README.md

@@ -1,53 +1,54 @@
 # KMath
-Kotlin MATHematics library is intended as a kotlin based analog of numpy python library. Contrary to `numpy`
-and `scipy` it is modular and has a lightweight core.
+The Kotlin MATHematics library is intended as a Kotlin-based analog to Python's `numpy` library. In contrast to `numpy` and `scipy` it is modular and has a lightweight core.
 
 ## Features
 
 * **Algebra**
-    * Mathematical operation entities like rings, spaces and fields with (**TODO** add example to wiki) 
-    * Basic linear algebra operations (summs products, etc) backed by `Space` API.
-    * Complex numbers backed by `Field` API (meaning that they will be useable in any structures like vectors and NDArrays).
-    * [In progress] advanced linear algebra operations like matrix inversions.
-* **Array-like structures** Full support of numpy-like ndarray including mixed arithmetic operations and function operations
-on arrays and numbers just like it works in python (with benefit of static type checking).
+    * Algebraic structures like rings, spaces and field (**TODO** add example to wiki)
+    * Basic linear algebra operations (sums, products, etc.), backed by the `Space` API.
+    * Complex numbers backed by the `Field` API (meaning that they will be usable in any structure like vectors and N-dimensional arrays).
+    * [In progress] advanced linear algebra operations like matrix inversion and LU decomposition.
+* **Array-like structures** Full support of [numpy-like ndarrays](https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.ndarray.html) including mixed arithmetic operations and function operations over arrays and numbers just like in Python (with the added benefit of static type checking).
 
-* **Expressions** Expressions are one of the ultimate goals of kmath. It is planned to be able to write some mathematical
-expression once an then apply it to different types of objects by providing different context. Expressions could be used
-for a wide variety of purposes from high performance calculations to code generation.
+* **Expressions** Expressions are one of the ultimate goals of KMath. By writing a single mathematical expression
+once, users will be able to apply different types of objects to the expression by providing a context. Exceptions
+can be used for a wide variety of purposes from high performance calculations to code generation.
 
 ## Planned features
 
 * **Common mathematics** It is planned to gradually wrap most parts of [Apache commons-math](http://commons.apache.org/proper/commons-math/) 
-library in kotlin code and maybe rewrite some parts to better suite kotlin programming paradigm. There is no fixed priority list for that. Feel free
-to submit a future request if you want something to be done first.
+library in Kotlin code and maybe rewrite some parts to better suit the Kotlin programming paradigm, however there is no fixed roadmap for that. Feel free
+to submit a feature request if you want something to be done first.
 
 * **Messaging** A mathematical notation to support multi-language and multi-node communication for mathematical tasks.
 
 ## Multi-platform support
-KMath is developed as a multi-platform library, which means that most of interfaces are declared in common module.
-Implementation is also done in common module wherever it is possible. In some cases features are delegated to 
-platform even if they could be done in common module because of platform performance optimization. 
-Currently the main focus of development is the JVM platform, contribution of implementations for Kotlin - Native and
-Kotlin - JS is welcome. 
+
+KMath is developed as a multi-platform library, which means that most of interfaces are declared in the [common module](kmath-core/src/commonMain).
+Implementation is also done in the common module wherever possible. In some cases, features are delegated to
+platform-specific implementations even if they could be done in the common module for performance reasons.
+Currently, the JVM is the main focus of development, however Kotlin/Native and Kotlin/JS contributions are also welcome.
 
 ## Performance
-The calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve 
-both performance and flexibility. We expect to firstly focus on creating convenient universal API and then work on 
-increasing performance for specific cases. We expect the worst KMath performance still be better than natural python,
-but worse than optimized native/scipy (mostly due to boxing operations on primitive numbers). The best performance 
-of optimized parts should be better than scipy.
+
+Calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve
+both performance and flexibility. We expect to focus on creating convenient universal API first and then work on
+increasing performance for specific cases. We expect the worst KMath benchmarks will perform better than native Python,
+but worse than optimized native/SciPy (mostly due to boxing operations on primitive numbers). The best performance
+of optimized parts should be better than SciPy.
 
 ## Releases
 
-The project is currently in pre-release stage. Nightly builds could be used by adding additional repository to (groovy) gradle config:
+The project is currently in pre-release stage. Nightly builds can be used by adding an additional repository to the Gradle config like so:
+
 ```groovy
 repositories {
     maven { url = "http://npm.mipt.ru:8081/artifactory/gradle-dev" }
     mavenCentral()
 } 
 ```
-or for kotlin gradle dsl:
+
+or for the Gradle Kotlin DSL:
 
 ```kotlin
 repositories {
@@ -56,16 +57,20 @@ repositories {
 } 
 ```
 
-Then use regular dependency like
+Then use a regular dependency like so:
+
 ```groovy
 compile(group: 'scientifik', name: 'kmath-core', version: '0.0.1-SNAPSHOT')
 ```
-or in kotlin
+
+or in the Gradle Kotlin DSL:
+
 ```kotlin
 compile(group = "scientifik", name = "kmath-core", version = "0.0.1-SNAPSHOT")
 ```
 
-Work builds could be obtained with [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath). 
+Working builds can be obtained here: [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath).
 
 ## Contributing
+
 The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.

benchmarks/build.gradle

@@ -0,0 +1,39 @@
+plugins {
+    id "java"
+    id "me.champeau.gradle.jmh" version "0.4.8"
+    id 'org.jetbrains.kotlin.jvm'
+}
+
+repositories {
+    maven { url 'https://dl.bintray.com/kotlin/kotlin-eap' }
+    maven{ url "http://dl.bintray.com/kyonifer/maven"}
+    mavenCentral()
+}
+
+dependencies {
+    implementation project(":kmath-core")
+    implementation project(":kmath-coroutines")
+    implementation project(":kmath-commons")
+    implementation project(":kmath-koma")
+    implementation group: "com.kyonifer", name:"koma-core-ejml", version: "0.12"
+    implementation "org.jetbrains.kotlinx:kotlinx-io-jvm:0.1.5"
+    //compile "org.jetbrains.kotlin:kotlin-stdlib-jdk8"
+    //jmh project(':kmath-core')
+}
+
+jmh{
+    warmupIterations = 1
+}
+
+jmhClasses.dependsOn(compileKotlin)
+
+compileKotlin {
+    kotlinOptions {
+        jvmTarget = "1.8"
+    }
+}
+compileTestKotlin {
+    kotlinOptions {
+        jvmTarget = "1.8"
+    }
+}

benchmarks/src/jmh/kotlin/scientifik/kmath/structures/ArrayBenchmark.kt

@@ -0,0 +1,48 @@
+package scientifik.kmath.structures
+
+import org.openjdk.jmh.annotations.Benchmark
+import org.openjdk.jmh.annotations.Scope
+import org.openjdk.jmh.annotations.State
+import java.nio.IntBuffer
+
+
+@State(Scope.Benchmark)
+open class ArrayBenchmark {
+
+    @Benchmark
+    fun benchmarkArrayRead() {
+        var res = 0
+        for (i in 1..size) {
+            res += array[size - i]
+        }
+    }
+
+    @Benchmark
+    fun benchmarkBufferRead() {
+        var res = 0
+        for (i in 1..size) {
+            res += arrayBuffer.get(size - i)
+        }
+    }
+
+    @Benchmark
+    fun nativeBufferRead() {
+        var res = 0
+        for (i in 1..size) {
+            res += nativeBuffer.get(size - i)
+        }
+    }
+    
+    companion object {
+        val size = 1000
+        
+        val array = IntArray(size) { it }
+        val arrayBuffer = IntBuffer.wrap(array)
+        val nativeBuffer = IntBuffer.allocate(size).also {
+            for (i in 0 until size) {
+                it.put(i, i)
+            }
+
+        }
+    }
+}

benchmarks/src/jmh/kotlin/scientifik/kmath/structures/BufferBenchmark.kt

@@ -1,10 +1,10 @@
 package scientifik.kmath.structures
 
-import org.openjdk.jmh.annotations.*
+import org.openjdk.jmh.annotations.Benchmark
+import org.openjdk.jmh.annotations.Scope
+import org.openjdk.jmh.annotations.State
 import scientifik.kmath.operations.Complex
 
-@Warmup(iterations = 1)
-@Measurement(iterations = 5)
 @State(Scope.Benchmark)
 open class BufferBenchmark {
 
@@ -22,7 +22,7 @@ open class BufferBenchmark {
 
     @Benchmark
     fun complexBufferReadWrite() {
-        val buffer = Complex.createBuffer(size/2)
+        val buffer = MutableBuffer.complex(size / 2)
         (0 until size / 2).forEach {
             buffer[it] = Complex(it.toDouble(), -it.toDouble())
         }
@@ -33,6 +33,6 @@ open class BufferBenchmark {
     }
 
     companion object {
-        const val size = 1000
+        const val size = 100
     }
 }

benchmarks/src/jmh/kotlin/scientifik/kmath/structures/NDFieldBenchmark.kt

@@ -0,0 +1,69 @@
+package scientifik.kmath.structures
+
+import org.openjdk.jmh.annotations.Benchmark
+import scientifik.kmath.operations.RealField
+
+open class NDFieldBenchmark {
+
+    @Benchmark
+    fun autoFieldAdd() {
+        bufferedField.run {
+            var res: NDBuffer<Double> = one
+            repeat(n) {
+                res += one
+            }
+        }
+    }
+
+    @Benchmark
+    fun autoElementAdd() {
+        var res = genericField.one
+        repeat(n) {
+            res += 1.0
+        }
+    }
+
+    @Benchmark
+    fun specializedFieldAdd() {
+        specializedField.run {
+            var res: NDBuffer<Double> = one
+            repeat(n) {
+                res += 1.0
+            }
+        }
+    }
+
+
+    @Benchmark
+    fun lazyFieldAdd() {
+        lazyNDField.run {
+            var res = one
+            repeat(n) {
+                res += one
+            }
+
+            res.elements().sumByDouble { it.second }
+        }
+    }
+
+
+    @Benchmark
+    fun boxingFieldAdd() {
+        genericField.run {
+            var res: NDBuffer<Double> = one
+            repeat(n) {
+                res += one
+            }
+        }
+    }
+
+    companion object {
+        val dim = 1000
+        val n = 100
+
+        val bufferedField = NDField.auto(RealField, intArrayOf(dim, dim))
+        val specializedField = NDField.real(intArrayOf(dim, dim))
+        val genericField = NDField.buffered(intArrayOf(dim, dim), RealField)
+        val lazyNDField = NDField.lazy(intArrayOf(dim, dim), RealField)
+    }
+}

benchmarks/src/main/kotlin/scientifik/kmath/linear/LinearAlgebraBenchmark.kt

@@ -0,0 +1,61 @@
+package scientifik.kmath.linear
+
+import koma.matrix.ejml.EJMLMatrixFactory
+import kotlin.random.Random
+import kotlin.system.measureTimeMillis
+
+fun main() {
+    val random = Random(12224)
+    val dim = 100
+    //creating invertible matrix
+    val u = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
+    val l = Matrix.real(dim, dim) { i, j -> if (i >= j) random.nextDouble() else 0.0 }
+    val matrix = l dot u
+
+    val n = 500 // iterations
+
+    val solver = LUSolver.real
+
+    repeat(50) {
+        val res = solver.inverse(matrix)
+    }
+
+    val inverseTime = measureTimeMillis {
+        repeat(n) {
+            val res = solver.inverse(matrix)
+        }
+    }
+
+    println("[kmath] Inversion of $n matrices $dim x $dim finished in $inverseTime millis")
+
+    //commons-math
+
+    val cmContext = CMMatrixContext
+
+    val commonsTime = measureTimeMillis {
+        cmContext.run {
+            val cm = matrix.toCM()             //avoid overhead on conversion
+            repeat(n) {
+                val res = inverse(cm)
+            }
+        }
+    }
+
+
+    println("[commons-math] Inversion of $n matrices $dim x $dim finished in $commonsTime millis")
+
+    //koma-ejml
+
+    val komaContext = KomaMatrixContext(EJMLMatrixFactory())
+
+    val komaTime = measureTimeMillis {
+        komaContext.run {
+            val km = matrix.toKoma()      //avoid overhead on conversion
+            repeat(n) {
+                val res = inverse(km)
+            }
+        }
+    }
+
+    println("[koma-ejml] Inversion of $n matrices $dim x $dim finished in $komaTime millis")
+}

benchmarks/src/main/kotlin/scientifik/kmath/linear/MultiplicationBenchmark.kt

@@ -0,0 +1,45 @@
+package scientifik.kmath.linear
+
+import koma.matrix.ejml.EJMLMatrixFactory
+import kotlin.random.Random
+import kotlin.system.measureTimeMillis
+
+fun main() {
+    val random = Random(12224)
+    val dim = 1000
+    //creating invertible matrix
+    val matrix1 = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
+    val matrix2 = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
+
+//    //warmup
+//    matrix1 dot matrix2
+
+    CMMatrixContext.run {
+        val cmMatrix1 = matrix1.toCM()
+        val cmMatrix2 = matrix2.toCM()
+
+        val cmTime = measureTimeMillis {
+            cmMatrix1 dot cmMatrix2
+        }
+
+        println("CM implementation time: $cmTime")
+    }
+
+
+    KomaMatrixContext(EJMLMatrixFactory()).run {
+        val komaMatrix1 = matrix1.toKoma()
+        val komaMatrix2 = matrix2.toKoma()
+
+        val komaTime = measureTimeMillis {
+            komaMatrix1 dot komaMatrix2
+        }
+
+        println("Koma-ejml implementation time: $komaTime")
+    }
+
+    val genericTime = measureTimeMillis {
+        val res = matrix1 dot matrix2
+    }
+
+    println("Generic implementation time: $genericTime")
+}

benchmarks/src/main/kotlin/scientifik/kmath/structures/ComplexNDBenchmark.kt

@@ -0,0 +1,34 @@
+package scientifik.kmath.structures
+
+import kotlin.system.measureTimeMillis
+
+fun main() {
+    val dim = 1000
+    val n = 1000
+
+    val realField = NDField.real(dim, dim)
+    val complexField = NDField.complex(dim, dim)
+
+
+    val realTime = measureTimeMillis {
+        realField.run {
+            var res: NDBuffer<Double> = one
+            repeat(n) {
+                res += 1.0
+            }
+        }
+    }
+
+    println("Real addition completed in $realTime millis")
+
+    val complexTime = measureTimeMillis {
+        complexField.run {
+            var res: ComplexNDElement = one
+            repeat(n) {
+                res += 1.0
+            }
+        }
+    }
+
+    println("Complex addition completed in $complexTime millis")
+}

benchmarks/src/main/kotlin/scientifik/kmath/structures/NDFieldBenchmark.kt

@@ -0,0 +1,77 @@
+package scientifik.kmath.structures
+
+import kotlinx.coroutines.GlobalScope
+import scientifik.kmath.operations.RealField
+import kotlin.system.measureTimeMillis
+
+fun main(args: Array<String>) {
+    val dim = 1000
+    val n = 1000
+
+    // automatically build context most suited for given type.
+    val autoField = NDField.auto(RealField, dim, dim)
+    // specialized nd-field for Double. It works as generic Double field as well
+    val specializedField = NDField.real(dim, dim)
+    //A generic boxing field. It should be used for objects, not primitives.
+    val genericField = NDField.buffered(intArrayOf(dim, dim), RealField)
+
+
+    val autoTime = measureTimeMillis {
+        autoField.run {
+            var res = one
+            repeat(n) {
+                res += 1.0
+            }
+        }
+    }
+
+    println("Automatic field addition completed in $autoTime millis")
+
+    val elementTime = measureTimeMillis {
+        var res = genericField.one
+        repeat(n) {
+            res += 1.0
+        }
+    }
+
+    println("Element addition completed in $elementTime millis")
+
+    val specializedTime = measureTimeMillis {
+        specializedField.run {
+            var res: NDBuffer<Double> = one
+            repeat(n) {
+                res += 1.0
+            }
+        }
+    }
+
+    println("Specialized addition completed in $specializedTime millis")
+
+
+    val lazyTime = measureTimeMillis {
+        val res = specializedField.one.mapAsync(GlobalScope) {
+            var c = 0.0
+            repeat(n) {
+                c += 1.0
+            }
+            c
+        }
+
+        res.elements().forEach { it.second }
+    }
+
+    println("Lazy addition completed in $lazyTime millis")
+
+    val genericTime = measureTimeMillis {
+        //genericField.run(action)
+        genericField.run {
+            var res: NDBuffer<Double> = one
+            repeat(n) {
+                res += 1.0
+            }
+        }
+    }
+
+    println("Generic addition completed in $genericTime millis")
+
+}

benchmarks/src/main/kotlin/scientifik/kmath/structures/StructureReadBenchmark.kt

@@ -0,0 +1,36 @@
+package scientifik.kmath.structures
+
+import kotlin.system.measureTimeMillis
+
+fun main(args: Array<String>) {
+    val n = 6000
+
+    val array = DoubleArray(n * n) { 1.0 }
+    val buffer = DoubleBuffer(array)
+    val strides = DefaultStrides(intArrayOf(n, n))
+
+    val structure = BufferNDStructure(strides, buffer)
+
+    measureTimeMillis {
+        var res: Double = 0.0
+        strides.indices().forEach { res = structure[it] }
+    } // warmup
+
+    val time1 = measureTimeMillis {
+        var res: Double = 0.0
+        strides.indices().forEach { res = structure[it] }
+    }
+    println("Structure reading finished in $time1 millis")
+
+    val time2 = measureTimeMillis {
+        var res: Double = 0.0
+        strides.indices().forEach { res = buffer[strides.offset(it)] }
+    }
+    println("Buffer reading finished in $time2 millis")
+
+    val time3 = measureTimeMillis {
+        var res: Double = 0.0
+        strides.indices().forEach { res = array[strides.offset(it)] }
+    }
+    println("Array reading finished in $time3 millis")
+}

benchmarks/src/main/kotlin/scientifik/kmath/structures/StructureWriteBenchmark.kt

@@ -0,0 +1,39 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.structures.Buffer.Companion.DoubleBufferFactory
+import kotlin.system.measureTimeMillis
+
+
+fun main(args: Array<String>) {
+
+    val n = 6000
+
+    val structure = NDStructure.build(intArrayOf(n, n), DoubleBufferFactory) { 1.0 }
+
+    structure.mapToBuffer { it + 1 } // warm-up
+
+    val time1 = measureTimeMillis {
+        val res = structure.mapToBuffer { it + 1 }
+    }
+    println("Structure mapping finished in $time1 millis")
+
+    val array = DoubleArray(n * n) { 1.0 }
+
+    val time2 = measureTimeMillis {
+        val target = DoubleArray(n * n)
+        val res = array.forEachIndexed { index, value ->
+            target[index] = value + 1
+        }
+    }
+    println("Array mapping finished in $time2 millis")
+
+    val buffer = DoubleBuffer(DoubleArray(n * n) { 1.0 })
+
+    val time3 = measureTimeMillis {
+        val target = DoubleBuffer(DoubleArray(n * n))
+        val res = array.forEachIndexed { index, value ->
+            target[index] = value + 1
+        }
+    }
+    println("Buffer mapping finished in $time3 millis")
+}

build.gradle.kts

@@ -1,13 +1,13 @@
-buildscript {
-    extra["kotlinVersion"] = "1.3.11"
-    extra["ioVersion"] = "0.1.2-dev-2"
-    extra["coroutinesVersion"] = "1.0.1"
+import org.jetbrains.kotlin.gradle.dsl.KotlinMultiplatformExtension
 
-    val kotlinVersion: String by extra
-    val ioVersion: String by extra
-    val coroutinesVersion: String by extra
+buildscript {
+    val kotlinVersion: String by rootProject.extra("1.3.21")
+    val ioVersion: String by rootProject.extra("0.1.5")
+    val coroutinesVersion: String by rootProject.extra("1.1.1")
+    val atomicfuVersion: String by rootProject.extra("0.12.1")
 
     repositories {
+        //maven("https://dl.bintray.com/kotlin/kotlin-eap")
         jcenter()
     }
 
@@ -18,16 +18,37 @@ buildscript {
 }
 
 plugins {
-    id("com.jfrog.artifactory") version "4.8.1"  apply false
-//    id("org.jetbrains.kotlin.multiplatform") apply false
+    id("com.jfrog.artifactory") version "4.9.1" apply false
 }
 
 allprojects {
+    if (project.name.startsWith("kmath")) {
         apply(plugin = "maven-publish")
         apply(plugin = "com.jfrog.artifactory")
+    }
 
     group = "scientifik"
-    version = "0.0.2-dev-1"
+    version = "0.0.3-dev"
+
+    repositories {
+        //maven("https://dl.bintray.com/kotlin/kotlin-eap")
+        jcenter()
+    }
+
+    extensions.findByType<KotlinMultiplatformExtension>()?.apply {
+        jvm {
+            compilations.all {
+                kotlinOptions {
+                    jvmTarget = "1.8"
+                }
+            }
+        }
+        targets.all {
+            sourceSets.all {
+                languageSettings.progressiveMode = true
+            }
+        }
+    }
 }
 
 if (file("artifactory.gradle").exists()) {

doc/algebra.md

@@ -0,0 +1,70 @@
+# Algebra and algebra elements
+
+The mathematical operations in `kmath` are generally separated from mathematical objects.
+This means that in order to perform an operation, say `+`, one needs two objects of a type `T` and
+and algebra context which defines appropriate operation, say `Space<T>`. Next one needs to run actual operation
+in the context:
+
+```kotlin
+val a: T
+val b: T
+val space: Space<T>
+
+val c = space.run{a + b}
+```
+
+From the first glance, this distinction seems to be a needless complication, but in fact one needs
+to remember that in mathematics, one could define different operations on the same objects. For example,
+one could use different types of geometry for vectors.
+
+## Algebra hierarchy
+
+Mathematical contexts have the following hierarchy:
+
+**Space** <- **Ring** <- **Field**
+
+All classes follow abstract mathematical constructs.
+[Space](http://mathworld.wolfram.com/Space.html) defines `zero` element, addition operation and multiplication by constant,
+[Ring](http://mathworld.wolfram.com/Ring.html) adds multiplication and unit `one` element,
+[Field](http://mathworld.wolfram.com/Field.html) adds division operation.
+
+Typical case of `Field` is the `RealField` which works on doubles. And typical case of `Space` is a `VectorSpace`.
+
+In some cases algebra context could hold additional operation like `exp` or `sin`, in this case it inherits appropriate
+interface. Also a context could have an operation which produces an element outside of its context. For example
+`Matrix` `dot` operation produces a matrix with new dimensions which could not be compatible with initial matrix in
+terms of linear operations.
+
+## Algebra element
+
+In order to achieve more familiar behavior (where you apply operations directly to mathematica objects), without involving contexts
+`kmath` introduces special type objects called `MathElement`. A `MathElement` is basically some object coupled to
+a mathematical context. For example `Complex` is the pair of real numbers representing real and imaginary parts,
+but it also holds reference to the `ComplexField` singleton which allows to perform direct operations on `Complex`
+numbers without explicit involving the context like:
+
+```kotlin
+    val c1 = Complex(1.0, 1.0)
+    val c2 = Complex(1.0, -1.0)
+    val c3 = c1 + c2 + 3.0.toComplex()
+    //or with field notation:
+    val c4 = ComplexField.run{c1 + i - 2.0}
+```
+
+Both notations have their pros and cons.
+
+The hierarchy for algebra elements follows the hierarchy for the corresponding algebra.
+
+**MathElement** <- **SpaceElement** <- **RingElement** <- **FieldElement**
+
+**MathElement** is the generic common ancestor of the class with context.
+
+One important distinction between algebra elements and algebra contexts is that algebra element has three type parameters:
+
+1. The type of elements, field operates on.
+2. The self-type of the element returned from operation (must be algebra element).
+3. The type of the algebra over first type-parameter.
+
+The middle type is needed in case algebra members do not store context. For example, it is not possible to add
+a context to regular `Double`. The element performs automatic conversions from context types and back.
+One should used context operations in all important places. The performance of element operations is not guaranteed.

doc/buffers.md

@@ -0,0 +1 @@
+**TODO**

doc/contexts.md

@@ -0,0 +1,73 @@
+# Context-oriented mathematics
+
+## The problem
+
+A known problem for implementing mathematics in statically-typed languages (but not only in them) is that different
+sets of mathematical operators can be defined on the same mathematical objects. Sometimes there is no single way to
+treat some operations, including basic arithmetic operations, on a Java/Kotlin `Number`. Sometimes there are different ways to
+define the same structure, such as Euclidean and elliptic geometry vector spaces over real vectors. Another problem arises when
+one wants to add some kind of behavior to an existing entity. In dynamic languages those problems are usually solved
+by adding dynamic context-specific behaviors at runtime, but this solution has a lot of drawbacks.
+
+## Context-oriented approach
+
+One possible solution to these problems is to divorce numerical representations from behaviors.
+For example in Kotlin one can define a separate class which represents some entity without any operations,
+ex. a complex number:
+
+```kotlin
+data class Complex(val re: Double, val im: Double)
+```
+
+And then to define a separate class or singleton, representing an operation on those complex numbers:
+
+```kotlin
+object ComplexOperations {
+    operator fun Complex.plus(other: Complex) = Complex(re + other.re, im + other.im)
+    operator fun Complex.minus(other: Complex) = Complex(re - other.re, im - other.im)
+}
+```
+
+In Java, applying such external operations could be very cumbersome, but Kotlin has a unique feature which allows us
+implement this naturally: [extensions with receivers](https://kotlinlang.org/docs/reference/extensions.html#extension-functions).
+In Kotlin, an operation on complex number could be implemented as:
+
+```kotlin
+with(ComplexOperations) { c1 + c2 - c3 }
+```
+
+Kotlin also allows the creation of functions with receivers:
+
+```kotlin
+fun ComplexOperations.doSomethingWithComplex(c1: Complex, c2: Complex, c3: Complex) = c1 + c2 - c3
+
+ComplexOperations.doComethingWithComplex(c1, c2, c3)
+```
+
+In fact, whole parts of a program may be run within a mathematical context or even multiple nested contexts.
+
+In KMath, contexts are not only responsible for operations, but also for raw object creation and advanced features.
+
+## Other possibilities
+
+### Type classes
+
+An obvious candidate to get more or less the same functionality is the type class, which allows one to bind a behavior to
+a specific type without modifying the type itself. On the plus side, type classes do not require explicit context
+declaration, so the code looks cleaner. On the minus side, if there are different sets of behaviors for the same types,
+it is impossible to combine them into one module. Also, unlike type classes, context can have parameters or even
+state. For example in KMath, sizes and strides for `NDElement` or `Matrix` could be moved to context to optimize
+performance in case of a large amount of structures.
+
+### Wildcard imports and importing-on-demand
+
+Sometimes, one may wish to use a single context throughout a file. In this case, is possible to import all members
+from a package or file, via `import context.complex.*`. Effectively, this is the same as enclosing an entire file
+with a single context. However when using multiple contexts, this technique can introduce operator ambiguity, due to
+namespace pollution. If there are multiple scoped contexts which define the same operation, it is still possible to
+to import specific operations as needed, without using an explicit context with extension functions, for example:
+
+```
+import context.complex.op1
+import context.quaternion.op2
+```

doc/expressions.md

@@ -0,0 +1,26 @@
+# Expressions
+
+**Experimental: this API is in early stage and could change any time**
+
+Expressions is an experimental feature which allows to construct lazily or immediately calculated parametric mathematical 
+expressions.
+
+The potential use-cases for it (so far) are following:
+
+* Lazy evaluation (in general simple lambda is better, but there are some border cases)
+
+* Automatic differentiation in single-dimension and in multiple dimensions
+
+* Generation of mathematical syntax trees with subsequent code generation for other languages
+
+* Maybe symbolic computations (needs additional research)
+
+The workhorse of this API is `Expression` interface which exposes single `operator fun invoke(arguments: Map<String, T>): T`
+method. `ExpressionContext` is used to generate expressions and introduce variables.
+
+Currently there are two implementations:
+
+* Generic `ExpressionField` in `kmath-core` which allows construction of custom lazy expressions
+
+* Auto-differentiation expression in `kmath-commons` module allows to use full power of `DerivativeStructure` 
+from commons-math. **TODO: add example**

doc/histograms.md

@@ -0,0 +1 @@
+**TODO**

doc/linear.md

@@ -0,0 +1 @@
+**TODO**

doc/nd-performance.md

@@ -0,0 +1,127 @@
+# Performance for n-dimensional structures operations
+
+One of the most sought after features of mathematical libraries is the high-performance operations on n-dimensional
+structures. In `kmath` performance depends on which particular context was used for operation.
+
+Let us consider following contexts:
+```kotlin
+    // specialized nd-field for Double. It works as generic Double field as well
+    val specializedField = NDField.real(intArrayOf(dim, dim))
+
+    // automatically build context most suited for given type.
+    val autoField = NDField.auto(intArrayOf(dim, dim), RealField)
+
+    //A field implementing lazy computations. All elements are computed on-demand
+    val lazyField = NDField.lazy(intArrayOf(dim, dim), RealField)
+
+    //A generic boxing field. It should be used for objects, not primitives.
+    val genericField = NDField.buffered(intArrayOf(dim, dim), RealField)
+```
+Now let us perform several tests and see which implementation is best suited for each case:
+
+## Test case
+
+In order to test performance we will take 2d-structures with `dim = 1000` and add a structure filled with `1.0`
+to it `n = 1000` times.
+
+## Specialized
+The code to run this looks like:
+```kotlin
+    specializedField.run {
+        var res = one
+        repeat(n) {
+            res += 1.0
+        }
+    }
+```
+The performance of this code is the best of all tests since it inlines all operations and is specialized for operation
+with doubles. We will measure everything else relative to this one, so time for this test will be `1x` (real time
+on my computer is about 4.5 seconds). The only problem with this approach is that it requires to specify type
+from the beginning. Everyone do so anyway, so it is the recommended approach.
+
+## Automatic
+Let's do the same with automatic field inference:
+```kotlin
+    autoField.run {
+        var res = one
+        repeat(n) {
+            res += 1.0
+        }
+    }
+```
+Ths speed of this operation is approximately the same as for specialized case since `NDField.auto` just
+returns the same `RealNDField` in this case. Of course it is usually better to use specialized method to be sure.
+
+## Lazy
+Lazy field does not produce a structure when asked, instead it generates an empty structure and fills it on-demand
+using coroutines to parallelize computations.
+When one calls
+```kotlin
+    lazyField.run {
+        var res = one
+        repeat(n) {
+            res += 1.0
+        }
+    }
+```
+The result will be calculated almost immediately but the result will be empty. In order to get the full result
+structure one needs to call all its elements. In this case computation overhead will be huge. So this field never
+should be used if one expects to use the full result structure. Though if one wants only small fraction, it could
+save a lot of time.
+
+This field still could be used with reasonable performance if call code is changed:
+```kotlin
+    lazyField.run {
+        val res = one.map {
+            var c = 0.0
+            repeat(n) {
+                c += 1.0
+            }
+            c
+        }
+
+        res.elements().forEach { it.second }
+    }
+```
+In this case it completes in about `4x-5x` time due to boxing.
+
+## Boxing
+The boxing field produced by
+```kotlin
+    genericField.run {
+        var res = one
+        repeat(n) {
+            res += 1.0
+        }
+    }
+```
+obviously is the slowest one, because it requires to box and unbox the `double` on each operation. It takes about
+`15x` time (**TODO: there seems to be a problem here, it should be slow, but not that slow**). This field should
+never be used for primitives.
+
+## Element operation
+Let us also check the speed for direct operations on elements:
+```kotlin
+    var res = genericField.one
+    repeat(n) {
+        res += 1.0
+    }
+```
+One would expect to be at least as slow as field operation, but in fact, this one takes only `2x` time to complete.
+It happens, because in this particular case it does not use actual `NDField` but instead calculated directly
+via extension function.
+
+## What about python?
+
+Usually it is bad idea to compare the direct numerical operation performance in different languages, but it hard to
+work completely without frame of reference. In this case, simple numpy code:
+```python
+res = np.ones((1000,1000))
+for i in range(1000):
+    res = res + 1.0
+```
+gives the completion time of about `1.1x`, which means that specialized kotlin code in fact is working faster (I think it is
+because better memory management). Of course if one writes `res += 1.0`, the performance will be different,
+but it would be differenc case, because numpy overrides `+=` with in-place operations. In-place operations are
+available in `kmath` with `MutableNDStructure` but there is no field for it (one can still work with mapping
+functions).

