Merge pull request #24 from altavir/dev

dev

README.md

@@ -58,11 +58,11 @@ repositories {
 
 Then use regular dependency like
 ```groovy
-compile(group: 'scientifik', name: 'kmath-core-jvm', version: '0.0.1-SNAPSHOT')
+compile(group: 'scientifik', name: 'kmath-core', version: '0.0.1-SNAPSHOT')
 ```
 or in kotlin
 ```kotlin
-compile(group = "scientifik", name = "kmath-core-jvm", version = "0.0.1-SNAPSHOT")
+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). 

build.gradle

@@ -1,24 +0,0 @@
-buildscript {
-    ext.kotlin_version = '1.3.0'
-
-    repositories {
-        jcenter()
-    }
-
-    dependencies {
-        classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
-        classpath "org.jfrog.buildinfo:build-info-extractor-gradle:4+"
-    }
-}
-
-allprojects {
-    apply plugin: 'maven-publish'
-    apply plugin: "com.jfrog.artifactory"
-
-    group = 'scientifik'
-    version = '0.0.1-SNAPSHOT'
-}
-
-if(file('artifactory.gradle').exists()){
-    apply from: 'artifactory.gradle'
-}

build.gradle.kts

@@ -0,0 +1,35 @@
+buildscript {
+    extra["kotlinVersion"] = "1.3.11"
+    extra["ioVersion"] = "0.1.2-dev-2"
+    extra["coroutinesVersion"] = "1.0.1"
+
+    val kotlinVersion: String by extra
+    val ioVersion: String by extra
+    val coroutinesVersion: String by extra
+
+    repositories {
+        jcenter()
+    }
+
+    dependencies {
+        classpath("org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlinVersion")
+        classpath("org.jfrog.buildinfo:build-info-extractor-gradle:4+")
+    }
+}
+
+plugins {
+    id("com.jfrog.artifactory") version "4.8.1"  apply false
+//    id("org.jetbrains.kotlin.multiplatform") apply false
+}
+
+allprojects {
+    apply(plugin = "maven-publish")
+    apply(plugin = "com.jfrog.artifactory")
+
+    group = "scientifik"
+    version = "0.0.2-dev-1"
+}
+
+if(file("artifactory.gradle").exists()){
+    apply(from = "artifactory.gradle")
+}

kmath-core/build.gradle

@@ -1,10 +1,5 @@
 plugins {
-    id 'kotlin-multiplatform'
+    id "org.jetbrains.kotlin.multiplatform"
-}
-
-repositories {
-    maven { url = 'http://dl.bintray.com/kotlin/kotlin-eap' }
-    mavenCentral()
 }
 
 kotlin {
@@ -19,7 +14,7 @@ kotlin {
     sourceSets {
         commonMain {
             dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-stdlib-common'
+                api 'org.jetbrains.kotlin:kotlin-stdlib-common'
             }
         }
         commonTest {
@@ -30,7 +25,7 @@ kotlin {
         }
         jvmMain {
             dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
+                api 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
             }
         }
         jvmTest {
@@ -41,7 +36,7 @@ kotlin {
         }
         jsMain {
             dependencies {
-                implementation 'org.jetbrains.kotlin:kotlin-stdlib-js'
+                api 'org.jetbrains.kotlin:kotlin-stdlib-js'
             }
         }
         jsTest {

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

@@ -1,63 +1,42 @@
 package scientifik.kmath.histogram
 
-import scientifik.kmath.linear.RealVector
 import scientifik.kmath.linear.toVector
-import scientifik.kmath.structures.Buffer
+import scientifik.kmath.structures.*
-import scientifik.kmath.structures.NDStructure
-import scientifik.kmath.structures.ndStructure
 import kotlin.math.floor
 
-class MultivariateBin(override val center: RealVector, val sizes: RealVector, val counter: LongCounter = LongCounter()) : Bin<Double> {
+private operator fun RealPoint.minus(other: RealPoint) = ListBuffer((0 until size).map { get(it) - other[it] })
-    init {
-        if (center.size != sizes.size) error("Dimension mismatch in bin creation. Expected ${center.size}, but found ${sizes.size}")
-    }
 
-    override fun contains(vector: Buffer<out Double>): Boolean {
+private inline fun <T> Buffer<out Double>.mapIndexed(crossinline mapper: (Int, Double) -> T): Sequence<T> = (0 until size).asSequence().map { mapper(it, get(it)) }
-        if (vector.size != center.size) error("Dimension mismatch for input vector. Expected ${center.size}, but found ${vector.size}")
-        return vector.asSequence().mapIndexed { i, value -> value in (center[i] - sizes[i] / 2)..(center[i] + sizes[i] / 2) }.all { it }
-    }
-
-    override val value: Number get() = counter.sum()
-    internal operator fun inc() = this.also { counter.increment() }
-
-    override val dimension: Int get() = center.size
-}
 
 /**
- * Uniform multivariate histogram with fixed borders. Based on NDStructure implementation with complexity of m for bin search, where m is the number of dimensions
+ * 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: RealVector,
+        private val lower: RealPoint,
-        private val upper: RealVector,
+        private val upper: RealPoint,
         private val binNums: IntArray = IntArray(lower.size) { 20 }
-) : Histogram<Double, MultivariateBin> {
+) : MutableHistogram<Double, PhantomBin<Double>> {
+
+
+    private val strides = DefaultStrides(IntArray(binNums.size) { binNums[it] + 2 })
+
+    private val values: NDStructure<LongCounter> = ndStructure(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())
 
     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).any { it <= 0 }) error("Range for one of axis is not strictly positive")
+        if ((upper - lower).asSequence().any { it <= 0 }) error("Range for one of axis is not strictly positive")
     }
 
 
     override val dimension: Int get() = lower.size
 
-    //TODO optimize binSize performance if needed
-    private val binSize = (upper - lower).mapIndexed { index, value -> value / binNums[index] }.toVector()
-
-    private val bins: NDStructure<MultivariateBin> by lazy {
-        val actualSizes = IntArray(binNums.size) { binNums[it] + 2 }
-        ndStructure(actualSizes) { indexArray ->
-            val center = indexArray.mapIndexed { axis, index ->
-                when (index) {
-                    0 -> Double.NEGATIVE_INFINITY
-                    actualSizes[axis] -> Double.POSITIVE_INFINITY
