, result, 0)
+    }
+//
+//    override fun DS<T, A>.minus(arg: DS): DS<T, A> = transformDataBuffer { result ->
+//        subtract(data, 0, arg.data, 0, result, 0)
+//    }
+
+    override operator fun DS<T, A>.plus(other: Number): DS<T, A> = transformDataBuffer {
+        it[0] += number(other)
+    }
+
+//
+//    override operator fun DS<T, A>.minus(other: Number): DS<T, A> =
+//        this + (-other.toDouble())
+
+    override operator fun Number.plus(other: DS<T, A>): DS<T, A> = other + this
+    override operator fun Number.minus(other: DS<T, A>): DS<T, A> = other - this
+}
+
+@UnstableKMathAPI
+public class DerivativeStructureRingExpression<T, A>(
+    public val algebra: A,
+    public val bufferFactory: MutableBufferFactory<T>,
+    public val function: DSRing<T, A>.() -> DS<T, A>,
+) : DifferentiableExpression<T> where A : Ring<T>, A : ScaleOperations<T>, A : NumericAlgebra<T> {
+    override operator fun invoke(arguments: Map<Symbol, T>): T =
+        DSRing(algebra, bufferFactory, 0, arguments).function().value
+
+    override fun derivativeOrNull(symbols: List<Symbol>): Expression<T> = Expression { arguments ->
+        with(
+            DSRing(
+                algebra,
+                bufferFactory,
+                symbols.size,
+                arguments
+            )
+        ) { function().derivative(symbols) }
+    }
+}
+
+/**
+ * A field over commons-math [DerivativeStructure].
+ *
+ * @property order The derivation order.
+ * @param bindings The map of bindings values. All bindings are considered free parameters.
+ */
+@UnstableKMathAPI
+public class DSField<T, A : ExtendedField<T>>(
+    algebra: A,
+    bufferFactory: MutableBufferFactory<T>,
+    order: Int,
+    bindings: Map<Symbol, T>,
+) : DSRing<T, A>(algebra, bufferFactory, order, bindings), ExtendedField<DS<T, A>> {
+    override fun number(value: Number): DS<T, A> = const(algebra.number(value))
+
+    override fun divide(left: DS<T, A>, right: DS<T, A>): DS<T, A> = left.transformDataBuffer { result ->
+        compiler.divide(left.data, 0, right.data, 0, result, 0)
+    }
+
+    override fun sin(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.sin(arg.data, 0, result, 0)
+    }
+
+    override fun cos(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.cos(arg.data, 0, result, 0)
+    }
+
+    override fun tan(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.tan(arg.data, 0, result, 0)
+    }
+
+    override fun asin(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.asin(arg.data, 0, result, 0)
+    }
+
+    override fun acos(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.acos(arg.data, 0, result, 0)
+    }
+
+    override fun atan(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.atan(arg.data, 0, result, 0)
+    }
+
+    override fun sinh(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.sinh(arg.data, 0, result, 0)
+    }
+
+    override fun cosh(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.cosh(arg.data, 0, result, 0)
+    }
+
+    override fun tanh(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.tanh(arg.data, 0, result, 0)
+    }
+
+    override fun asinh(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.asinh(arg.data, 0, result, 0)
+    }
+
+    override fun acosh(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.acosh(arg.data, 0, result, 0)
+    }
+
+    override fun atanh(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.atanh(arg.data, 0, result, 0)
+    }
+
+    override fun power(arg: DS<T, A>, pow: Number): DS<T, A> = when (pow) {
+        is Int -> arg.transformDataBuffer { result ->
+            compiler.pow(arg.data, 0, pow, result, 0)
+        }
+        else -> arg.transformDataBuffer { result ->
+            compiler.pow(arg.data, 0, pow.toDouble(), result, 0)
+        }
+    }
+
+    override fun sqrt(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.sqrt(arg.data, 0, result, 0)
+    }
+
+    public fun power(arg: DS<T, A>, pow: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.pow(arg.data, 0, pow.data, 0, result, 0)
+    }
+
+    override fun exp(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.exp(arg.data, 0, result, 0)
+    }
+
+    override fun ln(arg: DS<T, A>): DS<T, A> = arg.transformDataBuffer { result ->
+        compiler.ln(arg.data, 0, result, 0)
+    }
+}
+
+@UnstableKMathAPI
+public class DSFieldExpression<T, A : ExtendedField<T>>(
+    public val algebra: A,
+    public val bufferFactory: MutableBufferFactory<T>,
+    public val function: DSField<T, A>.() -> DS<T, A>,
+) : DifferentiableExpression<T> {
+    override operator fun invoke(arguments: Map<Symbol, T>): T =
+        DSField(algebra, bufferFactory, 0, arguments).function().value
+
+    override fun derivativeOrNull(symbols: List<Symbol>): Expression<T> = Expression { arguments ->
+        DSField(
+            algebra,
+            bufferFactory,
+            symbols.size,
+            arguments,
+        ).run { function().derivative(symbols) }
+    }
+}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSCompiler.kt

@@ -5,11 +5,11 @@
 
 package space.kscience.kmath.expressions
 
+
 import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.MutableBuffer
 import space.kscience.kmath.structures.MutableBufferFactory
-import kotlin.math.max
 import kotlin.math.min
 
 internal fun <T> MutableBuffer<T>.fill(element: T, fromIndex: Int = 0, toIndex: Int = size) {
@@ -52,20 +52,20 @@ internal fun <T> MutableBuffer<T>.fill(element: T, fromIndex: Int = 0, toIndex:
  *
  * @property freeParameters Number of free parameters.
  * @property order Derivation order.
- * @see DerivativeStructure
+ * @see DS
  */
-internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
+public class DSCompiler<T, out A : Algebra<T>> internal constructor(
-    val algebra: A,
+    public val algebra: A,
-    val bufferFactory: MutableBufferFactory<T>,
+    public val bufferFactory: MutableBufferFactory<T>,
-    val freeParameters: Int,
+    public val freeParameters: Int,
-    val order: Int,
+    public val order: Int,
     valueCompiler: DSCompiler<T, A>?,
     derivativeCompiler: DSCompiler<T, A>?,
 ) {
     /**
      * Number of partial derivatives (including the single 0 order derivative element).
      */
-    val sizes: Array<IntArray> by lazy {
+    public val sizes: Array<IntArray> by lazy {
         compileSizes(
             freeParameters,
             order,
@@ -76,7 +76,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
     /**
      * Indirection array for partial derivatives.
      */
-    val derivativesIndirection: Array<IntArray> by lazy {
+    internal val derivativesIndirection: Array<IntArray> by lazy {
         compileDerivativesIndirection(
             freeParameters, order,
             valueCompiler, derivativeCompiler,
@@ -86,7 +86,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
     /**
      * Indirection array of the lower derivative elements.
      */
-    val lowerIndirection: IntArray by lazy {
+    internal val lowerIndirection: IntArray by lazy {
         compileLowerIndirection(
             freeParameters, order,
             valueCompiler, derivativeCompiler,
@@ -96,7 +96,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
     /**
      * Indirection arrays for multiplication.
      */
-    val multIndirection: Array<Array<IntArray>> by lazy {
+    internal val multIndirection: Array<Array<IntArray>> by lazy {
         compileMultiplicationIndirection(
             freeParameters, order,
             valueCompiler, derivativeCompiler, lowerIndirection,
@@ -106,7 +106,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
     /**
      * Indirection arrays for function composition.
      */
-    val compositionIndirection: Array<Array<IntArray>> by lazy {
+    internal val compositionIndirection: Array<Array<IntArray>> by lazy {
         compileCompositionIndirection(
             freeParameters, order,
             valueCompiler, derivativeCompiler,
@@ -120,8 +120,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
      * This number includes the single 0 order derivative element, which is
      * guaranteed to be stored in the first element of the array.
      */
-    val size: Int
+    public val size: Int get() = sizes[freeParameters][order]
-        get() = sizes[freeParameters][order]
 
     /**
      * Get the index of a partial derivative in the array.
@@ -148,7 +147,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
      * @return index of the partial derivative.
      * @see getPartialDerivativeOrders
      */
-    fun getPartialDerivativeIndex(vararg orders: Int): Int {
+    public fun getPartialDerivativeIndex(vararg orders: Int): Int {
         // safety check
         require(orders.size == freeParameters) { "dimension mismatch: ${orders.size} and $freeParameters" }
         return getPartialDerivativeIndex(freeParameters, order, sizes, *orders)
@@ -163,7 +162,7 @@ internal class DSCompiler<T, out A : Algebra<T>> internal constructor(
      * @return orders derivation orders with respect to each parameter
      * @see getPartialDerivativeIndex
      */
-    fun getPartialDerivativeOrders(index: Int): IntArray = derivativesIndirection[index]
+    public fun getPartialDerivativeOrders(index: Int): IntArray = derivativesIndirection[index]
 }
 
 /**
@@ -178,7 +177,7 @@ internal fun <T, A> DSCompiler<T, A>.ln(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : ExponentialOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -211,7 +210,7 @@ internal fun <T, A> DSCompiler<T, A>.pow(
     operandOffset: Int,
     n: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : PowerOperations<T> = algebra {
     if (n == 0) {
         // special case, x^0 = 1 for all x
@@ -267,7 +266,7 @@ internal fun <T, A> DSCompiler<T, A>.exp(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Ring<T>, A : ScaleOperations<T>, A : ExponentialOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -290,7 +289,7 @@ internal fun <T, A> DSCompiler<T, A>.sqrt(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : PowerOperations<T> = algebra {
     // create the function value and derivatives
     // [x^(1/n), (1/n)x^((1/n)-1), (1-n)/n^2x^((1/n)-2), ... ]
@@ -351,7 +350,7 @@ internal fun <T, A> DSCompiler<T, A>.pow(
     operandOffset: Int,
     p: Double,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Ring<T>, A : NumericAlgebra<T>, A : PowerOperations<T>, A : ScaleOperations<T> = algebra {
     // create the function value and derivatives
     // [x^p, px^(p-1), p(p-1)x^(p-2), ... ]
@@ -387,7 +386,7 @@ internal fun <T, A> DSCompiler<T, A>.tan(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Ring<T>, A : TrigonometricOperations<T>, A : ScaleOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -469,7 +468,7 @@ internal fun <T, A> DSCompiler<T, A>.sin(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Ring<T>, A : ScaleOperations<T>, A : TrigonometricOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -497,7 +496,7 @@ internal fun <T, A> DSCompiler<T, A>.acos(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : TrigonometricOperations<T>, A : PowerOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -559,7 +558,7 @@ internal fun <T, A> DSCompiler<T, A>.asin(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : TrigonometricOperations<T>, A : PowerOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -618,7 +617,7 @@ internal fun <T, A> DSCompiler<T, A>.atan(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : TrigonometricOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -678,7 +677,7 @@ internal fun <T, A> DSCompiler<T, A>.cosh(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Ring<T>, A : ScaleOperations<T>, A : ExponentialOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -708,7 +707,7 @@ internal fun <T, A> DSCompiler<T, A>.tanh(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : ExponentialOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -765,7 +764,7 @@ internal fun <T, A> DSCompiler<T, A>.acosh(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : ExponentialOperations<T>, A : PowerOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -857,7 +856,7 @@ internal fun <T, A> DSCompiler<T, A>.sinh(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : ExponentialOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -964,7 +963,7 @@ internal fun <T, A> DSCompiler<T, A>.asinh(
     operand: Buffer<T>,
     operandOffset: Int,
     result: MutableBuffer<T>,
-    resultOffset: Int
+    resultOffset: Int,
 ) where A : Field<T>, A : ExponentialOperations<T>, A : PowerOperations<T> = algebra {
     // create the function value and derivatives
     val function = bufferFactory(1 + order) { zero }
@@ -1109,59 +1108,6 @@ internal fun <T, A> DSCompiler<T, A>.atanh(
     compose(operand, operandOffset, function, result, resultOffset)
 }
 