doc/operations.md

@@ -0,0 +1,40 @@
+## Spaces and fields
+
+An obvious first choice of mathematical objects to implement in a context-oriented style are algebraic elements like spaces,
+rings and fields. Those are located in the `scientifik.kmath.operations.Algebra.kt` file. Alongside common contexts, the file includes definitions for algebra elements like `FieldElement`. A `FieldElement` object
+stores a reference to the `Field` which contains additive and multiplicative operations, meaning
+it has one fixed context attached and does not require explicit external context. So those `MathElements` can be operated without context:
+
+```kotlin
+val c1 = Complex(1.0, 2.0)
+val c2 = ComplexField.i
+val c3 = c1 + c2
+```
+
+`ComplexField` also features special operations to mix complex and real numbers, for example:
+
+```kotlin
+val c1 = Complex(1.0, 2.0)
+val c2 = ComplexField.run{ c1 - 1.0} // Returns: [re:0.0, im: 2.0]
+val c3 = ComplexField.run{ c1 - i*2.0}
+```
+
+**Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
+that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) and [KEEP-176](https://github.com/Kotlin/KEEP/pull/176) for updates.
+
+## Nested fields
+
+Contexts allow one to build more complex structures. For example, it is possible to create a `Matrix` from complex elements like so:
+
+```kotlin
+val element = NDElement.complex(shape = intArrayOf(2,2)){ index: IntArray ->
+    Complex(index[0].toDouble() - index[1].toDouble(), index[0].toDouble() + index[1].toDouble())
+}
+```
+
+The `element` in this example is a member of the `Field` of 2-d structures, each element of which is a member of its own
+`ComplexField`. The important thing is one does not need to create a special n-d class to hold complex
+numbers and implement operations on it, one just needs to provide a field for its elements.
+
+**Note**: Fields themselves do not solve the problem of JVM boxing, but it is possible to solve with special contexts like
+`BufferSpec`. This feature is in development phase.

gradle/wrapper/gradle-wrapper.properties

@@ -0,0 +1,5 @@
+distributionBase=GRADLE_USER_HOME
+distributionPath=wrapper/dists
+distributionUrl=https\://services.gradle.org/distributions/gradle-5.0-bin.zip
+zipStoreBase=GRADLE_USER_HOME
+zipStorePath=wrapper/dists

gradlew

@@ -0,0 +1,172 @@
+#!/usr/bin/env sh
+
+##############################################################################
+##
+##  Gradle start up script for UN*X
+##
+##############################################################################
+
+# Attempt to set APP_HOME
+# Resolve links: $0 may be a link
+PRG="$0"
+# Need this for relative symlinks.
+while [ -h "$PRG" ] ; do
+    ls=`ls -ld "$PRG"`
+    link=`expr "$ls" : '.*-> \(.*\)$'`
+    if expr "$link" : '/.*' > /dev/null; then
+        PRG="$link"
+    else
+        PRG=`dirname "$PRG"`"/$link"
+    fi
+done
+SAVED="`pwd`"
+cd "`dirname \"$PRG\"`/" >/dev/null
+APP_HOME="`pwd -P`"
+cd "$SAVED" >/dev/null
+
+APP_NAME="Gradle"
+APP_BASE_NAME=`basename "$0"`
+
+# Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+DEFAULT_JVM_OPTS='"-Xmx64m"'
+
+# Use the maximum available, or set MAX_FD != -1 to use that value.
+MAX_FD="maximum"
+
+warn () {
+    echo "$*"
+}
+
+die () {
+    echo
+    echo "$*"
+    echo
+    exit 1
+}
+
+# OS specific support (must be 'true' or 'false').
+cygwin=false
+msys=false
+darwin=false
+nonstop=false
+case "`uname`" in
+  CYGWIN* )
+    cygwin=true
+    ;;
+  Darwin* )
+    darwin=true
+    ;;
+  MINGW* )
+    msys=true
+    ;;
+  NONSTOP* )
+    nonstop=true
+    ;;
+esac
+
+CLASSPATH=$APP_HOME/gradle/wrapper/gradle-wrapper.jar
+
+# Determine the Java command to use to start the JVM.
+if [ -n "$JAVA_HOME" ] ; then
+    if [ -x "$JAVA_HOME/jre/sh/java" ] ; then
+        # IBM's JDK on AIX uses strange locations for the executables
+        JAVACMD="$JAVA_HOME/jre/sh/java"
+    else
+        JAVACMD="$JAVA_HOME/bin/java"
+    fi
+    if [ ! -x "$JAVACMD" ] ; then
+        die "ERROR: JAVA_HOME is set to an invalid directory: $JAVA_HOME
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+    fi
+else
+    JAVACMD="java"
+    which java >/dev/null 2>&1 || die "ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+fi
+
+# Increase the maximum file descriptors if we can.
+if [ "$cygwin" = "false" -a "$darwin" = "false" -a "$nonstop" = "false" ] ; then
+    MAX_FD_LIMIT=`ulimit -H -n`
+    if [ $? -eq 0 ] ; then
+        if [ "$MAX_FD" = "maximum" -o "$MAX_FD" = "max" ] ; then
+            MAX_FD="$MAX_FD_LIMIT"
+        fi
+        ulimit -n $MAX_FD
+        if [ $? -ne 0 ] ; then
+            warn "Could not set maximum file descriptor limit: $MAX_FD"
+        fi
+    else
+        warn "Could not query maximum file descriptor limit: $MAX_FD_LIMIT"
+    fi
+fi
+
+# For Darwin, add options to specify how the application appears in the dock
+if $darwin; then
+    GRADLE_OPTS="$GRADLE_OPTS \"-Xdock:name=$APP_NAME\" \"-Xdock:icon=$APP_HOME/media/gradle.icns\""
+fi
+
+# For Cygwin, switch paths to Windows format before running java
+if $cygwin ; then
+    APP_HOME=`cygpath --path --mixed "$APP_HOME"`
+    CLASSPATH=`cygpath --path --mixed "$CLASSPATH"`
+    JAVACMD=`cygpath --unix "$JAVACMD"`
+
+    # We build the pattern for arguments to be converted via cygpath
+    ROOTDIRSRAW=`find -L / -maxdepth 1 -mindepth 1 -type d 2>/dev/null`
+    SEP=""
+    for dir in $ROOTDIRSRAW ; do
+        ROOTDIRS="$ROOTDIRS$SEP$dir"
+        SEP="|"
+    done
+    OURCYGPATTERN="(^($ROOTDIRS))"
+    # Add a user-defined pattern to the cygpath arguments
+    if [ "$GRADLE_CYGPATTERN" != "" ] ; then
+        OURCYGPATTERN="$OURCYGPATTERN|($GRADLE_CYGPATTERN)"
+    fi
+    # Now convert the arguments - kludge to limit ourselves to /bin/sh
+    i=0
+    for arg in "$@" ; do
+        CHECK=`echo "$arg"|egrep -c "$OURCYGPATTERN" -`
+        CHECK2=`echo "$arg"|egrep -c "^-"`                                 ### Determine if an option
+
+        if [ $CHECK -ne 0 ] && [ $CHECK2 -eq 0 ] ; then                    ### Added a condition
+            eval `echo args$i`=`cygpath --path --ignore --mixed "$arg"`
+        else
+            eval `echo args$i`="\"$arg\""
+        fi
+        i=$((i+1))
+    done
+    case $i in
+        (0) set -- ;;
+        (1) set -- "$args0" ;;
+        (2) set -- "$args0" "$args1" ;;
+        (3) set -- "$args0" "$args1" "$args2" ;;
+        (4) set -- "$args0" "$args1" "$args2" "$args3" ;;
+        (5) set -- "$args0" "$args1" "$args2" "$args3" "$args4" ;;
+        (6) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" ;;
+        (7) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" ;;
+        (8) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" ;;
+        (9) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" "$args8" ;;
+    esac
+fi
+
+# Escape application args
+save () {
+    for i do printf %s\\n "$i" | sed "s/'/'\\\\''/g;1s/^/'/;\$s/\$/' \\\\/" ; done
+    echo " "
+}
+APP_ARGS=$(save "$@")
+
+# Collect all arguments for the java command, following the shell quoting and substitution rules
+eval set -- $DEFAULT_JVM_OPTS $JAVA_OPTS $GRADLE_OPTS "\"-Dorg.gradle.appname=$APP_BASE_NAME\"" -classpath "\"$CLASSPATH\"" org.gradle.wrapper.GradleWrapperMain "$APP_ARGS"
+
+# by default we should be in the correct project dir, but when run from Finder on Mac, the cwd is wrong
+if [ "$(uname)" = "Darwin" ] && [ "$HOME" = "$PWD" ]; then
+  cd "$(dirname "$0")"
+fi
+
+exec "$JAVACMD" "$@"

gradlew.bat

@@ -0,0 +1,84 @@
+@if "%DEBUG%" == "" @echo off
+@rem ##########################################################################
+@rem
+@rem  Gradle startup script for Windows
+@rem
+@rem ##########################################################################
+
+@rem Set local scope for the variables with windows NT shell
+if "%OS%"=="Windows_NT" setlocal
+
+set DIRNAME=%~dp0
+if "%DIRNAME%" == "" set DIRNAME=.
+set APP_BASE_NAME=%~n0
+set APP_HOME=%DIRNAME%
+
+@rem Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+set DEFAULT_JVM_OPTS="-Xmx64m"
+
+@rem Find java.exe
+if defined JAVA_HOME goto findJavaFromJavaHome
+
+set JAVA_EXE=java.exe
+%JAVA_EXE% -version >NUL 2>&1
+if "%ERRORLEVEL%" == "0" goto init
+
+echo.
+echo ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:findJavaFromJavaHome
+set JAVA_HOME=%JAVA_HOME:"=%
+set JAVA_EXE=%JAVA_HOME%/bin/java.exe
+
+if exist "%JAVA_EXE%" goto init
+
+echo.
+echo ERROR: JAVA_HOME is set to an invalid directory: %JAVA_HOME%
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:init
+@rem Get command-line arguments, handling Windows variants
+
+if not "%OS%" == "Windows_NT" goto win9xME_args
+
+:win9xME_args
+@rem Slurp the command line arguments.
+set CMD_LINE_ARGS=
+set _SKIP=2
+
+:win9xME_args_slurp
+if "x%~1" == "x" goto execute
+
+set CMD_LINE_ARGS=%*
+
+:execute
+@rem Setup the command line
+
+set CLASSPATH=%APP_HOME%\gradle\wrapper\gradle-wrapper.jar
+
+@rem Execute Gradle
+"%JAVA_EXE%" %DEFAULT_JVM_OPTS% %JAVA_OPTS% %GRADLE_OPTS% "-Dorg.gradle.appname=%APP_BASE_NAME%" -classpath "%CLASSPATH%" org.gradle.wrapper.GradleWrapperMain %CMD_LINE_ARGS%
+
+:end
+@rem End local scope for the variables with windows NT shell
+if "%ERRORLEVEL%"=="0" goto mainEnd
+
+:fail
+rem Set variable GRADLE_EXIT_CONSOLE if you need the _script_ return code instead of
+rem the _cmd.exe /c_ return code!
+if  not "" == "%GRADLE_EXIT_CONSOLE%" exit 1
+exit /b 1
+
+:mainEnd
+if "%OS%"=="Windows_NT" endlocal
+
+:omega

kmath-commons/build.gradle.kts

@@ -0,0 +1,13 @@
+plugins {
+    kotlin("jvm")
+}
+
+description = "Commons math binding for kmath"
+
+dependencies {
+    api(project(":kmath-core"))
+    api(project(":kmath-sequential"))
+    api("org.apache.commons:commons-math3:3.6.1")
+    testImplementation("org.jetbrains.kotlin:kotlin-test")
+    testImplementation("org.jetbrains.kotlin:kotlin-test-junit")
+}

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

@@ -0,0 +1,129 @@
+package scientifik.kmath.expressions
+
+import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
+import scientifik.kmath.operations.ExtendedField
+import scientifik.kmath.operations.ExtendedFieldOperations
+import scientifik.kmath.operations.Field
+import kotlin.properties.ReadOnlyProperty
+import kotlin.reflect.KProperty
+
+/**
+ * A field wrapping commons-math derivative structures
+ */
+class DerivativeStructureField(val order: Int, val parameters: Map<String, Double>) :
+    ExtendedField<DerivativeStructure> {
+
+    override val zero: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size) }
+
+    override val one: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size, 1.0) }
+
+    private val variables: Map<String, DerivativeStructure> = parameters.mapValues { (key, value) ->
+        DerivativeStructure(parameters.size, order, parameters.keys.indexOf(key), value)
+    }
+
+    val variable = object : ReadOnlyProperty<Any?, DerivativeStructure> {
+        override fun getValue(thisRef: Any?, property: KProperty<*>): DerivativeStructure {
+            return variables[property.name] ?: error("A variable with name ${property.name} does not exist")
+        }
+    }
+
+    fun variable(name: String, default: DerivativeStructure? = null): DerivativeStructure =
+        variables[name] ?: default ?: error("A variable with name $name does not exist")
+
+
+    fun Number.const() = DerivativeStructure(order, parameters.size, toDouble())
+
+    fun DerivativeStructure.deriv(parName: String, order: Int = 1): Double {
+        return deriv(mapOf(parName to order))
+    }
+
+    fun DerivativeStructure.deriv(orders: Map<String, Int>): Double {
+        return getPartialDerivative(*parameters.keys.map { orders[it] ?: 0 }.toIntArray())
+    }
+
+    fun DerivativeStructure.deriv(vararg orders: Pair<String, Int>): Double = deriv(mapOf(*orders))
+
+    override fun add(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.add(b)
+
+    override fun multiply(a: DerivativeStructure, k: Number): DerivativeStructure = when (k) {
+        is Double -> a.multiply(k)
+        is Int -> a.multiply(k)
+        else -> a.multiply(k.toDouble())
+    }
+
+    override fun multiply(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.multiply(b)
+
+    override fun divide(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.divide(b)
+
+    override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
+
+    override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
+
+    override fun power(arg: DerivativeStructure, pow: Number): DerivativeStructure = when (pow) {
+        is Double -> arg.pow(pow)
+        is Int -> arg.pow(pow)
+        else -> arg.pow(pow.toDouble())
+    }
+
+    fun power(arg: DerivativeStructure, pow: DerivativeStructure): DerivativeStructure = arg.pow(pow)
+
+    override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
+
+    override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
+
+    operator fun DerivativeStructure.plus(n: Number): DerivativeStructure = add(n.toDouble())
+    operator fun DerivativeStructure.minus(n: Number): DerivativeStructure = subtract(n.toDouble())
+    operator fun Number.plus(s: DerivativeStructure) = s + this
+    operator fun Number.minus(s: DerivativeStructure) = s - this
+}
+
+/**
+ * A constructs that creates a derivative structure with required order on-demand
+ */
+class DiffExpression(val function: DerivativeStructureField.() -> DerivativeStructure) : Expression<Double> {
+    override fun invoke(arguments: Map<String, Double>): Double = DerivativeStructureField(0, arguments)
+        .run(function).value
+
+    /**
+     * Get the derivative expression with given orders
+     * TODO make result [DiffExpression]
+     */
+    fun derivative(orders: Map<String, Int>): Expression<Double> {
+        return object : Expression<Double> {
+            override fun invoke(arguments: Map<String, Double>): Double =
+                DerivativeStructureField(orders.values.max() ?: 0, arguments)
+                    .run {
+                        function().deriv(orders)
+                    }
+        }
+    }
+
+    //TODO add gradient and maybe other vector operators
+}
+
+fun DiffExpression.derivative(vararg orders: Pair<String, Int>) = derivative(mapOf(*orders))
+fun DiffExpression.derivative(name: String) = derivative(name to 1)
+
+/**
+ * A context for [DiffExpression] (not to be confused with [DerivativeStructure])
+ */
+object DiffExpressionContext : ExpressionContext<Double>, Field<DiffExpression> {
+    override fun variable(name: String, default: Double?) = DiffExpression { variable(name, default?.const()) }
+
+    override fun const(value: Double): DiffExpression = DiffExpression { value.const() }
+
+    override fun add(a: DiffExpression, b: DiffExpression) = DiffExpression { a.function(this) + b.function(this) }
+
+    override val zero = DiffExpression { 0.0.const() }
+
+    override fun multiply(a: DiffExpression, k: Number) = DiffExpression { a.function(this) * k }
+
+    override val one = DiffExpression { 1.0.const() }
+
+    override fun multiply(a: DiffExpression, b: DiffExpression) = DiffExpression { a.function(this) * b.function(this) }
+
+    override fun divide(a: DiffExpression, b: DiffExpression) = DiffExpression { a.function(this) / b.function(this) }
+}
+
+
+

kmath-commons/src/main/kotlin/scientifik/kmath/linear/CMMatrix.kt

@@ -0,0 +1,93 @@
+package scientifik.kmath.linear
+
+import org.apache.commons.math3.linear.*
+import org.apache.commons.math3.linear.RealMatrix
+import org.apache.commons.math3.linear.RealVector
+
+class CMMatrix(val origin: RealMatrix, features: Set<MatrixFeature>? = null) : Matrix<Double> {
+    override val rowNum: Int get() = origin.rowDimension
+    override val colNum: Int get() = origin.columnDimension
+
+    override val features: Set<MatrixFeature> = features ?: sequence<MatrixFeature> {
+        if(origin is DiagonalMatrix) yield(DiagonalFeature)
+    }.toSet()
+
+    override fun suggestFeature(vararg features: MatrixFeature) =
+        CMMatrix(origin, this.features + features)
+
+    override fun get(i: Int, j: Int): Double = origin.getEntry(i, j)
+}
+
+fun Matrix<Double>.toCM(): CMMatrix = if (this is CMMatrix) {
+    this
+} else {
+    //TODO add feature analysis
+    val array = Array(rowNum) { i -> DoubleArray(colNum) { j -> get(i, j) } }
+    CMMatrix(Array2DRowRealMatrix(array))
+}
+
+fun RealMatrix.toMatrix() = CMMatrix(this)
+
+class CMVector(val origin: RealVector) : Point<Double> {
+    override val size: Int get() = origin.dimension
+
+    override fun get(index: Int): Double = origin.getEntry(index)
+
+    override fun iterator(): Iterator<Double> = origin.toArray().iterator()
+}
+
+fun Point<Double>.toCM(): CMVector = if (this is CMVector) {
+    this
+} else {
+    val array = DoubleArray(size) { this[it] }
+    CMVector(ArrayRealVector(array))
+}
+
+fun RealVector.toPoint() = CMVector(this)
+
+object CMMatrixContext : MatrixContext<Double>, LinearSolver<Double> {
+
+    override fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> Double): CMMatrix {
+        val array = Array(rows) { i -> DoubleArray(columns) { j -> initializer(i, j) } }
+        return CMMatrix(Array2DRowRealMatrix(array))
+    }
+
+    override fun solve(a: Matrix<Double>, b: Matrix<Double>): CMMatrix {
+        val decomposition = LUDecomposition(a.toCM().origin)
+        return decomposition.solver.solve(b.toCM().origin).toMatrix()
+    }
+
+    override fun solve(a: Matrix<Double>, b: Point<Double>): CMVector {
+        val decomposition = LUDecomposition(a.toCM().origin)
+        return decomposition.solver.solve(b.toCM().origin).toPoint()
+    }
+
+    override fun inverse(a: Matrix<Double>): CMMatrix {
+        val decomposition = LUDecomposition(a.toCM().origin)
+        return decomposition.solver.inverse.toMatrix()
+    }
+
+    override fun Matrix<Double>.dot(other: Matrix<Double>) =
+        CMMatrix(this.toCM().origin.multiply(other.toCM().origin))
+
+    override fun Matrix<Double>.dot(vector: Point<Double>): CMVector =
+        CMVector(this.toCM().origin.preMultiply(vector.toCM().origin))
+
+
+    override fun Matrix<Double>.unaryMinus(): CMMatrix =
+        produce(rowNum, colNum) { i, j -> -get(i, j) }
+
+    override fun Matrix<Double>.plus(b: Matrix<Double>) =
+        CMMatrix(this.toCM().origin.multiply(b.toCM().origin))
+
+    override fun Matrix<Double>.minus(b: Matrix<Double>) =
+        CMMatrix(this.toCM().origin.subtract(b.toCM().origin))
+
+    override fun Matrix<Double>.times(value: Double) =
+        CMMatrix(this.toCM().origin.scalarMultiply(value.toDouble()))
+}
+
+operator fun CMMatrix.plus(other: CMMatrix): CMMatrix = CMMatrix(this.origin.add(other.origin))
+operator fun CMMatrix.minus(other: CMMatrix): CMMatrix = CMMatrix(this.origin.subtract(other.origin))
+
+infix fun CMMatrix.dot(other: CMMatrix): CMMatrix = CMMatrix(this.origin.multiply(other.origin))

kmath-commons/src/main/kotlin/scientifik/kmath/transform/Transformations.kt

@@ -0,0 +1,86 @@
+package scientifik.kmath.transform
+
+import org.apache.commons.math3.transform.*
+import scientifik.kmath.operations.Complex
+import scientifik.kmath.sequential.Processor
+import scientifik.kmath.sequential.Producer
+import scientifik.kmath.sequential.map
+import scientifik.kmath.structures.*
+
+
+/**
+ *
+ */
+object Transformations {
+
+    private fun Buffer<Complex>.toArray(): Array<org.apache.commons.math3.complex.Complex> =
+        Array(size) { org.apache.commons.math3.complex.Complex(get(it).re, get(it).im) }
+
+    private fun Buffer<Double>.asArray() = if (this is DoubleBuffer) {
+        array
+    } else {
+        DoubleArray(size) { i -> get(i) }
+    }
+
+    /**
+     * Create a virtual buffer on top of array
+     */
+    private fun Array<org.apache.commons.math3.complex.Complex>.asBuffer() = VirtualBuffer<Complex>(size) {
+        val value = get(it)
+        Complex(value.real, value.imaginary)
+    }
+
+    fun fourier(
+        normalization: DftNormalization = DftNormalization.STANDARD,
+        direction: TransformType = TransformType.FORWARD
+    ): BufferTransform<Complex, Complex> = {
+        FastFourierTransformer(normalization).transform(it.toArray(), direction).asBuffer()
+    }
+
+    fun realFourier(
+        normalization: DftNormalization = DftNormalization.STANDARD,
+        direction: TransformType = TransformType.FORWARD
+    ): BufferTransform<Double, Complex> = {
+        FastFourierTransformer(normalization).transform(it.asArray(), direction).asBuffer()
+    }
+
+    fun sine(
+        normalization: DstNormalization = DstNormalization.STANDARD_DST_I,
+        direction: TransformType = TransformType.FORWARD
+    ): BufferTransform<Double, Double> = {
+        FastSineTransformer(normalization).transform(it.asArray(), direction).asBuffer()
+    }
+
+    fun cosine(
+        normalization: DctNormalization = DctNormalization.STANDARD_DCT_I,
+        direction: TransformType = TransformType.FORWARD
+    ): BufferTransform<Double, Double> = {
+        FastCosineTransformer(normalization).transform(it.asArray(), direction).asBuffer()
+    }
+
+    fun hadamard(
+        direction: TransformType = TransformType.FORWARD
+    ): BufferTransform<Double, Double> = {
+        FastHadamardTransformer().transform(it.asArray(), direction).asBuffer()
+    }
+}
+
+/**
+ * Process given [Producer] with commons-math fft transformation
+ */
+fun Producer<Buffer<Complex>>.FFT(
+    normalization: DftNormalization = DftNormalization.STANDARD,
+    direction: TransformType = TransformType.FORWARD
+): Processor<Buffer<Complex>, Buffer<Complex>> {
+    val transform = Transformations.fourier(normalization, direction)
+    return map { transform(it) }
+}
+
+@JvmName("realFFT")
+fun Producer<Buffer<Double>>.FFT(
+    normalization: DftNormalization = DftNormalization.STANDARD,
+    direction: TransformType = TransformType.FORWARD
+): Processor<Buffer<Double>, Buffer<Complex>> {
+    val transform = Transformations.realFourier(normalization, direction)
+    return map { transform(it) }
+}

kmath-commons/src/test/kotlin/scientifik/kmath/expressions/AutoDiffTest.kt

@@ -0,0 +1,31 @@
+package scientifik.kmath.expressions
+
+import org.junit.Test
+import kotlin.test.assertEquals
+
+inline fun <R> diff(order: Int, vararg parameters: Pair<String, Double>, block: DerivativeStructureField.() -> R) =
+    DerivativeStructureField(order, mapOf(*parameters)).run(block)
+
+class AutoDiffTest {
+    @Test
+    fun derivativeStructureFieldTest() {
+        val res = diff(3, "x" to 1.0, "y" to 1.0) {
+            val x by variable
+            val y = variable("y")
+            val z = x * (-sin(x * y) + y)
+            z.deriv("x")
+        }
+    }
+
+    @Test
+    fun autoDifTest() {
+        val f = DiffExpression {
+            val x by variable
+            val y by variable
+            x.pow(2) + 2 * x * y + y.pow(2) + 1
+        }
+
+        assertEquals(10.0, f("x" to 1.0, "y" to 2.0))
+        assertEquals(6.0, f.derivative("x")("x" to 1.0, "y" to 2.0))
+    }
+}

kmath-core/build.gradle

@@ -1,52 +0,0 @@
-plugins {
-    id "org.jetbrains.kotlin.multiplatform"
-}
-
-kotlin {
-    targets {
-        fromPreset(presets.jvm, 'jvm')
-        fromPreset(presets.js, 'js')
-        // For ARM, preset should be changed to presets.iosArm32 or presets.iosArm64
-        // For Linux, preset should be changed to e.g. presets.linuxX64
-        // For MacOS, preset should be changed to e.g. presets.macosX64
-        //fromPreset(presets.mingwX64, 'mingw')
-    }
-    sourceSets {
-        commonMain {
-            dependencies {
-                api 'org.jetbrains.kotlin:kotlin-stdlib-common'
-            }
-        }
-        commonTest {
-            dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-test-common'
-                implementation 'org.jetbrains.kotlin:kotlin-test-annotations-common'
-            }
-        }
-        jvmMain {
-            dependencies {
-                api 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
-            }
-        }
-        jvmTest {
-            dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-test'
-                implementation 'org.jetbrains.kotlin:kotlin-test-junit'
-            }
-        }
-        jsMain {
-            dependencies {
-                api 'org.jetbrains.kotlin:kotlin-stdlib-js'
-            }
-        }
-        jsTest {
-            dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-test-js'
-            }
-        }
-//        mingwMain {
-//        }
-//        mingwTest {
-//        }
-    }
-}

kmath-core/build.gradle.kts

@@ -0,0 +1,51 @@
+plugins {
+    kotlin("multiplatform")
+}
+
+val ioVersion: String by rootProject.extra
+
+
+kotlin {
+    jvm()
+    js()
+
+    sourceSets {
+        val commonMain by getting {
+            dependencies {
+                api(project(":kmath-memory"))
+                api(kotlin("stdlib"))
+            }
+        }
+        val commonTest by getting {
+            dependencies {
+                implementation(kotlin("test-common"))
+                implementation(kotlin("test-annotations-common"))
+            }
+        }
+        val jvmMain by getting {
+            dependencies {
+                api(kotlin("stdlib-jdk8"))
+            }
+        }
+        val jvmTest by getting {
+            dependencies {
+                implementation(kotlin("test"))
+                implementation(kotlin("test-junit"))
+            }
+        }
+        val jsMain by getting {
+            dependencies {
+                api(kotlin("stdlib-js"))
+            }
+        }
+        val jsTest by getting {
+            dependencies {
+                implementation(kotlin("test-js"))
+            }
+        }
+//        mingwMain {
+//        }
+//        mingwTest {
+//        }
+    }
+}

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

@@ -1,48 +1,64 @@
 package scientifik.kmath.expressions
 
 import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Ring
 import scientifik.kmath.operations.Space
 
-
+/**
+ * An elementary function that could be invoked on a map of arguments
+ */
 interface Expression<T> {
     operator fun invoke(arguments: Map<String, T>): T
 }
 
 operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
 
+/**
+ * A context for expression construction
+ */
 interface ExpressionContext<T> {
+    /**
+     * Introduce a variable into expression context
+     */
     fun variable(name: String, default: T? = null): Expression<T>
 