-                    else -> lower[axis] + (index - 1) * binSize[axis]
-                }
-            }.toVector()
-            MultivariateBin(center, binSize)
-        }
-    }
 
     /**
      * Get internal [NDStructure] bin index for given axis
@@ -70,17 +49,60 @@ class FastHistogram(
         }
     }
 
+    private fun getIndex(point: Buffer<out Double>): IntArray = IntArray(dimension) { getIndex(it, point[it]) }
 
-    override fun get(point: Buffer<out Double>): MultivariateBin? {
+    private fun getValue(index: IntArray): Long {
-        val index = IntArray(dimension) { getIndex(it, point[it]) }
+        return values[index].sum()
-        return bins[index]
     }
 
-    override fun put(point: Buffer<out Double>) {
+    fun getValue(point: Buffer<out Double>): Long {
-        this[point]?.inc() ?: error("Could not find appropriate bin (should not be possible)")
+        return getValue(getIndex(point))
     }
 
-    override fun iterator(): Iterator<MultivariateBin> = bins.asSequence().map { it.second }.iterator()
+    private fun getTemplate(index: IntArray): BinTemplate<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)
+    }
+
+    fun getTemplate(point: Buffer<out Double>): BinTemplate<Double> {
+        return getTemplate(getIndex(point))
+    }
+
+    override fun get(point: Buffer<out Double>): PhantomBin<Double>? {
+        val index = getIndex(point)
+        return PhantomBin(getTemplate(index), getValue(index))
+    }
+
+    override fun put(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())
+    }.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())
+    }
 
     companion object {
 
@@ -108,8 +130,8 @@ class FastHistogram(
          */
         fun fromRanges(vararg ranges: Pair<ClosedFloatingPointRange<Double>, Int>): FastHistogram {
             return FastHistogram(
-                    ranges.map { it.first.start }.toVector(),
+                    ListBuffer(ranges.map { it.first.start }),
-                    ranges.map { it.first.endInclusive }.toVector(),
+                    ListBuffer(ranges.map { it.first.endInclusive }),
                     ranges.map { it.second }.toIntArray()
             )
         }

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

@@ -1,15 +1,19 @@
 package scientifik.kmath.histogram
 
-import scientifik.kmath.operations.Space
 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: Buffer<out T>): Boolean
+    operator fun contains(vector: Point<out T>): Boolean
     val dimension: Int
 }
 
@@ -21,7 +25,7 @@ interface Bin<T: Any> : Domain<T> {
      * The value of this bin
      */
     val value: Number
-    val center: Buffer<T>
+    val center: Point<T>
 }
 
 interface Histogram<T: Any, out B : Bin<T>> : Iterable<B> {
@@ -29,34 +33,31 @@ interface Histogram<T: Any, out B : Bin<T>> : Iterable<B> {
     /**
      * Find existing bin, corresponding to given coordinates
      */
-    operator fun get(point: Buffer<out T>): B?
+    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: Buffer<out T>)
+    fun put(point: Point<out T>, weight: Double = 1.0)
 }
 
-fun <T: Any> Histogram<T,*>.put(vararg point: T) = put(ArrayBuffer(point))
+fun <T: Any> MutableHistogram<T,*>.put(vararg point: T) = put(ArrayBuffer(point))
 
-fun <T: Any> Histogram<T,*>.fill(sequence: Iterable<Buffer<T>>) = sequence.forEach { put(it) }
+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> Histogram<T, *>.fill(buider: suspend SequenceScope<Buffer<T>>.() -> Unit) = fill(sequence(buider).asIterable())
+fun <T: Any> MutableHistogram<T, *>.fill(buider: suspend SequenceScope<Point<T>>.() -> Unit) = fill(sequence(buider).asIterable())
-
-/**
- * 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>>
-}

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

@@ -0,0 +1,63 @@
+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/LUDecomposition.kt

@@ -1,5 +1,7 @@
 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
@@ -9,7 +11,7 @@ import kotlin.math.absoluteValue
 /**
  * Implementation based on Apache common-maths LU-decomposition
  */
-abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
+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.  */
@@ -31,7 +33,7 @@ abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
      * L is a lower-triangular matrix
      * @return the L matrix (or null if decomposed matrix is singular)
      */
-    val l: Matrix<out T> by lazy {
+    val l: Matrix<out T, F> by lazy {
         matrix.context.produce { i, j ->
             when {
                 j < i -> lu[i, j]
@@ -48,7 +50,7 @@ abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
      * U is an upper-triangular matrix
      * @return the U matrix (or null if decomposed matrix is singular)
      */
-    val u: Matrix<out T> by lazy {
+    val u: Matrix<out T, F> by lazy {
         matrix.context.produce { i, j ->
             if (j >= i) lu[i, j] else field.zero
         }
@@ -64,7 +66,7 @@ abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
      * @return the P rows permutation matrix (or null if decomposed matrix is singular)
      * @see .getPivot
      */
-    val p: Matrix<out T> by lazy {
+    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
@@ -181,7 +183,7 @@ abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
 
 }
 
-class RealLUDecomposition(matrix: Matrix<Double>, private val singularityThreshold: Double = DEFAULT_TOO_SMALL) : LUDecomposition<Double>(matrix) {
+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
     }
@@ -194,12 +196,12 @@ class RealLUDecomposition(matrix: Matrix<Double>, private val singularityThresho
 
 
 /** Specialized solver.  */
-object RealLUSolver : LinearSolver<Double> {
+object RealLUSolver : LinearSolver<Double, DoubleField> {
 
 
-    fun decompose(mat: Matrix<Double>, threshold: Double = 1e-11): RealLUDecomposition = RealLUDecomposition(mat, threshold)
+    fun decompose(mat: Matrix<Double, DoubleField>, threshold: Double = 1e-11): RealLUDecomposition = RealLUDecomposition(mat, threshold)
 