-/**
- * Get the compiler for number of free parameters and order.
- *
- * @param parameters number of free parameters.
- * @param order derivation order.
- * @return cached rules set.
- */
-internal fun <T, A : Algebra<T>> getCompiler(
-    algebra: A,
-    bufferFactory: MutableBufferFactory<T>,
-    parameters: Int,
-    order: Int
-): DSCompiler<T, A> {
-    // get the cached compilers
-    val cache: Array<Array<DSCompiler<T, A>?>>? = null
-
-    // we need to create more compilers
-    val maxParameters: Int = max(parameters, cache?.size ?: 0)
-    val maxOrder: Int = max(order, if (cache == null) 0 else cache[0].size)
-    val newCache: Array<Array<DSCompiler<T, A>?>> = Array(maxParameters + 1) { arrayOfNulls(maxOrder + 1) }
-
-    if (cache != null) {
-        // preserve the already created compilers
-        for (i in cache.indices) {
-            cache[i].copyInto(newCache[i], endIndex = cache[i].size)
-        }
-    }
-
-    // create the array in increasing diagonal order
-
-    // create the array in increasing diagonal order
-    for (diag in 0..parameters + order) {
-        for (o in max(0, diag - parameters)..min(order, diag)) {
-            val p: Int = diag - o
-            if (newCache[p][o] == null) {
-                val valueCompiler: DSCompiler<T, A>? = if (p == 0) null else newCache[p - 1][o]!!
-                val derivativeCompiler: DSCompiler<T, A>? = if (o == 0) null else newCache[p][o - 1]!!
-
-                newCache[p][o] = DSCompiler(
-                    algebra,
-                    bufferFactory,
-                    p,
-                    o,
-                    valueCompiler,
-                    derivativeCompiler,
-                )
-            }
-        }
-    }
-
-    return newCache[parameters][order]!!
-}
-
 /**
  * Compile the sizes array.
  *

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DerivativeStructure.kt

@@ -1,186 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
- */
-
-package space.kscience.kmath.expressions
-
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.NumericAlgebra
-import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.ScaleOperations
-import space.kscience.kmath.structures.MutableBuffer
-
-/**
- * Class representing both the value and the differentials of a function.
- *
- * This class is the workhorse of the differentiation package.
- *
- * This class is an implementation of the extension to Rall's numbers described in Dan Kalman's paper [Doubly Recursive
- * Multivariate Automatic Differentiation](http://www1.american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf),
- * Mathematics Magazine, vol. 75, no. 3, June 2002. Rall's numbers are an extension to the real numbers used
- * throughout mathematical expressions; they hold the derivative together with the value of a function. Dan Kalman's
- * derivative structures hold all partial derivatives up to any specified order, with respect to any number of free
- * parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free
- * parameter, and real numbers can be seen as derivative structures with zero order derivative and no free parameters.
- *
- * Derived from
- * [Commons Math's `DerivativeStructure`](https://github.com/apache/commons-math/blob/924f6c357465b39beb50e3c916d5eb6662194175/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java).
- */
-@UnstableKMathAPI
-public open class DerivativeStructure<T, A> internal constructor(
-    internal val derivativeAlgebra: DerivativeStructureRing<T, A>,
-    internal val compiler: DSCompiler<T, A>,
-) where A : Ring<T>, A : NumericAlgebra<T>, A : ScaleOperations<T> {
-    /**
-     * Combined array holding all values.
-     */
-    internal var data: MutableBuffer<T> =
-        derivativeAlgebra.bufferFactory(compiler.size) { derivativeAlgebra.algebra.zero }
-
-    /**
-     * Build an instance with all values and derivatives set to 0.
-     *
-     * @param parameters number of free parameters.
-     * @param order derivation order.
-     */
-    public constructor (
-        derivativeAlgebra: DerivativeStructureRing<T, A>,
-        parameters: Int,
-        order: Int,
-    ) : this(
-        derivativeAlgebra,
-        getCompiler<T, A>(derivativeAlgebra.algebra, derivativeAlgebra.bufferFactory, parameters, order),
-    )
-
-    /**
-     * Build an instance representing a constant value.
-     *
-     * @param parameters number of free parameters.
-     * @param order derivation order.
-     * @param value value of the constant.
-     * @see DerivativeStructure
-     */
-    public constructor (
-        derivativeAlgebra: DerivativeStructureRing<T, A>,
-        parameters: Int,
-        order: Int,
-        value: T,
-    ) : this(
-        derivativeAlgebra,
-        parameters,
-        order,
-    ) {
-        data[0] = value
-    }
-
-    /**
-     * Build an instance representing a variable.
-     *
-     * Instances built using this constructor are considered to be the free variables with respect to which
-     * differentials are computed. As such, their differential with respect to themselves is +1.
-     *
-     * @param parameters number of free parameters.
-     * @param order derivation order.
-     * @param index index of the variable (from 0 to `parameters - 1`).
-     * @param value value of the variable.
-     */
-    public constructor (
-        derivativeAlgebra: DerivativeStructureRing<T, A>,
-        parameters: Int,
-        order: Int,
-        index: Int,
-        value: T,
-    ) : this(derivativeAlgebra, parameters, order, value) {
-        require(index < parameters) { "number is too large: $index >= $parameters" }
-
-        if (order > 0) {
-            // the derivative of the variable with respect to itself is 1.
-            data[getCompiler(derivativeAlgebra.algebra, derivativeAlgebra.bufferFactory, index, order).size] =
-                derivativeAlgebra.algebra.one
-        }
-    }
-
-    /**
-     * Build an instance from all its derivatives.
-     *
-     * @param parameters number of free parameters.
-     * @param order derivation order.
-     * @param derivatives derivatives sorted according to [DSCompiler.getPartialDerivativeIndex].
-     */
-    public constructor (
-        derivativeAlgebra: DerivativeStructureRing<T, A>,
-        parameters: Int,
-        order: Int,
-        vararg derivatives: T,
-    ) : this(
-        derivativeAlgebra,
-        parameters,
-        order,
-    ) {
-        require(derivatives.size == data.size) { "dimension mismatch: ${derivatives.size} and ${data.size}" }
-        data = derivativeAlgebra.bufferFactory(data.size) { derivatives[it] }
-    }
-
-    /**
-     * Copy constructor.
-     *
-     * @param ds instance to copy.
-     */
-    internal constructor(ds: DerivativeStructure<T, A>) : this(ds.derivativeAlgebra, ds.compiler) {
-        this.data = ds.data.copy()
-    }
-
-    /**
-     * The number of free parameters.
-     */
-    public val freeParameters: Int
-        get() = compiler.freeParameters
-
-    /**
-     * The derivation order.
-     */
-    public val order: Int
-        get() = compiler.order
-
-    /**
-     * The value part of the derivative structure.
-     *
-     * @see getPartialDerivative
-     */
-    public val value: T
-        get() = data[0]
-
-    /**
-     * Get a partial derivative.
-     *
-     * @param orders derivation orders with respect to each variable (if all orders are 0, the value is returned).
-     * @return partial derivative.
-     * @see value
-     */
-    public fun getPartialDerivative(vararg orders: Int): T = data[compiler.getPartialDerivativeIndex(*orders)]
-
-
-    /**
-     * Test for the equality of two derivative structures.
-     *
-     * Derivative structures are considered equal if they have the same number
-     * of free parameters, the same derivation order, and the same derivatives.
-     *
-     * @return `true` if two derivative structures are equal.
-     */
-    public override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-
-        if (other is DerivativeStructure<*, *>) {
-            return ((freeParameters == other.freeParameters) &&
-                    (order == other.order) &&
-                    data == other.data)
-        }
-
-        return false
-    }
-
-    public override fun hashCode(): Int =
-        227 + 229 * freeParameters + 233 * order + 239 * data.hashCode()
-}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DerivativeStructureExpression.kt