+    /**
+     * A constant expression which does not depend on arguments
+     */
     fun const(value: T): Expression<T>
 }
 
 internal class VariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T {
-        return arguments[name] ?: default ?: error("The parameter not found: $name")
-    }
+    override fun invoke(arguments: Map<String, T>): T =
+        arguments[name] ?: default ?: error("Parameter not found: $name")
 }
 
 internal class ConstantExpression<T>(val value: T) : Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = value
 }
 
-internal class SumExpression<T>(val context: Space<T>, val first: Expression<T>, val second: Expression<T>) : Expression<T> {
+internal class SumExpression<T>(val context: Space<T>, val first: Expression<T>, val second: Expression<T>) :
+    Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = context.add(first.invoke(arguments), second.invoke(arguments))
 }
 
-internal class ProductExpression<T>(val context: Field<T>, val first: Expression<T>, val second: Expression<T>) : Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T = context.multiply(first.invoke(arguments), second.invoke(arguments))
+internal class ProductExpression<T>(val context: Ring<T>, val first: Expression<T>, val second: Expression<T>) :
+    Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T =
+        context.multiply(first.invoke(arguments), second.invoke(arguments))
 }
 
-internal class ConstProductExpession<T>(val context: Field<T>, val expr: Expression<T>, val const: Double) : Expression<T> {
+internal class ConstProductExpession<T>(val context: Space<T>, val expr: Expression<T>, val const: Number) :
+    Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
 }
 
-internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) : Expression<T> {
+internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) :
+    Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = context.divide(expr.invoke(arguments), second.invoke(arguments))
 }
 
-class FieldExpressionContext<T>(val field: Field<T>) : Field<Expression<T>>, ExpressionContext<T> {
+class ExpressionField<T>(val field: Field<T>) : Field<Expression<T>>, ExpressionContext<T> {
 
     override val zero: Expression<T> = ConstantExpression(field.zero)
 
@@ -54,9 +70,20 @@ class FieldExpressionContext<T>(val field: Field<T>) : Field<Expression<T>>, Exp
 
     override fun add(a: Expression<T>, b: Expression<T>): Expression<T> = SumExpression(field, a, b)
 
-    override fun multiply(a: Expression<T>, k: Double): Expression<T> = ConstProductExpession(field, a, k)
+    override fun multiply(a: Expression<T>, k: Number): Expression<T> = ConstProductExpession(field, a, k)
 
     override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> = ProductExpression(field, a, b)
 
     override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> = DivExpession(field, a, b)
+
+
+    operator fun Expression<T>.plus(arg: T) = this + const(arg)
+    operator fun Expression<T>.minus(arg: T) = this - const(arg)
+    operator fun Expression<T>.times(arg: T) = this * const(arg)
+    operator fun Expression<T>.div(arg: T) = this / const(arg)
+
+    operator fun T.plus(arg: Expression<T>) = arg + this
+    operator fun T.minus(arg: Expression<T>) = arg - this
+    operator fun T.times(arg: Expression<T>) = arg * this
+    operator fun T.div(arg: Expression<T>) = arg / this
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/histogram/Counters.kt

@@ -1,20 +0,0 @@
-package scientifik.kmath.histogram
-
-/*
- * Common representation for atomic counters
- */
-
-
-expect class LongCounter(){
-    fun	decrement()
-    fun	increment()
-    fun	reset()
-    fun	sum(): Long
-    fun add(l:Long)
-}
-
-expect class DoubleCounter(){
-    fun	reset()
-    fun	sum(): Double
-    fun add(d: Double)
-}

kmath-core/src/commonMain/kotlin/scientifik/kmath/histogram/Histogram.kt

@@ -1,63 +0,0 @@
-package scientifik.kmath.histogram
-
-import scientifik.kmath.structures.ArrayBuffer
-import scientifik.kmath.structures.Buffer
-import scientifik.kmath.structures.DoubleBuffer
-
-typealias Point<T> = Buffer<T>
-
-typealias RealPoint = Buffer<Double>
-
-/**
- * A simple geometric domain
- * TODO move to geometry module
- */
-interface Domain<T: Any> {
-    operator fun contains(vector: Point<out T>): Boolean
-    val dimension: Int
-}
-
-/**
- * The bin in the histogram. The histogram is by definition always done in the real space
- */
-interface Bin<T: Any> : Domain<T> {
-    /**
-     * The value of this bin
-     */
-    val value: Number
-    val center: Point<T>
-}
-
-interface Histogram<T: Any, out B : Bin<T>> : Iterable<B> {
-
-    /**
-     * Find existing bin, corresponding to given coordinates
-     */
-    operator fun get(point: Point<out T>): B?
-
-    /**
-     * Dimension of the histogram
-     */
-    val dimension: Int
-
-}
-
-interface MutableHistogram<T: Any, out B : Bin<T>>: Histogram<T,B>{
-
-    /**
-     * Increment appropriate bin
-     */
-    fun put(point: Point<out T>, weight: Double = 1.0)
-}
-
-fun <T: Any> MutableHistogram<T,*>.put(vararg point: T) = put(ArrayBuffer(point))
-
-fun MutableHistogram<Double,*>.put(vararg point: Number) = put(DoubleBuffer(point.map { it.toDouble() }.toDoubleArray()))
-fun MutableHistogram<Double,*>.put(vararg point: Double) = put(DoubleBuffer(point))
-
-fun <T: Any> MutableHistogram<T,*>.fill(sequence: Iterable<Point<T>>) = sequence.forEach { put(it) }
-
-/**
- * Pass a sequence builder into histogram
- */
-fun <T: Any> MutableHistogram<T, *>.fill(buider: suspend SequenceScope<Point<T>>.() -> Unit) = fill(sequence(buider).asIterable())

kmath-core/src/commonMain/kotlin/scientifik/kmath/histogram/PhantomHistogram.kt

@@ -1,63 +0,0 @@
-package scientifik.kmath.histogram
-
-import scientifik.kmath.linear.Vector
-import scientifik.kmath.operations.Space
-import scientifik.kmath.structures.NDStructure
-import scientifik.kmath.structures.asSequence
-
-data class BinTemplate<T : Comparable<T>>(val center: Vector<T, *>, val sizes: Point<T>) {
-    fun contains(vector: Point<out T>): Boolean {
-        if (vector.size != center.size) error("Dimension mismatch for input vector. Expected ${center.size}, but found ${vector.size}")
-        val upper = center.context.run { center + sizes / 2.0}
-        val lower =  center.context.run {center - sizes / 2.0}
-        return vector.asSequence().mapIndexed { i, value ->
-            value in lower[i]..upper[i]
-        }.all { it }
-    }
-}
-
-/**
- * A space to perform arithmetic operations on histograms
- */
-interface HistogramSpace<T : Any, B : Bin<T>, H : Histogram<T, B>> : Space<H> {
-    /**
-     * Rules for performing operations on bins
-     */
-    val binSpace: Space<Bin<T>>
-}
-
-class PhantomBin<T : Comparable<T>>(val template: BinTemplate<T>, override val value: Number) : Bin<T> {
-
-    override fun contains(vector: Point<out T>): Boolean = template.contains(vector)
-
-    override val dimension: Int
-        get() = template.center.size
-
-    override val center: Point<T>
-        get() = template.center
-
-}
-
-/**
- * Immutable histogram with explicit structure for content and additional external bin description.
- * Bin search is slow, but full histogram algebra is supported.
- * @param bins map a template into structure index
- */
-class PhantomHistogram<T : Comparable<T>>(
-        val bins: Map<BinTemplate<T>, IntArray>,
-        val data: NDStructure<Number>
-) : Histogram<T, PhantomBin<T>> {
-
-    override val dimension: Int
-        get() = data.dimension
-
-    override fun iterator(): Iterator<PhantomBin<T>> {
-        return bins.asSequence().map { entry -> PhantomBin(entry.key, data[entry.value]) }.iterator()
-    }
-
-    override fun get(point: Point<out T>): PhantomBin<T>? {
-        val template = bins.keys.find { it.contains(point) }
-        return template?.let { PhantomBin(it, data[bins[it]!!]) }
-    }
-
-}

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/BufferMatrix.kt

@@ -0,0 +1,100 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.structures.*
+
+/**
+ * Basic implementation of Matrix space based on [NDStructure]
+ */
+class BufferMatrixContext<T : Any, R : Ring<T>>(
+    override val elementContext: R,
+    private val bufferFactory: BufferFactory<T>
+) : GenericMatrixContext<T, R> {
+
+    override fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> T): BufferMatrix<T> {
+        val buffer = bufferFactory(rows * columns) { offset -> initializer(offset / columns, offset % columns) }
+        return BufferMatrix(rows, columns, buffer)
+    }
+
+    override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
+}
+
+class BufferMatrix<T : Any>(
+    override val rowNum: Int,
+    override val colNum: Int,
+    val buffer: Buffer<out T>,
+    override val features: Set<MatrixFeature> = emptySet()
+) : Matrix<T> {
+
+    init {
+        if (buffer.size != rowNum * colNum) {
+            error("Dimension mismatch for matrix structure")
+        }
+    }
+
+
+    override val shape: IntArray get() = intArrayOf(rowNum, colNum)
+
+    override fun suggestFeature(vararg features: MatrixFeature) =
+        BufferMatrix(rowNum, colNum, buffer, this.features + features)
+
+    override fun get(index: IntArray): T = get(index[0], index[1])
+
+    override fun get(i: Int, j: Int): T = buffer[i * colNum + j]
+
+    override fun elements(): Sequence<Pair<IntArray, T>> = sequence {
+        for (i in 0 until rowNum) {
+            for (j in 0 until colNum) {
+                yield(intArrayOf(i, j) to get(i, j))
+            }
+        }
+    }
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        return when (other) {
+            is NDStructure<*> -> return NDStructure.equals(this, other)
+            else -> false
+        }
+    }
+
+    override fun hashCode(): Int {
+        var result = buffer.hashCode()
+        result = 31 * result + features.hashCode()
+        return result
+    }
+
+    override fun toString(): String {
+        return if (rowNum <= 5 && colNum <= 5) {
+            "Matrix(rowsNum = $rowNum, colNum = $colNum, features=$features)\n" +
+                    rows.asSequence().joinToString(prefix = "(", postfix = ")", separator = "\n ") {
+                        it.asSequence().joinToString(separator = "\t") { it.toString() }
+                    }
+        } else {
+            "Matrix(rowsNum = $rowNum, colNum = $colNum, features=$features)"
+        }
+    }
+}
+
+/**
+ * Optimized dot product for real matrices
+ */
+infix fun BufferMatrix<Double>.dot(other: BufferMatrix<Double>): BufferMatrix<Double> {
+    if (this.colNum != other.rowNum) error("Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})")
+
+    val array = DoubleArray(this.rowNum * other.colNum)
+
+    val a = this.buffer.array
+    val b = other.buffer.array
+
+    for (i in (0 until rowNum)) {
+        for (j in (0 until other.colNum)) {
+            for (k in (0 until colNum)) {
+                array[i * other.colNum + j] += a[i * colNum + k] * b[k * other.colNum + j]
+            }
+        }
+    }
+
+    val buffer = DoubleBuffer(array)
+    return BufferMatrix(rowNum, other.colNum, buffer)
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUDecomposition.kt

@@ -1,251 +0,0 @@
-package scientifik.kmath.linear
-
-import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.operations.Field
-import scientifik.kmath.structures.MutableNDStructure
-import scientifik.kmath.structures.NDStructure
-import scientifik.kmath.structures.genericNdStructure
-import scientifik.kmath.structures.get
-import kotlin.math.absoluteValue
-
-/**
- * Implementation based on Apache common-maths LU-decomposition
- */
-abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matrix<T, F>) {
-
-    private val field get() = matrix.context.field
-    /** Entries of LU decomposition.  */
-    internal val lu: NDStructure<T>
-    /** Pivot permutation associated with LU decomposition.  */
-    internal val pivot: IntArray
-    /** Parity of the permutation associated with the LU decomposition.  */
-    private var even: Boolean = false
-
-    init {
-        val pair = calculateLU()
-        lu = pair.first
-        pivot = pair.second
-    }
-
-    /**
-     * Returns the matrix L of the decomposition.
-     *
-     * L is a lower-triangular matrix
-     * @return the L matrix (or null if decomposed matrix is singular)
-     */
-    val l: Matrix<out T, F> by lazy {
-        matrix.context.produce { i, j ->
-            when {
-                j < i -> lu[i, j]
-                j == i -> matrix.context.field.one
-                else -> matrix.context.field.zero
-            }
-        }
-    }
-
-
-    /**
-     * Returns the matrix U of the decomposition.
-     *
-     * U is an upper-triangular matrix
-     * @return the U matrix (or null if decomposed matrix is singular)
-     */
-    val u: Matrix<out T, F> by lazy {
-        matrix.context.produce { i, j ->
-            if (j >= i) lu[i, j] else field.zero
-        }
-    }
-
-    /**
-     * Returns the P rows permutation matrix.
-     *
-     * P is a sparse matrix with exactly one element set to 1.0 in
-     * each row and each column, all other elements being set to 0.0.
-     *
-     * The positions of the 1 elements are given by the [ pivot permutation vector][.getPivot].
-     * @return the P rows permutation matrix (or null if decomposed matrix is singular)
-     * @see .getPivot
-     */
-    val p: Matrix<out T, F> by lazy {
-        matrix.context.produce { i, j ->
-            //TODO ineffective. Need sparse matrix for that
-            if (j == pivot[i]) field.one else field.zero
-        }
-    }
-
-    /**
-     * Return the determinant of the matrix
-     * @return determinant of the matrix
-     */
-    val determinant: T
-        get() {
-            with(matrix.context.field) {
-                var determinant = if (even) one else -one
-                for (i in 0 until matrix.rows) {
-                    determinant *= lu[i, i]
-                }
-                return determinant
-            }
-        }
-
-    /**
-     * In-place transformation for [MutableNDArray], using given transformation for each element
-     */
-    operator fun <T> MutableNDStructure<T>.set(i: Int, j: Int, value: T) {
-        this[intArrayOf(i, j)] = value
-    }
-
-    abstract fun isSingular(value: T): Boolean
-
-    private fun abs(value: T) = if (value > matrix.context.field.zero) value else with(matrix.context.field) { -value }
-
-    private fun calculateLU(): Pair<NDStructure<T>, IntArray> {
-        if (matrix.rows != matrix.columns) {
-            error("LU decomposition supports only square matrices")
-        }
-
-        val m = matrix.columns
-        val pivot = IntArray(matrix.rows)
-        //TODO fix performance
-        val lu: MutableNDStructure<T> = genericNdStructure(intArrayOf(matrix.rows, matrix.columns)) { index -> matrix[index[0], index[1]] }
-
-
-        with(matrix.context.field) {
-            // Initialize permutation array and parity
-            for (row in 0 until m) {
-                pivot[row] = row
-            }
-            even = true
-
-            // Loop over columns
-            for (col in 0 until m) {
-
-                // upper
-                for (row in 0 until col) {
-                    var sum = lu[row, col]
-                    for (i in 0 until row) {
-                        sum -= lu[row, i] * lu[i, col]
-                    }
-                    lu[row, col] = sum
-                }
-
-                // lower
-                val max = (col until m).maxBy { row ->
-                    var sum = lu[row, col]
-                    for (i in 0 until col) {
-                        sum -= lu[row, i] * lu[i, col]
-                    }
-                    //luRow[col] = sum
-                    lu[row, col] = sum
-
-                    abs(sum)
-                } ?: col
-
-                // Singularity check
-                if (isSingular(lu[max, col])) {
-                    error("Singular matrix")
-                }
-
-                // Pivot if necessary
-                if (max != col) {
-                    //var tmp = zero
-                    //val luMax = lu[max]
-                    //val luCol = lu[col]
-                    for (i in 0 until m) {
-                        lu[max, i] = lu[col, i]
-                        lu[col, i] = lu[max, i]
-                    }
-                    val temp = pivot[max]
-                    pivot[max] = pivot[col]
-                    pivot[col] = temp
-                    even = !even
-                }
-
-                // Divide the lower elements by the "winning" diagonal elt.
-                val luDiag = lu[col, col]
-                for (row in col + 1 until m) {
-                    lu[row, col] = lu[row, col] / luDiag
-//                    lu[row, col] /= luDiag
-                }
-            }
-        }
-        return Pair(lu, pivot)
-    }
-
-    /**
-     * Returns the pivot permutation vector.
-     * @return the pivot permutation vector
-     * @see .getP
-     */
-    fun getPivot(): IntArray {
-        return pivot.copyOf()
-    }
-
-}
-
-class RealLUDecomposition(matrix: RealMatrix, private val singularityThreshold: Double = DEFAULT_TOO_SMALL) : LUDecomposition<Double, DoubleField>(matrix) {
-    override fun isSingular(value: Double): Boolean {
-        return value.absoluteValue < singularityThreshold
-    }
-
-    companion object {
-        /** Default bound to determine effective singularity in LU decomposition.  */
-        private const val DEFAULT_TOO_SMALL = 1e-11
-    }
-}
-
-
-/** Specialized solver.  */
-object RealLUSolver : LinearSolver<Double, DoubleField> {
-
-
-    fun decompose(mat: Matrix<Double, DoubleField>, threshold: Double = 1e-11): RealLUDecomposition = RealLUDecomposition(mat, threshold)
-
-    override fun solve(a: RealMatrix, b: RealMatrix): RealMatrix {
-        val decomposition = decompose(a, a.context.field.zero)
-
-        if (b.rows != a.rows) {
-            error("Matrix dimension mismatch expected ${a.rows}, but got ${b.rows}")
-        }
-
-        // Apply permutations to b
-        val bp = Array(a.rows) { DoubleArray(b.columns) }
-        for (row in 0 until a.rows) {
-            val bpRow = bp[row]
-            val pRow = decomposition.pivot[row]
-            for (col in 0 until b.columns) {
-                bpRow[col] = b[pRow, col]
-            }
-        }
-
-        // Solve LY = b
-        for (col in 0 until a.rows) {
-            val bpCol = bp[col]
-            for (i in col + 1 until a.rows) {
-                val bpI = bp[i]
-                val luICol = decomposition.lu[i, col]
-                for (j in 0 until b.columns) {
-                    bpI[j] -= bpCol[j] * luICol
-                }
-            }
-        }
-
-        // Solve UX = Y
-        for (col in a.rows - 1 downTo 0) {
-            val bpCol = bp[col]
-            val luDiag = decomposition.lu[col, col]
-            for (j in 0 until b.columns) {
-                bpCol[j] /= luDiag
-            }
-            for (i in 0 until col) {
-                val bpI = bp[i]
-                val luICol = decomposition.lu[i, col]
-                for (j in 0 until b.columns) {
-                    bpI[j] -= bpCol[j] * luICol
-                }
-            }
-        }
-
-        return a.context.produce { i, j -> bp[i][j] }
-    }
-}

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt

@@ -0,0 +1,205 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.structures.MutableBuffer
+import scientifik.kmath.structures.MutableBuffer.Companion.boxing
+import scientifik.kmath.structures.MutableBufferFactory
+import scientifik.kmath.structures.NDStructure
+import scientifik.kmath.structures.get
+
+class LUPDecomposition<T : Comparable<T>>(
+    private val elementContext: Ring<T>,
+    internal val lu: NDStructure<T>,
+    val pivot: IntArray,
+    private val even: Boolean
+) : LUPDecompositionFeature<T>, DeterminantFeature<T> {
+
+    /**
+     * Returns the matrix L of the decomposition.
+     *
+     * L is a lower-triangular matrix with [Ring.one] in diagonal
+     */
+    override val l: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1], setOf(LFeature)) { i, j ->
+        when {
+            j < i -> lu[i, j]
+            j == i -> elementContext.one
+            else -> elementContext.zero
+        }
+    }
+
+
+    /**
+     * Returns the matrix U of the decomposition.
+     *
+     * U is an upper-triangular matrix including the diagonal
+     */
+    override val u: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1], setOf(UFeature)) { i, j ->
+        if (j >= i) lu[i, j] else elementContext.zero
+    }
+
+
+    /**
+     * Returns the P rows permutation matrix.
+     *
+     * P is a sparse matrix with exactly one element set to [Ring.one] in
+     * each row and each column, all other elements being set to [Ring.zero].
+     */
+    override val p: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
+        if (j == pivot[i]) elementContext.one else elementContext.zero
+    }
+
+
+    /**
+     * Return the determinant of the matrix
+     * @return determinant of the matrix
+     */
+    override val determinant: T by lazy {
+        with(elementContext) {
+            (0 until lu.shape[0]).fold(if (even) one else -one) { value, i -> value * lu[i, i] }
+        }
+    }
+
+}
+
+
+class LUSolver<T : Comparable<T>, F : Field<T>>(
+    val context: GenericMatrixContext<T, F>,
+    val bufferFactory: MutableBufferFactory<T> = ::boxing,
+    val singularityCheck: (T) -> Boolean
+) : LinearSolver<T> {
+
+
+    private fun abs(value: T) =
+        if (value > context.elementContext.zero) value else with(context.elementContext) { -value }
+
+    fun buildDecomposition(matrix: Matrix<T>): LUPDecomposition<T> {
+        if (matrix.rowNum != matrix.colNum) {
+            error("LU decomposition supports only square matrices")
+        }
+
+        val m = matrix.colNum
+        val pivot = IntArray(matrix.rowNum)
+
+        val lu = Mutable2DStructure.create(matrix.rowNum, matrix.colNum, bufferFactory) { i, j ->
+            matrix[i, j]
+        }
+
+
+        with(context.elementContext) {
+            // Initialize permutation array and parity
+            for (row in 0 until m) {
+                pivot[row] = row
+            }
+            var even = true
+
+            // Loop over columns
+            for (col in 0 until m) {
+
+                // upper
+                for (row in 0 until col) {
+                    var sum = lu[row, col]
+                    for (i in 0 until row) {
+                        sum -= lu[row, i] * lu[i, col]
+                    }
+                    lu[row, col] = sum
+                }
+
+                // lower
+                val max = (col until m).maxBy { row ->
+                    var sum = lu[row, col]
+                    for (i in 0 until col) {
+                        sum -= lu[row, i] * lu[i, col]
+                    }
+                    lu[row, col] = sum
+
+                    abs(sum)
+                } ?: col
+
+                // Singularity check
+                if (singularityCheck(lu[max, col])) {
+                    error("Singular matrix")
+                }
+
+                // Pivot if necessary
+                if (max != col) {
+                    for (i in 0 until m) {
+                        lu[max, i] = lu[col, i]
+                        lu[col, i] = lu[max, i]
+                    }
+                    val temp = pivot[max]
+                    pivot[max] = pivot[col]
+                    pivot[col] = temp
+                    even = !even
+                }
+
+                // Divide the lower elements by the "winning" diagonal elt.
+                val luDiag = lu[col, col]
+                for (row in col + 1 until m) {
+                    lu[row, col] = lu[row, col] / luDiag
+                }
+            }
+            return LUPDecomposition(context.elementContext, lu, pivot, even)
+        }
+    }
+
+    /**
+     * Produce a matrix with added decomposition feature
+     */
+    fun decompose(matrix: Matrix<T>): Matrix<T> {
+        if (matrix.hasFeature<LUPDecomposition<*>>()) {
+            return matrix
+        } else {
+            val decomposition = buildDecomposition(matrix)
+            return VirtualMatrix.wrap(matrix, decomposition)
+        }
+    }
+
+
+    override fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
+        if (b.rowNum != a.colNum) {
+            error("Matrix dimension mismatch expected ${a.rowNum}, but got ${b.colNum}")
+        }
+
+        // Use existing decomposition if it is provided by matrix
+        val decomposition = a.getFeature() ?: buildDecomposition(a)
+
+        with(decomposition) {
+            with(context.elementContext) {
+                // Apply permutations to b
+                val bp = Mutable2DStructure.create(a.rowNum, a.colNum, bufferFactory) { i, j ->
+                    b[pivot[i], j]
+                }
+
+                // Solve LY = b
+                for (col in 0 until a.rowNum) {
+                    for (i in col + 1 until a.rowNum) {
+                        for (j in 0 until b.colNum) {
+                            bp[i, j] -= bp[col, j] * lu[i, col]
+                        }
+                    }
+                }
+
+                // Solve UX = Y
+                for (col in a.rowNum - 1 downTo 0) {
+                    for (j in 0 until b.colNum) {
+                        bp[col, j] /= lu[col, col]
+                    }
+                    for (i in 0 until col) {
+                        for (j in 0 until b.colNum) {
+                            bp[i, j] -= bp[col, j] * lu[i, col]
+                        }
+                    }
+                }
+
+                return context.produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
+            }
+        }
+    }
+
+    override fun inverse(a: Matrix<T>): Matrix<T> = solve(a, context.one(a.rowNum, a.colNum))
+
+    companion object {
+        val real = LUSolver(MatrixContext.real, MutableBuffer.Companion::auto) { it < 1e-11 }
+    }
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt

@@ -1,62 +1,45 @@
 package scientifik.kmath.linear
 
-import scientifik.kmath.operations.DoubleField
 import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.Norm
+import scientifik.kmath.operations.RealField
+import scientifik.kmath.structures.VirtualBuffer
+import scientifik.kmath.structures.asSequence
 
 
 /**
  * A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
  */
-interface LinearSolver<T : Any, F : Field<T>> {
-    fun solve(a: Matrix<T, F>, b: Matrix<T, F>): Matrix<T, F>
-    fun solve(a: Matrix<T, F>, b: Vector<T, F>): Vector<T, F> = solve(a, b.toMatrix()).toVector()
-    fun inverse(a: Matrix<T, F>): Matrix<T, F> = solve(a, Matrix.diagonal(a.rows, a.columns, a.context.field))
+interface LinearSolver<T : Any>  {
+    fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
+    fun solve(a: Matrix<T>, b: Point<T>): Point<T> = solve(a, b.toMatrix()).toVector()
+    fun inverse(a: Matrix<T>): Matrix<T>
 }
 
 /**
  * Convert vector to array (copying content of array)
  */
-fun <T : Any> Array<T>.toVector(field: Field<T>) = Vector.of(size, field) { this[it] }
+fun <T : Any> Array<T>.toVector(field: Field<T>) = Vector.generic(size, field) { this[it] }
+
+fun DoubleArray.toVector() = Vector.real(this.size) { this[it] }
+fun List<Double>.toVector() = Vector.real(this.size) { this[it] }
+
+object VectorL2Norm : Norm<Point<out Number>, Double> {
+    override fun norm(arg: Point<out Number>): Double =
+        kotlin.math.sqrt(arg.asSequence().sumByDouble { it.toDouble() })
+}
+
+typealias RealVector = Vector<Double, RealField>
+typealias RealMatrix = Matrix<Double>
+
 
-fun DoubleArray.toVector() = Vector.ofReal(this.size) { this[it] }
-fun List<Double>.toVector() = Vector.ofReal(this.size) { this[it] }
 
 /**
  * Convert matrix to vector if it is possible
  */
-fun <T : Any, F : Field<T>> Matrix<T, F>.toVector(): Vector<T, F> {
-    return when {
-        this.columns == 1 -> {
-//            if (this is ArrayMatrix) {
-//                //Reuse existing underlying array
-//                ArrayVector(ArrayVectorSpace(rows, context.field, context.ndFactory), array)
-//            } else {
-//                //Generic vector
-//                vector(rows, context.field) { get(it, 0) }
-//            }
-            Vector.of(rows, context.field) { get(it, 0) }
-        }
-        else -> error("Can't convert matrix with more than one column to vector")
-    }
-}
+fun <T: Any> Matrix<T>.toVector(): Point<T> =
+    if (this.colNum == 1) {
+        VirtualBuffer(rowNum){ get(it, 0) }
+    } else error("Can't convert matrix with more than one column to vector")
 
-fun <T : Any, F : Field<T>> Vector<T, F>.toMatrix(): Matrix<T, F> {
-//    return if (this is ArrayVector) {
-//        //Reuse existing underlying array
-//        ArrayMatrix(ArrayMatrixSpace(size, 1, context.field, context.ndFactory), array)
-//    } else {
-//        //Generic vector
-//        matrix(size, 1, context.field) { i, j -> get(i) }
-//    }
-    return Matrix.of(size, 1, context.space) { i, _ -> get(i) }
-}
-
-object VectorL2Norm : Norm<Vector<out Number, *>, Double> {
-    override fun norm(arg: Vector<out Number, *>): Double {
-        return kotlin.math.sqrt(arg.sumByDouble { it.toDouble() })
-    }
-}
-
-typealias RealVector = Vector<Double, DoubleField>
-typealias RealMatrix = Matrix<Double, DoubleField>
+fun <T: Any> Point<T>.toMatrix(): Matrix<T> = VirtualMatrix(size, 1) { i, _ -> get(i) }

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/Matrix.kt

@@ -1,187 +1,214 @@
 package scientifik.kmath.linear
 
-import scientifik.kmath.operations.*
+import scientifik.kmath.operations.RealField
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.operations.sum
 import scientifik.kmath.structures.*
+import scientifik.kmath.structures.Buffer.Companion.DoubleBufferFactory
+import scientifik.kmath.structures.Buffer.Companion.boxing
+import kotlin.math.sqrt
+
+
+interface MatrixContext<T : Any> {
+    /**
+     * Produce a matrix with this context and given dimensions
+     */
+    fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> T): Matrix<T>
+
+    infix fun Matrix<T>.dot(other: Matrix<T>): Matrix<T>
+
+    infix fun Matrix<T>.dot(vector: Point<T>): Point<T>
+
+    operator fun Matrix<T>.unaryMinus(): Matrix<T>
+
+    operator fun Matrix<T>.plus(b: Matrix<T>): Matrix<T>
+
+    operator fun Matrix<T>.minus(b: Matrix<T>): Matrix<T>
+
+    operator fun Matrix<T>.times(value: T): Matrix<T>
+
+    operator fun T.times(m: Matrix<T>): Matrix<T> = m * this
+
+    companion object {
+        /**
+         * Non-boxing double matrix
+         */
+        val real = BufferMatrixContext(RealField, DoubleBufferFactory)
 
         /**
- * The space for linear elements. Supports scalar product alongside with standard linear operations.
- * @param T type of individual element of the vector or matrix
- * @param V the type of vector space element
+         * A structured matrix with custom buffer
          */
-abstract class MatrixSpace<T : Any, F : Ring<T>>(val rows: Int, val columns: Int, val field: F) : Space<Matrix<T, F>> {
+        fun <T : Any, R : Ring<T>> buffered(
+            ring: R,
+            bufferFactory: BufferFactory<T> = ::boxing
+        ): GenericMatrixContext<T, R> =
+            BufferMatrixContext(ring, bufferFactory)
 