-    override fun solve(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
+    override fun solve(a: RealMatrix, b: RealMatrix): RealMatrix {
         val decomposition = decompose(a, a.context.field.zero)
 
         if (b.rows != a.rows) {

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

@@ -2,282 +2,16 @@ package scientifik.kmath.linear
 
 import scientifik.kmath.operations.DoubleField
 import scientifik.kmath.operations.Field
-import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.Norm
-import scientifik.kmath.operations.SpaceElement
-import scientifik.kmath.structures.*
 
-/**
- * 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
- */
-abstract class MatrixSpace<T : Any>(val rows: Int, val columns: Int, val field: Field<T>) : Space<Matrix<T>> {
-
-    /**
-     * Produce the element of this space
-     */
-    abstract fun produce(initializer: (Int, Int) -> T): Matrix<T>
-
-    /**
-     * 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>
-
-    override val zero: Matrix<T> by lazy {
-        produce { _, _ -> field.zero }
-    }
-
-//    val one: Matrix<T> by lazy {
-//        produce { i, j -> if (i == j) field.one else field.zero }
-//    }
-
-    override fun add(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
-        return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
-    }
-
-    override fun multiply(a: Matrix<T>, k: Double): Matrix<T> {
-        //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 } }
-    }
-
-    /**
-     * Dot product. Throws exception on dimension mismatch
-     */
-    fun multiply(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
-        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) }
-        }
-    }
-
-    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> Matrix<T>.dot(b: Matrix<T>): Matrix<T> = this.context.multiply(this, b)
-
-/**
- * A matrix-like structure
- */
-interface Matrix<T : Any> : SpaceElement<Matrix<T>, MatrixSpace<T>> {
-    /**
-     * Number of rows
-     */
-    val rows: Int
-    /**
-     * Number of columns
-     */
-    val columns: Int
-
-    /**
-     * 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 val self: Matrix<T>
-        get() = this
-
-    fun transpose(): Matrix<T> {
-        return object : Matrix<T> {
-            override val context: MatrixSpace<T> = 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]
-        }
-    }
-
-    companion object {
-
-        /**
-         * Create [ArrayMatrix] with custom field
-         */
-        fun <T : Any> of(rows: Int, columns: Int, field: Field<T>, 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> diagonal(rows: Int, columns: Int, field: Field<T>, values: (Int) -> T = { field.one }): Matrix<T> {
-            return of(rows, columns, field) { i, j -> if (i == j) values(i) else field.zero }
-        }
-
-        /**
-         * 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
-        }
-    }
-}
-
-
-/**
- * A linear space for vectors
- */
-abstract class VectorSpace<T : Any>(val size: Int, val field: Field<T>) : Space<Vector<T>> {
-
-    abstract fun produce(initializer: (Int) -> T): Vector<T>
-
-    override val zero: Vector<T> by lazy { produce { field.zero } }
-
-    override fun add(a: Vector<T>, b: Vector<T>): Vector<T> = produce { with(field) { a[it] + b[it] } }
-
-    override fun multiply(a: Vector<T>, k: Double): Vector<T> = produce { with(field) { a[it] * k } }
-}
-
-
-interface Vector<T : Any> : SpaceElement<Vector<T>, VectorSpace<T>>, Buffer<T>, Iterable<T> {
-    override val size: Int get() = context.size
-
-    companion object {
-        /**
-         * Create vector with custom field
-         */
-        fun <T : Any> of(size: Int, field: Field<T>, initializer: (Int) -> T) =
-                ArrayVector(ArrayVectorSpace(size, field), initializer)
-
-        /**
-         * Create vector of [Double]
-         */
-        fun ofReal(size: Int, initializer: (Int) -> Double) =
-                ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), 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
-        }
-    }
-}
-
-typealias NDFieldFactory<T> = (IntArray) -> NDField<T>
-
-internal fun <T : Any> genericNDFieldFactory(field: Field<T>): NDFieldFactory<T> = { index -> GenericNDField(index, field) }
-internal val realNDFieldFactory: NDFieldFactory<Double> = { index -> GenericNDField(index, DoubleField) }
-
-
-/**
- * NDArray-based implementation of vector space. By default uses slow [SimpleNDField], but could be overridden with custom [NDField] factory.
- */
-class ArrayMatrixSpace<T : Any>(
-        rows: Int,
-        columns: Int,
-        field: Field<T>,
-        val ndFactory: NDFieldFactory<T> = genericNDFieldFactory(field)
-) : MatrixSpace<T>(rows, columns, field) {
-
-    val ndField by lazy {
-        ndFactory(intArrayOf(rows, columns))
-    }
-
-    override fun produce(initializer: (Int, Int) -> T): Matrix<T> = ArrayMatrix(this, initializer)
-
-    override fun produceSpace(rows: Int, columns: Int): ArrayMatrixSpace<T> {
-        return ArrayMatrixSpace(rows, columns, field, ndFactory)
-    }
-}
-
-class ArrayVectorSpace<T : Any>(
-        size: Int,
-        field: Field<T>,
-        val ndFactory: NDFieldFactory<T> = genericNDFieldFactory(field)
-) : VectorSpace<T>(size, field) {
-    val ndField by lazy {
-        ndFactory(intArrayOf(size))
-    }
-
-    override fun produce(initializer: (Int) -> T): Vector<T> = ArrayVector(this, initializer)
-}
-
-/**
- * Member of [ArrayMatrixSpace] which wraps 2-D array
- */
-class ArrayMatrix<T : Any> internal constructor(override val context: ArrayMatrixSpace<T>, val array: NDArray<T>) : Matrix<T> {
-
-    constructor(context: ArrayMatrixSpace<T>, initializer: (Int, Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0], list[1]) })
-
-    override val rows: Int get() = context.rows
-
-    override val columns: Int get() = context.columns
-
-    override fun get(i: Int, j: Int): T {
-        return array[i, j]
-    }
-
-    override val self: ArrayMatrix<T> get() = this
-}
-