@@ -1,332 +0,0 @@
-/*
- * Copyright 2018-2021 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
- */
-
-package space.kscience.kmath.expressions
-
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.*
-import space.kscience.kmath.structures.MutableBufferFactory
-import space.kscience.kmath.structures.indices
-
-/**
- * A class implementing both [DerivativeStructure] and [Symbol].
- */
-@UnstableKMathAPI
-public class DerivativeStructureSymbol<T, A>(
-    derivativeAlgebra: DerivativeStructureRing<T, A>,
-    size: Int,
-    order: Int,
-    index: Int,
-    symbol: Symbol,
-    value: T,
-) : Symbol by symbol, DerivativeStructure<T, A>(
-    derivativeAlgebra,
-    size,
-    order,
-    index,
-    value
-) where A : Ring<T>, A : NumericAlgebra<T>, A : ScaleOperations<T> {
-    override fun toString(): String = symbol.toString()
-    override fun equals(other: Any?): Boolean = (other as? Symbol) == symbol
-    override fun hashCode(): Int = symbol.hashCode()
-}
-
-/**
- * A ring over [DerivativeStructure].
- *
- * @property order The derivation order.
- * @param bindings The map of bindings values. All bindings are considered free parameters.
- */
-@UnstableKMathAPI
-public open class DerivativeStructureRing<T, A>(
-    public val algebra: A,
-    public val bufferFactory: MutableBufferFactory<T>,
-    public val order: Int,
-    bindings: Map<Symbol, T>,
-) : Ring<DerivativeStructure<T, A>>, ScaleOperations<DerivativeStructure<T, A>>,
-    NumericAlgebra<DerivativeStructure<T, A>>,
-    ExpressionAlgebra<T, DerivativeStructure<T, A>>,
-    NumbersAddOps<DerivativeStructure<T, A>> where A : Ring<T>, A : NumericAlgebra<T>, A : ScaleOperations<T> {
-    public val numberOfVariables: Int = bindings.size
-
-    override val zero: DerivativeStructure<T, A> by lazy {
-        DerivativeStructure(
-            this,
-            numberOfVariables,
-            order,
-        )
-    }
-
-    override val one: DerivativeStructure<T, A> by lazy {
-        DerivativeStructure(
-            this,
-            numberOfVariables,
-            order,
-            algebra.one,
-        )
-    }
-
-    override fun number(value: Number): DerivativeStructure<T, A> = const(algebra.number(value))
-
-    private val variables: Map<Symbol, DerivativeStructureSymbol<T, A>> =
-        bindings.entries.mapIndexed { index, (key, value) ->
-            key to DerivativeStructureSymbol(
-                this,
-                numberOfVariables,
-                order,
-                index,
-                key,
-                value,
-            )
-        }.toMap()
-
-    public override fun const(value: T): DerivativeStructure<T, A> =
-        DerivativeStructure(this, numberOfVariables, order, value)
-
-    override fun bindSymbolOrNull(value: String): DerivativeStructureSymbol<T, A>? = variables[StringSymbol(value)]
-
-    override fun bindSymbol(value: String): DerivativeStructureSymbol<T, A> =
-        bindSymbolOrNull(value) ?: error("Symbol '$value' is not supported in $this")
-
-    public fun bindSymbolOrNull(symbol: Symbol): DerivativeStructureSymbol<T, A>? = variables[symbol.identity]
-
-    public fun bindSymbol(symbol: Symbol): DerivativeStructureSymbol<T, A> =
-        bindSymbolOrNull(symbol.identity) ?: error("Symbol '${symbol}' is not supported in $this")
-
-    public fun DerivativeStructure<T, A>.derivative(symbols: List<Symbol>): T {
-        require(symbols.size <= order) { "The order of derivative ${symbols.size} exceeds computed order $order" }
-        val ordersCount = symbols.groupBy { it }.mapValues { it.value.size }
-        return getPartialDerivative(*variables.keys.map { ordersCount[it] ?: 0 }.toIntArray())
-    }
-
-    public fun DerivativeStructure<T, A>.derivative(vararg symbols: Symbol): T = derivative(symbols.toList())
-
-    override fun DerivativeStructure<T, A>.unaryMinus(): DerivativeStructure<T, A> {
-        val ds = DerivativeStructure(this@DerivativeStructureRing, compiler)
-        for (i in ds.data.indices) {
-            ds.data[i] = algebra { -data[i] }
-        }
-        return ds
-    }
-
-    override fun add(left: DerivativeStructure<T, A>, right: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        left.compiler.checkCompatibility(right.compiler)
-        val ds = DerivativeStructure(left)
-        left.compiler.add(left.data, 0, right.data, 0, ds.data, 0)
-        return ds
-    }
-
-    override fun scale(a: DerivativeStructure<T, A>, value: Double): DerivativeStructure<T, A> {
-        val ds = DerivativeStructure(a)
-        for (i in ds.data.indices) {
-            ds.data[i] = algebra { ds.data[i].times(value) }
-        }
-        return ds
-    }
-
-    override fun multiply(
-        left: DerivativeStructure<T, A>,
-        right: DerivativeStructure<T, A>
-    ): DerivativeStructure<T, A> {
-        left.compiler.checkCompatibility(right.compiler)
-        val result = DerivativeStructure(this, left.compiler)
-        left.compiler.multiply(left.data, 0, right.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun DerivativeStructure<T, A>.minus(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        compiler.checkCompatibility(arg.compiler)
-        val ds = DerivativeStructure(this)
-        compiler.subtract(data, 0, arg.data, 0, ds.data, 0)
-        return ds
-    }
-
-    override operator fun DerivativeStructure<T, A>.plus(other: Number): DerivativeStructure<T, A> {
-        val ds = DerivativeStructure(this)
-        ds.data[0] = algebra { ds.data[0] + number(other) }
-        return ds
-    }
-
-    override operator fun DerivativeStructure<T, A>.minus(other: Number): DerivativeStructure<T, A> =
-        this + -other.toDouble()
-
-    override operator fun Number.plus(other: DerivativeStructure<T, A>): DerivativeStructure<T, A> = other + this
-    override operator fun Number.minus(other: DerivativeStructure<T, A>): DerivativeStructure<T, A> = other - this
-}
-
-@UnstableKMathAPI
-public class DerivativeStructureRingExpression<T, A>(
-    public val algebra: A,
-    public val bufferFactory: MutableBufferFactory<T>,
-    public val function: DerivativeStructureRing<T, A>.() -> DerivativeStructure<T, A>,
-) : DifferentiableExpression<T> where A : Ring<T>, A : ScaleOperations<T>, A : NumericAlgebra<T> {
-    override operator fun invoke(arguments: Map<Symbol, T>): T =
-        DerivativeStructureRing(algebra, bufferFactory, 0, arguments).function().value
-
-    override fun derivativeOrNull(symbols: List<Symbol>): Expression<T> = Expression { arguments ->
-        with(
-            DerivativeStructureRing(
-                algebra,
-                bufferFactory,
-                symbols.size,
-                arguments
-            )
-        ) { function().derivative(symbols) }
-    }
-}
-
-/**
- * A field over commons-math [DerivativeStructure].
- *
- * @property order The derivation order.
- * @param bindings The map of bindings values. All bindings are considered free parameters.
- */
-@UnstableKMathAPI
-public class DerivativeStructureField<T, A : ExtendedField<T>>(
-    algebra: A,
-    bufferFactory: MutableBufferFactory<T>,
-    order: Int,
-    bindings: Map<Symbol, T>,
-) : DerivativeStructureRing<T, A>(algebra, bufferFactory, order, bindings), ExtendedField<DerivativeStructure<T, A>> {
-    override fun number(value: Number): DerivativeStructure<T, A> = const(algebra.number(value))
-
-    override fun divide(left: DerivativeStructure<T, A>, right: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        left.compiler.checkCompatibility(right.compiler)
-        val result = DerivativeStructure(this, left.compiler)
-        left.compiler.divide(left.data, 0, right.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun sin(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.sin(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun cos(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.cos(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun tan(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.tan(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun asin(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.asin(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun acos(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.acos(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun atan(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.atan(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun sinh(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.sinh(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun cosh(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.cosh(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun tanh(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.tanh(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun asinh(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.asinh(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun acosh(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.acosh(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun atanh(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.atanh(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun power(arg: DerivativeStructure<T, A>, pow: Number): DerivativeStructure<T, A> = when (pow) {
-        is Int -> {
-            val result = DerivativeStructure(this, arg.compiler)
-            arg.compiler.pow(arg.data, 0, pow, result.data, 0)
-            result
-        }
-        else -> {
-            val result = DerivativeStructure(this, arg.compiler)
-            arg.compiler.pow(arg.data, 0, pow.toDouble(), result.data, 0)
-            result
-        }
-    }
-
-    override fun sqrt(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.sqrt(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    public fun power(arg: DerivativeStructure<T, A>, pow: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        arg.compiler.checkCompatibility(pow.compiler)
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.pow(arg.data, 0, pow.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun exp(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.exp(arg.data, 0, result.data, 0)
-        return result
-    }
-
-    override fun ln(arg: DerivativeStructure<T, A>): DerivativeStructure<T, A> {
-        val result = DerivativeStructure(this, arg.compiler)
-        arg.compiler.ln(arg.data, 0, result.data, 0)
-        return result
-    }
-}
-
-@UnstableKMathAPI
-public class DerivativeStructureFieldExpression<T, A : ExtendedField<T>>(
-    public val algebra: A,
-    public val bufferFactory: MutableBufferFactory<T>,
-    public val function: DerivativeStructureField<T, A>.() -> DerivativeStructure<T, A>,
-) : DifferentiableExpression<T> {
-    override operator fun invoke(arguments: Map<Symbol, T>): T =
-        DerivativeStructureField(algebra, bufferFactory, 0, arguments).function().value
-
-    override fun derivativeOrNull(symbols: List<Symbol>): Expression<T> = Expression { arguments ->
-        with(
-            DerivativeStructureField(
-                algebra,
-                bufferFactory,
-                symbols.size,
-                arguments,
-            )
-        ) { function().derivative(symbols) }
-    }
-}

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

@@ -34,12 +34,12 @@ public abstract class FunctionalExpressionAlgebra<T, out A : Algebra<T>>(
     override fun binaryOperationFunction(operation: String): (left: Expression<T>, right: Expression<T>) -> Expression<T> =
         { left, right ->
             Expression { arguments ->
-                algebra.binaryOperationFunction(operation)(left.invoke(arguments), right.invoke(arguments))
+                algebra.binaryOperationFunction(operation)(left(arguments), right(arguments))
             }
         }
 
     override fun unaryOperationFunction(operation: String): (arg: Expression<T>) -> Expression<T> = { arg ->
-        Expression { arguments -> algebra.unaryOperationFunction(operation)(arg.invoke(arguments)) }
+        Expression { arguments -> algebra.unaryOperation(operation, arg(arguments)) }
     }
 }
 
@@ -164,8 +164,6 @@ public open class FunctionalExpressionExtendedField<T, out A : ExtendedField<T>>
 
     override fun binaryOperationFunction(operation: String): (left: Expression<T>, right: Expression<T>) -> Expression<T> =
         super<FunctionalExpressionField>.binaryOperationFunction(operation)
-
-    override fun bindSymbol(value: String): Expression<T> = super<FunctionalExpressionField>.bindSymbol(value)
 }
 
 public inline fun <T, A : Group<T>> A.expressionInGroup(

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MST.kt

@@ -24,7 +24,7 @@ public sealed interface MST {
     public data class Numeric(val value: Number) : MST
 
     /**
-     * A node containing an unary operation.
+     * A node containing a unary operation.
      *
      * @property operation the identifier of operation.
      * @property value the argument of this operation.
@@ -34,7 +34,7 @@ public sealed interface MST {
     /**
      * A node containing binary operation.
      *
-     * @property operation the identifier operation.
+     * @property operation the identifier of operation.
      * @property left the left operand.
      * @property right the right operand.
      */

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

@@ -343,10 +343,7 @@ public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.atanh(x: Au
 public class SimpleAutoDiffExtendedField<T : Any, F : ExtendedField<T>>(
     context: F,
     bindings: Map<Symbol, T>,
-) : ExtendedField<AutoDiffValue<T>>, ScaleOperations<AutoDiffValue<T>>,
+) : ExtendedField<AutoDiffValue<T>>, ScaleOperations<AutoDiffValue<T>>, SimpleAutoDiffField<T, F>(context, bindings) {
-    SimpleAutoDiffField<T, F>(context, bindings) {
-
-    override fun bindSymbol(value: String): AutoDiffValue<T> = super<SimpleAutoDiffField>.bindSymbol(value)
 
     override fun number(value: Number): AutoDiffValue<T> = const { number(value) }
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt

@@ -188,7 +188,7 @@ public interface LinearSpace<T, out A : Ring<T>> {
          */
         public fun <T : Any, A : Ring<T>> buffered(
             algebra: A,
-            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
+            bufferFactory: BufferFactory<T> = BufferFactory(Buffer.Companion::boxing),
         ): LinearSpace<T, A> = BufferedLinearSpace(BufferRingOps(algebra, bufferFactory))
 
         @Deprecated("use DoubleField.linearSpace")

kmath-core/src/commonMain/kotlin/space/kscience/kmath/misc/annotations.kt

@@ -27,5 +27,5 @@ public annotation class UnstableKMathAPI
     RequiresOptIn.Level.WARNING,
 )
 public annotation class PerformancePitfall(
-    val message: String = "Potential performance problem"
+    val message: String = "Potential performance problem",
 )

kmath-core/src/commonMain/kotlin/space/kscience/kmath/misc/sorting.kt

@@ -3,43 +3,71 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
+
 package space.kscience.kmath.misc
 
-import kotlin.comparisons.*
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.VirtualBuffer
 
 /**
- * Return a new list filled with buffer indices. Indice order is defined by sorting associated buffer value.
+ * Return a new array filled with buffer indices. Indices order is defined by sorting associated buffer value.
- * This feature allows to sort buffer values without reordering its content.
+ * This feature allows sorting buffer values without reordering its content.
  *
- * @return List of buffer indices, sorted by associated value.
+ * @return Buffer indices, sorted by associated value.
  */
-@PerformancePitfall
 @UnstableKMathAPI
-public fun <V: Comparable<V>> Buffer<V>.permSort() : IntArray = _permSortWith(compareBy<Int> { get(it) })
+public fun <V : Comparable<V>> Buffer<V>.indicesSorted(): IntArray = permSortIndicesWith(compareBy { get(it) })
+
+/**
+ * Create a zero-copy virtual buffer that contains the same elements but in ascending order
+ */
+@OptIn(UnstableKMathAPI::class)
+public fun <V : Comparable<V>> Buffer<V>.sorted(): Buffer<V> {
+    val permutations = indicesSorted()
+    return VirtualBuffer(size) { this[permutations[it]] }
+}
 
-@PerformancePitfall
 @UnstableKMathAPI
-public fun <V: Comparable<V>> Buffer<V>.permSortDescending() : IntArray = _permSortWith(compareByDescending<Int> { get(it) })
+public fun <V : Comparable<V>> Buffer<V>.indicesSortedDescending(): IntArray =
+    permSortIndicesWith(compareByDescending { get(it) })
+
+/**
+ * Create a zero-copy virtual buffer that contains the same elements but in descending order
+ */
+@OptIn(UnstableKMathAPI::class)
+public fun <V : Comparable<V>> Buffer<V>.sortedDescending(): Buffer<V> {
+    val permutations = indicesSortedDescending()
+    return VirtualBuffer(size) { this[permutations[it]] }
+}
 
-@PerformancePitfall
 @UnstableKMathAPI
-public fun <V, C: Comparable<C>> Buffer<V>.permSortBy(selector: (V) -> C) : IntArray = _permSortWith(compareBy<Int> { selector(get(it)) })
+public fun <V, C : Comparable<C>> Buffer<V>.indicesSortedBy(selector: (V) -> C): IntArray =
+    permSortIndicesWith(compareBy { selector(get(it)) })
+
+@OptIn(UnstableKMathAPI::class)
+public fun <V, C : Comparable<C>> Buffer<V>.sortedBy(selector: (V) -> C): Buffer<V> {
+    val permutations = indicesSortedBy(selector)
+    return VirtualBuffer(size) { this[permutations[it]] }
+}
 
-@PerformancePitfall
 @UnstableKMathAPI
-public fun <V, C: Comparable<C>> Buffer<V>.permSortByDescending(selector: (V) -> C) : IntArray = _permSortWith(compareByDescending<Int> { selector(get(it)) })
+public fun <V, C : Comparable<C>> Buffer<V>.indicesSortedByDescending(selector: (V) -> C): IntArray =
+    permSortIndicesWith(compareByDescending { selector(get(it)) })
+
+@OptIn(UnstableKMathAPI::class)
+public fun <V, C : Comparable<C>> Buffer<V>.sortedByDescending(selector: (V) -> C): Buffer<V> {
+    val permutations = indicesSortedByDescending(selector)
+    return VirtualBuffer(size) { this[permutations[it]] }
+}
 
-@PerformancePitfall
 @UnstableKMathAPI
-public fun <V> Buffer<V>.permSortWith(comparator : Comparator<V>) : IntArray = _permSortWith { i1, i2 -> comparator.compare(get(i1), get(i2)) }
+public fun <V> Buffer<V>.indicesSortedWith(comparator: Comparator<V>): IntArray =
+    permSortIndicesWith { i1, i2 -> comparator.compare(get(i1), get(i2)) }
 
-@PerformancePitfall
+private fun <V> Buffer<V>.permSortIndicesWith(comparator: Comparator<Int>): IntArray {
-@UnstableKMathAPI
+    if (size < 2) return IntArray(size) { 0 }
-private fun <V> Buffer<V>._permSortWith(comparator : Comparator<Int>) : IntArray {
-    if (size < 2) return IntArray(size)
 
-    /* TODO: optimisation : keep a constant big array of indices (Ex: from 0 to 4096), then create indice
+    /* TODO: optimisation : keep a constant big array of indices (Ex: from 0 to 4096), then create indices
      * arrays more efficiently by copying subpart of cached one. For bigger needs, we could copy entire
      * cached array, then fill remaining indices manually. Not done for now, because:
      *  1. doing it right would require some statistics about common used buffer sizes.
@@ -53,3 +81,12 @@ private fun <V> Buffer<V>._permSortWith(comparator : Comparator<Int>) : IntArray
      */
     return packedIndices.sortedWith(comparator).toIntArray()
 }
+
+/**
+ * Checks that the [Buffer] is sorted (ascending) and throws [IllegalArgumentException] if it is not.
+ */
+public fun <T : Comparable<T>> Buffer<T>.requireSorted() {
+    for (i in 0..(size - 2)) {
+        require(get(i + 1) >= get(i)) { "The buffer is not sorted at index $i" }
+    }
+}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt

@@ -10,25 +10,6 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
 import kotlin.reflect.KClass
 
-/**
- * An exception is thrown when the expected and actual shape of NDArray differ.
- *
- * @property expected the expected shape.
- * @property actual the actual shape.
- */
-public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) :
-    RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.")
-
-public typealias Shape = IntArray
-
-public fun Shape(shapeFirst: Int, vararg shapeRest: Int): Shape = intArrayOf(shapeFirst, *shapeRest)
-
-public interface WithShape {
-    public val shape: Shape
-
-    public val indices: ShapeIndexer get() = DefaultStrides(shape)
-}
-
 /**
  * The base interface for all ND-algebra implementations.
  *
@@ -194,7 +175,7 @@ public interface RingOpsND<T, out A : RingOps<T>> : RingOps<StructureND<T>>, Gro
     override fun multiply(left: StructureND<T>, right: StructureND<T>): StructureND<T> =
         zip(left, right) { aValue, bValue -> multiply(aValue, bValue) }
 
-    //TODO move to extensions after KEEP-176
+    //TODO move to extensions with context receivers
 
     /**
      * Multiplies an ND structure by an element of it.

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt

@@ -47,7 +47,7 @@ public interface BufferAlgebraND<T, out A : Algebra<T>> : AlgebraND<T, A> {
         zipInline(left.toBufferND(), right.toBufferND(), transform)
 
     public companion object {
-        public val defaultIndexerBuilder: (IntArray) -> ShapeIndexer = DefaultStrides.Companion::invoke
+        public val defaultIndexerBuilder: (IntArray) -> ShapeIndexer = ::Strides
     }
 }
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt

@@ -32,17 +32,22 @@ public open class BufferND<out T>(
 /**
  * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [BufferND]
  */
-public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
+public inline fun <T, R : Any> StructureND<T>.mapToBuffer(
-    factory: BufferFactory<R> = Buffer.Companion::auto,
+    factory: BufferFactory<R>,
     crossinline transform: (T) -> R,
-): BufferND<R> {
+): BufferND<R> = if (this is BufferND<T>)
-    return if (this is BufferND<T>)
     BufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) })
 else {
     val strides = DefaultStrides(shape)
     BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
 }
-}
+
+/**
+ * Transform structure to a new structure using inferred [BufferFactory]
+ */
+public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
+    crossinline transform: (T) -> R,
+): BufferND<R> = mapToBuffer(Buffer.Companion::auto, transform)
 
 /**
  * Represents [MutableStructureND] over [MutableBuffer].
@@ -64,7 +69,7 @@ public class MutableBufferND<T>(
  * Transform structure to a new structure using provided [MutableBufferFactory] and optimizing if argument is [MutableBufferND]
  */
 public inline fun <T, reified R : Any> MutableStructureND<T>.mapToMutableBuffer(
-    factory: MutableBufferFactory<R> = MutableBuffer.Companion::auto,
+    factory: MutableBufferFactory<R> = MutableBufferFactory(MutableBuffer.Companion::auto),
     crossinline transform: (T) -> R,
 ): MutableBufferND<R> {
     return if (this is MutableBufferND<T>)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Shape.kt

@@ -0,0 +1,35 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.nd
+
+/**
+ * An exception is thrown when the expected and actual shape of NDArray differ.
+ *
+ * @property expected the expected shape.
+ * @property actual the actual shape.
+ */
+public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) :
+    RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.")
+
+public class IndexOutOfShapeException(public val shape: Shape, public val index: IntArray) :
+    RuntimeException("Index ${index.contentToString()} is out of shape ${shape.contentToString()}")
+
+public typealias Shape = IntArray
+
+public fun Shape(shapeFirst: Int, vararg shapeRest: Int): Shape = intArrayOf(shapeFirst, *shapeRest)
+
+public interface WithShape {
+    public val shape: Shape
+
+    public val indices: ShapeIndexer get() = DefaultStrides(shape)
+}
+
+internal fun requireIndexInShape(index: IntArray, shape: Shape) {
+    if (index.size != shape.size) throw IndexOutOfShapeException(index, shape)
+    shape.forEachIndexed { axis, axisShape ->
+        if (index[axis] !in 0 until axisShape) throw IndexOutOfShapeException(index, shape)
+    }
+}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndexer.kt

@@ -66,7 +66,7 @@ public abstract class Strides: ShapeIndexer {
 /**
  * Simple implementation of [Strides].
  */
-public class DefaultStrides private constructor(override val shape: IntArray) : Strides() {
+public class DefaultStrides(override val shape: IntArray) : Strides() {
     override val linearSize: Int get() = strides[shape.size]
 