         /**
-     * Produce the element of this space
+         * Automatic buffered matrix, unboxed if it is possible
          */
-    abstract fun produce(initializer: (Int, Int) -> T): Matrix<T, F>
-
-    /**
-     * Produce new matrix space with given dimensions. The space produced could be raised from cache since [MatrixSpace] does not have mutable elements
-     */
-    abstract fun produceSpace(rows: Int, columns: Int): MatrixSpace<T, F>
-
-    override val zero: Matrix<T, F> by lazy {
-        produce { _, _ -> field.zero }
+        inline fun <reified T : Any, R : Ring<T>> auto(ring: R): GenericMatrixContext<T, R> =
+            buffered(ring, Buffer.Companion::auto)
+    }
 }
 
-//    val one: Matrix<T> by lazy {
-//        produce { i, j -> if (i == j) field.one else field.zero }
-//    }
+interface GenericMatrixContext<T : Any, R : Ring<T>> : MatrixContext<T> {
+    /**
+     * The ring context for matrix elements
+     */
+    val elementContext: R
 
-    override fun add(a: Matrix<T, F>, b: Matrix<T, F>): Matrix<T, F> {
-        return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
+    /**
+     * Produce a point compatible with matrix space
+     */
+    fun point(size: Int, initializer: (Int) -> T): Point<T>
+
+    override infix fun Matrix<T>.dot(other: Matrix<T>): Matrix<T> {
+        //TODO add typed error
+        if (this.colNum != other.rowNum) error("Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})")
+        return produce(rowNum, other.colNum) { i, j ->
+            val row = rows[i]
+            val column = other.columns[j]
+            with(elementContext) {
+                sum(row.asSequence().zip(column.asSequence(), ::multiply))
+            }
+        }
     }
 
-    override fun multiply(a: Matrix<T, F>, k: Double): Matrix<T, F> {
-        //TODO it is possible to implement scalable linear elements which normed values and adjustable scale to save memory and processing poser
-        return produce { i, j -> with(field) { a[i, j] * k } }
+    override infix fun Matrix<T>.dot(vector: Point<T>): Point<T> {
+        //TODO add typed error
+        if (this.colNum != vector.size) error("Matrix dot vector operation dimension mismatch: ($rowNum, $colNum) x (${vector.size})")
+        return point(rowNum) { i ->
+            val row = rows[i]
+            with(elementContext) {
+                sum(row.asSequence().zip(vector.asSequence(), ::multiply))
+            }
+        }
+    }
+
+    override operator fun Matrix<T>.unaryMinus() =
+        produce(rowNum, colNum) { i, j -> elementContext.run { -get(i, j) } }
+
+    override operator fun Matrix<T>.plus(b: Matrix<T>): Matrix<T> {
+        if (rowNum != b.rowNum || colNum != b.colNum) error("Matrix operation dimension mismatch. [$rowNum,$colNum] + [${b.rowNum},${b.colNum}]")
+        return produce(rowNum, colNum) { i, j -> elementContext.run { get(i, j) + b[i, j] } }
+    }
+
+    override operator fun Matrix<T>.minus(b: Matrix<T>): Matrix<T> {
+        if (rowNum != b.rowNum || colNum != b.colNum) error("Matrix operation dimension mismatch. [$rowNum,$colNum] - [${b.rowNum},${b.colNum}]")
+        return produce(rowNum, colNum) { i, j -> elementContext.run { get(i, j) + b[i, j] } }
+    }
+
+    operator fun Matrix<T>.times(number: Number): Matrix<T> =
+        produce(rowNum, colNum) { i, j -> elementContext.run { get(i, j) * number } }
+
+    operator fun Number.times(matrix: Matrix<T>): Matrix<T> = matrix * this
+
+    override fun Matrix<T>.times(value: T): Matrix<T> =
+        produce(rowNum, colNum) { i, j -> elementContext.run { get(i, j) * value } }
 }
 
 /**
-     * Dot product. Throws exception on dimension mismatch
+ * Specialized 2-d structure
  */
-    fun multiply(a: Matrix<T, F>, b: Matrix<T, F>): Matrix<T, F> {
-        if (a.rows != b.columns) {
-            //TODO replace by specific exception
-            error("Dimension mismatch in linear structure dot product: [${a.rows},${a.columns}]*[${b.rows},${b.columns}]")
-        }
-        return produceSpace(a.rows, b.columns).produce { i, j ->
-            (0 until a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
-        }
-    }
+interface Matrix<T : Any> : Structure2D<T> {
+    val rowNum: Int
+    val colNum: Int
 
-    override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-        if (other !is MatrixSpace<*,*>) return false
-
-        if (rows != other.rows) return false
-        if (columns != other.columns) return false
-        if (field != other.field) return false
-
-        return true
-    }
-
-    override fun hashCode(): Int {
-        var result = rows
-        result = 31 * result + columns
-        result = 31 * result + field.hashCode()
-        return result
-    }
-}
-
-infix fun <T : Any, F : Field<T>> Matrix<T, F>.dot(b: Matrix<T, F>): Matrix<T, F> = this.context.multiply(this, b)
+    val features: Set<MatrixFeature>
 
     /**
- * A matrix-like structure
+     * Suggest new feature for this matrix. The result is the new matrix that may or may not reuse existing data structure.
+     *
+     * The implementation does not guarantee to check that matrix actually have the feature, so one should be careful to
+     * add only those features that are valid.
      */
-interface Matrix<T : Any, F: Ring<T>> : SpaceElement<Matrix<T, F>, MatrixSpace<T, F>> {
-    /**
-     * Number of rows
-     */
-    val rows: Int
-    /**
-     * Number of columns
-     */
-    val columns: Int
+    fun suggestFeature(vararg features: MatrixFeature): Matrix<T>
 
-    /**
-     * Get element in row [i] and column [j]. Throws error in case of call ounside structure dimensions
-     */
-    operator fun get(i: Int, j: Int): T
+    override fun get(index: IntArray): T = get(index[0], index[1])
 
-    override val self: Matrix<T, F>
-        get() = this
+    override val shape: IntArray get() = intArrayOf(rowNum, colNum)
 
-    fun transpose(): Matrix<T, F> {
-        return object : Matrix<T, F> {
-            override val context: MatrixSpace<T, F> = this@Matrix.context
-            override val rows: Int = this@Matrix.columns
-            override val columns: Int = this@Matrix.rows
-            override fun get(i: Int, j: Int): T = this@Matrix[j, i]
+    val rows: Point<Point<T>>
+        get() = VirtualBuffer(rowNum) { i ->
+            VirtualBuffer(colNum) { j -> get(i, j) }
+        }
+
+    val columns: Point<Point<T>>
+        get() = VirtualBuffer(colNum) { j ->
+            VirtualBuffer(rowNum) { i -> get(i, j) }
+        }
+
+    override fun elements(): Sequence<Pair<IntArray, T>> = sequence {
+        for (i in (0 until rowNum)) {
+            for (j in (0 until colNum)) {
+                yield(intArrayOf(i, j) to get(i, j))
+            }
         }
     }
 
     companion object {
+        fun real(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
+            MatrixContext.real.produce(rows, columns, initializer)
 
         /**
-         * Create [ArrayMatrix] with custom field
+         * Build a square matrix from given elements.
          */
-        fun <T : Any, F: Field<T>> of(rows: Int, columns: Int, field: F, initializer: (Int, Int) -> T) =
-                ArrayMatrix(ArrayMatrixSpace(rows, columns, field), initializer)
-
-        /**
-         * Create [ArrayMatrix] of doubles. The implementation in general should be faster than generic one due to boxing.
-         */
-        fun ofReal(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
-                ArrayMatrix(ArrayMatrixSpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
-
-        /**
-         * Create a diagonal value matrix. By default value equals [Field.one].
-         */
-        fun <T : Any, F: Field<T>> diagonal(rows: Int, columns: Int, field: F, values: (Int) -> T = { field.one }): Matrix<T, F> {
-            return of(rows, columns, field) { i, j -> if (i == j) values(i) else field.zero }
+        fun <T : Any> square(vararg elements: T): Matrix<T> {
+            val size: Int = sqrt(elements.size.toDouble()).toInt()
+            if (size * size != elements.size) error("The number of elements ${elements.size} is not a full square")
+            val buffer = elements.asBuffer()
+            return BufferMatrix(size, size, buffer)
         }
 
-        /**
-         * Equality check on two generic matrices
-         */
-        fun equals(mat1: Matrix<*, *>, mat2: Matrix<*, *>): Boolean {
-            if (mat1 === mat2) return true
-            if (mat1.context != mat2.context) return false
-            for (i in 0 until mat1.rows) {
-                for (j in 0 until mat2.columns) {
-                    if (mat1[i, j] != mat2[i, j]) return false
-                }
-            }
-            return true
-        }
+        fun <T : Any> build(rows: Int, columns: Int): MatrixBuilder<T> = MatrixBuilder(rows, columns)
     }
 }
 
-
-
-
-typealias NDFieldFactory<T, F> = (IntArray) -> NDField<T, F>
-
-internal fun <T : Any, F : Field<T>> genericNDFieldFactory(field: F): NDFieldFactory<T, F> = { index -> GenericNDField(index, field) }
-internal val realNDFieldFactory: NDFieldFactory<Double, DoubleField> = { index -> ExtendedNDField(index, DoubleField) }
-
-
-/**
- * NDArray-based implementation of vector space. By default uses slow [GenericNDField], but could be overridden with custom [NDField] factory.
- */
-class ArrayMatrixSpace<T : Any, F : Field<T>>(
-        rows: Int,
-        columns: Int,
-        field: F,
-        val ndFactory: NDFieldFactory<T, F> = genericNDFieldFactory(field)
-) : MatrixSpace<T, F>(rows, columns, field) {
-
-    val ndField by lazy {
-        ndFactory(intArrayOf(rows, columns))
-    }
-
-    override fun produce(initializer: (Int, Int) -> T): Matrix<T, F> = ArrayMatrix(this, initializer)
-
-    override fun produceSpace(rows: Int, columns: Int): ArrayMatrixSpace<T, F> {
-        return ArrayMatrixSpace(rows, columns, field, ndFactory)
+class MatrixBuilder<T : Any>(val rows: Int, val columns: Int) {
+    operator fun invoke(vararg elements: T): Matrix<T> {
+        if (rows * columns != elements.size) error("The number of elements ${elements.size} is not equal $rows * $columns")
+        val buffer = elements.asBuffer()
+        return BufferMatrix(rows, columns, buffer)
     }
 }
 
 /**
- * Member of [ArrayMatrixSpace] which wraps 2-D array
+ * Check if matrix has the given feature class
  */
-class ArrayMatrix<T : Any, F : Field<T>> internal constructor(override val context: ArrayMatrixSpace<T, F>, val element: NDElement<T, F>) : Matrix<T, F> {
+inline fun <reified T : Any> Matrix<*>.hasFeature(): Boolean = features.find { it is T } != null
 
-    constructor(context: ArrayMatrixSpace<T, F>, initializer: (Int, Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0], list[1]) })
+/**
+ * Get the first feature matching given class. Does not guarantee that matrix has only one feature matching the criteria
+ */
+inline fun <reified T : Any> Matrix<*>.getFeature(): T? = features.filterIsInstance<T>().firstOrNull()
 
-    override val rows: Int get() = context.rows
-
-    override val columns: Int get() = context.columns
-
-    override fun get(i: Int, j: Int): T {
-        return element[i, j]
+/**
+ * Diagonal matrix of ones. The matrix is virtual no actual matrix is created
+ */
+fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R>.one(rows: Int, columns: Int): Matrix<T> =
+    VirtualMatrix<T>(rows, columns) { i, j ->
+        if (i == j) elementContext.one else elementContext.zero
     }
 
-    override val self: ArrayMatrix<T, F> get() = this
+
+/**
+ * A virtual matrix of zeroes
+ */
+fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R>.zero(rows: Int, columns: Int): Matrix<T> =
+    VirtualMatrix<T>(rows, columns) { _, _ -> elementContext.zero }
+
+class TransposedFeature<T : Any>(val original: Matrix<T>) : MatrixFeature
+
+/**
+ * Create a virtual transposed matrix without copying anything. `A.transpose().transpose() === A`
+ */
+fun <T : Any, R : Ring<T>> Matrix<T>.transpose(): Matrix<T> {
+    return this.getFeature<TransposedFeature<T>>()?.original ?: VirtualMatrix(
+        this.colNum,
+        this.rowNum,
+        setOf(TransposedFeature(this))
+    ) { i, j -> get(j, i) }
 }
+
+infix fun Matrix<Double>.dot(other: Matrix<Double>): Matrix<Double> = with(MatrixContext.real) { dot(other) }

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixFeatures.kt

@@ -0,0 +1,62 @@
+package scientifik.kmath.linear
+
+/**
+ * A marker interface representing some matrix feature like diagonal, sparce, zero, etc. Features used to optimize matrix
+ * operations performance in some cases.
+ */
+interface MatrixFeature
+
+/**
+ * The matrix with this feature is considered to have only diagonal non-null elements
+ */
+object DiagonalFeature : MatrixFeature
+
+/**
+ * Matrix with this feature has all zero elements
+ */
+object ZeroFeature : MatrixFeature
+
+/**
+ * Matrix with this feature have unit elements on diagonal and zero elements in all other places
+ */
+object UnitFeature : MatrixFeature
+
+/**
+ * Inverted matrix feature
+ */
+interface InverseMatrixFeature<T : Any> : MatrixFeature {
+    val inverse: Matrix<T>
+}
+
+/**
+ * A determinant container
+ */
+interface DeterminantFeature<T : Any> : MatrixFeature {
+    val determinant: T
+}
+
+@Suppress("FunctionName")
+fun <T: Any> DeterminantFeature(determinant: T) = object: DeterminantFeature<T>{
+    override val determinant: T = determinant
+}
+
+/**
+ * Lower triangular matrix
+ */
+object LFeature: MatrixFeature
+
+/**
+ * Upper triangular feature
+ */
+object UFeature: MatrixFeature
+
+/**
+ * TODO add documentation
+ */
+interface LUPDecompositionFeature<T : Any> : MatrixFeature {
+    val l: Matrix<T>
+    val u: Matrix<T>
+    val p: Matrix<T>
+}
+
+//TODO add sparse matrix feature

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/Mutable2DStructure.kt

@@ -0,0 +1,40 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.structures.MutableBuffer
+import scientifik.kmath.structures.MutableBufferFactory
+import scientifik.kmath.structures.MutableNDStructure
+
+class Mutable2DStructure<T>(val rowNum: Int, val colNum: Int, val buffer: MutableBuffer<T>) : MutableNDStructure<T> {
+    override val shape: IntArray
+        get() = intArrayOf(rowNum, colNum)
+
+    operator fun get(i: Int, j: Int): T = buffer[i * colNum + j]
+
+    override fun get(index: IntArray): T = get(index[0], index[1])
+
+    override fun elements(): Sequence<Pair<IntArray, T>> = sequence {
+        for (i in 0 until rowNum) {
+            for (j in 0 until colNum) {
+                yield(intArrayOf(i, j) to get(i, j))
+            }
+        }
+    }
+
+    operator fun set(i: Int, j: Int, value: T) {
+        buffer[i * colNum + j] = value
+    }
+
+    override fun set(index: IntArray, value: T) = set(index[0], index[1], value)
+
+    companion object {
+        fun <T> create(
+            rowNum: Int,
+            colNum: Int,
+            bufferFactory: MutableBufferFactory<T>,
+            init: (i: Int, j: Int) -> T
+        ): Mutable2DStructure<T> {
+            val buffer = bufferFactory(rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
+            return Mutable2DStructure(rowNum, colNum, buffer)
+        }
+    }
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/Vector.kt

@@ -1,103 +1,125 @@
 package scientifik.kmath.linear
 
-import scientifik.kmath.histogram.Point
-import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.RealField
 import scientifik.kmath.operations.Space
 import scientifik.kmath.operations.SpaceElement
-import scientifik.kmath.structures.NDElement
-import scientifik.kmath.structures.get
+import scientifik.kmath.structures.Buffer
+import scientifik.kmath.structures.BufferFactory
+import scientifik.kmath.structures.asSequence
+
+typealias Point<T> = Buffer<T>
 
 /**
  * A linear space for vectors.
  * Could be used on any point-like structure
  */
-abstract class VectorSpace<T : Any, S : Space<T>>(val size: Int, val space: S) : Space<Point<T>> {
+interface VectorSpace<T : Any, S : Space<T>> : Space<Point<T>> {
 
-    abstract fun produce(initializer: (Int) -> T): Vector<T, S>
+    val size: Int
 
-    override val zero: Vector<T, S> by lazy { produce { space.zero } }
+    val space: S
 
-    override fun add(a: Point<T>, b: Point<T>): Vector<T, S> = produce { with(space) { a[it] + b[it] } }
+    fun produce(initializer: (Int) -> T): Point<T>
 
-    override fun multiply(a: Point<T>, k: Double): Vector<T, S> = produce { with(space) { a[it] * k } }
+    /**
+     * Produce a space-element of this vector space for expressions
+     */
+    fun produceElement(initializer: (Int) -> T): Vector<T, S>
+
+    override val zero: Point<T> get() = produce { space.zero }
+
+    override fun add(a: Point<T>, b: Point<T>): Point<T> = produce { with(space) { a[it] + b[it] } }
+
+    override fun multiply(a: Point<T>, k: Number): Point<T> = produce { with(space) { a[it] * k } }
+
+    //TODO add basis
+
+    companion object {
+
+        private val realSpaceCache = HashMap<Int, BufferVectorSpace<Double, RealField>>()
+
+        /**
+         * Non-boxing double vector space
+         */
+        fun real(size: Int): BufferVectorSpace<Double, RealField> {
+            return realSpaceCache.getOrPut(size) { BufferVectorSpace(size, RealField, Buffer.DoubleBufferFactory) }
+        }
+
+        /**
+         * A structured vector space with custom buffer
+         */
+        fun <T : Any, S : Space<T>> buffered(
+            size: Int,
+            space: S,
+            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing
+        ): VectorSpace<T, S> = BufferVectorSpace(size, space, bufferFactory)
+
+        /**
+         * Automatic buffered vector, unboxed if it is possible
+         */
+        inline fun <reified T : Any, S : Space<T>> smart(size: Int, space: S): VectorSpace<T, S> =
+            buffered(size, space, Buffer.Companion::auto)
+    }
 }
 
 
 /**
  * A point coupled to the linear space
  */
-interface Vector<T : Any, S : Space<T>> : SpaceElement<Point<T>, VectorSpace<T, S>>, Point<T>, Iterable<T> {
+interface Vector<T : Any, S : Space<T>> : SpaceElement<Point<T>, Vector<T, S>, VectorSpace<T, S>>, Point<T> {
     override val size: Int get() = context.size
 
-    override operator fun plus(b: Point<T>): Vector<T, S> = context.add(self, b)
-    override operator fun minus(b: Point<T>): Vector<T, S> = context.add(self, context.multiply(b, -1.0))
-    override operator fun times(k: Number): Vector<T, S> = context.multiply(self, k.toDouble())
-    override operator fun div(k: Number): Vector<T, S> = context.multiply(self, 1.0 / k.toDouble())
+    override operator fun plus(b: Point<T>): Vector<T, S> = context.add(this, b).wrap()
+    override operator fun minus(b: Point<T>): Vector<T, S> = context.add(this, context.multiply(b, -1.0)).wrap()
+    override operator fun times(k: Number): Vector<T, S> = context.multiply(this, k.toDouble()).wrap()
+    override operator fun div(k: Number): Vector<T, S> = context.multiply(this, 1.0 / k.toDouble()).wrap()
 
     companion object {
         /**
          * Create vector with custom field
          */
-        fun <T : Any, F : Field<T>> of(size: Int, field: F, initializer: (Int) -> T) =
-                ArrayVector(ArrayVectorSpace(size, field), initializer)
+        fun <T : Any, S : Space<T>> generic(size: Int, field: S, initializer: (Int) -> T): Vector<T, S> =
+            VectorSpace.buffered(size, field).produceElement(initializer)
 
-        private val realSpaceCache = HashMap<Int, ArrayVectorSpace<Double, DoubleField>>()
+        fun real(size: Int, initializer: (Int) -> Double): Vector<Double, RealField> =
+            VectorSpace.real(size).produceElement(initializer)
 
-        private fun getRealSpace(size: Int): ArrayVectorSpace<Double, DoubleField> {
-            return realSpaceCache.getOrPut(size){ArrayVectorSpace(size, DoubleField, realNDFieldFactory)}
-        }
+        fun ofReal(vararg elements: Double): Vector<Double, RealField> =
+            VectorSpace.real(elements.size).produceElement { elements[it] }
 
-        /**
-         * Create vector of [Double]
-         */
-        fun ofReal(size: Int, initializer: (Int) -> Double) =
-                ArrayVector(getRealSpace(size), initializer)
-
-        fun ofReal(vararg point: Double) = point.toVector()
-
-        fun equals(v1: Vector<*, *>, v2: Vector<*, *>): Boolean {
-            if (v1 === v2) return true
-            if (v1.context != v2.context) return false
-            for (i in 0 until v2.size) {
-                if (v1[i] != v2[i]) return false
-            }
-            return true
-        }
     }
 }
 
-class ArrayVectorSpace<T : Any, F : Field<T>>(
-        size: Int,
-        field: F,
-        val ndFactory: NDFieldFactory<T, F> = genericNDFieldFactory(field)
-) : VectorSpace<T, F>(size, field) {
-    val ndField by lazy {
-        ndFactory(intArrayOf(size))
-    }
-
-    override fun produce(initializer: (Int) -> T): Vector<T, F> = ArrayVector(this, initializer)
+data class BufferVectorSpace<T : Any, S : Space<T>>(
+    override val size: Int,
+    override val space: S,
+    val bufferFactory: BufferFactory<T>
+) : VectorSpace<T, S> {
+    override fun produce(initializer: (Int) -> T) = bufferFactory(size, initializer)
+    override fun produceElement(initializer: (Int) -> T): Vector<T, S> = BufferVector(this, produce(initializer))
 }
 
 
-class ArrayVector<T : Any, F : Field<T>> internal constructor(override val context: VectorSpace<T, F>, val element: NDElement<T, F>) : Vector<T, F> {
-
-    constructor(context: ArrayVectorSpace<T, F>, initializer: (Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0]) })
+data class BufferVector<T : Any, S : Space<T>>(override val context: VectorSpace<T, S>, val buffer: Buffer<T>) :
+    Vector<T, S> {
 
     init {
-        if (context.size != element.shape[0]) {
+        if (context.size != buffer.size) {
             error("Array dimension mismatch")
         }
     }
 
     override fun get(index: Int): T {
-        return element[index]
+        return buffer[index]
     }
 
-    override val self: ArrayVector<T, F> get() = this
+    override fun unwrap(): Point<T> = this
 
-    override fun iterator(): Iterator<T> = (0 until size).map { element[it] }.iterator()
+    override fun Point<T>.wrap(): Vector<T, S> = BufferVector(context, this)
 
-    override fun toString(): String = this.joinToString(prefix = "[", postfix = "]", separator = ", ") { it.toString() }
+    override fun iterator(): Iterator<T> = (0 until size).map { buffer[it] }.iterator()
+
+    override fun toString(): String =
+        this.asSequence().joinToString(prefix = "[", postfix = "]", separator = ", ") { it.toString() }
 }
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VirtualMatrix.kt

@@ -0,0 +1,47 @@
+package scientifik.kmath.linear
+
+class VirtualMatrix<T : Any>(
+    override val rowNum: Int,
+    override val colNum: Int,
+    override val features: Set<MatrixFeature> = emptySet(),
+    val generator: (i: Int, j: Int) -> T
+) : Matrix<T> {
+    override fun get(i: Int, j: Int): T = generator(i, j)
+
+    override fun suggestFeature(vararg features: MatrixFeature) =
+        VirtualMatrix(rowNum, colNum, this.features + features, generator)
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other !is Matrix<*>) return false
+
+        if (rowNum != other.rowNum) return false
+        if (colNum != other.colNum) return false
+
+        return elements().all { (index, value) -> value == other[index] }
+    }
+
+    override fun hashCode(): Int {
+        var result = rowNum
+        result = 31 * result + colNum
+        result = 31 * result + features.hashCode()
+        result = 31 * result + generator.hashCode()
+        return result
+    }
+
+
+    companion object {
+        /**
+         * Wrap a matrix adding additional features to it
+         */
+        fun <T : Any> wrap(matrix: Matrix<T>, vararg features: MatrixFeature): Matrix<T> {
+            return if (matrix is VirtualMatrix) {
+                VirtualMatrix(matrix.rowNum, matrix.colNum, matrix.features + features, matrix.generator)
+            } else {
+                VirtualMatrix(matrix.rowNum, matrix.colNum, matrix.features + features) { i, j ->
+                    matrix[i, j]
+                }
+            }
+        }
+    }
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Cumulative.kt

@@ -1,59 +0,0 @@
-package scientifik.kmath.misc
-
-import kotlin.jvm.JvmName
-
-
-/**
- * Generic cumulative operation on iterator
- * @param T type of initial iterable
- * @param R type of resulting iterable
- * @param initial lazy evaluated
- */
-fun <T, R> Iterator<T>.cumulative(initial: R, operation: (T, R) -> R): Iterator<R> = object : Iterator<R> {
-    var state: R = initial
-    override fun hasNext(): Boolean = this@cumulative.hasNext()
-
-    override fun next(): R {
-        state = operation.invoke(this@cumulative.next(), state)
-        return state
-    }
-}
-
-fun <T, R> Iterable<T>.cumulative(initial: R, operation: (T, R) -> R): Iterable<R> = object : Iterable<R> {
-    override fun iterator(): Iterator<R> = this@cumulative.iterator().cumulative(initial, operation)
-}
-
-fun <T, R> Sequence<T>.cumulative(initial: R, operation: (T, R) -> R): Sequence<R> = object : Sequence<R> {
-    override fun iterator(): Iterator<R> = this@cumulative.iterator().cumulative(initial, operation)
-}
-
-fun <T, R> List<T>.cumulative(initial: R, operation: (T, R) -> R): List<R> = this.iterator().cumulative(initial, operation).asSequence().toList()
-
-//Cumulative sum
-
-@JvmName("cumulativeSumOfDouble")
-fun Iterable<Double>.cumulativeSum() = this.cumulative(0.0){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfInt")
-fun Iterable<Int>.cumulativeSum() = this.cumulative(0){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfLong")
-fun Iterable<Long>.cumulativeSum() = this.cumulative(0L){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfDouble")
-fun Sequence<Double>.cumulativeSum() = this.cumulative(0.0){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfInt")
-fun Sequence<Int>.cumulativeSum() = this.cumulative(0){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfLong")
-fun Sequence<Long>.cumulativeSum() = this.cumulative(0L){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfDouble")
-fun List<Double>.cumulativeSum() = this.cumulative(0.0){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfInt")
-fun List<Int>.cumulativeSum() = this.cumulative(0){ element, sum -> sum + element}
-
-@JvmName("cumulativeSumOfLong")
-fun List<Long>.cumulativeSum() = this.cumulative(0L){ element, sum -> sum + element}

kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt

@@ -8,8 +8,8 @@ package scientifik.kmath.misc
  *
  * If step is negative, the same goes from upper boundary downwards
  */
-fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double> {
-    return when {
+fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double> =
+        when {
             step == 0.0 -> error("Zero step in double progression")
             step > 0 -> sequence {
                 var current = start
@@ -26,12 +26,11 @@ fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double>
                 }
             }
         }
-}
 
 /**
  * Convert double range to array of evenly spaced doubles, where the size of array equals [numPoints]
  */
 fun ClosedFloatingPointRange<Double>.toGrid(numPoints: Int): DoubleArray {
-    if (numPoints < 2) error("Can't create grid with less than two points")
+    if (numPoints < 2) error("Can't create generic grid with less than two points")
     return DoubleArray(numPoints) { i -> start + (endInclusive - start) / (numPoints - 1) * i }
 }

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

@@ -1,37 +1,7 @@
 package scientifik.kmath.operations
 
 
-/**
- * The generic mathematics elements which is able to store its context
- * @param T the self type of the element
- * @param S the type of mathematical context for this element
- */
-interface MathElement<T, S> {
-    /**
-     * Self value. Needed for static type checking.
-     */
-    val self: T
-
-    /**
-     * The context this element belongs to
-     */
-    val context: S
-}
-
-/**
- * A general interface representing linear context of some kind.
- * The context defines sum operation for its elements and multiplication by real value.
- * One must note that in some cases context is a singleton class, but in some cases it
- * works as a context for operations inside it.
- *
- * TODO do we need commutative context?
- */
-interface Space<T> {
-    /**
-     * Neutral element for sum operation
-     */
-    val zero: T
-
+interface SpaceOperations<T> {
     /**
      * Addition operation for two context elements
      */
@@ -40,7 +10,7 @@ interface Space<T> {
     /**
      * Multiplication operation for context element and real number
      */
-    fun multiply(a: T, k: Double): T
+    fun multiply(a: T, k: Number): T
 
     //Operation to be performed in this context
     operator fun T.unaryMinus(): T = multiply(this, -1.0)
@@ -50,69 +20,61 @@ interface Space<T> {
     operator fun T.times(k: Number) = multiply(this, k.toDouble())
     operator fun T.div(k: Number) = multiply(this, 1.0 / k.toDouble())
     operator fun Number.times(b: T) = b * this
-
 }
 
+
 /**
- * The element of linear context
- * @param T  self type of the element. Needed for static type checking
- * @param S the type of space
+ * A general interface representing linear context of some kind.
+ * The context defines sum operation for its elements and multiplication by real value.
+ * One must note that in some cases context is a singleton class, but in some cases it
+ * works as a context for operations inside it.
+ *
+ * TODO do we need non-commutative context?
  */
-interface SpaceElement<T, S : Space<T>> : MathElement<T, S> {
-    operator fun plus(b: T): T = context.add(self, b)
-    operator fun minus(b: T): T = context.add(self, context.multiply(b, -1.0))
-    operator fun times(k: Number): T = context.multiply(self, k.toDouble())
-    operator fun div(k: Number): T = context.multiply(self, 1.0 / k.toDouble())
+interface Space<T> : SpaceOperations<T> {
+    /**
+     * Neutral element for sum operation
+     */
+    val zero: T
 }
 