-
-class ArrayVector<T : Any> internal constructor(override val context: ArrayVectorSpace<T>, val array: NDArray<T>) : Vector<T> {
-
-    constructor(context: ArrayVectorSpace<T>, initializer: (Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0]) })
-
-    init {
-        if (context.size != array.shape[0]) {
-            error("Array dimension mismatch")
-        }
-    }
-
-    override fun get(index: Int): T {
-        return array[index]
-    }
-
-    override val self: ArrayVector<T> get() = this
-
-    override fun iterator(): Iterator<T> = (0 until size).map { array[it] }.iterator()
-
-    override fun copy(): ArrayVector<T> = ArrayVector(context, array)
-
-    override fun toString(): String = this.joinToString(prefix = "[", postfix = "]", separator = ", ") { it.toString() }
-}
-
-typealias RealVector = Vector<Double>
 
 /**
  * A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
  */
-interface LinearSolver<T : Any> {
+interface LinearSolver<T : Any, F : Field<T>> {
-    fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
+    fun solve(a: Matrix<T, F>, b: Matrix<T, F>): Matrix<T, F>
-    fun solve(a: Matrix<T>, b: Vector<T>): Vector<T> = solve(a, b.toMatrix()).toVector()
+    fun solve(a: Matrix<T, F>, b: Vector<T, F>): Vector<T, F> = solve(a, b.toMatrix()).toVector()
-    fun inverse(a: Matrix<T>): Matrix<T> = solve(a, Matrix.diagonal(a.rows, a.columns, a.context.field))
+    fun inverse(a: Matrix<T, F>): Matrix<T, F> = solve(a, Matrix.diagonal(a.rows, a.columns, a.context.field))
 }
 
 /**
@@ -291,7 +25,7 @@ fun List<Double>.toVector() = Vector.ofReal(this.size) { this[it] }
 /**
  * Convert matrix to vector if it is possible
  */
-fun <T : Any> Matrix<T>.toVector(): Vector<T> {
+fun <T : Any, F : Field<T>> Matrix<T, F>.toVector(): Vector<T, F> {
     return when {
         this.columns == 1 -> {
 //            if (this is ArrayMatrix) {
@@ -307,7 +41,7 @@ fun <T : Any> Matrix<T>.toVector(): Vector<T> {
     }
 }
 
-fun <T : Any> Vector<T>.toMatrix(): Matrix<T> {
+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)
@@ -315,6 +49,14 @@ fun <T : Any> Vector<T>.toMatrix(): Matrix<T> {
 //        //Generic vector
 //        matrix(size, 1, context.field) { i, j -> get(i) }
 //    }
-    return Matrix.of(size, 1, context.field) { i, _ -> 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>

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

@@ -0,0 +1,187 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.operations.*
+import scientifik.kmath.structures.*
+
+/**
+ * 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
+ */
+abstract class MatrixSpace<T : Any, F : Ring<T>>(val rows: Int, val columns: Int, val field: F) : Space<Matrix<T, F>> {
+
+    /**
+     * Produce the element of this space
+     */
+    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 }
+    }
+
+//    val one: Matrix<T> by lazy {
+//        produce { i, j -> if (i == j) field.one else field.zero }
+//    }
+
+    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] } }
+    }
+
+    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 } }
+    }
+
+    /**
+     * Dot product. Throws exception on dimension mismatch
+     */
+    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) }
+        }
+    }
+
+    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)
+
+/**
+ * A matrix-like structure
+ */
+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
+
+    /**
+     * 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 val self: Matrix<T, F>
+        get() = this
+
+    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]
+        }
+    }
+
+    companion object {
+
+        /**
+         * Create [ArrayMatrix] with custom field
+         */
+        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 }
+        }
+
+        /**
+         * 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
+        }
+    }
+}
+
+
+
+
+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)
+    }
+}
+
+/**
+ * Member of [ArrayMatrixSpace] which wraps 2-D array
+ */
+class ArrayMatrix<T : Any, F : Field<T>> internal constructor(override val context: ArrayMatrixSpace<T, F>, val element: NDElement<T, F>) : Matrix<T, F> {
+
+    constructor(context: ArrayMatrixSpace<T, F>, initializer: (Int, Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0], list[1]) })
+
+    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]
+    }
+
+    override val self: ArrayMatrix<T, F> get() = this
+}

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

@@ -0,0 +1,103 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.histogram.Point
+import scientifik.kmath.operations.DoubleField
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.SpaceElement
+import scientifik.kmath.structures.NDElement
+import scientifik.kmath.structures.get
+
+/**
+ * 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>> {
+
+    abstract fun produce(initializer: (Int) -> T): Vector<T, S>
+
+    override val zero: Vector<T, S> by lazy { produce { space.zero } }
+
+    override fun add(a: Point<T>, b: Point<T>): Vector<T, S> = produce { with(space) { a[it] + b[it] } }
+
+    override fun multiply(a: Point<T>, k: Double): Vector<T, S> = produce { with(space) { a[it] * k } }
+}
+
+
+/**
+ * A point coupled to the linear space
+ */
+interface Vector<T : Any, S : Space<T>> : SpaceElement<Point<T>, VectorSpace<T, S>>, Point<T>, Iterable<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())
+
+    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)
+
+        private val realSpaceCache = HashMap<Int, ArrayVectorSpace<Double, DoubleField>>()
+
+        private fun getRealSpace(size: Int): ArrayVectorSpace<Double, DoubleField> {
+            return realSpaceCache.getOrPut(size){ArrayVectorSpace(size, DoubleField, realNDFieldFactory)}
+        }
+
+        /**
+         * 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)
+}
+
+
+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]) })
+
+    init {
+        if (context.size != element.shape[0]) {