     /**
@@ -112,6 +112,7 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
         /**
          * Cached builder for default strides
          */
+        @Deprecated("Replace by Strides(shape)")
         public operator fun invoke(shape: IntArray): Strides =
             defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
     }
@@ -119,3 +120,8 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
 
 @ThreadLocal
 private val defaultStridesCache = HashMap<IntArray, Strides>()
+
+/**
+ * Cached builder for default strides
+ */
+public fun Strides(shape: IntArray): Strides = defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt

@@ -138,6 +138,10 @@ private class MutableStructure2DWrapper<T>(val structure: MutableStructureND<T>)
     override fun equals(other: Any?): Boolean = false
 
     override fun hashCode(): Int = 0
+
+    override fun toString(): String {
+        return StructureND.toString(structure)
+    }
 }
 
 /**

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt

@@ -101,7 +101,7 @@ public interface StructureND<out T> : Featured<StructureFeature>, WithShape {
             val bufferRepr: String = when (structure.shape.size) {
                 1 -> (0 until structure.shape[0]).map { structure[it] }
                     .joinToString(prefix = "[", postfix = "]", separator = ", ")
-                2 -> (0 until structure.shape[0]).joinToString(prefix = "[", postfix = "]", separator = ", ") { i ->
+                2 -> (0 until structure.shape[0]).joinToString(prefix = "[\n", postfix = "\n]", separator = ",\n") { i ->
                     (0 until structure.shape[1]).joinToString(prefix = "  [", postfix = "]", separator = ", ") { j ->
                         structure[i, j].toString()
                     }
@@ -120,7 +120,7 @@ public interface StructureND<out T> : Featured<StructureFeature>, WithShape {
          */
         public fun <T> buffered(
             strides: Strides,
-            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
+            bufferFactory: BufferFactory<T> = BufferFactory(Buffer.Companion::boxing),
             initializer: (IntArray) -> T,
         ): BufferND<T> = BufferND(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
 
@@ -140,7 +140,7 @@ public interface StructureND<out T> : Featured<StructureFeature>, WithShape {
 
         public fun <T> buffered(
             shape: IntArray,
-            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
+            bufferFactory: BufferFactory<T> = BufferFactory(Buffer.Companion::boxing),
             initializer: (IntArray) -> T,
         ): BufferND<T> = buffered(DefaultStrides(shape), bufferFactory, initializer)
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/VirtualStructureND.kt

@@ -0,0 +1,30 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.nd
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+
+public open class VirtualStructureND<T>(
+    override val shape: Shape,
+    public val producer: (IntArray) -> T,
+) : StructureND<T> {
+    override fun get(index: IntArray): T {
+        requireIndexInShape(index, shape)
+        return producer(index)
+    }
+}
+
+@UnstableKMathAPI
+public class VirtualDoubleStructureND(
+    shape: Shape,
+    producer: (IntArray) -> Double,
+) : VirtualStructureND<Double>(shape, producer)
+
+@UnstableKMathAPI
+public class VirtualIntStructureND(
+    shape: Shape,
+    producer: (IntArray) -> Int,
+) : VirtualStructureND<Int>(shape, producer)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/operationsND.kt

@@ -0,0 +1,32 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.nd
+
+public fun <T> StructureND<T>.roll(axis: Int, step: Int = 1): StructureND<T> {
+    require(axis in shape.indices) { "Axis $axis is outside of shape dimensions: [0, ${shape.size})" }
+    return VirtualStructureND(shape) { index ->
+        val newIndex: IntArray = IntArray(index.size) { indexAxis ->
+            if (indexAxis == axis) {
+                (index[indexAxis] + step).mod(shape[indexAxis])
+            } else {
+                index[indexAxis]
+            }
+        }
+        get(newIndex)
+    }
+}
+
+public fun <T> StructureND<T>.roll(pair: Pair<Int, Int>, vararg others: Pair<Int, Int>): StructureND<T> {
+    val axisMap: Map<Int, Int> = mapOf(pair, *others)
+    require(axisMap.keys.all { it in shape.indices }) { "Some of axes ${axisMap.keys} is outside of shape dimensions: [0, ${shape.size})" }
+    return VirtualStructureND(shape) { index ->
+        val newIndex: IntArray = IntArray(index.size) { indexAxis ->
+            val offset = axisMap[indexAxis] ?: 0
+            (index[indexAxis] + offset).mod(shape[indexAxis])
+        }
+        get(newIndex)
+    }
+}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt

@@ -5,7 +5,6 @@
 
 package space.kscience.kmath.operations
 
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.DoubleBuffer
@@ -53,7 +52,7 @@ public interface BufferAlgebra<T, out A : Algebra<T>> : Algebra<Buffer<T>> {
  */
 private inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapInline(
     buffer: Buffer<T>,
-    crossinline block: A.(T) -> T
+    crossinline block: A.(T) -> T,
 ): Buffer<T> = bufferFactory(buffer.size) { elementAlgebra.block(buffer[it]) }
 
 /**
@@ -61,7 +60,7 @@ private inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapInline(
  */
 private inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapIndexedInline(
     buffer: Buffer<T>,
-    crossinline block: A.(index: Int, arg: T) -> T
+    crossinline block: A.(index: Int, arg: T) -> T,
 ): Buffer<T> = bufferFactory(buffer.size) { elementAlgebra.block(it, buffer[it]) }
 
 /**
@@ -70,7 +69,7 @@ private inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapIndexedInline(
 private inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.zipInline(
     l: Buffer<T>,
     r: Buffer<T>,
-    crossinline block: A.(l: T, r: T) -> T
+    crossinline block: A.(l: T, r: T) -> T,
 ): Buffer<T> {
     require(l.size == r.size) { "Incompatible buffer sizes. left: ${l.size}, right: ${r.size}" }
     return bufferFactory(l.size) { elementAlgebra.block(l[it], r[it]) }
@@ -152,10 +151,11 @@ public val ShortRing.bufferAlgebra: BufferRingOps<Short, ShortRing>
 public open class BufferFieldOps<T, A : Field<T>>(
     elementAlgebra: A,
     bufferFactory: BufferFactory<T>,
-) : BufferRingOps<T, A>(elementAlgebra, bufferFactory), BufferAlgebra<T, A>, FieldOps<Buffer<T>>, ScaleOperations<Buffer<T>> {
+) : BufferRingOps<T, A>(elementAlgebra, bufferFactory), BufferAlgebra<T, A>, FieldOps<Buffer<T>>,
+    ScaleOperations<Buffer<T>> {
 
-    override fun add(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l + r }
+//    override fun add(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l + r }
-    override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l * r }
+//    override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l * r }
     override fun divide(left: Buffer<T>, right: Buffer<T>): Buffer<T> = zipInline(left, right) { l, r -> l / r }
 
     override fun scale(a: Buffer<T>, value: Double): Buffer<T> = a.map { scale(it, value) }
@@ -168,7 +168,7 @@ public open class BufferFieldOps<T, A : Field<T>>(
 public class BufferField<T, A : Field<T>>(
     elementAlgebra: A,
     bufferFactory: BufferFactory<T>,
-    override val size: Int
+    override val size: Int,
 ) : BufferFieldOps<T, A>(elementAlgebra, bufferFactory), Field<Buffer<T>>, WithSize {
 
     override val zero: Buffer<T> = bufferFactory(size) { elementAlgebra.zero }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt

@@ -6,12 +6,10 @@
 package space.kscience.kmath.operations
 
 import space.kscience.kmath.linear.Point
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.asBuffer
-
 import kotlin.math.*
 
 /**
@@ -21,7 +19,7 @@ public abstract class DoubleBufferOps : BufferAlgebra<Double, DoubleField>, Exte
     Norm<Buffer<Double>, Double> {
 
     override val elementAlgebra: DoubleField get() = DoubleField
-    override val bufferFactory: BufferFactory<Double> get() = ::DoubleBuffer
+    override val bufferFactory: BufferFactory<Double> get() = BufferFactory(::DoubleBuffer)
 
     override fun Buffer<Double>.map(block: DoubleField.(Double) -> Double): DoubleBuffer =
         mapInline { DoubleField.block(it) }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/bufferOperation.kt

@@ -61,31 +61,39 @@ public inline fun <reified T> Buffer<T>.toTypedArray(): Array<T> = Array(size, :
 /**
  * Create a new buffer from this one with the given mapping function and using [Buffer.Companion.auto] buffer factory.
  */
-public inline fun <T : Any, reified R : Any> Buffer<T>.map(block: (T) -> R): Buffer<R> =
+public inline fun <T, reified R : Any> Buffer<T>.map(block: (T) -> R): Buffer<R> =
     Buffer.auto(size) { block(get(it)) }
 
 /**
  * Create a new buffer from this one with the given mapping function.
  * Provided [bufferFactory] is used to construct the new buffer.
  */
-public inline fun <T : Any, R : Any> Buffer<T>.map(
+public inline fun <T, R> Buffer<T>.map(
     bufferFactory: BufferFactory<R>,
     crossinline block: (T) -> R,
 ): Buffer<R> = bufferFactory(size) { block(get(it)) }
 
 /**
- * Create a new buffer from this one with the given indexed mapping function.
+ * Create a new buffer from this one with the given mapping (indexed) function.
- * Provided [BufferFactory] is used to construct the new buffer.
+ * Provided [bufferFactory] is used to construct the new buffer.
  */
-public inline fun <T : Any, reified R : Any> Buffer<T>.mapIndexed(
+public inline fun <T, R> Buffer<T>.mapIndexed(
-    bufferFactory: BufferFactory<R> = Buffer.Companion::auto,
+    bufferFactory: BufferFactory<R>,
     crossinline block: (index: Int, value: T) -> R,
 ): Buffer<R> = bufferFactory(size) { block(it, get(it)) }
 
+/**
+ * Create a new buffer from this one with the given indexed mapping function.
+ * Provided [BufferFactory] is used to construct the new buffer.
+ */
+public inline fun <T, reified R : Any> Buffer<T>.mapIndexed(
+    crossinline block: (index: Int, value: T) -> R,
+): Buffer<R> = BufferFactory<R>(Buffer.Companion::auto).invoke(size) { block(it, get(it)) }
+
 /**
  * Fold given buffer according to [operation]
  */
-public inline fun <T : Any, R> Buffer<T>.fold(initial: R, operation: (acc: R, T) -> R): R {
+public inline fun <T, R> Buffer<T>.fold(initial: R, operation: (acc: R, T) -> R): R {
     var accumulator = initial
     for (index in this.indices) accumulator = operation(accumulator, get(index))
     return accumulator
@@ -95,9 +103,9 @@ public inline fun <T : Any, R> Buffer<T>.fold(initial: R, operation: (acc: R, T)
  * Zip two buffers using given [transform].
  */
 @UnstableKMathAPI
-public inline fun <T1 : Any, T2 : Any, reified R : Any> Buffer<T1>.zip(
+public inline fun <T1, T2 : Any, reified R : Any> Buffer<T1>.zip(
     other: Buffer<T2>,
-    bufferFactory: BufferFactory<R> = Buffer.Companion::auto,
+    bufferFactory: BufferFactory<R> = BufferFactory(Buffer.Companion::auto),
     crossinline transform: (T1, T2) -> R,
 ): Buffer<R> {
     require(size == other.size) { "Buffer size mismatch in zip: expected $size but found ${other.size}" }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt

@@ -14,14 +14,18 @@ import kotlin.reflect.KClass
  *
  * @param T the type of buffer.
  */
-public typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
+public fun interface BufferFactory<T> {
+    public operator fun invoke(size: Int, builder: (Int) -> T): Buffer<T>
+}
 
 /**
  * Function that produces [MutableBuffer] from its size and function that supplies values.
  *
  * @param T the type of buffer.
  */
-public typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
+public fun interface MutableBufferFactory<T>: BufferFactory<T>{
+    override fun invoke(size: Int, builder: (Int) -> T): MutableBuffer<T>
+}
 
 /**
  * A generic read-only random-access structure for both primitives and objects.
@@ -105,6 +109,16 @@ public interface Buffer<out T> {
  */
 public val Buffer<*>.indices: IntRange get() = 0 until size
 
+public fun <T> Buffer<T>.first(): T {
+    require(size > 0) { "Can't get the first element of empty buffer" }
+    return get(0)
+}
+
+public fun <T> Buffer<T>.last(): T {
+    require(size > 0) { "Can't get the last element of empty buffer" }
+    return get(size - 1)
+}
+
 /**
  * Immutable wrapper for [MutableBuffer].
  *

kmath-core/src/commonTest/kotlin/space/kscience/kmath/expressions/DerivativeStructureExpressionTest.kt

@@ -19,10 +19,10 @@ import kotlin.test.assertFails
 internal inline fun diff(
     order: Int,
     vararg parameters: Pair<Symbol, Double>,
-    block: DerivativeStructureField<Double, DoubleField>.() -> Unit,
+    block: DSField<Double, DoubleField>.() -> Unit,
 ) {
     contract { callsInPlace(block, InvocationKind.EXACTLY_ONCE) }
-    DerivativeStructureField(DoubleField, ::DoubleBuffer, order, mapOf(*parameters)).block()
+    DSField(DoubleField, ::DoubleBuffer, order, mapOf(*parameters)).block()
 }
 
 internal class AutoDiffTest {
@@ -30,7 +30,7 @@ internal class AutoDiffTest {
     private val y by symbol
 
     @Test
-    fun derivativeStructureFieldTest() {
+    fun dsAlgebraTest() {
         diff(2, x to 1.0, y to 1.0) {
             val x = bindSymbol(x)//by binding()
             val y = bindSymbol("y")
@@ -44,8 +44,8 @@ internal class AutoDiffTest {
     }
 
     @Test
-    fun autoDifTest() {
+    fun dsExpressionTest() {
-        val f = DerivativeStructureFieldExpression(DoubleField, ::DoubleBuffer) {
+        val f = DSFieldExpression(DoubleField, ::DoubleBuffer) {
             val x by binding
             val y by binding
             x.pow(2) + 2 * x * y + y.pow(2) + 1

kmath-core/src/commonTest/kotlin/space/kscience/kmath/misc/PermSortTest.kt

@@ -6,14 +6,13 @@
 package space.kscience.kmath.misc
 
 import space.kscience.kmath.misc.PermSortTest.Platform.*
-import kotlin.random.Random
-import kotlin.test.Test
-import kotlin.test.assertEquals
-import kotlin.test.assertTrue
-
 import space.kscience.kmath.structures.IntBuffer
 import space.kscience.kmath.structures.asBuffer
+import kotlin.random.Random
+import kotlin.test.Test
 import kotlin.test.assertContentEquals
+import kotlin.test.assertEquals
+import kotlin.test.assertTrue
 
 class PermSortTest {
 
@@ -29,9 +28,9 @@ class PermSortTest {
     @Test
     fun testOnEmptyBuffer() {
         val emptyBuffer = IntBuffer(0) {it}
-        var permutations = emptyBuffer.permSort()
+        var permutations = emptyBuffer.indicesSorted()
         assertTrue(permutations.isEmpty(), "permutation on an empty buffer should return an empty result")
-        permutations = emptyBuffer.permSortDescending()
+        permutations = emptyBuffer.indicesSortedDescending()
         assertTrue(permutations.isEmpty(), "permutation on an empty buffer should return an empty result")
     }
 
@@ -47,25 +46,25 @@ class PermSortTest {
 
     @Test
     fun testPermSortBy() {
-        val permutations = platforms.permSortBy { it.name }
+        val permutations = platforms.indicesSortedBy { it.name }
         val expected = listOf(ANDROID, JS, JVM, NATIVE, WASM)
         assertContentEquals(expected, permutations.map { platforms[it] }, "Ascending PermSort by name")
     }
 
     @Test
     fun testPermSortByDescending() {
-        val permutations = platforms.permSortByDescending { it.name }
+        val permutations = platforms.indicesSortedByDescending { it.name }
         val expected = listOf(WASM, NATIVE, JVM, JS, ANDROID)
         assertContentEquals(expected, permutations.map { platforms[it] }, "Descending PermSort by name")
     }
 
     @Test
     fun testPermSortWith() {
-        var permutations = platforms.permSortWith { p1, p2 -> p1.name.length.compareTo(p2.name.length) }
+        var permutations = platforms.indicesSortedWith { p1, p2 -> p1.name.length.compareTo(p2.name.length) }
         val expected = listOf(JS, JVM, WASM, NATIVE, ANDROID)
         assertContentEquals(expected, permutations.map { platforms[it] }, "PermSort using custom ascending comparator")
 
-        permutations = platforms.permSortWith(compareByDescending { it.name.length })
+        permutations = platforms.indicesSortedWith(compareByDescending { it.name.length })
         assertContentEquals(expected.reversed(), permutations.map { platforms[it] }, "PermSort using custom descending comparator")
     }
 
@@ -75,7 +74,7 @@ class PermSortTest {
         println("Test randomization seed: $seed")
 
         val buffer = Random(seed).buffer(bufferSize)
-        val indices = buffer.permSort()
+        val indices = buffer.indicesSorted()
 
         assertEquals(bufferSize, indices.size)
         // Ensure no doublon is present in indices
@@ -87,7 +86,7 @@ class PermSortTest {
             assertTrue(current <= next, "Permutation indices not properly sorted")
         }
 
-        val descIndices = buffer.permSortDescending()
+        val descIndices = buffer.indicesSortedDescending()
         assertEquals(bufferSize, descIndices.size) 
         // Ensure no doublon is present in indices
         assertEquals(descIndices.toSet().size, descIndices.size)

kmath-core/src/commonTest/kotlin/space/kscience/kmath/nd/NdOperationsTest.kt

@@ -0,0 +1,28 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.nd
+
+import space.kscience.kmath.operations.DoubleField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class NdOperationsTest {
+    @Test
+    fun roll() {
+        val structure = DoubleField.ndAlgebra.structureND(5, 5) { index ->
+            index.sumOf { it.toDouble() }
+        }
+
+        println(StructureND.toString(structure))
+
+        val rolled = structure.roll(0,-1)
+
+        println(StructureND.toString(rolled))
+
+        assertEquals(4.0, rolled[0, 0])
+    }
+
+}

kmath-coroutines/README.md

@@ -0,0 +1,32 @@
+# Module kmath-coroutines
+
+
+
+## Usage
+
+## Artifact:
+
+The Maven coordinates of this project are `space.kscience:kmath-coroutines:0.3.0`.
+
+**Gradle Groovy:**
+```groovy
+repositories {
+    maven { url 'https://repo.kotlin.link' }
+    mavenCentral()
+}
+
+dependencies {
+    implementation 'space.kscience:kmath-coroutines:0.3.0'
+}
+```
+**Gradle Kotlin DSL:**
+```kotlin
+repositories {
+    maven("https://repo.kotlin.link")
+    mavenCentral()
+}
+
+dependencies {
+    implementation("space.kscience:kmath-coroutines:0.3.0")
+}
+```

kmath-coroutines/src/jvmMain/kotlin/space/kscience/kmath/structures/LazyStructureND.kt

@@ -18,12 +18,12 @@ public class LazyStructureND<out T>(
 ) : StructureND<T> {
     private val cache: MutableMap<IntArray, Deferred<T>> = HashMap()
 
-    public fun deferred(index: IntArray): Deferred<T> = cache.getOrPut(index) {
+    public fun async(index: IntArray): Deferred<T> = cache.getOrPut(index) {
         scope.async(context = Dispatchers.Math) { function(index) }
     }
 
-    public suspend fun await(index: IntArray): T = deferred(index).await()
+    public suspend fun await(index: IntArray): T = async(index).await()
-    override operator fun get(index: IntArray): T = runBlocking { deferred(index).await() }
+    override operator fun get(index: IntArray): T = runBlocking { async(index).await() }
 
     @OptIn(PerformancePitfall::class)
     override fun elements(): Sequence<Pair<IntArray, T>> {
@@ -33,8 +33,8 @@ public class LazyStructureND<out T>(
     }
 }
 
-public fun <T> StructureND<T>.deferred(index: IntArray): Deferred<T> =
+public fun <T> StructureND<T>.async(index: IntArray): Deferred<T> =
-    if (this is LazyStructureND<T>) deferred(index) else CompletableDeferred(get(index))
+    if (this is LazyStructureND<T>) this@async.async(index) else CompletableDeferred(get(index))
 
 public suspend fun <T> StructureND<T>.await(index: IntArray): T =
     if (this is LazyStructureND<T>) await(index) else get(index)

kmath-dimensions/README.md

@@ -0,0 +1,32 @@
+# Module kmath-dimensions
+
+A proof of concept module for adding type-safe dimensions to structures
+
+## Usage
+
+## Artifact:
+
+The Maven coordinates of this project are `space.kscience:kmath-dimensions:0.3.0`.
+
+**Gradle Groovy:**
+```groovy
+repositories {
+    maven { url 'https://repo.kotlin.link' }
+    mavenCentral()
+}
+
+dependencies {
+    implementation 'space.kscience:kmath-dimensions:0.3.0'
+}
+```
+**Gradle Kotlin DSL:**
+```kotlin
+repositories {
+    maven("https://repo.kotlin.link")
+    mavenCentral()
+}
+
+dependencies {
+    implementation("space.kscience:kmath-dimensions:0.3.0")
+}
+```

kmath-ejml/README.md

@@ -9,17 +9,17 @@ EJML based linear algebra implementation.
 