-/**
- * The same as {@link Space} but with additional multiplication operation
- */
-interface Ring<T> : Space<T> {
-    /**
-     * neutral operation for multiplication
-     */
-    val one: T
-
+interface RingOperations<T> : SpaceOperations<T> {
     /**
      * Multiplication for two field elements
      */
     fun multiply(a: T, b: T): T
 
     operator fun T.times(b: T): T = multiply(this, b)
-
 }
 
 /**
- * Ring element
+ * The same as {@link Space} but with additional multiplication operation
  */
-interface RingElement<T, S : Ring<T>> : SpaceElement<T, S> {
-    override val context: S
+interface Ring<T> : Space<T>, RingOperations<T> {
+    /**
+     * neutral operation for multiplication
+     */
+    val one: T
 
-    operator fun times(b: T): T = context.multiply(self, b)
+//    operator fun T.plus(b: Number) = this.plus(b * one)
+//    operator fun Number.plus(b: T) = b + this
+//
+//    operator fun T.minus(b: Number) = this.minus(b * one)
+//    operator fun Number.minus(b: T) = -b + this
+}
+
+/**
+ * All ring operations but without neutral elements
+ */
+interface FieldOperations<T> : RingOperations<T> {
+    fun divide(a: T, b: T): T
+
+    operator fun T.div(b: T): T = divide(this, b)
 }
 
 /**
  * Four operations algebra
  */
-interface Field<T> : Ring<T> {
-    fun divide(a: T, b: T): T
-
-    operator fun T.div(b: T): T = divide(this, b)
+interface Field<T> : Ring<T>, FieldOperations<T> {
     operator fun Number.div(b: T) = this * divide(one, b)
-
-    operator fun T.plus(b: Number) = this.plus(b * one)
-    operator fun Number.plus(b: T) = b + this
-
-    operator fun T.minus(b: Number) = this.minus(b * one)
-    operator fun Number.minus(b: T) = -b + this
-}
-
-/**
- * Field element
- */
-interface FieldElement<T, S : Field<T>> : RingElement<T, S> {
-    override val context: S
-
-    operator fun div(b: T): T = context.divide(self, b)
 }

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

@@ -0,0 +1,48 @@
+package scientifik.kmath.operations
+
+/**
+ * The generic mathematics elements which is able to store its context
+ * @param T the type of space operation results
+ * @param I self type of the element. Needed for static type checking
+ * @param C the type of mathematical context for this element
+ */
+interface MathElement<C> {
+    /**
+     * The context this element belongs to
+     */
+    val context: C
+}
+
+interface MathWrapper<T, I> {
+    fun unwrap(): T
+    fun T.wrap(): I
+}
+
+/**
+ * The element of linear context
+ * @param T the type of space operation results
+ * @param I self type of the element. Needed for static type checking
+ * @param S the type of space
+ */
+interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement<S>, MathWrapper<T, I> {
+
+    operator fun plus(b: T) = context.add(unwrap(), b).wrap()
+    operator fun minus(b: T) = context.add(unwrap(), context.multiply(b, -1.0)).wrap()
+    operator fun times(k: Number) = context.multiply(unwrap(), k.toDouble()).wrap()
+    operator fun div(k: Number) = context.multiply(unwrap(), 1.0 / k.toDouble()).wrap()
+}
+
+/**
+ * Ring element
+ */
+interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T, I, R> {
+    operator fun times(b: T) = context.multiply(unwrap(), b).wrap()
+}
+
+/**
+ * Field element
+ */
+interface FieldElement<T, I : FieldElement<T, I, F>, F : Field<T>> : RingElement<T, I, F> {
+    override val context: F
+    operator fun div(b: T) = context.divide(unwrap(), b).wrap()
+}

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

@@ -0,0 +1,7 @@
+package scientifik.kmath.operations
+
+import scientifik.kmath.structures.Buffer
+import scientifik.kmath.structures.asSequence
+
+fun <T> Space<T>.sum(data : Iterable<T>): T = data.fold(zero) { left, right -> add(left,right) }
+fun <T> Space<T>.sum(data : Sequence<T>): T = data.fold(zero) { left, right -> add(left, right) }

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

@@ -1,45 +1,97 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.structures.Buffer
+import scientifik.kmath.structures.MutableBuffer
+import scientifik.kmath.structures.ObjectBuffer
+import scientifik.memory.MemoryReader
+import scientifik.memory.MemorySpec
+import scientifik.memory.MemoryWriter
+import kotlin.math.*
+
 /**
  * A field for complex numbers
  */
-object ComplexField : Field<Complex> {
+object ComplexField : ExtendedFieldOperations<Complex>, Field<Complex> {
     override val zero: Complex = Complex(0.0, 0.0)
 
-    override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
-
-    override fun multiply(a: Complex, k: Double): Complex = Complex(a.re * k, a.im * k)
-
     override val one: Complex = Complex(1.0, 0.0)
 
-    override fun multiply(a: Complex, b: Complex): Complex = Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
+    val i = Complex(0.0, 1.0)
 
-    override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
+    override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
 
+    override fun multiply(a: Complex, k: Number): Complex = Complex(a.re * k.toDouble(), a.im * k.toDouble())
+
+    override fun multiply(a: Complex, b: Complex): Complex =
+        Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
+
+    override fun divide(a: Complex, b: Complex): Complex {
+        val norm = b.square
+        return Complex((a.re * b.re + a.im * b.im) / norm, (a.re * b.im - a.im * b.re) / norm)
+    }
+
+    override fun sin(arg: Complex): Complex = i / 2 * (exp(-i * arg) - exp(i * arg))
+
+    override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
+
+    override fun power(arg: Complex, pow: Number): Complex =
+        arg.abs.pow(pow.toDouble()) * (cos(pow.toDouble() * arg.theta) + i * sin(pow.toDouble() * arg.theta))
+
+    override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
+
+    override fun ln(arg: Complex): Complex = ln(arg.abs) + i * atan2(arg.im, arg.re)
+
+    operator fun Double.plus(c: Complex) = add(this.toComplex(), c)
+
+    operator fun Double.minus(c: Complex) = add(this.toComplex(), -c)
+
+    operator fun Complex.plus(d: Double) = d + this
+
+    operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
+
+    operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
 }
 
 /**
  * Complex number class
  */
-data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
-    override val self: Complex get() = this
-    override val context: ComplexField
-        get() = ComplexField
+data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Complex, ComplexField> {
+    override fun unwrap(): Complex = this
+
+    override fun Complex.wrap(): Complex = this
+
+    override val context: ComplexField get() = ComplexField
 
     /**
      * A complex conjugate
      */
-    val conjugate: Complex
-        get() = Complex(re, -im)
+    val conjugate: Complex get() = Complex(re, -im)
 
-    val square: Double
-        get() = re * re + im * im
+    val square: Double get() = re * re + im * im
 
-    val abs: Double
-        get() = kotlin.math.sqrt(square)
+    val abs: Double get() = sqrt(square)
 
-    companion object {
+    val theta: Double get() = atan(im / re)
 
+    companion object : MemorySpec<Complex> {
+        override val objectSize: Int = 16
+
+        override fun MemoryReader.read(offset: Int): Complex =
+            Complex(readDouble(offset), readDouble(offset + 8))
+
+        override fun MemoryWriter.write(offset: Int, value: Complex) {
+            writeDouble(offset, value.re)
+            writeDouble(offset + 8, value.im)
+        }
+    }
 }
 
+fun Double.toComplex() = Complex(this, 0.0)
+
+fun Buffer.Companion.complex(size: Int, init: (Int) -> Complex): Buffer<Complex> {
+    return ObjectBuffer.create(Complex, size, init)
+}
+
+fun MutableBuffer.Companion.complex(size: Int, init: (Int) -> Complex): Buffer<Complex> {
+    return ObjectBuffer.create(Complex, size, init)
 }

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

@@ -1,89 +0,0 @@
-package scientifik.kmath.operations
-
-import kotlin.math.pow
-
-/**
- * Advanced Number-like field that implements basic operations
- */
-interface ExtendedField<N : Any> :
-        Field<N>,
-        TrigonometricOperations<N>,
-        PowerOperations<N>,
-        ExponentialOperations<N>
-
-
-/**
- * Field for real values
- */
-object RealField : ExtendedField<Real>, Norm<Real, Real> {
-    override val zero: Real = Real(0.0)
-    override fun add(a: Real, b: Real): Real = Real(a.value + b.value)
-    override val one: Real = Real(1.0)
-    override fun multiply(a: Real, b: Real): Real = Real(a.value * b.value)
-    override fun multiply(a: Real, k: Double): Real = Real(a.value * k)
-    override fun divide(a: Real, b: Real): Real = Real(a.value / b.value)
-
-    override fun sin(arg: Real): Real = Real(kotlin.math.sin(arg.value))
-    override fun cos(arg: Real): Real = Real(kotlin.math.cos(arg.value))
-
-    override fun power(arg: Real, pow: Double): Real = Real(arg.value.pow(pow))
-
-    override fun exp(arg: Real): Real = Real(kotlin.math.exp(arg.value))
-
-    override fun ln(arg: Real): Real = Real(kotlin.math.ln(arg.value))
-
-    override fun norm(arg: Real): Real = Real(kotlin.math.abs(arg.value))
-}
-
-/**
- * Real field element wrapping double.
- *
- * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
- */
-inline class Real(val value: Double) : FieldElement<Real, RealField> {
-
-    //values are dynamically calculated to save memory
-    override val self
-        get() = this
-
-    override val context
-        get() = RealField
-
-    companion object {
-
-    }
-}
-
-/**
- * A field for double without boxing. Does not produce appropriate field element
- */
-object DoubleField : ExtendedField<Double>, Norm<Double, Double> {
-    override val zero: Double = 0.0
-    override fun add(a: Double, b: Double): Double = a + b
-    override fun multiply(a: Double, @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE") b: Double): Double = a * b
-    override val one: Double = 1.0
-    override fun divide(a: Double, b: Double): Double = a / b
-
-    override fun sin(arg: Double): Double = kotlin.math.sin(arg)
-    override fun cos(arg: Double): Double = kotlin.math.cos(arg)
-
-    override fun power(arg: Double, pow: Double): Double = arg.pow(pow)
-
-    override fun exp(arg: Double): Double = kotlin.math.exp(arg)
-
-    override fun ln(arg: Double): Double = kotlin.math.ln(arg)
-
-    override fun norm(arg: Double): Double = kotlin.math.abs(arg)
-}
-
-/**
- * A field for double without boxing. Does not produce appropriate field element
- */
-object IntField : Field<Int>{
-    override val zero: Int = 0
-    override fun add(a: Int, b: Int): Int = a + b
-    override fun multiply(a: Int, b: Int): Int = a * b
-    override fun multiply(a: Int, k: Double): Int = (k*a).toInt()
-    override val one: Int = 1
-    override fun divide(a: Int, b: Int): Int = a / b
-}

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

@@ -0,0 +1,109 @@
+package scientifik.kmath.operations
+
+import kotlin.math.pow
+
+/**
+ * Advanced Number-like field that implements basic operations
+ */
+interface ExtendedFieldOperations<T> :
+    FieldOperations<T>,
+    TrigonometricOperations<T>,
+    PowerOperations<T>,
+    ExponentialOperations<T>
+
+interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T>
+
+/**
+ * Real field element wrapping double.
+ *
+ * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
+ */
+inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
+    override fun unwrap(): Double = value
+
+    override fun Double.wrap(): Real = Real(value)
+
+    override val context get() = RealField
+
+    companion object
+}
+
+/**
+ * A field for double without boxing. Does not produce appropriate field element
+ */
+@Suppress("EXTENSION_SHADOWED_BY_MEMBER")
+object RealField : Field<Double>, ExtendedFieldOperations<Double>, Norm<Double, Double> {
+    override val zero: Double = 0.0
+    override fun add(a: Double, b: Double): Double = a + b
+    override fun multiply(a: Double, b: Double): Double = a * b
+    override fun multiply(a: Double, k: Number): Double = a * k.toDouble()
+
+    override val one: Double = 1.0
+    override fun divide(a: Double, b: Double): Double = a / b
+
+    override fun sin(arg: Double): Double = kotlin.math.sin(arg)
+    override fun cos(arg: Double): Double = kotlin.math.cos(arg)
+
+    override fun power(arg: Double, pow: Number): Double = arg.pow(pow.toDouble())
+
+    override fun exp(arg: Double): Double = kotlin.math.exp(arg)
+    override fun ln(arg: Double): Double = kotlin.math.ln(arg)
+
+    override fun norm(arg: Double): Double = kotlin.math.abs(arg)
+
+    override fun Double.unaryMinus(): Double = -this
+
+    override fun Double.minus(b: Double): Double = this - b
+}
+
+/**
+ * A field for [Int] without boxing. Does not produce corresponding field element
+ */
+object IntRing : Ring<Int>, Norm<Int, Int> {
+    override val zero: Int = 0
+    override fun add(a: Int, b: Int): Int = a + b
+    override fun multiply(a: Int, b: Int): Int = a * b
+    override fun multiply(a: Int, k: Number): Int = (k * a)
+    override val one: Int = 1
+
+    override fun norm(arg: Int): Int = arg
+}
+
+/**
+ * A field for [Short] without boxing. Does not produce appropriate field element
+ */
+object ShortRing : Ring<Short>, Norm<Short, Short> {
+    override val zero: Short = 0
+    override fun add(a: Short, b: Short): Short = (a + b).toShort()
+    override fun multiply(a: Short, b: Short): Short = (a * b).toShort()
+    override fun multiply(a: Short, k: Number): Short = (a * k)
+    override val one: Short = 1
+
+    override fun norm(arg: Short): Short = arg
+}
+
+/**
+ * A field for [Byte] values
+ */
+object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
+    override val zero: Byte = 0
+    override fun add(a: Byte, b: Byte): Byte = (a + b).toByte()
+    override fun multiply(a: Byte, b: Byte): Byte = (a * b).toByte()
+    override fun multiply(a: Byte, k: Number): Byte = (a * k)
+    override val one: Byte = 1
+
+    override fun norm(arg: Byte): Byte = arg
+}
+
+/**
+ * A field for [Long] values
+ */
+object LongRing : Ring<Long>, Norm<Long, Long> {
+    override val zero: Long = 0
+    override fun add(a: Long, b: Long): Long = (a + b)
+    override fun multiply(a: Long, b: Long): Long = (a * b)
+    override fun multiply(a: Long, k: Number): Long = (a * k)
+    override val one: Long = 1
+
+    override fun norm(arg: Long): Long = arg
+}

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

@@ -10,7 +10,7 @@ package scientifik.kmath.operations
  * It also allows to override behavior for optional operations
  *
  */
-interface TrigonometricOperations<T> : Field<T> {
+interface TrigonometricOperations<T> : FieldOperations<T> {
     fun sin(arg: T): T
     fun cos(arg: T): T
 
@@ -19,10 +19,10 @@ interface TrigonometricOperations<T> : Field<T> {
     fun ctg(arg: T): T = cos(arg) / sin(arg)
 }
 
-fun <T : FieldElement<T, out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
-fun <T : FieldElement<T, out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
-fun <T : FieldElement<T, out TrigonometricOperations<T>>> tg(arg: T): T = arg.context.tg(arg)
-fun <T : FieldElement<T, out TrigonometricOperations<T>>> ctg(arg: T): T = arg.context.ctg(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> tg(arg: T): T = arg.context.tg(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> ctg(arg: T): T = arg.context.ctg(arg)
 
 /* Power and roots */
 
@@ -30,12 +30,13 @@ fun <T : FieldElement<T, out TrigonometricOperations<T>>> ctg(arg: T): T = arg.c
  * A context extension to include power operations like square roots, etc
  */
 interface PowerOperations<T> {
-    fun power(arg: T, pow: Double): T
+    fun power(arg: T, pow: Number): T
+    fun sqrt(arg: T) = power(arg, 0.5)
 }
 
-infix fun <T : MathElement<T, out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
-fun <T : MathElement<T, out PowerOperations<T>>> sqrt(arg: T): T = arg pow 0.5
-fun <T : MathElement<T, out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
+infix fun <T : MathElement<out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
+fun <T : MathElement<out PowerOperations<T>>> sqrt(arg: T): T = arg pow 0.5
+fun <T : MathElement<out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
 
 /* Exponential */
 
@@ -44,11 +45,11 @@ interface ExponentialOperations<T> {
     fun ln(arg: T): T
 }
 
-fun <T : MathElement<T, out ExponentialOperations<T>>> exp(arg: T): T = arg.context.exp(arg)
-fun <T : MathElement<T, out ExponentialOperations<T>>> ln(arg: T): T = arg.context.ln(arg)
+fun <T : MathElement<out ExponentialOperations<T>>> exp(arg: T): T = arg.context.exp(arg)
+fun <T : MathElement<out ExponentialOperations<T>>> ln(arg: T): T = arg.context.ln(arg)
 
-interface Norm<in T, out R> {
+interface Norm<in T: Any, out R> {
     fun norm(arg: T): R
 }
 
-fun <T : MathElement<T, out Norm<T, R>>, R> norm(arg: T): R = arg.context.norm(arg)
+fun <T : MathElement<out Norm<T, R>>, R> norm(arg: T): R = arg.context.norm(arg)

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

@@ -0,0 +1,73 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.FieldElement
+
+
+class BoxingNDField<T, F : Field<T>>(
+    override val shape: IntArray,
+    override val elementContext: F,
+    val bufferFactory: BufferFactory<T>
+) : BufferedNDField<T, F> {
+
+    override val strides: Strides = DefaultStrides(shape)
+
+    fun buildBuffer(size: Int, initializer: (Int) -> T): Buffer<T> =
+        bufferFactory(size, initializer)
+
+    override fun check(vararg elements: NDBuffer<T>) {
+        if (!elements.all { it.strides == this.strides }) error("Element strides are not the same as context strides")
+    }
+
+    override val zero by lazy { produce { zero } }
+    override val one by lazy { produce { one } }
+
+    override fun produce(initializer: F.(IntArray) -> T) =
+        BufferedNDFieldElement(
+            this,
+            buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) })
+
+    override fun map(arg: NDBuffer<T>, transform: F.(T) -> T): BufferedNDFieldElement<T, F> {
+        check(arg)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(arg.strides.linearSize) { offset -> elementContext.transform(arg.buffer[offset]) })
+
+//        val buffer = arg.buffer.transform { _, value -> elementContext.transform(value) }
+//        return BufferedNDFieldElement(this, buffer)
+
+    }
+
+    override fun mapIndexed(
+        arg: NDBuffer<T>,
+        transform: F.(index: IntArray, T) -> T
+    ): BufferedNDFieldElement<T, F> {
+        check(arg)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(arg.strides.linearSize) { offset ->
+                elementContext.transform(
+                    arg.strides.index(offset),
+                    arg.buffer[offset]
+                )
+            })
+
+//        val buffer =
+//            arg.buffer.transform { offset, value -> elementContext.transform(arg.strides.index(offset), value) }
+//        return BufferedNDFieldElement(this, buffer)
+    }
+
+    override fun combine(
+        a: NDBuffer<T>,
+        b: NDBuffer<T>,
+        transform: F.(T, T) -> T
+    ): BufferedNDFieldElement<T, F> {
+        check(a, b)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
+    }
+
+    override fun NDBuffer<T>.toElement(): FieldElement<NDBuffer<T>, *, out BufferedNDField<T, F>> =
+        BufferedNDFieldElement(this@BoxingNDField, buffer)
+}

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

@@ -0,0 +1,43 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.*
+
+interface BufferedNDAlgebra<T, C>: NDAlgebra<T, C, NDBuffer<T>>{
+    val strides: Strides
+
+    override fun check(vararg elements: NDBuffer<T>) {
+        if (!elements.all { it.strides == this.strides }) error("Strides mismatch")
+    }
+
+    /**
+     * Convert any [NDStructure] to buffered structure using strides from this context.
+     * If the structure is already [NDBuffer], conversion is free. If not, it could be expensive because iteration over indexes
+     *
+     * If the argument is [NDBuffer] with different strides structure, the new element will be produced.
+     */
+    fun NDStructure<T>.toBuffer(): NDBuffer<T> {
+        return if (this is NDBuffer<T> && this.strides == this@BufferedNDAlgebra.strides) {
+            this
+        } else {
+            produce { index -> get(index) }
+        }
+    }
+
+    /**
+     * Convert a buffer to element of this algebra
+     */
+    fun NDBuffer<T>.toElement(): MathElement<out BufferedNDAlgebra<T, C>>
+}
+
+
+interface BufferedNDSpace<T, S : Space<T>> : NDSpace<T, S, NDBuffer<T>>, BufferedNDAlgebra<T,S>  {
+    override fun NDBuffer<T>.toElement(): SpaceElement<NDBuffer<T>, *, out BufferedNDSpace<T, S>>
+}
+
+interface BufferedNDRing<T, R : Ring<T>> : NDRing<T, R, NDBuffer<T>>, BufferedNDSpace<T, R> {
+    override fun NDBuffer<T>.toElement(): RingElement<NDBuffer<T>, *, out BufferedNDRing<T, R>>
+}
+
+interface BufferedNDField<T, F : Field<T>> : NDField<T, F, NDBuffer<T>>, BufferedNDRing<T, F> {
+    override fun NDBuffer<T>.toElement(): FieldElement<NDBuffer<T>, *, out BufferedNDField<T, F>>
+}

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

@@ -0,0 +1,88 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.*
+
+/**
+ * Base interface for an element with context, containing strides
+ */
+interface BufferedNDElement<T, C> : NDBuffer<T>, NDElement<T, C, NDBuffer<T>> {
+    override val context: BufferedNDAlgebra<T, C>
+
+    override val strides get() = context.strides
+
+    override val shape: IntArray get() = context.shape
+}
+
+class BufferedNDSpaceElement<T, S : Space<T>>(
+    override val context: BufferedNDSpace<T, S>,
+    override val buffer: Buffer<T>
+) : BufferedNDElement<T, S>, SpaceElement<NDBuffer<T>, BufferedNDSpaceElement<T, S>, BufferedNDSpace<T, S>> {
+
+    override fun unwrap(): NDBuffer<T> = this
+
+    override fun NDBuffer<T>.wrap(): BufferedNDSpaceElement<T, S> {
+        context.check(this)
+        return BufferedNDSpaceElement(context, buffer)
+    }
+}
+
+class BufferedNDRingElement<T, R : Ring<T>>(
+    override val context: BufferedNDRing<T, R>,
+    override val buffer: Buffer<T>
+) : BufferedNDElement<T, R>, RingElement<NDBuffer<T>, BufferedNDRingElement<T, R>, BufferedNDRing<T, R>> {
+
+    override fun unwrap(): NDBuffer<T> = this
+
+    override fun NDBuffer<T>.wrap(): BufferedNDRingElement<T, R> {
+        context.check(this)
+        return BufferedNDRingElement(context, buffer)
+    }
+}
+
+class BufferedNDFieldElement<T, F : Field<T>>(
+    override val context: BufferedNDField<T, F>,
+    override val buffer: Buffer<T>
+) : BufferedNDElement<T, F>, FieldElement<NDBuffer<T>, BufferedNDFieldElement<T, F>, BufferedNDField<T, F>> {
+
+    override fun unwrap(): NDBuffer<T> = this
+
+    override fun NDBuffer<T>.wrap(): BufferedNDFieldElement<T, F> {
+        context.check(this)
+        return BufferedNDFieldElement(context, buffer)
+    }
+}
+
+
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy
+ */
+operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferedNDElement<T, F>) =
+    ndElement.context.run { map(ndElement) { invoke(it) }.toElement() }
+
+/* plus and minus */
+
+/**
+ * Summation operation for [BufferedNDElement] and single element
+ */
+operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.plus(arg: T) =
+    context.map(this) { it + arg }.wrap()
+
+/**
+ * Subtraction operation between [BufferedNDElement] and single element
+ */
+operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.minus(arg: T) =
+    context.map(this) { it - arg }.wrap()
+
+/* prod and div */
+
+/**
+ * Product operation for [BufferedNDElement] and single element
+ */
+operator fun <T : Any, F : Ring<T>> BufferedNDElement<T, F>.times(arg: T) =
+    context.map(this) { it * arg }.wrap()
+
+/**
+ * Division operation between [BufferedNDElement] and single element
+ */
+operator fun <T : Any, F : Field<T>> BufferedNDElement<T, F>.div(arg: T) =
+    context.map(this) { it / arg }.wrap()

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

@@ -1,20 +1,70 @@
 package scientifik.kmath.structures
 
 
+typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
+typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
+
+
 /**
  * A generic random access structure for both primitives and objects
  */
 interface Buffer<T> {
 
+    /**
+     * The size of the buffer
+     */
     val size: Int
 
+    /**
+     * Get element at given index
+     */
     operator fun get(index: Int): T
 
+    /**
+     * Iterate over all elements
+     */
     operator fun iterator(): Iterator<T>
+
+    /**
+     * Check content eqiality with another buffer
+     */
+    fun contentEquals(other: Buffer<*>): Boolean =
+        asSequence().mapIndexed { index, value -> value == other[index] }.all { it }
+
+    companion object {
+
+        /**
+         * Create a boxing buffer of given type
+         */
+        inline fun <T> boxing(size: Int, initializer: (Int) -> T): Buffer<T> = ListBuffer(List(size, initializer))
+
+        /**
+         * Create most appropriate immutable buffer for given type avoiding boxing wherever possible
+         */
+        @Suppress("UNCHECKED_CAST")
+        inline fun <reified T : Any> auto(size: Int, crossinline initializer: (Int) -> T): Buffer<T> {
+            return when (T::class) {
+                Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as Buffer<T>
+                Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as Buffer<T>
+                Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as Buffer<T>
+                Long::class -> LongBuffer(LongArray(size) { initializer(it) as Long }) as Buffer<T>
+                else -> boxing(size, initializer)
+            }
+        }
+
+        val DoubleBufferFactory: BufferFactory<Double> =
+            { size, initializer -> DoubleBuffer(DoubleArray(size, initializer)) }
+        val ShortBufferFactory: BufferFactory<Short> =
+            { size, initializer -> ShortBuffer(ShortArray(size, initializer)) }
+        val IntBufferFactory: BufferFactory<Int> = { size, initializer -> IntBuffer(IntArray(size, initializer)) }
+        val LongBufferFactory: BufferFactory<Long> = { size, initializer -> LongBuffer(LongArray(size, initializer)) }
+    }
 }
 
 fun <T> Buffer<T>.asSequence(): Sequence<T> = iterator().asSequence()
 
+fun <T> Buffer<T>.asIterable(): Iterable<T> = iterator().asSequence().asIterable()
+
 interface MutableBuffer<T> : Buffer<T> {
     operator fun set(index: Int, value: T)
 
@@ -22,10 +72,32 @@ interface MutableBuffer<T> : Buffer<T> {
      * A shallow copy of the buffer
      */
     fun copy(): MutableBuffer<T>
+
+    companion object {
+        /**
+         * Create a boxing mutable buffer of given type
+         */
+        inline fun <T> boxing(size: Int, initializer: (Int) -> T): MutableBuffer<T> =
+            MutableListBuffer(MutableList(size, initializer))
+
+        /**
+         * Create most appropriate mutable buffer for given type avoiding boxing wherever possible
+         */
+        @Suppress("UNCHECKED_CAST")
+        inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): MutableBuffer<T> {
+            return when (T::class) {
+                Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as MutableBuffer<T>
+                Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as MutableBuffer<T>
+                Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as MutableBuffer<T>
+                Long::class -> LongBuffer(LongArray(size) { initializer(it) as Long }) as MutableBuffer<T>
+                else -> boxing(size, initializer)
+            }
+        }
+    }
 }
 
 
-inline class ListBuffer<T>(private val list: List<T>) : Buffer<T> {
+inline class ListBuffer<T>(val list: List<T>) : Buffer<T> {
 
     override val size: Int
         get() = list.size
@@ -35,7 +107,12 @@ inline class ListBuffer<T>(private val list: List<T>) : Buffer<T> {
     override fun iterator(): Iterator<T> = list.iterator()
 }
 
-inline class MutableListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T> {
+fun <T> List<T>.asBuffer() = ListBuffer(this)
+
+@Suppress("FunctionName")
+inline fun <T> ListBuffer(size: Int, init: (Int) -> T) = List(size, init).asBuffer()
+
+inline class MutableListBuffer<T>(val list: MutableList<T>) : MutableBuffer<T> {
 
     override val size: Int
         get() = list.size
@@ -47,12 +124,11 @@ inline class MutableListBuffer<T>(private val list: MutableList<T>) : MutableBuf
     }
 
     override fun iterator(): Iterator<T> = list.iterator()
-
     override fun copy(): MutableBuffer<T> = MutableListBuffer(ArrayList(list))
 }
 
 class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
-    //Can't inline because array invariant
+    //Can't inline because array is invariant
     override val size: Int
         get() = array.size
 
@@ -67,9 +143,10 @@ class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
     override fun copy(): MutableBuffer<T> = ArrayBuffer(array.copyOf())
 }
 
-inline class DoubleBuffer(private val array: DoubleArray) : MutableBuffer<Double> {
-    override val size: Int
-        get() = array.size
+fun <T> Array<T>.asBuffer() = ArrayBuffer(this)
+
+inline class DoubleBuffer(val array: DoubleArray) : MutableBuffer<Double> {
+    override val size: Int get() = array.size
 
     override fun get(index: Int): Double = array[index]
 
@@ -77,14 +154,45 @@ inline class DoubleBuffer(private val array: DoubleArray) : MutableBuffer<Double
         array[index] = value
     }
 
-    override fun iterator(): Iterator<Double> = array.iterator()
+    override fun iterator() = array.iterator()
 
     override fun copy(): MutableBuffer<Double> = DoubleBuffer(array.copyOf())
 }
 
-inline class IntBuffer(private val array: IntArray) : MutableBuffer<Int> {
-    override val size: Int
-        get() = array.size
+@Suppress("FunctionName")
+inline fun DoubleBuffer(size: Int, init: (Int) -> Double) = DoubleBuffer(DoubleArray(size) { init(it) })
+
+/**
+ * Transform buffer of doubles into array for high performance operations
+ */
+val Buffer<out Double>.array: DoubleArray
+    get() = if (this is DoubleBuffer) {
+        array
+    } else {
+        DoubleArray(size) { get(it) }
+    }
+
+fun DoubleArray.asBuffer() = DoubleBuffer(this)
+
+inline class ShortBuffer(val array: ShortArray) : MutableBuffer<Short> {
+    override val size: Int get() = array.size
+
+    override fun get(index: Int): Short = array[index]
+
+    override fun set(index: Int, value: Short) {
+        array[index] = value
+    }
+
+    override fun iterator() = array.iterator()
+
+    override fun copy(): MutableBuffer<Short> = ShortBuffer(array.copyOf())
+
+}
+
+fun ShortArray.asBuffer() = ShortBuffer(this)
+
+inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
+    override val size: Int get() = array.size
 
     override fun get(index: Int): Int = array[index]
 