+            error("Array dimension mismatch")
+        }
+    }
+
+    override fun get(index: Int): T {
+        return element[index]
+    }
+
+    override val self: ArrayVector<T, F> get() = this
+
+    override fun iterator(): Iterator<T> = (0 until size).map { element[it] }.iterator()
+
+    override fun toString(): String = this.joinToString(prefix = "[", postfix = "]", separator = ", ") { it.toString() }
+}
+

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

@@ -38,4 +38,8 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Compl
     val abs: Double
         get() = kotlin.math.sqrt(square)
 
+    companion object {
+
+    }
+
 }

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

@@ -2,10 +2,20 @@ 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 : Field<Real>, TrigonometricOperations<Real>, PowerOperations<Real>, ExponentialOperations<Real> {
+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)
@@ -13,33 +23,24 @@ object RealField : Field<Real>, TrigonometricOperations<Real>, PowerOperations<R
     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 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 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 exp(arg: Real): Real = Real(kotlin.math.exp(arg.value))
 
-    override fun ln(arg: Real): Real  = Real(kotlin.math.ln(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 could be replaced by inline class in kotlin 1.3 if it would allow to avoid boxing
+ * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
  */
-data class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
+inline class Real(val value: Double) : FieldElement<Real, RealField> {
-    /*
-     * The class uses composition instead of inheritance since Double is final
-     */
-
-    override fun toByte(): Byte = value.toByte()
-    override fun toChar(): Char = value.toChar()
-    override fun toDouble(): Double = value
-    override fun toFloat(): Float = value.toFloat()
-    override fun toInt(): Int = value.toInt()
-    override fun toLong(): Long = value.toLong()
-    override fun toShort(): Short = value.toShort()
 
     //values are dynamically calculated to save memory
     override val self
@@ -48,24 +49,41 @@ data class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
     override val context
         get() = RealField
 
+    companion object {
+
+    }
 }
 
 /**
  * A field for double without boxing. Does not produce appropriate field element
  */
-object DoubleField : Field<Double>, TrigonometricOperations<Double>, PowerOperations<Double>, ExponentialOperations<Double> {
+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 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 power(arg: Double, pow: Double): Double = arg.pow(pow)
 
-    override fun exp(arg: Double): Double  =kotlin.math.exp(arg)
+    override fun exp(arg: Double): Double = kotlin.math.exp(arg)
 
-    override fun ln(arg: Double): Double  = kotlin.math.ln(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/OptionalOperations.kt

@@ -46,3 +46,9 @@ interface ExponentialOperations<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)
+
+interface Norm<in T, out R> {
+    fun norm(arg: T): R
+}
+
+fun <T : MathElement<T, out Norm<T, R>>, R> norm(arg: T): R = arg.context.norm(arg)

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

@@ -2,30 +2,40 @@ package scientifik.kmath.structures
 
 
 /**
- * A generic linear buffer for both primitives and objects
+ * A generic random access structure for both primitives and objects
  */
-interface Buffer<T> : Iterable<T> {
+interface Buffer<T> {
 
     val size: Int
 
     operator fun get(index: Int): T
 
-    /**
+    operator fun iterator(): Iterator<T>
-     * A shallow copy of the buffer
-     */
-    fun copy(): Buffer<T>
 }
 
+fun <T> Buffer<T>.asSequence(): Sequence<T> = iterator().asSequence()
+
 interface MutableBuffer<T> : Buffer<T> {
     operator fun set(index: Int, value: T)
 
     /**
      * A shallow copy of the buffer
      */
-    override fun copy(): MutableBuffer<T>
+    fun copy(): MutableBuffer<T>
 }
 
-inline class ListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T> {
+
+inline class ListBuffer<T>(private val list: List<T>) : Buffer<T> {
+
+    override val size: Int
+        get() = list.size
+
+    override fun get(index: Int): T = list[index]
+
+    override fun iterator(): Iterator<T> = list.iterator()
+}
+
+inline class MutableListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T> {
 
     override val size: Int
         get() = list.size
@@ -36,12 +46,13 @@ inline class ListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T>
         list[index] = value
     }
 
-    override fun iterator(): Iterator<T>  = list.iterator()
+    override fun iterator(): Iterator<T> = list.iterator()
 
-    override fun copy(): MutableBuffer<T> = ListBuffer(ArrayList(list))
+    override fun copy(): MutableBuffer<T> = MutableListBuffer(ArrayList(list))
 }
 
 class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
+    //Can't inline because array invariant
     override val size: Int
         get() = array.size
 
@@ -51,12 +62,12 @@ class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
         array[index] = value
     }
 
-    override fun iterator(): Iterator<T>  = array.iterator()
+    override fun iterator(): Iterator<T> = array.iterator()
 
     override fun copy(): MutableBuffer<T> = ArrayBuffer(array.copyOf())
 }
 
-class DoubleBuffer(private val array: DoubleArray) : MutableBuffer<Double> {
+inline class DoubleBuffer(private val array: DoubleArray) : MutableBuffer<Double> {
     override val size: Int
         get() = array.size
 
@@ -66,15 +77,63 @@ class DoubleBuffer(private val array: DoubleArray) : MutableBuffer<Double> {
         array[index] = value
     }
 
-    override fun iterator(): Iterator<Double>  = array.iterator()
+    override fun iterator(): Iterator<Double> = array.iterator()
 
     override fun copy(): MutableBuffer<Double> = DoubleBuffer(array.copyOf())
 }
 