 ## Artifact:
 
-The Maven coordinates of this project are `space.kscience:kmath-ejml:0.3.0-dev-17`.
+The Maven coordinates of this project are `space.kscience:kmath-ejml:0.3.0`.
 
-**Gradle:**
+**Gradle Groovy:**
-```gradle
+```groovy
 repositories {
     maven { url 'https://repo.kotlin.link' }
     mavenCentral()
 }
 
 dependencies {
-    implementation 'space.kscience:kmath-ejml:0.3.0-dev-17'
+    implementation 'space.kscience:kmath-ejml:0.3.0'
 }
 ```
 **Gradle Kotlin DSL:**
@@ -30,6 +30,6 @@ repositories {
 }
 
 dependencies {
-    implementation("space.kscience:kmath-ejml:0.3.0-dev-17")
+    implementation("space.kscience:kmath-ejml:0.3.0")
 }
 ```

kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/_generated.kt

@@ -271,7 +271,9 @@ public object EjmlLinearSpaceDDRM : EjmlLinearSpace<Double, DoubleField, DMatrix
             }
 
             else -> null
-        }?.let(type::cast)
+        }?.let{
+            type.cast(it)
+        }
     }
 
     /**
@@ -505,7 +507,9 @@ public object EjmlLinearSpaceFDRM : EjmlLinearSpace<Float, FloatField, FMatrixRM
             }
 
             else -> null
-        }?.let(type::cast)
+        }?.let{
+            type.cast(it)
+        }
     }
 
     /**
@@ -734,7 +738,9 @@ public object EjmlLinearSpaceDSCC : EjmlLinearSpace<Double, DoubleField, DMatrix
             }
 
             else -> null
-        }?.let(type::cast)
+        }?.let{
+            type.cast(it)
+        }
     }
 
     /**
@@ -963,7 +969,9 @@ public object EjmlLinearSpaceFSCC : EjmlLinearSpace<Float, FloatField, FMatrixSp
             }
 
             else -> null
-        }?.let(type::cast)
+        }?.let{
+            type.cast(it)
+        }
     }
 
     /**

kmath-ejml/src/test/kotlin/space/kscience/kmath/ejml/EjmlMatrixTest.kt

@@ -3,6 +3,8 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
+@file:OptIn(PerformancePitfall::class)
+
 package space.kscience.kmath.ejml
 
 import org.ejml.data.DMatrixRMaj
@@ -18,11 +20,11 @@ import kotlin.random.Random
 import kotlin.random.asJavaRandom
 import kotlin.test.*
 
-@OptIn(PerformancePitfall::class)
+internal fun <T : Any> assertMatrixEquals(expected: StructureND<T>, actual: StructureND<T>) {
-fun <T : Any> assertMatrixEquals(expected: StructureND<T>, actual: StructureND<T>) {
     assertTrue { StructureND.contentEquals(expected, actual) }
 }
 
+@OptIn(UnstableKMathAPI::class)
 internal class EjmlMatrixTest {
     private val random = Random(0)
 

kmath-for-real/README.md

@@ -9,17 +9,17 @@ Specialization of KMath APIs for Double numbers.
 
 ## Artifact:
 
-The Maven coordinates of this project are `space.kscience:kmath-for-real:0.3.0-dev-17`.
+The Maven coordinates of this project are `space.kscience:kmath-for-real:0.3.0`.
 
-**Gradle:**
+**Gradle Groovy:**
-```gradle
+```groovy
 repositories {
     maven { url 'https://repo.kotlin.link' }
     mavenCentral()
 }
 
 dependencies {
-    implementation 'space.kscience:kmath-for-real:0.3.0-dev-17'
+    implementation 'space.kscience:kmath-for-real:0.3.0'
 }
 ```
 **Gradle Kotlin DSL:**
@@ -30,6 +30,6 @@ repositories {
 }
 
 dependencies {
-    implementation("space.kscience:kmath-for-real:0.3.0-dev-17")
+    implementation("space.kscience:kmath-for-real:0.3.0")
 }
 ```

kmath-for-real/build.gradle.kts

@@ -21,19 +21,22 @@ readme {
 
     feature(
         id = "DoubleVector",
-        description = "Numpy-like operations for Buffers/Points",
         ref = "src/commonMain/kotlin/space/kscience/kmath/real/DoubleVector.kt"
-    )
+    ){
+        "Numpy-like operations for Buffers/Points"
+    }
 
     feature(
         id = "DoubleMatrix",
-        description = "Numpy-like operations for 2d real structures",
         ref = "src/commonMain/kotlin/space/kscience/kmath/real/DoubleMatrix.kt"
-    )
+    ){
+        "Numpy-like operations for 2d real structures"
+    }
 
     feature(
         id = "grids",
-        description = "Uniform grid generators",
         ref = "src/commonMain/kotlin/space/kscience/kmath/structures/grids.kt"
-    )
+    ){
+        "Uniform grid generators"
+    }
 }

kmath-functions/README.md

@@ -11,17 +11,17 @@ Functions and interpolations.
 
 ## Artifact:
 
-The Maven coordinates of this project are `space.kscience:kmath-functions:0.3.0-dev-17`.
+The Maven coordinates of this project are `space.kscience:kmath-functions:0.3.0`.
 
-**Gradle:**
+**Gradle Groovy:**
-```gradle
+```groovy
 repositories {
     maven { url 'https://repo.kotlin.link' }
     mavenCentral()
 }
 
 dependencies {
-    implementation 'space.kscience:kmath-functions:0.3.0-dev-17'
+    implementation 'space.kscience:kmath-functions:0.3.0'
 }
 ```
 **Gradle Kotlin DSL:**
@@ -32,6 +32,6 @@ repositories {
 }
 
 dependencies {
-    implementation("space.kscience:kmath-functions:0.3.0-dev-17")
+    implementation("space.kscience:kmath-functions:0.3.0")
 }
 ```

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

@@ -7,6 +7,6 @@ package space.kscience.kmath.functions
 
 import space.kscience.kmath.structures.Buffer
 
-public typealias UnivariateFunction<T> = (T) -> T
+public typealias Function1D<T> = (T) -> T
 
-public typealias MultivariateFunction<T> = (Buffer<T>) -> T
+public typealias FunctionND<T> = (Buffer<T>) -> T

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt

@@ -28,6 +28,8 @@ public fun <T : Comparable<T>> PiecewisePolynomial<T>.integrate(algebra: Field<T
 /**
  * Compute definite integral of given [PiecewisePolynomial] piece by piece in a given [range]
  * Requires [UnivariateIntegrationNodes] or [IntegrationRange] and [IntegrandMaxCalls]
+ *
+ * TODO use context receiver for algebra
  */
 @UnstableKMathAPI
 public fun <T : Comparable<T>> PiecewisePolynomial<T>.integrate(
@@ -98,6 +100,7 @@ public object DoubleSplineIntegrator : UnivariateIntegrator<Double> {
     }
 }
 
+@Suppress("unused")
 @UnstableKMathAPI
 public inline val DoubleField.splineIntegrator: UnivariateIntegrator<Double>
     get() = DoubleSplineIntegrator

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/Interpolator.kt

@@ -9,6 +9,7 @@ package space.kscience.kmath.interpolation
 
 import space.kscience.kmath.data.XYColumnarData
 import space.kscience.kmath.functions.PiecewisePolynomial
+import space.kscience.kmath.functions.asFunction
 import space.kscience.kmath.functions.value
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.Ring
@@ -59,3 +60,33 @@ public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
     val pointSet = XYColumnarData.of(data.map { it.first }.asBuffer(), data.map { it.second }.asBuffer())
     return interpolatePolynomials(pointSet)
 }
+
+public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
+    x: Buffer<T>,
+    y: Buffer<T>,
+): (T) -> T? = interpolatePolynomials(x, y).asFunction(algebra)
+
+public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
+    data: Map<T, T>,
+): (T) -> T? = interpolatePolynomials(data).asFunction(algebra)
+
+public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
+    data: List<Pair<T, T>>,
+): (T) -> T? = interpolatePolynomials(data).asFunction(algebra)
+
+
+public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
+    x: Buffer<T>,
+    y: Buffer<T>,
+    defaultValue: T,
+): (T) -> T = interpolatePolynomials(x, y).asFunction(algebra, defaultValue)
+
+public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
+    data: Map<T, T>,
+    defaultValue: T,
+): (T) -> T = interpolatePolynomials(data).asFunction(algebra, defaultValue)
+
+public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
+    data: List<Pair<T, T>>,
+    defaultValue: T,
+): (T) -> T = interpolatePolynomials(data).asFunction(algebra, defaultValue)

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/LinearInterpolator.kt

@@ -22,6 +22,7 @@ internal fun <T : Comparable<T>> insureSorted(points: XYColumnarData<*, T, *>) {
  * Reference JVM implementation: https://github.com/apache/commons-math/blob/master/src/main/java/org/apache/commons/math4/analysis/interpolation/LinearInterpolator.java
  */
 public class LinearInterpolator<T : Comparable<T>>(override val algebra: Field<T>) : PolynomialInterpolator<T> {
+
     @OptIn(UnstableKMathAPI::class)
     override fun interpolatePolynomials(points: XYColumnarData<T, T, T>): PiecewisePolynomial<T> = algebra {
         require(points.size > 0) { "Point array should not be empty" }
@@ -37,3 +38,6 @@ public class LinearInterpolator<T : Comparable<T>>(override val algebra: Field<T
         }
     }
 }
+
+public val <T : Comparable<T>> Field<T>.linearInterpolator: LinearInterpolator<T>
+    get() = LinearInterpolator(this)

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt

@@ -72,8 +72,12 @@ public class SplineInterpolator<T : Comparable<T>>(
             }
         }
     }
+}
 
-    public companion object {
+
-        public val double: SplineInterpolator<Double> = SplineInterpolator(DoubleField, ::DoubleBuffer)
+public fun <T : Comparable<T>> Field<T>.splineInterpolator(
-    }
+    bufferFactory: MutableBufferFactory<T>,
-}
+): SplineInterpolator<T> = SplineInterpolator(this, bufferFactory)
+
+public val DoubleField.splineInterpolator: SplineInterpolator<Double>
+    get() = SplineInterpolator(this, ::DoubleBuffer)

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/interpolation/LinearInterpolatorTest.kt

@@ -5,8 +5,6 @@
 
 package space.kscience.kmath.interpolation
 
-import space.kscience.kmath.functions.PiecewisePolynomial
-import space.kscience.kmath.functions.asFunction
 import space.kscience.kmath.operations.DoubleField
 import kotlin.test.Test
 import kotlin.test.assertEquals
@@ -21,8 +19,8 @@ internal class LinearInterpolatorTest {
             3.0 to 4.0
         )
 