@@ -92,17 +200,55 @@ inline class IntBuffer(private val array: IntArray) : MutableBuffer<Int> {
         array[index] = value
     }
 
-    override fun iterator(): Iterator<Int> = array.iterator()
+    override fun iterator() = array.iterator()
 
     override fun copy(): MutableBuffer<Int> = IntBuffer(array.copyOf())
+
 }
 
-inline class ReadOnlyBuffer<T>(private val buffer: MutableBuffer<T>) : Buffer<T> {
+fun IntArray.asBuffer() = IntBuffer(this)
+
+inline class LongBuffer(val array: LongArray) : MutableBuffer<Long> {
+    override val size: Int get() = array.size
+
+    override fun get(index: Int): Long = array[index]
+
+    override fun set(index: Int, value: Long) {
+        array[index] = value
+    }
+
+    override fun iterator() = array.iterator()
+
+    override fun copy(): MutableBuffer<Long> = LongBuffer(array.copyOf())
+
+}
+
+fun LongArray.asBuffer() = LongBuffer(this)
+
+inline class ReadOnlyBuffer<T>(val buffer: MutableBuffer<T>) : Buffer<T> {
     override val size: Int get() = buffer.size
 
     override fun get(index: Int): T = buffer.get(index)
 
-    override fun iterator(): Iterator<T> = buffer.iterator()
+    override fun iterator() = buffer.iterator()
+}
+
+/**
+ * A buffer with content calculated on-demand. The calculated contect is not stored, so it is recalculated on each call.
+ * Useful when one needs single element from the buffer.
+ */
+class VirtualBuffer<T>(override val size: Int, private val generator: (Int) -> T) : Buffer<T> {
+    override fun get(index: Int): T = generator(index)
+
+    override fun iterator(): Iterator<T> = (0 until size).asSequence().map(generator).iterator()
+
+    override fun contentEquals(other: Buffer<*>): Boolean {
+        return if (other is VirtualBuffer) {
+            this.size == other.size && this.generator == other.generator
+        } else {
+            super.contentEquals(other)
+        }
+    }
 }
 
 /**
@@ -115,25 +261,6 @@ fun <T> Buffer<T>.asReadOnly(): Buffer<T> = if (this is MutableBuffer) {
 }
 
 /**
- * Create most appropriate immutable buffer for given type avoiding boxing wherever possible
+ * Typealias for buffer transformations
  */
-@Suppress("UNCHECKED_CAST")
-inline fun <reified T : Any> buffer(size: Int, noinline initializer: (Int) -> T): Buffer<T> {
-    return when (T::class) {
-        Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as Buffer<T>
-        Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as Buffer<T>
-        else -> ArrayBuffer(Array(size, initializer))
-    }
-}
-
-/**
- * Create most appropriate mutable buffer for given type avoiding boxing wherever possible
- */
-@Suppress("UNCHECKED_CAST")
-inline fun <reified T : Any> mutableBuffer(size: Int, noinline initializer: (Int) -> T): MutableBuffer<T> {
-    return when (T::class) {
-        Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as MutableBuffer<T>
-        Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as MutableBuffer<T>
-        else -> ArrayBuffer(Array(size, initializer))
-    }
-}
+typealias BufferTransform<T, R> = (Buffer<T>) -> Buffer<R>

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

@@ -0,0 +1,134 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.Complex
+import scientifik.kmath.operations.ComplexField
+import scientifik.kmath.operations.FieldElement
+import scientifik.kmath.operations.complex
+
+typealias ComplexNDElement = BufferedNDFieldElement<Complex, ComplexField>
+
+/**
+ * An optimized nd-field for complex numbers
+ */
+class ComplexNDField(override val shape: IntArray) :
+    BufferedNDField<Complex, ComplexField>,
+    ExtendedNDField<Complex, ComplexField, NDBuffer<Complex>> {
+
+    override val strides: Strides = DefaultStrides(shape)
+
+    override val elementContext: ComplexField get() = ComplexField
+    override val zero by lazy { produce { zero } }
+    override val one by lazy { produce { one } }
+
+    inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Complex): Buffer<Complex> =
+        Buffer.complex(size) { initializer(it) }
+
+    /**
+     * Inline transform an NDStructure to another structure
+     */
+    override fun map(
+        arg: NDBuffer<Complex>,
+        transform: ComplexField.(Complex) -> Complex
+    ): ComplexNDElement {
+        check(arg)
+        val array = buildBuffer(arg.strides.linearSize) { offset -> ComplexField.transform(arg.buffer[offset]) }
+        return BufferedNDFieldElement(this, array)
+    }
+
+    override fun produce(initializer: ComplexField.(IntArray) -> Complex): ComplexNDElement {
+        val array = buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
+        return BufferedNDFieldElement(this, array)
+    }
+
+    override fun mapIndexed(
+        arg: NDBuffer<Complex>,
+        transform: ComplexField.(index: IntArray, Complex) -> Complex
+    ): ComplexNDElement {
+        check(arg)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(arg.strides.linearSize) { offset ->
+                elementContext.transform(
+                    arg.strides.index(offset),
+                    arg.buffer[offset]
+                )
+            })
+    }
+
+    override fun combine(
+        a: NDBuffer<Complex>,
+        b: NDBuffer<Complex>,
+        transform: ComplexField.(Complex, Complex) -> Complex
+    ): ComplexNDElement {
+        check(a, b)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
+    }
+
+    override fun NDBuffer<Complex>.toElement(): FieldElement<NDBuffer<Complex>, *, out BufferedNDField<Complex, ComplexField>> =
+        BufferedNDFieldElement(this@ComplexNDField, buffer)
+
+    override fun power(arg: NDBuffer<Complex>, pow: Number) = map(arg) { power(it, pow) }
+
+    override fun exp(arg: NDBuffer<Complex>) = map(arg) { exp(it) }
+
+    override fun ln(arg: NDBuffer<Complex>) = map(arg) { ln(it) }
+
+    override fun sin(arg: NDBuffer<Complex>) = map(arg) { sin(it) }
+
+    override fun cos(arg: NDBuffer<Complex>) = map(arg) { cos(it) }
+
+}
+
+
+/**
+ * Fast element production using function inlining
+ */
+inline fun BufferedNDField<Complex, ComplexField>.produceInline(crossinline initializer: ComplexField.(Int) -> Complex): ComplexNDElement {
+    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.initializer(offset) }
+    return BufferedNDFieldElement(this, buffer)
+}
+
+/**
+ * Map one [ComplexNDElement] using function with indexes
+ */
+inline fun ComplexNDElement.mapIndexed(crossinline transform: ComplexField.(index: IntArray, Complex) -> Complex) =
+    context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
+
+/**
+ * Map one [ComplexNDElement] using function without indexes
+ */
+inline fun ComplexNDElement.map(crossinline transform: ComplexField.(Complex) -> Complex): ComplexNDElement {
+    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.transform(buffer[offset]) }
+    return BufferedNDFieldElement(context, buffer)
+}
+
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy
+ */
+operator fun Function1<Complex, Complex>.invoke(ndElement: ComplexNDElement) =
+    ndElement.map { this@invoke(it) }
+
+
+/* plus and minus */
+
+/**
+ * Summation operation for [BufferedNDElement] and single element
+ */
+operator fun ComplexNDElement.plus(arg: Complex) =
+    map { it + arg }
+
+/**
+ * Subtraction operation between [BufferedNDElement] and single element
+ */
+operator fun ComplexNDElement.minus(arg: Complex) =
+    map { it - arg }
+
+operator fun ComplexNDElement.plus(arg: Double) =
+    map { it + arg }
+
+operator fun ComplexNDElement.minus(arg: Double) =
+    map { it - arg }
+
+fun NDField.Companion.complex(vararg shape: Int) = ComplexNDField(shape)

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

@@ -1,42 +1,46 @@
 package scientifik.kmath.structures
 
-import scientifik.kmath.operations.ExponentialOperations
-import scientifik.kmath.operations.ExtendedField
-import scientifik.kmath.operations.PowerOperations
-import scientifik.kmath.operations.TrigonometricOperations
+import scientifik.kmath.operations.*
 
 
-/**
- * NDField that supports [ExtendedField] operations on its elements
- */
-class ExtendedNDField<N : Any, F : ExtendedField<N>>(shape: IntArray, field: F) : NDField<N, F>(shape, field),
-        TrigonometricOperations<NDElement<N, F>>,
-        PowerOperations<NDElement<N, F>>,
-        ExponentialOperations<NDElement<N, F>> {
-
-    override fun produceStructure(initializer: F.(IntArray) -> N): NDStructure<N> {
-        return genericNdStructure(shape) { field.initializer(it) }
-    }
-
-    override fun power(arg: NDElement<N, F>, pow: Double): NDElement<N, F> {
-        return arg.transform { d -> with(field) { power(d, pow) } }
-    }
-
-    override fun exp(arg: NDElement<N, F>): NDElement<N, F> {
-        return arg.transform { d -> with(field) { exp(d) } }
-    }
-
-    override fun ln(arg: NDElement<N, F>): NDElement<N, F> {
-        return arg.transform { d -> with(field) { ln(d) } }
-    }
-
-    override fun sin(arg: NDElement<N, F>): NDElement<N, F> {
-        return arg.transform { d -> with(field) { sin(d) } }
-    }
-
-    override fun cos(arg: NDElement<N, F>): NDElement<N, F> {
-        return arg.transform { d -> with(field) { cos(d) } }
-    }
-}
+interface ExtendedNDField<T : Any, F, N : NDStructure<T>> :
+    NDField<T, F, N>,
+    TrigonometricOperations<N>,
+    PowerOperations<N>,
+    ExponentialOperations<N>
+        where F : ExtendedFieldOperations<T>, F : Field<T>
+
+
+///**
+// * NDField that supports [ExtendedField] operations on its elements
+// */
+//class ExtendedNDFieldWrapper<T : Any, F : ExtendedField<T>, N : NDStructure<T>>(private val ndField: NDField<T, F, N>) :
+//    ExtendedNDField<T, F, N>, NDField<T, F, N> by ndField {
+//
+//    override val shape: IntArray get() = ndField.shape
+//    override val elementContext: F get() = ndField.elementContext
+//
+//    override fun produce(initializer: F.(IntArray) -> T) = ndField.produce(initializer)
+//
+//    override fun power(arg: N, pow: Double): N {
+//        return produce { with(elementContext) { power(arg[it], pow) } }
+//    }
+//
+//    override fun exp(arg: N): N {
+//        return produce { with(elementContext) { exp(arg[it]) } }
+//    }
+//
+//    override fun ln(arg: N): N {
+//        return produce { with(elementContext) { ln(arg[it]) } }
+//    }
+//
+//    override fun sin(arg: N): N {
+//        return produce { with(elementContext) { sin(arg[it]) } }
+//    }
+//
+//    override fun cos(arg: N): N {
+//        return produce { with(elementContext) { cos(arg[it]) } }
+//    }
+//}
 
 

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

@@ -1,20 +0,0 @@
-package scientifik.kmath.structures
-
-//
-//class LazyStructureField<T: Any>(val field: Field<T>): Field<LazyStructure<T>>{
-//
-//}
-//
-//class LazyStructure<T : Any> : NDStructure<T> {
-//
-//    override val shape: IntArray
-//        get() = TODO("not implemented") //To change initializer of created properties use File | Settings | File Templates.
-//
-//    override fun get(index: IntArray): T {
-//        TODO("not implemented") //To change body of created functions use File | Settings | File Templates.
-//    }
-//
-//    override fun iterator(): Iterator<Pair<IntArray, T>> {
-//        TODO("not implemented") //To change body of created functions use File | Settings | File Templates.
-//    }
-//}

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

@@ -0,0 +1,144 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.operations.Space
+import kotlin.jvm.JvmName
+
+
+/**
+ * An exception is thrown when the expected ans actual shape of NDArray differs
+ */
+class ShapeMismatchException(val expected: IntArray, val actual: IntArray) : RuntimeException()
+
+
+/**
+ * The base interface for all nd-algebra implementations
+ * @param T the type of nd-structure element
+ * @param C the type of the element context
+ * @param N the type of the structure
+ */
+interface NDAlgebra<T, C, N : NDStructure<T>> {
+    val shape: IntArray
+    val elementContext: C
+
+    /**
+     * Produce a new [N] structure using given initializer function
+     */
+    fun produce(initializer: C.(IntArray) -> T): N
+
+    /**
+     * Map elements from one structure to another one
+     */
+    fun map(arg: N, transform: C.(T) -> T): N
+
+    /**
+     * Map indexed elements
+     */
+    fun mapIndexed(arg: N, transform: C.(index: IntArray, T) -> T): N
+
+    /**
+     * Combine two structures into one
+     */
+    fun combine(a: N, b: N, transform: C.(T, T) -> T): N
+
+    /**
+     * Check if given elements are consistent with this context
+     */
+    fun check(vararg elements: N) {
+        elements.forEach {
+            if (!shape.contentEquals(it.shape)) {
+                throw ShapeMismatchException(shape, it.shape)
+            }
+        }
+    }
+
+    /**
+     * element-by-element invoke a function working on [T] on a [NDStructure]
+     */
+    operator fun Function1<T, T>.invoke(structure: N) = map(structure) { value -> this@invoke(value) }
+}
+
+/**
+ * An nd-space over element space
+ */
+interface NDSpace<T, S : Space<T>, N : NDStructure<T>> : Space<N>, NDAlgebra<T, S, N> {
+    /**
+     * Element-by-element addition
+     */
+    override fun add(a: N, b: N): N = combine(a, b) { aValue, bValue -> add(aValue, bValue) }
+
+    /**
+     * Multiply all elements by constant
+     */
+    override fun multiply(a: N, k: Number): N = map(a) { multiply(it, k) }
+
+    operator fun N.plus(arg: T) = map(this) { value -> add(arg, value) }
+    operator fun N.minus(arg: T) = map(this) { value -> add(arg, -value) }
+
+    operator fun T.plus(arg: N) = map(arg) { value -> add(this@plus, value) }
+    operator fun T.minus(arg: N) = map(arg) { value -> add(-this@minus, value) }
+}
+
+/**
+ * An nd-ring over element ring
+ */
+interface NDRing<T, R : Ring<T>, N : NDStructure<T>> : Ring<N>, NDSpace<T, R, N> {
+
+    /**
+     * Element-by-element multiplication
+     */
+    override fun multiply(a: N, b: N): N = combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
+
+    operator fun N.times(arg: T) = map(this) { value -> multiply(arg, value) }
+    operator fun T.times(arg: N) = map(arg) { value -> multiply(this@times, value) }
+}
+
+/**
+ * Field for n-dimensional structures.
+ * @param shape - the list of dimensions of the array
+ * @param elementField - operations field defined on individual array element
+ * @param T - the type of the element contained in ND structure
+ * @param F - field of structure elements
+ * @param R - actual nd-element type of this field
+ */
+interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F, N> {
+
+    /**
+     * Element-by-element division
+     */
+    override fun divide(a: N, b: N): N = combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
+
+    operator fun N.div(arg: T) = map(this) { value -> divide(arg, value) }
+    operator fun T.div(arg: N) = map(arg) { divide(it, this@div) }
+
+    companion object {
+
+        private val realNDFieldCache = HashMap<IntArray, RealNDField>()
+
+        /**
+         * Create a nd-field for [Double] values or pull it from cache if it was created previously
+         */
+        fun real(vararg shape: Int) = realNDFieldCache.getOrPut(shape) { RealNDField(shape) }
+
+        /**
+         * Create a nd-field with boxing generic buffer
+         */
+        fun <T : Any, F : Field<T>> buffered(
+            shape: IntArray,
+            field: F,
+            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing
+        ) =
+            BoxingNDField(shape, field, bufferFactory)
+
+        /**
+         * Create a most suitable implementation for nd-field using reified class.
+         */
+        @Suppress("UNCHECKED_CAST")
+        inline fun <reified T : Any, F : Field<T>> auto(field: F, vararg shape: Int): BufferedNDField<T, F> =
+            when {
+                T::class == Double::class -> real(*shape) as BufferedNDField<T, F>
+                else -> BoxingNDField(shape, field, Buffer.Companion::auto)
+            }
+    }
+}

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

@@ -0,0 +1,132 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.RealField
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.operations.Space
+
+/**
+ * The root for all [NDStructure] based algebra elements. Does not implement algebra element root because of problems with recursive self-types
+ * @param T  the type of the element of the structure
+ * @param C the type of the context for the element
+ * @param N the type of the underlying [NDStructure]
+ */
+interface NDElement<T, C, N : NDStructure<T>> : NDStructure<T> {
+
+    val context: NDAlgebra<T, C, N>
+
+    fun unwrap(): N
+
+    fun N.wrap(): NDElement<T, C, N>
+
+    companion object {
+        /**
+         * Create a optimized NDArray of doubles
+         */
+        fun real(shape: IntArray, initializer: RealField.(IntArray) -> Double = { 0.0 }) =
+            NDField.real(*shape).produce(initializer)
+
+
+        fun real1D(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }) =
+            real(intArrayOf(dim)) { initializer(it[0]) }
+
+
+        fun real2D(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }) =
+            real(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
+
+        fun real3D(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }) =
+            real(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
+
+
+        /**
+         * Simple boxing NDArray
+         */
+        fun <T : Any, F : Field<T>> buffered(
+            shape: IntArray,
+            field: F,
+            initializer: F.(IntArray) -> T
+        ): BufferedNDElement<T, F> {
+            val ndField = BoxingNDField(shape, field, Buffer.Companion::boxing)
+            return ndField.produce(initializer)
+        }
+
+        inline fun <reified T : Any, F : Field<T>> auto(
+            shape: IntArray,
+            field: F,
+            noinline initializer: F.(IntArray) -> T
+        ): BufferedNDFieldElement<T, F> {
+            val ndField = NDField.auto(field, *shape)
+            return BufferedNDFieldElement(ndField, ndField.produce(initializer).buffer)
+        }
+    }
+}
+
+
+fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.mapIndexed(transform: C.(index: IntArray, T) -> T) =
+    context.mapIndexed(unwrap(), transform).wrap()
+
+fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.map(transform: C.(T) -> T) = context.map(unwrap(), transform).wrap()
+
+
+/**
+ * Element by element application of any operation on elements to the whole [NDElement]
+ */
+operator fun <T, C, N : NDStructure<T>> Function1<T, T>.invoke(ndElement: NDElement<T, C, N>) =
+    ndElement.map { value -> this@invoke(value) }
+
+/* plus and minus */
+
+/**
+ * Summation operation for [NDElement] and single element
+ */
+operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.plus(arg: T) =
+    map { value -> arg + value }
+
+/**
+ * Subtraction operation between [NDElement] and single element
+ */
+operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.minus(arg: T) =
+    map { value -> arg - value }
+
+/* prod and div */
+
+/**
+ * Product operation for [NDElement] and single element
+ */
+operator fun <T, R : Ring<T>, N : NDStructure<T>> NDElement<T, R, N>.times(arg: T) =
+    map { value -> arg * value }
+
+/**
+ * Division operation between [NDElement] and single element
+ */
+operator fun <T, F : Field<T>, N : NDStructure<T>> NDElement<T, F, N>.div(arg: T) =
+    map { value -> arg / value }
+
+
+//    /**
+//     * Reverse sum operation
+//     */
+//    operator fun T.plus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@plus + arg[index] }
+//    }
+//
+//    /**
+//     * Reverse minus operation
+//     */
+//    operator fun T.minus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@minus - arg[index] }
+//    }
+//
+//    /**
+//     * Reverse product operation
+//     */
+//    operator fun T.times(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@times * arg[index] }
+//    }
+//
+//    /**
+//     * Reverse division operation
+//     */
+//    operator fun T.div(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@div / arg[index] }
+//    }

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

@@ -1,209 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.operations.Field
-import scientifik.kmath.operations.FieldElement
-
-/**
- * An exception is thrown when the expected ans actual shape of NDArray differs
- */
-class ShapeMismatchException(val expected: IntArray, val actual: IntArray) : RuntimeException()
-
-/**
- * Field for n-dimensional arrays.
- * @param shape - the list of dimensions of the array
- * @param field - operations field defined on individual array element
- * @param T the type of the element contained in NDArray
- */
-abstract class NDField<T, F : Field<T>>(val shape: IntArray, val field: F) : Field<NDElement<T, F>> {
-
-    abstract fun produceStructure(initializer: F.(IntArray) -> T): NDStructure<T>
-
-    /**
-     * Create new instance of NDArray using field shape and given initializer
-     * The producer takes list of indices as argument and returns contained value
-     */
-    fun produce(initializer: F.(IntArray) -> T): NDElement<T, F> = NDStructureElement(this, produceStructure(initializer))
-
-    override val zero: NDElement<T, F> by lazy {
-        produce { zero }
-    }
-
-    /**
-     * Check the shape of given NDArray and throw exception if it does not coincide with shape of the field
-     */
-    private fun checkShape(vararg elements: NDElement<T, F>) {
-        elements.forEach {
-            if (!shape.contentEquals(it.shape)) {
-                throw ShapeMismatchException(shape, it.shape)
-            }
-        }
-    }
-
-    /**
-     * Element-by-element addition
-     */
-    override fun add(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
-        checkShape(a, b)
-        return produce { with(field) { a[it] + b[it] } }
-    }
-
-    /**
-     * Multiply all elements by cinstant
-     */
-    override fun multiply(a: NDElement<T, F>, k: Double): NDElement<T, F> {
-        checkShape(a)
-        return produce { with(field) { a[it] * k } }
-    }
-
-    override val one: NDElement<T, F>
-        get() = produce { one }
-
-    /**
-     * Element-by-element multiplication
-     */
-    override fun multiply(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
-        checkShape(a)
-        return produce { with(field) { a[it] * b[it] } }
-    }
-
-    /**
-     * Element-by-element division
-     */
-    override fun divide(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
-        checkShape(a)
-        return produce { with(field) { a[it] / b[it] } }
-    }
-
-//    /**
-//     * Reverse sum operation
-//     */
-//    operator fun T.plus(arg: NDElement<T, F>): NDElement<T, F> = arg + this
-//
-//    /**
-//     * Reverse minus operation
-//     */
-//    operator fun T.minus(arg: NDElement<T, F>): NDElement<T, F> = arg.transformIndexed { _, value ->
-//        with(arg.context.field) {
-//            this@minus - value
-//        }
-//    }
-//
-//    /**
-//     * Reverse product operation
-//     */
-//    operator fun T.times(arg: NDElement<T, F>): NDElement<T, F> = arg * this
-//
-//    /**
-//     * Reverse division operation
-//     */
-//    operator fun T.div(arg: NDElement<T, F>): NDElement<T, F> = arg.transformIndexed { _, value ->
-//        with(arg.context.field) {
-//            this@div / value
-//        }
-//    }
-}
-
-
-interface NDElement<T, F : Field<T>>: FieldElement<NDElement<T, F>, NDField<T, F>>, NDStructure<T>
-
-inline fun <T, F : Field<T>> NDElement<T, F>.transformIndexed(crossinline action: F.(IntArray, T) -> T): NDElement<T, F> = context.produce { action(it, get(*it)) }
-inline fun <T, F : Field<T>> NDElement<T, F>.transform(crossinline action: F.(T) -> T): NDElement<T, F> = context.produce { action(get(*it)) }
-
-
-/**
- *  Read-only [NDStructure] coupled to the context.
- */
-class NDStructureElement<T, F : Field<T>>(override val context: NDField<T, F>, private val structure: NDStructure<T>) : NDElement<T,F>, NDStructure<T> by structure {
-
-    //TODO ensure structure is immutable
-
-    override val self: NDElement<T, F>  get() = this
-}
-
-/**
- * Element by element application of any operation on elements to the whole array. Just like in numpy
- */
-operator fun <T, F : Field<T>> Function1<T, T>.invoke(ndElement: NDElement<T, F>): NDElement<T, F> = ndElement.transform {value -> this@invoke(value) }
-
-/* plus and minus */
-
-/**
- * Summation operation for [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.plus(arg: T): NDElement<T, F> = transform {value ->
-    with(context.field) {
-        arg + value
-    }
-}
-
-/**
- * Subtraction operation between [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.minus(arg: T): NDElement<T, F> = transform {value ->
-    with(context.field) {
-        arg - value
-    }
-}
-
-/* prod and div */
-
-/**
- * Product operation for [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.times(arg: T): NDElement<T, F> = transform { value ->
-    with(context.field) {
-        arg * value
-    }
-}
-
-/**
- * Division operation between [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.div(arg: T): NDElement<T, F> = transform { value ->
-    with(context.field) {
-        arg / value
-    }
-}
-
-class GenericNDField<T : Any, F : Field<T>>(shape: IntArray, field: F) : NDField<T, F>(shape, field) {
-    override fun produceStructure(initializer: F.(IntArray) -> T): NDStructure<T> = genericNdStructure(shape) { field.initializer(it) }
-}
-
-//typealias NDFieldFactory<T> = (IntArray)->NDField<T>
-
-object NDArrays {
-    /**
-     * Create a platform-optimized NDArray of doubles
-     */
-    fun realNDArray(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
-        return ExtendedNDField(shape, DoubleField).produce(initializer)
-    }
-
-    fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
-        return realNDArray(intArrayOf(dim)) { initializer(it[0]) }
-    }
-
-    fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
-        return realNDArray(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
-    }
-
-    fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
-        return realNDArray(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
-    }
-
-    inline fun produceReal(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDElement<Double, DoubleField>) =
-            ExtendedNDField(shape, DoubleField).run(block)
-
-//    /**
-//     * Simple boxing NDField
-//     */
-//    fun <T : Any> fieldFactory(field: Field<T>): NDFieldFactory<T> = { shape -> GenericNDField(shape, field) }
-
-    /**
-     * Simple boxing NDArray
-     */
-    fun <T : Any, F : Field<T>> create(field: F, shape: IntArray, initializer: (IntArray) -> T): NDElement<T, F> {
-        return GenericNDField(shape, field).produce { initializer(it) }
-    }
-}

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

@@ -11,6 +11,45 @@ interface NDStructure<T> {
     operator fun get(index: IntArray): T
 
     fun elements(): Sequence<Pair<IntArray, T>>
+
+    companion object {
+        fun equals(st1: NDStructure<*>, st2: NDStructure<*>): Boolean {
+            return when {
+                st1 === st2 -> true
+                st1 is BufferNDStructure<*> && st2 is BufferNDStructure<*> && st1.strides == st2.strides -> st1.buffer.contentEquals(
+                    st2.buffer
+                )
+                else -> st1.elements().all { (index, value) -> value == st2[index] }
+            }
+        }
+
+        /**
+         * Create a NDStructure with explicit buffer factory
+         *
+         * Strides should be reused if possible
+         */
+        fun <T> build(
+            strides: Strides,
+            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
+            initializer: (IntArray) -> T
+        ) =
+            BufferNDStructure(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
+
+        /**
+         * Inline create NDStructure with non-boxing buffer implementation if it is possible
+         */
+        inline fun <reified T : Any> auto(strides: Strides, crossinline initializer: (IntArray) -> T) =
+            BufferNDStructure(strides, Buffer.auto(strides.linearSize) { i -> initializer(strides.index(i)) })
+
+        fun <T> build(
+            shape: IntArray,
+            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
+            initializer: (IntArray) -> T
+        ) = build(DefaultStrides(shape), bufferFactory, initializer)
+
+        inline fun <reified T : Any> auto(shape: IntArray, crossinline initializer: (IntArray) -> T) =
+            auto(DefaultStrides(shape), initializer)
+    }
 }
 
 operator fun <T> NDStructure<T>.get(vararg index: Int): T = get(index)
@@ -19,7 +58,7 @@ interface MutableNDStructure<T> : NDStructure<T> {
     operator fun set(index: IntArray, value: T)
 }
 
-fun <T> MutableNDStructure<T>.transformInPlace(action: (IntArray, T) -> T) {
+fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T) {
     elements().forEach { (index, oldValue) ->
         this[index] = action(index, oldValue)
     }
@@ -49,6 +88,9 @@ interface Strides {
      */
     fun index(offset: Int): IntArray
 
+    /**
+     * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides
+     */
     val linearSize: Int
 
     /**
@@ -60,7 +102,7 @@ interface Strides {
     }
 }
 
-class DefaultStrides(override val shape: IntArray) : Strides {
+class DefaultStrides private constructor(override val shape: IntArray) : Strides {
     /**
      * Strides for memory access
      */
@@ -77,7 +119,7 @@ class DefaultStrides(override val shape: IntArray) : Strides {
 
     override fun offset(index: IntArray): Int {
         return index.mapIndexed { i, value ->
-            if (value < 0 || value >= shape[i]) {
+            if (value < 0 || value >= this.shape[i]) {
                 throw RuntimeException("Index $value out of shape bounds: (0,${this.shape[i]})")
             }
             value * strides[i]
@@ -98,19 +140,40 @@ class DefaultStrides(override val shape: IntArray) : Strides {
 
     override val linearSize: Int
         get() = strides[shape.size]
+
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other !is DefaultStrides) return false
+
+        if (!shape.contentEquals(other.shape)) return false
+
+        return true
     }
 
-abstract class GenericNDStructure<T, B : Buffer<T>> : NDStructure<T> {
-    protected abstract val buffer: B
-    protected abstract val strides: Strides
+    override fun hashCode(): Int {
+        return shape.contentHashCode()
+    }
+
+    companion object {
+        private val defaultStridesCache = HashMap<IntArray, Strides>()
+
+        /**
+         * Cached builder for default strides
+         */
+        operator fun invoke(shape: IntArray): Strides = defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
+    }
+}
+
+interface NDBuffer<T> : NDStructure<T> {
+    val buffer: Buffer<T>
+    val strides: Strides
 
     override fun get(index: IntArray): T = buffer[strides.offset(index)]
 
-    override val shape: IntArray
-        get() = strides.shape
+    override val shape: IntArray get() = strides.shape
 
-    override fun elements()=
-            strides.indices().map { it to this[it] }
+    override fun elements() = strides.indices().map { it to this[it] }
 }
 