-inline fun <reified T : Any> buffer(size: Int, noinline initializer: (Int) -> T): Buffer<T> {
+inline class IntBuffer(private val array: IntArray) : MutableBuffer<Int> {
-    return ArrayBuffer(Array(size, initializer))
+    override val size: Int
+        get() = array.size
+
+    override fun get(index: Int): Int = array[index]
+
+    override fun set(index: Int, value: Int) {
+        array[index] = value
+    }
+
+    override fun iterator(): Iterator<Int> = array.iterator()
+
+    override fun copy(): MutableBuffer<Int> = IntBuffer(array.copyOf())
 }
 
-inline fun <reified T : Any> mutableBuffer(size: Int, noinline initializer: (Int) -> T): MutableBuffer<T> {
+inline class ReadOnlyBuffer<T>(private val buffer: MutableBuffer<T>) : Buffer<T> {
-    return ArrayBuffer(Array(size, initializer))
+    override val size: Int get() = buffer.size
+
+    override fun get(index: Int): T = buffer.get(index)
+
+    override fun iterator(): Iterator<T> = buffer.iterator()
+}
+
+/**
+ * Convert this buffer to read-only buffer
+ */
+fun <T> Buffer<T>.asReadOnly(): Buffer<T> = if (this is MutableBuffer) {
+    ReadOnlyBuffer(this)
+} else {
+    this
+}
+
+/**
+ * Create most appropriate immutable buffer for given type avoiding boxing wherever possible
+ */
+@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))
+    }
 }

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

@@ -0,0 +1,42 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.ExponentialOperations
+import scientifik.kmath.operations.ExtendedField
+import scientifik.kmath.operations.PowerOperations
+import scientifik.kmath.operations.TrigonometricOperations
+
+
+/**
+ * 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) } }
+    }
+}
+
+

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

@@ -0,0 +1,20 @@
+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/NDField.kt

@@ -15,25 +15,25 @@ class ShapeMismatchException(val expected: IntArray, val actual: IntArray) : Run
  * @param field - operations field defined on individual array element
  * @param T the type of the element contained in NDArray
  */
-abstract class NDField<T>(val shape: IntArray, val field: Field<T>) : Field<NDArray<T>> {
+abstract class NDField<T, F : Field<T>>(val shape: IntArray, val field: F) : Field<NDElement<T, F>> {
 
-    abstract fun produceStructure(initializer: (IntArray) -> T): NDStructure<T>
+    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: (IntArray) -> T): NDArray<T> = NDArray(this, produceStructure(initializer))
+    fun produce(initializer: F.(IntArray) -> T): NDElement<T, F> = NDStructureElement(this, produceStructure(initializer))
 
-    override val zero: NDArray<T> by lazy {
+    override val zero: NDElement<T, F> by lazy {
-        produce { this.field.zero }
+        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 arrays: NDArray<T>) {
+    private fun checkShape(vararg elements: NDElement<T, F>) {
-        arrays.forEach {
+        elements.forEach {
             if (!shape.contentEquals(it.shape)) {
                 throw ShapeMismatchException(shape, it.shape)
             }
@@ -43,7 +43,7 @@ abstract class NDField<T>(val shape: IntArray, val field: Field<T>) : Field<NDAr
     /**
      * Element-by-element addition
      */
-    override fun add(a: NDArray<T>, b: NDArray<T>): NDArray<T> {
+    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] } }
     }
@@ -51,18 +51,18 @@ abstract class NDField<T>(val shape: IntArray, val field: Field<T>) : Field<NDAr
     /**
      * Multiply all elements by cinstant
      */
-    override fun multiply(a: NDArray<T>, k: Double): NDArray<T> {
+    override fun multiply(a: NDElement<T, F>, k: Double): NDElement<T, F> {
         checkShape(a)
         return produce { with(field) { a[it] * k } }
     }
 
-    override val one: NDArray<T>
+    override val one: NDElement<T, F>
-        get() = produce { this.field.one }
+        get() = produce { one }
 
     /**
      * Element-by-element multiplication
      */
-    override fun multiply(a: NDArray<T>, b: NDArray<T>): NDArray<T> {
+    override fun multiply(a: NDElement<T, F>, b: NDElement<T, F>): NDElement<T, F> {
         checkShape(a)
         return produce { with(field) { a[it] * b[it] } }
     }
@@ -70,73 +70,77 @@ abstract class NDField<T>(val shape: IntArray, val field: Field<T>) : Field<NDAr
     /**
      * Element-by-element division
      */
-    override fun divide(a: NDArray<T>, b: NDArray<T>): NDArray<T> {
+    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
+//     * Reverse sum operation
-     */
+//     */
-    operator fun <T> T.plus(arg: NDArray<T>): NDArray<T> = arg + this
+//    operator fun T.plus(arg: NDElement<T, F>): NDElement<T, F> = arg + this
-
+//
-    /**
+//    /**
-     * Reverse minus operation
+//     * Reverse minus operation
-     */
+//     */
-    operator fun <T> T.minus(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
+//    operator fun T.minus(arg: NDElement<T, F>): NDElement<T, F> = arg.transformIndexed { _, value ->
-        with(arg.context.field) {
+//        with(arg.context.field) {
-            this@minus - value
+//            this@minus - value
-        }
+//        }
-    }
+//    }
-
+//
-    /**
+//    /**
-     * Reverse product operation
+//     * Reverse product operation
-     */
+//     */
-    operator fun <T> T.times(arg: NDArray<T>): NDArray<T> = arg * this
+//    operator fun T.times(arg: NDElement<T, F>): NDElement<T, F> = arg * this
-
+//
-    /**
+//    /**
-     * Reverse division operation
+//     * Reverse division operation
-     */
+//     */
-    operator fun <T> T.div(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
+//    operator fun T.div(arg: NDElement<T, F>): NDElement<T, F> = arg.transformIndexed { _, value ->
-        with(arg.context.field) {
+//        with(arg.context.field) {
-            this@div / value
+//            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)) }
+
+
 /**
- *  Immutable [NDStructure] coupled to the context. Emulates Python ndarray
+ *  Read-only [NDStructure] coupled to the context.