-        val polynomial: PiecewisePolynomial<Double> = LinearInterpolator(DoubleField).interpolatePolynomials(data)
+        //val polynomial: PiecewisePolynomial<Double> = DoubleField.linearInterpolator.interpolatePolynomials(data)
-        val function = polynomial.asFunction(DoubleField)
+        val function = DoubleField.linearInterpolator.interpolate(data)
         assertEquals(null, function(-1.0))
         assertEquals(0.5, function(0.5))
         assertEquals(2.0, function(1.5))

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/interpolation/SplineInterpolatorTest.kt

@@ -5,8 +5,6 @@
 
 package space.kscience.kmath.interpolation
 
-import space.kscience.kmath.functions.PiecewisePolynomial
-import space.kscience.kmath.functions.asFunction
 import space.kscience.kmath.operations.DoubleField
 import kotlin.math.PI
 import kotlin.math.sin
@@ -21,9 +19,10 @@ internal class SplineInterpolatorTest {
             x to sin(x)
         }
 
-        val polynomial: PiecewisePolynomial<Double> = SplineInterpolator.double.interpolatePolynomials(data)
+        //val polynomial: PiecewisePolynomial<Double> = DoubleField.splineInterpolator.interpolatePolynomials(data)
+
+        val function = DoubleField.splineInterpolator.interpolate(data, Double.NaN)
 
-        val function = polynomial.asFunction(DoubleField, Double.NaN)
         assertEquals(Double.NaN, function(-1.0))
         assertEquals(sin(0.5), function(0.5), 0.1)
         assertEquals(sin(1.5), function(1.5), 0.1)

kmath-geometry/README.md

@@ -0,0 +1,32 @@
+# Module kmath-geometry
+
+
+
+## Usage
+
+## Artifact:
+
+The Maven coordinates of this project are `space.kscience:kmath-geometry:0.3.0`.
+
+**Gradle Groovy:**
+```groovy
+repositories {
+    maven { url 'https://repo.kotlin.link' }
+    mavenCentral()
+}
+
+dependencies {
+    implementation 'space.kscience:kmath-geometry:0.3.0'
+}
+```
+**Gradle Kotlin DSL:**
+```kotlin
+repositories {
+    maven("https://repo.kotlin.link")
+    mavenCentral()
+}
+
+dependencies {
+    implementation("space.kscience:kmath-geometry:0.3.0")
+}
+```

kmath-geometry/build.gradle.kts

@@ -6,7 +6,7 @@ plugins {
 
 kotlin.sourceSets.commonMain {
     dependencies {
-        api(project(":kmath-core"))
+        api(projects.kmath.kmathComplex)
     }
 }
 

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean2DSpace.kt

@@ -6,12 +6,10 @@
 package space.kscience.kmath.geometry
 
 import space.kscience.kmath.linear.Point
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.operations.invoke
 import kotlin.math.sqrt
 
-@OptIn(UnstableKMathAPI::class)
 public interface Vector2D : Point<Double>, Vector {
     public val x: Double
     public val y: Double
@@ -29,7 +27,6 @@ public interface Vector2D : Point<Double>, Vector {
 public val Vector2D.r: Double
     get() = Euclidean2DSpace { norm() }
 
-@Suppress("FunctionName")
 public fun Vector2D(x: Double, y: Double): Vector2D = Vector2DImpl(x, y)
 
 private data class Vector2DImpl(

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean3DSpace.kt

@@ -6,12 +6,11 @@
 package space.kscience.kmath.geometry
 
 import space.kscience.kmath.linear.Point
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.structures.Buffer
 import kotlin.math.sqrt
 
-@OptIn(UnstableKMathAPI::class)
 public interface Vector3D : Point<Double>, Vector {
     public val x: Double
     public val y: Double
@@ -31,6 +30,19 @@ public interface Vector3D : Point<Double>, Vector {
 @Suppress("FunctionName")
 public fun Vector3D(x: Double, y: Double, z: Double): Vector3D = Vector3DImpl(x, y, z)
 
+public fun Buffer<Double>.asVector3D(): Vector3D = object : Vector3D {
+    init {
+        require(this@asVector3D.size == 3) { "Buffer of size 3 is required for Vector3D" }
+    }
+
+    override val x: Double get() = this@asVector3D[0]
+    override val y: Double get() = this@asVector3D[1]
+    override val z: Double get() = this@asVector3D[2]
+
+    override fun toString(): String = this@asVector3D.toString()
+
+}
+
 public val Vector3D.r: Double get() = Euclidean3DSpace { norm() }
 
 private data class Vector3DImpl(

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/projections.kt

@@ -5,6 +5,8 @@
 
 package space.kscience.kmath.geometry
 
+//TODO move vector to receiver
+
 /**
  * Project vector onto a line.
  * @param vector to project

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/rotations3D.kt

@@ -0,0 +1,116 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.geometry
+
+import space.kscience.kmath.complex.Quaternion
+import space.kscience.kmath.complex.QuaternionField
+import space.kscience.kmath.complex.reciprocal
+import space.kscience.kmath.linear.LinearSpace
+import space.kscience.kmath.linear.Matrix
+import space.kscience.kmath.linear.linearSpace
+import space.kscience.kmath.linear.matrix
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.operations.DoubleField
+import kotlin.math.pow
+import kotlin.math.sqrt
+
+internal fun Vector3D.toQuaternion(): Quaternion = Quaternion(0.0, x, y, z)
+
+/**
+ * Angle in radians denoted by this quaternion rotation
+ */
+public val Quaternion.theta: Double get() = kotlin.math.acos(w) * 2
+
+/**
+ * An axis of quaternion rotation
+ */
+public val Quaternion.vector: Vector3D
+    get() {
+        val sint2 = sqrt(1 - w * w)
+
+        return object : Vector3D {
+            override val x: Double get() = this@vector.x / sint2
+            override val y: Double get() = this@vector.y / sint2
+            override val z: Double get() = this@vector.z / sint2
+            override fun toString(): String = listOf(x, y, z).toString()
+        }
+    }
+
+/**
+ * Rotate a vector in a [Euclidean3DSpace]
+ */
+public fun Euclidean3DSpace.rotate(vector: Vector3D, q: Quaternion): Vector3D = with(QuaternionField) {
+    val p = vector.toQuaternion()
+    (q * p * q.reciprocal).vector
+}
+
+/**
+ * Use a composition of quaternions to create a rotation
+ */
+public fun Euclidean3DSpace.rotate(vector: Vector3D, composition: QuaternionField.() -> Quaternion): Vector3D =
+    rotate(vector, QuaternionField.composition())
+
+public fun Euclidean3DSpace.rotate(vector: Vector3D, matrix: Matrix<Double>): Vector3D {
+    require(matrix.colNum == 3 && matrix.rowNum == 3) { "Square 3x3 rotation matrix is required" }
+    return with(DoubleField.linearSpace) { matrix.dot(vector).asVector3D() }
+}
+
+/**
+ * Convert a [Quaternion] to a rotation matrix
+ */
+@OptIn(UnstableKMathAPI::class)
+public fun Quaternion.toRotationMatrix(
+    linearSpace: LinearSpace<Double, *> = DoubleField.linearSpace,
+): Matrix<Double> {
+    val s = QuaternionField.norm(this).pow(-2)
+    return linearSpace.matrix(3, 3)(
+        1.0 - 2 * s * (y * y + z * z), 2 * s * (x * y - z * w), 2 * s * (x * z + y * w),
+        2 * s * (x * y + z * w), 1.0 - 2 * s * (x * x + z * z), 2 * s * (y * z - x * w),
+        2 * s * (x * z - y * w), 2 * s * (y * z + x * w), 1.0 - 2 * s * (x * x + y * y)
+    )
+}
+
+/**
+ * taken from https://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
+ */
+public fun Quaternion.Companion.fromRotationMatrix(matrix: Matrix<Double>): Quaternion {
+    require(matrix.colNum == 3 && matrix.rowNum == 3) { "Rotation matrix should be 3x3 but is ${matrix.rowNum}x${matrix.colNum}" }
+    val trace = matrix[0, 0] + matrix[1, 1] + matrix[2, 2]
+
+    return if (trace > 0) {
+        val s = sqrt(trace + 1.0) * 2 // S=4*qw
+        Quaternion(
+            w = 0.25 * s,
+            x = (matrix[2, 1] - matrix[1, 2]) / s,
+            y = (matrix[0, 2] - matrix[2, 0]) / s,
+            z = (matrix[1, 0] - matrix[0, 1]) / s,
+        )
+    } else if ((matrix[0, 0] > matrix[1, 1]) && (matrix[0, 0] > matrix[2, 2])) {
+        val s = sqrt(1.0 + matrix[0, 0] - matrix[1, 1] - matrix[2, 2]) * 2 // S=4*qx
+        Quaternion(
+            w = (matrix[2, 1] - matrix[1, 2]) / s,
+            x = 0.25 * s,
+            y = (matrix[0, 1] + matrix[1, 0]) / s,
+            z = (matrix[0, 2] + matrix[2, 0]) / s,
+        )
+    } else if (matrix[1, 1] > matrix[2, 2]) {
+        val s = sqrt(1.0 + matrix[1, 1] - matrix[0, 0] - matrix[2, 2]) * 2 // S=4*qy
+        Quaternion(
+            w = (matrix[0, 2] - matrix[2, 0]) / s,
+            x = (matrix[0, 1] + matrix[1, 0]) / s,
+            y = 0.25 * s,
+            z = (matrix[1, 2] + matrix[2, 1]) / s,
+        )
+    } else {
+        val s = sqrt(1.0 + matrix[2, 2] - matrix[0, 0] - matrix[1, 1]) * 2 // S=4*qz
+        Quaternion(
+            w = (matrix[1, 0] - matrix[0, 1]) / s,
+            x = (matrix[0, 2] + matrix[2, 0]) / s,
+            y = (matrix[1, 2] + matrix[2, 1]) / s,
+            z = 0.25 * s,
+        )
+    }
+}

kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/RotationTest.kt

@@ -0,0 +1,35 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.geometry
+
+import space.kscience.kmath.complex.Quaternion
+import space.kscience.kmath.complex.normalized
+import space.kscience.kmath.testutils.assertBufferEquals
+import kotlin.test.Test
+
+class RotationTest {
+
+    @Test
+    fun rotations() = with(Euclidean3DSpace) {
+        val vector = Vector3D(1.0, 1.0, 1.0)
+        val q = Quaternion(1.0, 2.0, -3.0, 4.0).normalized()
+        val rotatedByQ = rotate(vector, q)
+        val matrix = q.toRotationMatrix()
+        val rotatedByM = rotate(vector,matrix)
+
+        assertBufferEquals(rotatedByQ, rotatedByM, 1e-4)
+    }
+
+    @Test
+    fun rotationConversion() {
+
+        val q = Quaternion(1.0, 2.0, -3.0, 4.0).normalized()
+
+        val matrix = q.toRotationMatrix()
+
+        assertBufferEquals(q, Quaternion.fromRotationMatrix(matrix))
+    }
+}