 /**
@@ -119,29 +182,58 @@ abstract class GenericNDStructure<T, B : Buffer<T>> : NDStructure<T> {
 class BufferNDStructure<T>(
     override val strides: Strides,
     override val buffer: Buffer<T>
-) : GenericNDStructure<T, Buffer<T>>() {
+) : NDBuffer<T> {
 
     init {
         if (strides.linearSize != buffer.size) {
             error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
         }
     }
+
+    override fun get(index: IntArray): T = buffer[strides.offset(index)]
+
+    override val shape: IntArray get() = strides.shape
+
+    override fun elements() = strides.indices().map { it to this[it] }
+
+    override fun equals(other: Any?): Boolean {
+        return when {
+            this === other -> true
+            other is BufferNDStructure<*> && this.strides == other.strides -> this.buffer.contentEquals(other.buffer)
+            other is NDStructure<*> -> elements().all { (index, value) -> value == other[index] }
+            else -> false
+        }
     }
 
-inline fun <reified T : Any> ndStructure(strides: Strides, noinline initializer: (IntArray) -> T) =
-        BufferNDStructure<T>(strides, buffer(strides.linearSize) { i -> initializer(strides.index(i)) })
-
-inline fun <reified T : Any> ndStructure(shape: IntArray, noinline initializer: (IntArray) -> T) =
-        ndStructure(DefaultStrides(shape), initializer)
-
+    override fun hashCode(): Int {
+        var result = strides.hashCode()
+        result = 31 * result + buffer.hashCode()
+        return result
+    }
+}
 
 /**
- * Mutable ND buffer based on linear [Buffer]
+ * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [BufferNDStructure]
+ */
+inline fun <T, reified R : Any> NDStructure<T>.mapToBuffer(
+    factory: BufferFactory<R> = Buffer.Companion::auto,
+    crossinline transform: (T) -> R
+): BufferNDStructure<R> {
+    return if (this is BufferNDStructure<T>) {
+        BufferNDStructure(this.strides, factory.invoke(strides.linearSize) { transform(buffer[it]) })
+    } else {
+        val strides = DefaultStrides(shape)
+        BufferNDStructure(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
+    }
+}
+
+/**
+ * Mutable ND buffer based on linear [autoBuffer]
  */
 class MutableBufferNDStructure<T>(
     override val strides: Strides,
     override val buffer: MutableBuffer<T>
-) : GenericNDStructure<T, MutableBuffer<T>>(), MutableNDStructure<T> {
+) : NDBuffer<T>, MutableNDStructure<T> {
 
     init {
         if (strides.linearSize != buffer.size) {
@@ -152,25 +244,10 @@ class MutableBufferNDStructure<T>(
     override fun set(index: IntArray, value: T) = buffer.set(strides.offset(index), value)
 }
 
-/**
- * Create optimized mutable structure for given type
- */
-inline fun <reified T : Any> mutableNdStructure(strides: Strides, noinline initializer: (IntArray) -> T) =
-        MutableBufferNDStructure(strides, mutableBuffer(strides.linearSize) { i -> initializer(strides.index(i)) })
-
-inline fun <reified T : Any> mutableNdStructure(shape: IntArray, noinline initializer: (IntArray) -> T) =
-        mutableNdStructure(DefaultStrides(shape), initializer)
-
-/**
- * Create universal mutable structure
- */
-fun <T> genericNdStructure(shape: IntArray, initializer: (IntArray) -> T): MutableBufferNDStructure<T> {
-    val strides = DefaultStrides(shape)
-    val sequence = sequence {
-        strides.indices().forEach {
-            yield(initializer(it))
-        }
-    }
-    val buffer = MutableListBuffer(sequence.toMutableList())
-    return MutableBufferNDStructure(strides, buffer)
+inline fun <reified T : Any> NDStructure<T>.combine(
+    struct: NDStructure<T>,
+    crossinline block: (T, T) -> T
+): NDStructure<T> {
+    if (!this.shape.contentEquals(struct.shape)) error("Shape mismatch in structure combination")
+    return NDStructure.auto(shape) { block(this[it], struct[it]) }
 }

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

@@ -0,0 +1,48 @@
+package scientifik.kmath.structures
+
+import scientifik.memory.*
+
+/**
+ * A non-boxing buffer based on [ByteBuffer] storage
+ */
+open class ObjectBuffer<T : Any>(protected val memory: Memory, protected val spec: MemorySpec<T>) : Buffer<T> {
+
+    override val size: Int get() = memory.size / spec.objectSize
+
+    private val reader = memory.reader()
+
+    override fun get(index: Int): T = reader.read(spec, spec.objectSize * index)
+
+    override fun iterator(): Iterator<T> = (0 until size).asSequence().map { get(it) }.iterator()
+
+
+    companion object {
+        fun <T : Any> create(spec: MemorySpec<T>, size: Int) =
+            ObjectBuffer(Memory.allocate(size * spec.objectSize), spec)
+
+        inline fun <T : Any> create(
+            spec: MemorySpec<T>,
+            size: Int,
+            crossinline initializer: (Int) -> T
+        ): ObjectBuffer<T> =
+            MutableObjectBuffer(Memory.allocate(size * spec.objectSize), spec).also { buffer ->
+                (0 until size).forEach {
+                    buffer[it] = initializer(it)
+                }
+            }
+    }
+}
+
+class MutableObjectBuffer<T : Any>(memory: Memory, spec: MemorySpec<T>) : ObjectBuffer<T>(memory, spec),
+    MutableBuffer<T> {
+
+    private val writer = memory.writer()
+
+    override fun set(index: Int, value: T) = writer.write(spec, spec.objectSize * index, value)
+
+    override fun copy(): MutableBuffer<T> = MutableObjectBuffer(memory.copy(), spec)
+
+    companion object {
+
+    }
+}

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

@@ -0,0 +1,153 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.ExtendedFieldOperations
+import scientifik.kmath.operations.Field
+import kotlin.math.*
+
+
+/**
+ * A simple field over linear buffers of [Double]
+ */
+object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
+    override fun add(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+        require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
+        return if (a is DoubleBuffer && b is DoubleBuffer) {
+            val aArray = a.array
+            val bArray = b.array
+            DoubleBuffer(DoubleArray(a.size) { aArray[it] + bArray[it] })
+        } else {
+            DoubleBuffer(DoubleArray(a.size) { a[it] + b[it] })
+        }
+    }
+
+    override fun multiply(a: Buffer<Double>, k: Number): DoubleBuffer {
+        val kValue = k.toDouble()
+        return if (a is DoubleBuffer) {
+            val aArray = a.array
+            DoubleBuffer(DoubleArray(a.size) { aArray[it] * kValue })
+        } else {
+            DoubleBuffer(DoubleArray(a.size) { a[it] * kValue })
+        }
+    }
+
+    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+        require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
+        return if (a is DoubleBuffer && b is DoubleBuffer) {
+            val aArray = a.array
+            val bArray = b.array
+            DoubleBuffer(DoubleArray(a.size) { aArray[it] * bArray[it] })
+        } else {
+            DoubleBuffer(DoubleArray(a.size) { a[it] * b[it] })
+        }
+    }
+
+    override fun divide(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+        require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
+        return if (a is DoubleBuffer && b is DoubleBuffer) {
+            val aArray = a.array
+            val bArray = b.array
+            DoubleBuffer(DoubleArray(a.size) { aArray[it] / bArray[it] })
+        } else {
+            DoubleBuffer(DoubleArray(a.size) { a[it] / b[it] })
+        }
+    }
+
+    override fun sin(arg: Buffer<Double>): DoubleBuffer {
+        return if (arg is DoubleBuffer) {
+            val array = arg.array
+            DoubleBuffer(DoubleArray(arg.size) { sin(array[it]) })
+        } else {
+            DoubleBuffer(DoubleArray(arg.size) { sin(arg[it]) })
+        }
+    }
+
+    override fun cos(arg: Buffer<Double>): DoubleBuffer {
+        return if (arg is DoubleBuffer) {
+            val array = arg.array
+            DoubleBuffer(DoubleArray(arg.size) { cos(array[it]) })
+        } else {
+            DoubleBuffer(DoubleArray(arg.size) { cos(arg[it]) })
+        }
+    }
+
+    override fun power(arg: Buffer<Double>, pow: Number): DoubleBuffer {
+        return if (arg is DoubleBuffer) {
+            val array = arg.array
+            DoubleBuffer(DoubleArray(arg.size) { array[it].pow(pow.toDouble()) })
+        } else {
+            DoubleBuffer(DoubleArray(arg.size) { arg[it].pow(pow.toDouble()) })
+        }
+    }
+
+    override fun exp(arg: Buffer<Double>): DoubleBuffer {
+        return if (arg is DoubleBuffer) {
+            val array = arg.array
+            DoubleBuffer(DoubleArray(arg.size) { exp(array[it]) })
+        } else {
+            DoubleBuffer(DoubleArray(arg.size) { exp(arg[it]) })
+        }
+    }
+
+    override fun ln(arg: Buffer<Double>): DoubleBuffer {
+        return if (arg is DoubleBuffer) {
+            val array = arg.array
+            DoubleBuffer(DoubleArray(arg.size) { ln(array[it]) })
+        } else {
+            DoubleBuffer(DoubleArray(arg.size) { ln(arg[it]) })
+        }
+    }
+}
+
+class RealBufferField(val size: Int) : Field<Buffer<Double>>, ExtendedFieldOperations<Buffer<Double>> {
+
+    override val zero: Buffer<Double> by lazy { DoubleBuffer(size) { 0.0 } }
+
+    override val one: Buffer<Double> by lazy { DoubleBuffer(size) { 1.0 } }
+
+    override fun add(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
+        return RealBufferFieldOperations.add(a, b)
+    }
+
+    override fun multiply(a: Buffer<Double>, k: Number): DoubleBuffer {
+        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
+        return RealBufferFieldOperations.multiply(a, k)
+    }
+
+    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
+        return RealBufferFieldOperations.multiply(a, b)
+    }
+
+
+    override fun divide(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
+        return RealBufferFieldOperations.divide(a, b)
+    }
+
+    override fun sin(arg: Buffer<Double>): DoubleBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.sin(arg)
+    }
+
+    override fun cos(arg: Buffer<Double>): DoubleBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.cos(arg)
+    }
+
+    override fun power(arg: Buffer<Double>, pow: Number): DoubleBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.power(arg, pow)
+    }
+
+    override fun exp(arg: Buffer<Double>): DoubleBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.exp(arg)
+    }
+
+    override fun ln(arg: Buffer<Double>): DoubleBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.ln(arg)
+    }
+
+}

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

@@ -0,0 +1,121 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.FieldElement
+import scientifik.kmath.operations.RealField
+
+typealias RealNDElement = BufferedNDFieldElement<Double, RealField>
+
+class RealNDField(override val shape: IntArray) :
+    BufferedNDField<Double, RealField>,
+    ExtendedNDField<Double, RealField, NDBuffer<Double>> {
+
+    override val strides: Strides = DefaultStrides(shape)
+
+    override val elementContext: RealField get() = RealField
+    override val zero by lazy { produce { zero } }
+    override val one by lazy { produce { one } }
+
+    inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Double): Buffer<Double> =
+        DoubleBuffer(DoubleArray(size) { initializer(it) })
+
+    /**
+     * Inline transform an NDStructure to
+     */
+    override fun map(
+        arg: NDBuffer<Double>,
+        transform: RealField.(Double) -> Double
+    ): RealNDElement {
+        check(arg)
+        val array = buildBuffer(arg.strides.linearSize) { offset -> RealField.transform(arg.buffer[offset]) }
+        return BufferedNDFieldElement(this, array)
+    }
+
+    override fun produce(initializer: RealField.(IntArray) -> Double): RealNDElement {
+        val array = buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
+        return BufferedNDFieldElement(this, array)
+    }
+
+    override fun mapIndexed(
+        arg: NDBuffer<Double>,
+        transform: RealField.(index: IntArray, Double) -> Double
+    ): RealNDElement {
+        check(arg)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(arg.strides.linearSize) { offset ->
+                elementContext.transform(
+                    arg.strides.index(offset),
+                    arg.buffer[offset]
+                )
+            })
+    }
+
+    override fun combine(
+        a: NDBuffer<Double>,
+        b: NDBuffer<Double>,
+        transform: RealField.(Double, Double) -> Double
+    ): RealNDElement {
+        check(a, b)
+        return BufferedNDFieldElement(
+            this,
+            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
+    }
+
+    override fun NDBuffer<Double>.toElement(): FieldElement<NDBuffer<Double>, *, out BufferedNDField<Double, RealField>> =
+        BufferedNDFieldElement(this@RealNDField, buffer)
+
+    override fun power(arg: NDBuffer<Double>, pow: Number) = map(arg) { power(it, pow) }
+
+    override fun exp(arg: NDBuffer<Double>) = map(arg) { exp(it) }
+
+    override fun ln(arg: NDBuffer<Double>) = map(arg) { ln(it) }
+
+    override fun sin(arg: NDBuffer<Double>) = map(arg) { sin(it) }
+
+    override fun cos(arg: NDBuffer<Double>) = map(arg) { cos(it) }
+
+}
+
+
+/**
+ * Fast element production using function inlining
+ */
+inline fun BufferedNDField<Double, RealField>.produceInline(crossinline initializer: RealField.(Int) -> Double): RealNDElement {
+    val array = DoubleArray(strides.linearSize) { offset -> RealField.initializer(offset) }
+    return BufferedNDFieldElement(this, DoubleBuffer(array))
+}
+
+/**
+ * Map one [RealNDElement] using function with indexes
+ */
+inline fun RealNDElement.mapIndexed(crossinline transform: RealField.(index: IntArray, Double) -> Double) =
+    context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
+
+/**
+ * Map one [RealNDElement] using function without indexes
+ */
+inline fun RealNDElement.map(crossinline transform: RealField.(Double) -> Double): RealNDElement {
+    val array = DoubleArray(strides.linearSize) { offset -> RealField.transform(buffer[offset]) }
+    return BufferedNDFieldElement(context, DoubleBuffer(array))
+}
+
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy
+ */
+operator fun Function1<Double, Double>.invoke(ndElement: RealNDElement) =
+    ndElement.map { this@invoke(it) }
+
+
+/* plus and minus */
+
+/**
+ * Summation operation for [BufferedNDElement] and single element
+ */
+operator fun RealNDElement.plus(arg: Double) =
+    map { it + arg }
+
+/**
+ * Subtraction operation between [BufferedNDElement] and single element
+ */
+operator fun RealNDElement.minus(arg: Double) =
+    map { it - arg }

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

@@ -0,0 +1,96 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.RingElement
+import scientifik.kmath.operations.ShortRing
+
+
+typealias ShortNDElement = BufferedNDRingElement<Short, ShortRing>
+
+class ShortNDRing(override val shape: IntArray) :
+    BufferedNDRing<Short, ShortRing> {
+
+    override val strides: Strides = DefaultStrides(shape)
+
+    override val elementContext: ShortRing get() = ShortRing
+    override val zero by lazy { produce { ShortRing.zero } }
+    override val one by lazy { produce { ShortRing.one } }
+
+    inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Short): Buffer<Short> =
+        ShortBuffer(ShortArray(size) { initializer(it) })
+
+    /**
+     * Inline transform an NDStructure to
+     */
+    override fun map(
+        arg: NDBuffer<Short>,
+        transform: ShortRing.(Short) -> Short
+    ): ShortNDElement {
+        check(arg)
+        val array = buildBuffer(arg.strides.linearSize) { offset -> ShortRing.transform(arg.buffer[offset]) }
+        return BufferedNDRingElement(this, array)
+    }
+
+    override fun produce(initializer: ShortRing.(IntArray) -> Short): ShortNDElement {
+        val array = buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
+        return BufferedNDRingElement(this, array)
+    }
+
+    override fun mapIndexed(
+        arg: NDBuffer<Short>,
+        transform: ShortRing.(index: IntArray, Short) -> Short
+    ): ShortNDElement {
+        check(arg)
+        return BufferedNDRingElement(
+            this,
+            buildBuffer(arg.strides.linearSize) { offset ->
+                elementContext.transform(
+                    arg.strides.index(offset),
+                    arg.buffer[offset]
+                )
+            })
+    }
+
+    override fun combine(
+        a: NDBuffer<Short>,
+        b: NDBuffer<Short>,
+        transform: ShortRing.(Short, Short) -> Short
+    ): ShortNDElement {
+        check(a, b)
+        return BufferedNDRingElement(
+            this,
+            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
+    }
+
+    override fun NDBuffer<Short>.toElement(): RingElement<NDBuffer<Short>, *, out BufferedNDRing<Short, ShortRing>> =
+        BufferedNDRingElement(this@ShortNDRing, buffer)
+}
+
+
+/**
+ * Fast element production using function inlining
+ */
+inline fun BufferedNDRing<Short, ShortRing>.produceInline(crossinline initializer: ShortRing.(Int) -> Short): ShortNDElement {
+    val array = ShortArray(strides.linearSize) { offset -> ShortRing.initializer(offset) }
+    return BufferedNDRingElement(this, ShortBuffer(array))
+}
+
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy
+ */
+operator fun Function1<Short, Short>.invoke(ndElement: ShortNDElement) =
+    ndElement.context.produceInline { i -> invoke(ndElement.buffer[i]) }
+
+
+/* plus and minus */
+
+/**
+ * Summation operation for [StridedNDFieldElement] and single element
+ */
+operator fun ShortNDElement.plus(arg: Short) =
+    context.produceInline { i -> (buffer[i] + arg).toShort() }
+
+/**
+ * Subtraction operation between [StridedNDFieldElement] and single element
+ */
+operator fun ShortNDElement.minus(arg: Short) =
+    context.produceInline { i -> (buffer[i] - arg).toShort() }

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

@@ -0,0 +1,94 @@
+package scientifik.kmath.structures
+
+/**
+ * A structure that is guaranteed to be one-dimensional
+ */
+interface Structure1D<T> : NDStructure<T>, Buffer<T> {
+    override val dimension: Int get() = 1
+
+    override fun get(index: IntArray): T {
+        if (index.size != 1) error("Index dimension mismatch. Expected 1 but found ${index.size}")
+        return get(index[0])
+    }
+
+    override fun iterator(): Iterator<T> = (0 until size).asSequence().map { get(it) }.iterator()
+}
+
+/**
+ * A 1D wrapper for nd-structure
+ */
+private inline class Structure1DWrapper<T>(val structure: NDStructure<T>) : Structure1D<T> {
+
+    override val shape: IntArray get() = structure.shape
+    override val size: Int get() = structure.shape[0]
+
+    override fun get(index: Int): T = structure[index]
+
+    override fun elements(): Sequence<Pair<IntArray, T>> = structure.elements()
+}
+
+/**
+ * Represent a [NDStructure] as [Structure1D]. Throw error in case of dimension mismatch
+ */
+fun <T> NDStructure<T>.as1D(): Structure1D<T> = if (shape.size == 1) {
+    Structure1DWrapper(this)
+} else {
+    error("Can't create 1d-structure from ${shape.size}d-structure")
+}
+
+fun <T> NDBuffer<T>.as1D(): Structure1D<T> = if (shape.size == 1) {
+    Buffer1DWrapper(this.buffer)
+} else {
+    error("Can't create 1d-structure from ${shape.size}d-structure")
+}
+
+/**
+ * A structure wrapper for buffer
+ */
+private inline class Buffer1DWrapper<T>(val buffer: Buffer<T>) : Structure1D<T> {
+    override val shape: IntArray get() = intArrayOf(buffer.size)
+
+    override val size: Int get() = buffer.size
+
+    override fun elements(): Sequence<Pair<IntArray, T>> =
+        asSequence().mapIndexed { index, value -> intArrayOf(index) to value }
+
+    override fun get(index: Int): T = buffer.get(index)
+}
+
+/**
+ * Represent this buffer as 1D structure
+ */
+fun <T> Buffer<T>.asND(): Structure1D<T> = Buffer1DWrapper(this)
+
+/**
+ * A structure that is guaranteed to be two-dimensional
+ */
+interface Structure2D<T> : NDStructure<T> {
+    operator fun get(i: Int, j: Int): T
+
+    override fun get(index: IntArray): T {
+        if (index.size != 2) error("Index dimension mismatch. Expected 2 but found ${index.size}")
+        return get(index[0], index[1])
+    }
+}
+
+/**
+ * A 2D wrapper for nd-structure
+ */
+private inline class Structure2DWrapper<T>(val structure: NDStructure<T>) : Structure2D<T> {
+    override fun get(i: Int, j: Int): T = structure[i, j]
+
+    override val shape: IntArray get() = structure.shape
+
+    override fun elements(): Sequence<Pair<IntArray, T>> = structure.elements()
+}
+
+/**
+ * Represent a [NDStructure] as [Structure1D]. Throw error in case of dimension mismatch
+ */
+fun <T> NDStructure<T>.as2D(): Structure2D<T> = if (shape.size == 2) {
+    Structure2DWrapper(this)
+} else {
+    error("Can't create 2d-structure from ${shape.size}d-structure")
+}

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

@@ -2,17 +2,17 @@ package scientifik.kmath.expressions
 
 import scientifik.kmath.operations.Complex
 import scientifik.kmath.operations.ComplexField
-import scientifik.kmath.operations.DoubleField
+import scientifik.kmath.operations.RealField
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
-class FieldExpressionContextTest {
+class ExpressionFieldTest {
     @Test
     fun testExpression() {
-        val context = FieldExpressionContext(DoubleField)
+        val context = ExpressionField(RealField)
         val expression = with(context) {
             val x = variable("x", 2.0)
-            x * x + 2 * x + 1.0
+            x * x + 2 * x + one
         }
         assertEquals(expression("x" to 1.0), 4.0)
         assertEquals(expression(), 9.0)
@@ -20,10 +20,10 @@ class FieldExpressionContextTest {
 
     @Test
     fun testComplex() {
-        val context = FieldExpressionContext(ComplexField)
+        val context = ExpressionField(ComplexField)
         val expression = with(context) {
             val x = variable("x", Complex(2.0, 0.0))
-            x * x + 2 * x + 1.0
+            x * x + 2 * x + one
         }
         assertEquals(expression("x" to Complex(1.0, 0.0)), Complex(4.0, 0.0))
         assertEquals(expression(), Complex(9.0, 0.0))
@@ -31,23 +31,23 @@ class FieldExpressionContextTest {
 
     @Test
     fun separateContext() {
-        fun <T> FieldExpressionContext<T>.expression(): Expression<T>{
+        fun <T> ExpressionField<T>.expression(): Expression<T> {
             val x = variable("x")
-            return x * x + 2 * x + 1.0
+            return x * x + 2 * x + one
         }
 
-        val expression = FieldExpressionContext(DoubleField).expression()
+        val expression = ExpressionField(RealField).expression()
         assertEquals(expression("x" to 1.0), 4.0)
     }
 
     @Test
     fun valueExpression() {
-        val expressionBuilder: FieldExpressionContext<Double>.()->Expression<Double> = {
+        val expressionBuilder: ExpressionField<Double>.() -> Expression<Double> = {
             val x = variable("x")
-            x * x + 2 * x + 1.0
+            x * x + 2 * x + one
         }
 
-        val expression = FieldExpressionContext(DoubleField).expressionBuilder()
+        val expression = ExpressionField(RealField).expressionBuilder()
         assertEquals(expression("x" to 1.0), 4.0)
     }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/ArrayMatrixTest.kt

@@ -1,34 +0,0 @@
-package scientifik.kmath.linear
-
-import kotlin.test.Test
-import kotlin.test.assertEquals
-
-class ArrayMatrixTest {
-
-    @Test
-    fun testSum() {
-        val vector1 = Vector.ofReal(5) { it.toDouble() }
-        val vector2 = Vector.ofReal(5) { 5 - it.toDouble() }
-        val sum = vector1 + vector2
-        assertEquals(5.0, sum[2])
-    }
-
-    @Test
-    fun testVectorToMatrix() {
-        val vector = Vector.ofReal(5) { it.toDouble() }
-        val matrix = vector.toMatrix()
-        assertEquals(4.0, matrix[4, 0])
-    }
-
-
-    @Test
-    fun testDot() {
-        val vector1 = Vector.ofReal(5) { it.toDouble() }
-        val vector2 = Vector.ofReal(5) { 5 - it.toDouble() }
-        val product = vector1.toMatrix() dot (vector2.toMatrix().transpose())
-
-
-        assertEquals(5.0, product[1, 0])
-        assertEquals(6.0, product[2, 2])
-    }
-}

kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt

@@ -0,0 +1,54 @@
+package scientifik.kmath.linear
+
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class MatrixTest {
+
+    @Test
+    fun testSum() {
+        val vector1 = Vector.real(5) { it.toDouble() }
+        val vector2 = Vector.real(5) { 5 - it.toDouble() }
+        val sum = vector1 + vector2
+        assertEquals(5.0, sum[2])
+    }
+
+    @Test
+    fun testVectorToMatrix() {
+        val vector = Vector.real(5) { it.toDouble() }
+        val matrix = vector.toMatrix()
+        assertEquals(4.0, matrix[4, 0])
+    }
+
+    @Test
+    fun testTranspose() {
+        val matrix = MatrixContext.real.one(3, 3)
+        val transposed = matrix.transpose()
+        assertEquals(matrix, transposed)
+    }
+
+
+    @Test
+    fun testDot() {
+        val vector1 = Vector.real(5) { it.toDouble() }
+        val vector2 = Vector.real(5) { 5 - it.toDouble() }
+
+        val matrix1 = vector1.toMatrix()
+        val matrix2 = vector2.toMatrix().transpose()
+        val product = MatrixContext.real.run { matrix1 dot matrix2 }
+
+
+        assertEquals(5.0, product[1, 0])
+        assertEquals(6.0, product[2, 2])
+    }
+
+    @Test
+    fun testBuilder() {
+        val matrix = Matrix.build<Double>(2, 3)(
+            1.0, 0.0, 0.0,
+            0.0, 1.0, 2.0
+        )
+
+        assertEquals(2.0, matrix[1, 2])
+    }
+}

kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt

@@ -1,21 +1,41 @@
 package scientifik.kmath.linear
 
-import scientifik.kmath.operations.DoubleField
 import kotlin.test.Test
-import kotlin.test.assertTrue
+import kotlin.test.assertEquals
 
 class RealLUSolverTest {
     @Test
     fun testInvertOne() {
-        val matrix = Matrix.diagonal(2, 2, DoubleField)
-        val inverted = RealLUSolver.inverse(matrix)
-        assertTrue { Matrix.equals(matrix,inverted) }
+        val matrix = MatrixContext.real.one(2, 2)
+        val inverted = LUSolver.real.inverse(matrix)
+        assertEquals(matrix, inverted)
     }
 
-//    @Test
-//    fun testInvert() {
-//        val matrix = realMatrix(2,2){}
-//        val inverted = RealLUSolver.inverse(matrix)
-//        assertTrue { Matrix.equals(matrix,inverted) }
-//    }
+    @Test
+    fun testInvert() {
+        val matrix = Matrix.square(
+            3.0, 1.0,
+            1.0, 3.0
+        )
+
+        val decomposed = LUSolver.real.decompose(matrix)
+        val decomposition = decomposed.getFeature<LUPDecomposition<Double>>()!!
+
+        //Check determinant
+        assertEquals(8.0, decomposition.determinant)
+
+        //Check decomposition
+        with(MatrixContext.real) {
+            assertEquals(decomposition.p dot matrix, decomposition.l dot decomposition.u)
+        }
+
+        val inverted = LUSolver.real.inverse(decomposed)
+
+        val expected = Matrix.square(
+            0.375, -0.125,
+            -0.125, 0.375
+        )
+
+        assertEquals(expected, inverted)
+    }
 }

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

@@ -6,11 +6,9 @@ import kotlin.test.assertEquals
 class RealFieldTest {
     @Test
     fun testSqrt() {
-
-        //fails because KT-27586
         val sqrt = with(RealField) {
             sqrt(25 * one)
         }
-        assertEquals(5.0, sqrt.value)
+        assertEquals(5.0, sqrt)
     }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/ComplexBufferSpecTest.kt

@@ -1,17 +1,14 @@
 package scientifik.kmath.structures
 
-import org.junit.Test
 import scientifik.kmath.operations.Complex
+import scientifik.kmath.operations.complex
+import kotlin.test.Test
 import kotlin.test.assertEquals
 
 class ComplexBufferSpecTest {
     @Test
     fun testComplexBuffer() {
-        val buffer = Complex.createBuffer(20)
-        (0 until 20).forEach {
-            buffer[it] = Complex(it.toDouble(), -it.toDouble())
-        }
-
+        val buffer = Buffer.complex(20) { Complex(it.toDouble(), -it.toDouble()) }
         assertEquals(Complex(5.0, -5.0), buffer[5])
     }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/GenericNDFieldTest.kt

@@ -1,16 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.structures.NDArrays.create
-import kotlin.test.Test
-import kotlin.test.assertEquals
-
-
-class GenericNDFieldTest{
-    @Test
-    fun testStrides(){
-        val ndArray = create(DoubleField, intArrayOf(10,10)){(it[0]+it[1]).toDouble()}
-        assertEquals(ndArray[5,5], 10.0)
-    }
-
-}

kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NDFieldTest.kt

@@ -0,0 +1,13 @@
+package scientifik.kmath.structures
+
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+
+class NDFieldTest {
+    @Test
+    fun testStrides() {
+        val ndArray = NDElement.real(intArrayOf(10, 10)) { (it[0] + it[1]).toDouble() }
+        assertEquals(ndArray[5, 5], 10.0)
+    }
+}

kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NumberNDFieldTest.kt

@@ -1,16 +1,15 @@
 package scientifik.kmath.structures
 
 import scientifik.kmath.operations.Norm
-import scientifik.kmath.structures.NDArrays.produceReal
-import scientifik.kmath.structures.NDArrays.real2DArray
+import scientifik.kmath.structures.NDElement.Companion.real2D
 import kotlin.math.abs
 import kotlin.math.pow
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
 class NumberNDFieldTest {
-    val array1 = real2DArray(3, 3) { i, j -> (i + j).toDouble() }
-    val array2 = real2DArray(3, 3) { i, j -> (i - j).toDouble() }
+    val array1 = real2D(3, 3) { i, j -> (i + j).toDouble() }
+    val array2 = real2D(3, 3) { i, j -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
@@ -27,7 +26,7 @@ class NumberNDFieldTest {
     @Test
     fun testGeneration() {
 