  */
-data class NDArray<T>(override val context: NDField<T>, private val structure: NDStructure<T>) : FieldElement<NDArray<T>, NDField<T>>, NDStructure<T> by structure {
+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: NDArray<T>
+    override val self: NDElement<T, F>  get() = this
-        get() = this
-
-    fun transform(action: (IntArray, T) -> T): NDArray<T> = context.produce { action(it, get(*it)) }
 }
 
 /**
  * Element by element application of any operation on elements to the whole array. Just like in numpy
  */
-operator fun <T> Function1<T, T>.invoke(ndArray: NDArray<T>): NDArray<T> = ndArray.transform { _, value -> this(value) }
+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 [NDArray] and single element
+ * Summation operation for [NDElement] and single element
  */
-operator fun <T> NDArray<T>.plus(arg: T): NDArray<T> = transform { _, value ->
+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 [NDArray] and single element
+ * Subtraction operation between [NDElement] and single element
  */
-operator fun <T> NDArray<T>.minus(arg: T): NDArray<T> = transform { _, value ->
+operator fun <T, F : Field<T>> NDElement<T, F>.minus(arg: T): NDElement<T, F> = transform {value ->
     with(context.field) {
         arg - value
     }
@@ -145,25 +149,25 @@ operator fun <T> NDArray<T>.minus(arg: T): NDArray<T> = transform { _, value ->
 /* prod and div */
 
 /**
- * Product operation for [NDArray] and single element
+ * Product operation for [NDElement] and single element
  */
-operator fun <T> NDArray<T>.times(arg: T): NDArray<T> = transform { _, value ->
+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 [NDArray] and single element
+ * Division operation between [NDElement] and single element
  */
-operator fun <T> NDArray<T>.div(arg: T): NDArray<T> = transform { _, value ->
+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>(shape: IntArray, field: Field<T>) : NDField<T>(shape, field) {
+class GenericNDField<T : Any, F : Field<T>>(shape: IntArray, field: F) : NDField<T, F>(shape, field) {
-    override fun produceStructure(initializer: (IntArray) -> T): NDStructure<T> = genericNdStructure(shape, initializer)
+    override fun produceStructure(initializer: F.(IntArray) -> T): NDStructure<T> = genericNdStructure(shape) { field.initializer(it) }
 }
 
 //typealias NDFieldFactory<T> = (IntArray)->NDField<T>
@@ -172,22 +176,25 @@ object NDArrays {
     /**
      * Create a platform-optimized NDArray of doubles
      */
-    fun realNDArray(shape: IntArray, initializer: (IntArray) -> Double = { 0.0 }): NDArray<Double> {
+    fun realNDArray(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
-        return GenericNDField(shape, DoubleField).produce(initializer)
+        return ExtendedNDField(shape, DoubleField).produce(initializer)
     }
 
-    fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDArray<Double> {
+    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 }): NDArray<Double> {
+    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 }): NDArray<Double> {
+    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
 //     */
@@ -196,7 +203,7 @@ object NDArrays {
     /**
      * Simple boxing NDArray
      */
-    fun <T : Any> create(field: Field<T>, shape: IntArray, initializer: (IntArray) -> T): NDArray<T> {
+    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

@@ -1,7 +1,7 @@
 package scientifik.kmath.structures
 
 
-interface NDStructure<T> : Iterable<Pair<IntArray, T>> {
+interface NDStructure<T> {
 
     val shape: IntArray
 
@@ -9,6 +9,8 @@ interface NDStructure<T> : Iterable<Pair<IntArray, T>> {
         get() = shape.size
 
     operator fun get(index: IntArray): T
+
+    fun elements(): Sequence<Pair<IntArray, T>>
 }
 
 operator fun <T> NDStructure<T>.get(vararg index: Int): T = get(index)
@@ -18,7 +20,7 @@ interface MutableNDStructure<T> : NDStructure<T> {
 }
 
 fun <T> MutableNDStructure<T>.transformInPlace(action: (IntArray, T) -> T) {
-    for ((index, oldValue) in this) {
+    elements().forEach { (index, oldValue) ->
         this[index] = action(index, oldValue)
     }
 }
@@ -76,22 +78,22 @@ class DefaultStrides(override val shape: IntArray) : Strides {
     override fun offset(index: IntArray): Int {
         return index.mapIndexed { i, value ->
             if (value < 0 || value >= shape[i]) {
-                throw RuntimeException("Index $value out of shape bounds: (0,${shape[i]})")
+                throw RuntimeException("Index $value out of shape bounds: (0,${this.shape[i]})")
             }
             value * strides[i]
         }.sum()
     }
 
     override fun index(offset: Int): IntArray {
-        return sequence {
+        val res = IntArray(shape.size)
-            var current = offset
+        var current = offset
-            var strideIndex = strides.size - 2
+        var strideIndex = strides.size - 2
-            while (strideIndex >= 0) {
+        while (strideIndex >= 0) {
-                yield(current / strides[strideIndex])
+            res[strideIndex] = (current / strides[strideIndex])
-                current %= strides[strideIndex]
+            current %= strides[strideIndex]
-                strideIndex--
+            strideIndex--
-            }
+        }
-        }.toList().reversed().toIntArray()
+        return res
     }
 
     override val linearSize: Int
@@ -107,8 +109,8 @@ abstract class GenericNDStructure<T, B : Buffer<T>> : NDStructure<T> {
     override val shape: IntArray
         get() = strides.shape
 
-    override fun iterator(): Iterator<Pair<IntArray, T>> =
+    override fun elements()=
-            strides.indices().map { it to this[it] }.iterator()
+            strides.indices().map { it to this[it] }
 }
 
 /**
@@ -126,10 +128,10 @@ class BufferNDStructure<T>(
     }
 }
 
-inline fun <reified T: Any> ndStructure(strides: Strides, noinline initializer: (IntArray) -> T) =
+inline fun <reified T : Any> ndStructure(strides: Strides, noinline initializer: (IntArray) -> T) =
-        BufferNDStructure<T>(strides, buffer(strides.linearSize){ i-> initializer(strides.index(i))})
+        BufferNDStructure<T>(strides, buffer(strides.linearSize) { i -> initializer(strides.index(i)) })
 
-inline fun <reified T: Any> ndStructure(shape: IntArray, noinline initializer: (IntArray) -> T) =
+inline fun <reified T : Any> ndStructure(shape: IntArray, noinline initializer: (IntArray) -> T) =
         ndStructure(DefaultStrides(shape), initializer)
 
 
@@ -153,22 +155,22 @@ class MutableBufferNDStructure<T>(
 /**
  * Create optimized mutable structure for given type
  */
-inline fun <reified T: Any> mutableNdStructure(strides: Strides, noinline initializer: (IntArray) -> T) =
+inline fun <reified T : Any> mutableNdStructure(strides: Strides, noinline initializer: (IntArray) -> T) =
-            MutableBufferNDStructure(strides, mutableBuffer(strides.linearSize) { i -> initializer(strides.index(i)) })
+        MutableBufferNDStructure(strides, mutableBuffer(strides.linearSize) { i -> initializer(strides.index(i)) })
 
-inline fun <reified T: Any> mutableNdStructure(shape: IntArray, noinline initializer: (IntArray) -> T) =
+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>{
+fun <T> genericNdStructure(shape: IntArray, initializer: (IntArray) -> T): MutableBufferNDStructure<T> {
     val strides = DefaultStrides(shape)
-    val sequence = sequence{
+    val sequence = sequence {
-        strides.indices().forEach{
+        strides.indices().forEach {
             yield(initializer(it))
         }
     }
-    val buffer = ListBuffer<T>(sequence.toMutableList())
+    val buffer = MutableListBuffer(sequence.toMutableList())
     return MutableBufferNDStructure(strides, buffer)
 }

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

@@ -39,4 +39,15 @@ class FieldExpressionContextTest {
         val expression = FieldExpressionContext(DoubleField).expression()
         assertEquals(expression("x" to 1.0), 4.0)
     }
+
+    @Test
+    fun valueExpression() {
+        val expressionBuilder: FieldExpressionContext<Double>.()->Expression<Double> = {
+            val x = variable("x")
+            x * x + 2 * x + 1.0
+        }
+
+        val expression = FieldExpressionContext(DoubleField).expressionBuilder()
+        assertEquals(expression("x" to 1.0), 4.0)
+    }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/histogram/MultivariateHistogramTest.kt

@@ -14,10 +14,11 @@ class MultivariateHistogramTest {
                 (-1.0..1.0),
                 (-1.0..1.0)
         )
-        histogram.put(0.6, 0.6)
+        histogram.put(0.55, 0.55)
         val bin = histogram.find { it.value.toInt() > 0 }!!