-        val array = real2DArray(3, 3) { i, j -> (i * 10 + j).toDouble() }
+        val array = real2D(3, 3) { i, j -> (i * 10 + j).toDouble() }
 
         for (i in 0..2) {
             for (j in 0..2) {
@@ -51,15 +50,20 @@ class NumberNDFieldTest {
         assertEquals(2.0, result[0, 2])
     }
 
-    object L2Norm : Norm<NDElement<out Number, *>, Double> {
-        override fun norm(arg: NDElement<out Number, *>): Double {
-            return kotlin.math.sqrt(arg.sumByDouble { it.second.toDouble() })
+    @Test
+    fun combineTest() {
+        val division = array1.combine(array2, Double::div)
+    }
+
+    object L2Norm : Norm<NDStructure<out Number>, Double> {
+        override fun norm(arg: NDStructure<out Number>): Double {
+            return kotlin.math.sqrt(arg.elements().sumByDouble { it.second.toDouble() })
         }
     }
 
     @Test
     fun testInternalContext() {
-        produceReal(array1.shape) {
+        NDField.real(*array1.shape).run {
             with(L2Norm) {
                 1 + norm(array1) + exp(array2)
             }

kmath-core/src/jsMain/kotlin/scientifik/kmath/histogram/Counters.kt

@@ -1,16 +0,0 @@
-package scientifik.kmath.histogram
-
-actual class LongCounter{
-    private var sum: Long = 0
-    actual fun decrement() {sum--}
-    actual fun increment() {sum++}
-    actual fun reset() {sum = 0}
-    actual fun sum(): Long = sum
-    actual fun add(l: Long) {sum+=l}
-}
-actual class DoubleCounter{
-    private var sum: Double = 0.0
-    actual fun reset() {sum = 0.0}
-    actual fun sum(): Double = sum
-    actual fun add(d: Double) {sum+=d}
-}

kmath-core/src/jvmMain/kotlin/scientifik/kmath/structures/BufferSpec.kt

@@ -1,55 +0,0 @@
-package scientifik.kmath.structures
-
-import java.nio.ByteBuffer
-
-
-/**
- * A specification for serialization and deserialization objects to buffer
- */
-interface BufferSpec<T : Any> {
-    fun fromBuffer(buffer: ByteBuffer): T
-    fun toBuffer(value: T): ByteBuffer
-}
-
-/**
- * A [BufferSpec] with fixed unit size. Allows storage of any object without boxing.
- */
-interface FixedSizeBufferSpec<T : Any> : BufferSpec<T> {
-    val unitSize: Int
-
-    /**
-     * Read an object from buffer in current position
-     */
-    fun ByteBuffer.readObject(): T {
-        val buffer = ByteArray(unitSize)
-        get(buffer)
-        return fromBuffer(ByteBuffer.wrap(buffer))
-    }
-
-    /**
-     * Read an object from buffer in given index (not buffer position
-     */
-    fun ByteBuffer.readObject(index: Int): T {
-        val dup = duplicate()
-        dup.position(index*unitSize)
-        return dup.readObject()
-    }
-
-    /**
-     * Write object to [ByteBuffer] in current buffer position
-     */
-    fun ByteBuffer.writeObject(obj: T) {
-        val buffer = toBuffer(obj).apply { rewind() }
-        assert(buffer.limit() == unitSize)
-        put(buffer)
-    }
-
-    /**
-     * Put an object in given index
-     */
-    fun ByteBuffer.writeObject(index: Int, obj: T) {
-        val dup = duplicate()
-        dup.position(index*unitSize)
-        dup.writeObject(obj)
-    }
-}

kmath-core/src/jvmMain/kotlin/scientifik/kmath/structures/ComplexBufferSpec.kt

@@ -1,25 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.Complex
-import java.nio.ByteBuffer
-
-object ComplexBufferSpec : FixedSizeBufferSpec<Complex> {
-    override val unitSize: Int = 16
-
-    override fun fromBuffer(buffer: ByteBuffer): Complex {
-        val re = buffer.getDouble(0)
-        val im = buffer.getDouble(8)
-        return Complex(re, im)
-    }
-
-    override fun toBuffer(value: Complex): ByteBuffer = ByteBuffer.allocate(16).apply {
-        putDouble(value.re)
-        putDouble(value.im)
-    }
-}
-
-/**
- * Create a mutable buffer which ignores boxing
- */
-fun Complex.Companion.createBuffer(size: Int) = ObjectBuffer.create(ComplexBufferSpec, size)
-

kmath-core/src/jvmMain/kotlin/scientifik/kmath/structures/ObjectBuffer.kt

@@ -1,28 +0,0 @@
-package scientifik.kmath.structures
-
-import java.nio.ByteBuffer
-
-class ObjectBuffer<T : Any>(private val buffer: ByteBuffer, private val spec: FixedSizeBufferSpec<T>) : MutableBuffer<T> {
-    override val size: Int
-        get() = buffer.limit() / spec.unitSize
-
-    override fun get(index: Int): T = with(spec) { buffer.readObject(index) }
-
-    override fun iterator(): Iterator<T> = (0 until size).asSequence().map { get(it) }.iterator()
-
-    override fun set(index: Int, value: T) = with(spec) { buffer.writeObject(index, value) }
-
-    override fun copy(): MutableBuffer<T> {
-        val dup = buffer.duplicate()
-        val copy = ByteBuffer.allocate(dup.capacity())
-        dup.rewind()
-        copy.put(dup)
-        copy.flip()
-        return ObjectBuffer(copy, spec)
-    }
-
-    companion object {
-        fun <T : Any> create(spec: FixedSizeBufferSpec<T>, size: Int) =
-                ObjectBuffer<T>(ByteBuffer.allocate(size * spec.unitSize), spec)
-    }
-}

kmath-core/src/jvmMain/kotlin/scientifik/kmath/structures/RealBufferSpec.kt

@@ -1,23 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.Real
-import java.nio.ByteBuffer
-
-object RealBufferSpec : FixedSizeBufferSpec<Real> {
-    override val unitSize: Int = 8
-
-    override fun fromBuffer(buffer: ByteBuffer): Real = Real(buffer.double)
-
-    override fun toBuffer(value: Real): ByteBuffer = ByteBuffer.allocate(8).apply { putDouble(value.value) }
-}
-
-object DoubleBufferSpec : FixedSizeBufferSpec<Double> {
-    override val unitSize: Int = 8
-
-    override fun fromBuffer(buffer: ByteBuffer): Double = buffer.double
-
-    override fun toBuffer(value: Double): ByteBuffer = ByteBuffer.allocate(8).apply { putDouble(value) }
-}
-
-fun Double.Companion.createBuffer(size: Int) = ObjectBuffer.create(DoubleBufferSpec, size)
-fun Real.Companion.createBuffer(size: Int) = ObjectBuffer.create(RealBufferSpec, size)

kmath-coroutines/build.gradle

@@ -1,42 +0,0 @@
-plugins {
-    id "org.jetbrains.kotlin.multiplatform"
-}
-
-kotlin {
-    targets {
-        fromPreset(presets.jvm, 'jvm')
-        // For ARM, preset should be changed to presets.iosArm32 or presets.iosArm64
-        // For Linux, preset should be changed to e.g. presets.linuxX64
-        // For MacOS, preset should be changed to e.g. presets.macosX64
-        //fromPreset(presets.mingwX64, 'mingw')
-    }
-    sourceSets {
-        commonMain {
-            dependencies {
-                api project(":kmath-core")
-                api "org.jetbrains.kotlinx:kotlinx-coroutines-core-common:$coroutinesVersion"
-            }
-        }
-        commonTest {
-            dependencies {
-                api 'org.jetbrains.kotlin:kotlin-test-common'
-                api 'org.jetbrains.kotlin:kotlin-test-annotations-common'
-            }
-        }
-        jvmMain {
-            dependencies {
-                api "org.jetbrains.kotlinx:kotlinx-coroutines-core:$coroutinesVersion"
-            }
-        }
-        jvmTest {
-            dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-test'
-                implementation 'org.jetbrains.kotlin:kotlin-test-junit'
-            }
-        }
-//        mingwMain {
-//        }
-//        mingwTest {
-//        }
-    }
-}

kmath-coroutines/build.gradle.kts

@@ -0,0 +1,46 @@
+plugins {
+    kotlin("multiplatform")
+}
+
+val coroutinesVersion: String by rootProject.extra
+
+kotlin {
+    jvm()
+    js()
+
+    sourceSets {
+        val commonMain by getting {
+            dependencies {
+                api(project(":kmath-core"))
+                api("org.jetbrains.kotlinx:kotlinx-coroutines-core-common:$coroutinesVersion")
+            }
+        }
+        val commonTest by getting {
+            dependencies {
+                implementation(kotlin("test-common"))
+                implementation(kotlin("test-annotations-common"))
+            }
+        }
+        val jvmMain by getting {
+            dependencies {
+                api("org.jetbrains.kotlinx:kotlinx-coroutines-core:$coroutinesVersion")
+            }
+        }
+        val jvmTest by getting {
+            dependencies {
+                implementation(kotlin("test"))
+                implementation(kotlin("test-junit"))
+            }
+        }
+        val jsMain by getting {
+            dependencies {
+                api("org.jetbrains.kotlinx:kotlinx-coroutines-core-js:$coroutinesVersion")
+            }
+        }
+        val jsTest by getting {
+            dependencies {
+                implementation(kotlin("test-js"))
+            }
+        }
+    }
+}

kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/structures/CoroutinesExtra.kt

@@ -6,6 +6,4 @@ import kotlinx.coroutines.Dispatchers
 import kotlin.coroutines.CoroutineContext
 import kotlin.coroutines.EmptyCoroutineContext
 
-expect fun <R> runBlocking(context: CoroutineContext = EmptyCoroutineContext, function: suspend CoroutineScope.()->R): R
-
 val Dispatchers.Math: CoroutineDispatcher get() = Dispatchers.Default

kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/structures/LazyNDField.kt

@@ -1,79 +0,0 @@
-package scientifik.kmath.structures
-
-import kotlinx.coroutines.*
-import scientifik.kmath.operations.Field
-
-class LazyNDField<T, F : Field<T>>(shape: IntArray, field: F, val scope: CoroutineScope = GlobalScope) : NDField<T, F>(shape, field) {
-
-    override fun produceStructure(initializer: F.(IntArray) -> T): NDStructure<T> = LazyNDStructure(this) { initializer(field, it) }
-
-
-    override fun add(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
-        return LazyNDStructure(this) { index ->
-            val aDeferred = a.deferred(index)
-            val bDeferred = b.deferred(index)
-            aDeferred.await() + bDeferred.await()
-        }
-    }
-
-    override fun multiply(a: NDElement<T, F>, k: Double): NDElement<T, F> {
-        return LazyNDStructure(this) { index -> a.await(index) * k }
-    }
-
-    override fun multiply(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
-        return LazyNDStructure(this) { index ->
-            val aDeferred = a.deferred(index)
-            val bDeferred = b.deferred(index)
-            aDeferred.await() * bDeferred.await()
-        }
-    }
-
-    override fun divide(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
-        return LazyNDStructure(this) { index ->
-            val aDeferred = a.deferred(index)
-            val bDeferred = b.deferred(index)
-            aDeferred.await() / bDeferred.await()
-        }
-    }
-}
-
-class LazyNDStructure<T, F : Field<T>>(override val context: LazyNDField<T, F>, val function: suspend F.(IntArray) -> T) : NDElement<T, F>, NDStructure<T> {
-    override val self: NDElement<T, F> get() = this
-    override val shape: IntArray get() = context.shape
-
-    private val cache = HashMap<IntArray, Deferred<T>>()
-
-    fun deferred(index: IntArray) = cache.getOrPut(index) { context.scope.async(context = Dispatchers.Math) { function.invoke(context.field, index) } }
-
-    suspend fun await(index: IntArray): T = deferred(index).await()
-
-    override fun get(index: IntArray): T = runBlocking {
-        deferred(index).await()
-    }
-
-    override fun elements(): Sequence<Pair<IntArray, T>> {
-        val strides = DefaultStrides(shape)
-        return strides.indices().map { index -> index to runBlocking { await(index) } }
-    }
-}
-
-fun <T> NDElement<T, *>.deferred(index: IntArray) = if (this is LazyNDStructure<T, *>) this.deferred(index) else CompletableDeferred(get(index))
-
-suspend fun <T> NDElement<T, *>.await(index: IntArray) = if (this is LazyNDStructure<T, *>) this.await(index) else get(index)
-
-fun <T, F : Field<T>> NDElement<T, F>.lazy(scope: CoroutineScope = GlobalScope): LazyNDStructure<T, F> {
-    return if (this is LazyNDStructure<T, F>) {
-        this
-    } else {
-        val context = LazyNDField(context.shape, context.field)
-        LazyNDStructure(context) { get(it) }
-    }
-}
-
-inline fun <T, F : Field<T>> LazyNDStructure<T, F>.transformIndexed(crossinline action: suspend F.(IntArray, T) -> T) = LazyNDStructure(context) { index ->
-    action.invoke(this, index, await(index))
-}
-
-inline fun <T, F : Field<T>> LazyNDStructure<T, F>.transform(crossinline action: suspend F.(T) -> T) = LazyNDStructure(context) { index ->
-    action.invoke(this, await(index))
-}

kmath-coroutines/src/commonTest/kotlin/scientifik/kmath/structures/LazyNDFieldTest.kt

@@ -1,20 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.IntField
-import kotlin.test.Test
-import kotlin.test.assertEquals
-
-
-class LazyNDFieldTest {
-    @Test
-    fun testLazyStructure() {
-        var counter = 0
-        val regularStructure = NDArrays.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] }
-        val result = (regularStructure.lazy() + 2).transform {
-            counter++
-            it * it
-        }
-        assertEquals(4, result[0,0,0])
-        assertEquals(1, counter)
-    }
-}

kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/structures/LazyNDStructure.kt

@@ -0,0 +1,47 @@
+package scientifik.kmath.structures
+
+import kotlinx.coroutines.*
+
+class LazyNDStructure<T>(
+    val scope: CoroutineScope,
+    override val shape: IntArray,
+    val function: suspend (IntArray) -> T
+) : NDStructure<T> {
+
+    private val cache = HashMap<IntArray, Deferred<T>>()
+
+    fun deferred(index: IntArray) = cache.getOrPut(index) {
+        scope.async(context = Dispatchers.Math) {
+            function(index)
+        }
+    }
+
+    suspend fun await(index: IntArray): T = deferred(index).await()
+
+    override fun get(index: IntArray): T = runBlocking {
+        deferred(index).await()
+    }
+
+    override fun elements(): Sequence<Pair<IntArray, T>> {
+        val strides = DefaultStrides(shape)
+        val res = runBlocking {
+            strides.indices().toList().map { index -> index to await(index) }
+        }
+        return res.asSequence()
+    }
+}
+
+fun <T> NDStructure<T>.deferred(index: IntArray) =
+    if (this is LazyNDStructure<T>) this.deferred(index) else CompletableDeferred(get(index))
+
+suspend fun <T> NDStructure<T>.await(index: IntArray) =
+    if (this is LazyNDStructure<T>) this.await(index) else get(index)
+
+/**
+ * PENDING would benifit from KEEP-176
+ */
+fun <T, R> NDStructure<T>.mapAsyncIndexed(scope: CoroutineScope, function: suspend (T, index: IntArray) -> R) =
+    LazyNDStructure(scope, shape) { index -> function(get(index), index) }
+
+fun <T, R> NDStructure<T>.mapAsync(scope: CoroutineScope, function: suspend (T) -> R) =
+    LazyNDStructure(scope, shape) { index -> function(get(index)) }

kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/structures/_CoroutinesExtra.kt

@@ -1,6 +0,0 @@
-package scientifik.kmath.structures
-
-import kotlinx.coroutines.CoroutineScope
-import kotlin.coroutines.CoroutineContext
-
-actual fun <R> runBlocking(context: CoroutineContext, function: suspend CoroutineScope.() -> R): R  = kotlinx.coroutines.runBlocking(context, function)

kmath-histograms/build.gradle.kts

@@ -0,0 +1,34 @@
+plugins {
+    kotlin("multiplatform")
+}
+
+kotlin {
+    jvm()
+    js()
+
+    sourceSets {
+
+        val commonMain by getting {
+            dependencies {
+                api(project(":kmath-core"))
+            }
+        }
+        val commonTest by getting {
+            dependencies {
+                implementation(kotlin("test-common"))
+                implementation(kotlin("test-annotations-common"))
+            }
+        }
+        val jvmTest by getting {
+            dependencies {
+                implementation(kotlin("test"))
+                implementation(kotlin("test-junit"))
+            }
+        }
+        val jsTest by getting {
+            dependencies {
+                implementation(kotlin("test-js"))
+            }
+        }
+    }
+}

kmath-histograms/src/commonMain/kotlin/scientifik/kmath/histogram/Counters.kt

@@ -0,0 +1,20 @@
+package scientifik.kmath.histogram
+
+/*
+ * Common representation for atomic counters
+ * TODO replace with atomics
+ */
+
+expect class LongCounter() {
+    fun decrement()
+    fun increment()
+    fun reset()
+    fun sum(): Long
+    fun add(l: Long)
+}
+
+expect class DoubleCounter() {
+    fun reset()
+    fun sum(): Double
+    fun add(d: Double)
+}

kmath-histograms/src/commonMain/kotlin/scientifik/kmath/histogram/Histogram.kt

@@ -0,0 +1,64 @@
+package scientifik.kmath.histogram
+
+import scientifik.kmath.linear.Point
+import scientifik.kmath.structures.ArrayBuffer
+import scientifik.kmath.structures.DoubleBuffer
+
+/**
+ * A simple geometric domain
+ * TODO move to geometry module
+ */
+interface Domain<T : Any> {
+    operator fun contains(vector: Point<out T>): Boolean
+    val dimension: Int
+}
+
+/**
+ * The bin in the histogram. The histogram is by definition always done in the real space
+ */
+interface Bin<T : Any> : Domain<T> {
+    /**
+     * The value of this bin
+     */
+    val value: Number
+    val center: Point<T>
+}
+
+interface Histogram<T : Any, out B : Bin<T>> : Iterable<B> {
+
+    /**
+     * Find existing bin, corresponding to given coordinates
+     */
+    operator fun get(point: Point<out T>): B?
+
+    /**
+     * Dimension of the histogram
+     */
+    val dimension: Int
+
+}
+
+interface MutableHistogram<T : Any, out B : Bin<T>> : Histogram<T, B> {
+
+    /**
+     * Increment appropriate bin
+     */
+    fun putWithWeight(point: Point<out T>, weight: Double)
+
+    fun put(point: Point<out T>) = putWithWeight(point, 1.0)
+}
+
+fun <T : Any> MutableHistogram<T, *>.put(vararg point: T) = put(ArrayBuffer(point))
+
+fun MutableHistogram<Double, *>.put(vararg point: Number) =
+    put(DoubleBuffer(point.map { it.toDouble() }.toDoubleArray()))
+
+fun MutableHistogram<Double, *>.put(vararg point: Double) = put(DoubleBuffer(point))
+
+fun <T : Any> MutableHistogram<T, *>.fill(sequence: Iterable<Point<T>>) = sequence.forEach { put(it) }
+
+/**
+ * Pass a sequence builder into histogram
+ */
+fun <T : Any> MutableHistogram<T, *>.fill(buider: suspend SequenceScope<Point<T>>.() -> Unit) =
+    fill(sequence(buider).asIterable())

kmath-histograms/src/commonMain/kotlin/scientifik/kmath/histogram/RealHistogram.kt

@@ -1,43 +1,66 @@
 package scientifik.kmath.histogram
 
+import scientifik.kmath.linear.Point
 import scientifik.kmath.linear.toVector
+import scientifik.kmath.operations.SpaceOperations
 import scientifik.kmath.structures.*
 import kotlin.math.floor
 
-private operator fun RealPoint.minus(other: RealPoint) = ListBuffer((0 until size).map { get(it) - other[it] })
 
-private inline fun <T> Buffer<out Double>.mapIndexed(crossinline mapper: (Int, Double) -> T): Sequence<T> = (0 until size).asSequence().map { mapper(it, get(it)) }
+data class BinDef<T : Comparable<T>>(val space: SpaceOperations<Point<T>>, val center: Point<T>, val sizes: Point<T>) {
+    fun contains(vector: Point<out T>): Boolean {
+        if (vector.size != center.size) error("Dimension mismatch for input vector. Expected ${center.size}, but found ${vector.size}")
+        val upper = space.run { center + sizes / 2.0 }
+        val lower = space.run { center - sizes / 2.0 }
+        return vector.asSequence().mapIndexed { i, value ->
+            value in lower[i]..upper[i]
+        }.all { it }
+    }
+}
+
+
+class MultivariateBin<T : Comparable<T>>(val def: BinDef<T>, override val value: Number) : Bin<T> {
+
+    override fun contains(vector: Point<out T>): Boolean = def.contains(vector)
+
+    override val dimension: Int
+        get() = def.center.size
+
+    override val center: Point<T>
+        get() = def.center
+
+}
 
 /**
  * Uniform multivariate histogram with fixed borders. Based on NDStructure implementation with complexity of m for bin search, where m is the number of dimensions.
  */
-class FastHistogram(
-        private val lower: RealPoint,
-        private val upper: RealPoint,
+class RealHistogram(
+    private val lower: Buffer<Double>,
+    private val upper: Buffer<Double>,
     private val binNums: IntArray = IntArray(lower.size) { 20 }
-) : MutableHistogram<Double, PhantomBin<Double>> {
+) : MutableHistogram<Double, MultivariateBin<Double>> {
 
 
     private val strides = DefaultStrides(IntArray(binNums.size) { binNums[it] + 2 })
 
-    private val values: NDStructure<LongCounter> = ndStructure(strides) { LongCounter() }
+    private val values: NDStructure<LongCounter> = NDStructure.auto(strides) { LongCounter() }
 
     //private val weight: NDStructure<DoubleCounter?> = ndStructure(strides){null}
 
-    //TODO optimize binSize performance if needed
-    private val binSize: RealPoint = ListBuffer((upper - lower).mapIndexed { index, value -> value / binNums[index] }.toList())
+
+    override val dimension: Int get() = lower.size
+
+
+    private val binSize = DoubleBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] }
 
     init {
         // argument checks
         if (lower.size != upper.size) error("Dimension mismatch in histogram lower and upper limits.")
         if (lower.size != binNums.size) error("Dimension mismatch in bin count.")
-        if ((upper - lower).asSequence().any { it <= 0 }) error("Range for one of axis is not strictly positive")
+        if ((0 until dimension).any { upper[it] - lower[it] < 0 }) error("Range for one of axis is not strictly positive")
     }
 
 
-    override val dimension: Int get() = lower.size
-
-
     /**
      * Get internal [NDStructure] bin index for given axis
      */
@@ -59,49 +82,41 @@ class FastHistogram(
         return getValue(getIndex(point))
     }
 
-    private fun getTemplate(index: IntArray): BinTemplate<Double> {
+    private fun getDef(index: IntArray): BinDef<Double> {
         val center = index.mapIndexed { axis, i ->
             when (i) {
                 0 -> Double.NEGATIVE_INFINITY
                 strides.shape[axis] - 1 -> Double.POSITIVE_INFINITY
                 else -> lower[axis] + (i.toDouble() - 0.5) * binSize[axis]
             }
-        }.toVector()
-        return BinTemplate(center, binSize)
+        }.asBuffer()
+        return BinDef(RealBufferFieldOperations, center, binSize)
     }
 
-    fun getTemplate(point: Buffer<out Double>): BinTemplate<Double> {
-        return getTemplate(getIndex(point))
+    fun getDef(point: Buffer<out Double>): BinDef<Double> {
+        return getDef(getIndex(point))
     }
 
-    override fun get(point: Buffer<out Double>): PhantomBin<Double>? {
+    override fun get(point: Buffer<out Double>): MultivariateBin<Double>? {
         val index = getIndex(point)
-        return PhantomBin(getTemplate(index), getValue(index))
+        return MultivariateBin(getDef(index), getValue(index))
     }
 
-    override fun put(point: Buffer<out Double>, weight: Double) {
+    override fun putWithWeight(point: Buffer<out Double>, weight: Double) {
         if (weight != 1.0) TODO("Implement weighting")
         val index = getIndex(point)
         values[index].increment()
     }
 
-    override fun iterator(): Iterator<PhantomBin<Double>> = values.elements().map { (index, value) ->
-        PhantomBin(getTemplate(index), value.sum())
+    override fun iterator(): Iterator<MultivariateBin<Double>> = values.elements().map { (index, value) ->
+        MultivariateBin(getDef(index), value.sum())
     }.iterator()
 
     /**
      * Convert this histogram into NDStructure containing bin values but not bin descriptions
      */
     fun asNDStructure(): NDStructure<Number> {
-        return ndStructure(this.values.shape) { values[it].sum() }
-    }
-
-    /**
-     * Create a phantom lightweight immutable copy of this histogram
-     */
-    fun asPhantomHistogram(): PhantomHistogram<Double> {
-        val binTemplates = values.elements().associate { (index, _) -> getTemplate(index) to index }
-        return PhantomHistogram(binTemplates, asNDStructure())
+        return NDStructure.auto(this.values.shape) { values[it].sum() }
     }
 
     companion object {
@@ -115,8 +130,11 @@ class FastHistogram(
          *)
          *```
          */
-        fun fromRanges(vararg ranges: ClosedFloatingPointRange<Double>): FastHistogram {
-            return FastHistogram(ranges.map { it.start }.toVector(), ranges.map { it.endInclusive }.toVector())
+        fun fromRanges(vararg ranges: ClosedFloatingPointRange<Double>): RealHistogram {
+            return RealHistogram(
+                ranges.map { it.start }.toVector(),
+                ranges.map { it.endInclusive }.toVector()
+            )
         }
 
         /**
@@ -128,8 +146,8 @@ class FastHistogram(
          *)
          *```
          */
-        fun fromRanges(vararg ranges: Pair<ClosedFloatingPointRange<Double>, Int>): FastHistogram {
-            return FastHistogram(
+        fun fromRanges(vararg ranges: Pair<ClosedFloatingPointRange<Double>, Int>): RealHistogram {
+            return RealHistogram(
                 ListBuffer(ranges.map { it.first.start }),
                 ListBuffer(ranges.map { it.first.endInclusive }),
                 ranges.map { it.second }.toIntArray()

kmath-histograms/src/commonTest/kotlin/scietifik/kmath/histogram/MultivariateHistogramTest.kt

@@ -1,5 +1,8 @@
-package scientifik.kmath.histogram
+package scietifik.kmath.histogram
 
+import scientifik.kmath.histogram.RealHistogram
+import scientifik.kmath.histogram.fill
+import scientifik.kmath.histogram.put
 import scientifik.kmath.linear.Vector
 import kotlin.random.Random
 import kotlin.test.Test
@@ -10,7 +13,7 @@ import kotlin.test.assertTrue
 class MultivariateHistogramTest {
     @Test
     fun testSinglePutHistogram() {
-        val histogram = FastHistogram.fromRanges(
+        val histogram = RealHistogram.fromRanges(
             (-1.0..1.0),
             (-1.0..1.0)
         )
@@ -23,7 +26,7 @@ class MultivariateHistogramTest {
 
     @Test
     fun testSequentialPut() {
-        val histogram = FastHistogram.fromRanges(
+        val histogram = RealHistogram.fromRanges(
             (-1.0..1.0),
             (-1.0..1.0),
             (-1.0..1.0)

kmath-histograms/src/jsMain/kotlin/scientifik/kmath/histogram/Counters.kt

@@ -0,0 +1,33 @@
+package scientifik.kmath.histogram
+
+actual class LongCounter {
+    private var sum: Long = 0
+    actual fun decrement() {
+        sum--
+    }
+
+    actual fun increment() {
+        sum++
+    }
+
+    actual fun reset() {
+        sum = 0
+    }
+
+    actual fun sum(): Long = sum
+    actual fun add(l: Long) {
+        sum += l
+    }
+}
+
+actual class DoubleCounter {
+    private var sum: Double = 0.0
+    actual fun reset() {
+        sum = 0.0
+    }
+
+    actual fun sum(): Double = sum
+    actual fun add(d: Double) {
+        sum += d
+    }
+}

kmath-histograms/src/jvmMain/kotlin/scientifik/kmath/histogram/UnivariateHistogram.kt

@@ -26,7 +26,8 @@ class UnivariateBin(val position: Double, val size: Double, val counter: LongCou
 /**
  * Univariate histogram with log(n) bin search speed
  */
-class UnivariateHistogram private constructor(private val factory: (Double) -> UnivariateBin) : MutableHistogram<Double,UnivariateBin> {
+class UnivariateHistogram private constructor(private val factory: (Double) -> UnivariateBin) :
+    MutableHistogram<Double, UnivariateBin> {
 
     private val bins: TreeMap<Double, UnivariateBin> = TreeMap()
 
@@ -58,7 +59,7 @@ class UnivariateHistogram private constructor(private val factory: (Double) -> U
         (get(value) ?: createBin(value)).inc()
     }
 
-    override fun put(point: Buffer<out Double>, weight: Double) {
+    override fun putWithWeight(point: Buffer<out Double>, weight: Double) {
         if (weight != 1.0) TODO("Implement weighting")
         put(point[0])
     }
@@ -75,8 +76,14 @@ class UnivariateHistogram private constructor(private val factory: (Double) -> U
             val sorted = borders.sortedArray()
             return UnivariateHistogram { value ->
                 when {
-                    value < sorted.first() -> UnivariateBin(Double.NEGATIVE_INFINITY, Double.MAX_VALUE)
-                    value > sorted.last() -> UnivariateBin(Double.POSITIVE_INFINITY, Double.MAX_VALUE)
+                    value < sorted.first() -> UnivariateBin(
+                        Double.NEGATIVE_INFINITY,
+                        Double.MAX_VALUE
+                    )
+                    value > sorted.last() -> UnivariateBin(
+                        Double.POSITIVE_INFINITY,
+                        Double.MAX_VALUE
+                    )
                     else -> {
                         val index = (0 until sorted.size).first { value > sorted[it] }
                         val left = sorted[index]

kmath-jmh/build.gradle

@@ -1,10 +0,0 @@
-plugins {
-    id "java"
-    id "kotlin"
-    id "me.champeau.gradle.jmh" version "0.4.7"
-}
-
-dependencies {
-    compile project(':kmath-core')
-    //jmh project(':kmath-core')
-}