-        assertTrue { bin.contains(Vector.ofReal(0.6, 0.6)) }
+        assertTrue { bin.contains(Vector.ofReal(0.55, 0.55)) }
-        assertFalse { bin.contains(Vector.ofReal(-0.6, 0.6)) }
+        assertTrue { bin.contains(Vector.ofReal(0.6, 0.5)) }
+        assertFalse { bin.contains(Vector.ofReal(-0.55, 0.55)) }
     }
 
     @Test

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

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

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

@@ -1,11 +1,14 @@
 package scientifik.kmath.structures
 
+import scientifik.kmath.operations.Norm
+import scientifik.kmath.structures.NDArrays.produceReal
 import scientifik.kmath.structures.NDArrays.real2DArray
+import kotlin.math.abs
 import kotlin.math.pow
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
-class RealNDFieldTest {
+class NumberNDFieldTest {
     val array1 = real2DArray(3, 3) { i, j -> (i + j).toDouble() }
     val array2 = real2DArray(3, 3) { i, j -> (i - j).toDouble() }
 
@@ -29,7 +32,7 @@ class RealNDFieldTest {
         for (i in 0..2) {
             for (j in 0..2) {
                 val expected = (i * 10 + j).toDouble()
-                assertEquals(expected, array[i, j],"Error at index [$i, $j]")
+                assertEquals(expected, array[i, j], "Error at index [$i, $j]")
             }
         }
     }
@@ -38,6 +41,28 @@ class RealNDFieldTest {
     fun testExternalFunction() {
         val function: (Double) -> Double = { x -> x.pow(2) + 2 * x + 1 }
         val result = function(array1) + 1.0
-        assertEquals(10.0, result[1,1])
+        assertEquals(10.0, result[1, 1])
+    }
+
+    @Test
+    fun testLibraryFunction() {
+        val abs: (Double) -> Double = ::abs
+        val result = abs(array2)
+        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 testInternalContext() {
+        produceReal(array1.shape) {
+            with(L2Norm) {
+                1 + norm(array1) + exp(array2)
+            }
+        }
     }
 }

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

@@ -26,7 +26,7 @@ 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) : Histogram<Double,UnivariateBin> {
+class UnivariateHistogram private constructor(private val factory: (Double) -> UnivariateBin) : MutableHistogram<Double,UnivariateBin> {
 
     private val bins: TreeMap<Double, UnivariateBin> = TreeMap()
 
@@ -58,7 +58,10 @@ class UnivariateHistogram private constructor(private val factory: (Double) -> U
         (get(value) ?: createBin(value)).inc()
     }
 
-    override fun put(point: Buffer<out Double>) = put(point[0])
+    override fun put(point: Buffer<out Double>, weight: Double) {
+        if (weight != 1.0) TODO("Implement weighting")
+        put(point[0])
+    }
 
     companion object {
         fun uniform(binSize: Double, start: Double = 0.0): UnivariateHistogram {

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

@@ -0,0 +1,55 @@
+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

@@ -0,0 +1,25 @@
+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

@@ -0,0 +1,28 @@
+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

@@ -0,0 +1,23 @@
+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-core/src/jvmTest/kotlin/scientifik/kmath/structures/ComplexBufferSpecTest.kt

@@ -0,0 +1,17 @@
+package scientifik.kmath.structures
+
+import org.junit.Test
+import scientifik.kmath.operations.Complex
+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())
+        }
+
+        assertEquals(Complex(5.0, -5.0), buffer[5])
+    }
+}

kmath-coroutines/build.gradle

@@ -0,0 +1,42 @@
+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/src/commonMain/kotlin/scientifik/kmath/structures/CoroutinesExtra.kt

@@ -0,0 +1,11 @@
+package scientifik.kmath.structures
+
+import kotlinx.coroutines.CoroutineDispatcher
+import kotlinx.coroutines.CoroutineScope
+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

@@ -0,0 +1,79 @@
+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

@@ -0,0 +1,20 @@
+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/_CoroutinesExtra.kt

@@ -0,0 +1,6 @@
+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-io/build.gradle

@@ -0,0 +1,55 @@
+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 project(":kmath-core")
+                implementation 'org.jetbrains.kotlin:kotlin-stdlib-common'
+                api "org.jetbrains.kotlinx:kotlinx-io:$ioVersion"
+            }
+        }
+        commonTest {
+            dependencies {
+                implementation 'org.jetbrains.kotlin:kotlin-test-common'
+                implementation 'org.jetbrains.kotlin:kotlin-test-annotations-common'
+            }
+        }
+        jvmMain {
+            dependencies {
+                implementation 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
+                api "org.jetbrains.kotlinx:kotlinx-io-jvm:$ioVersion"
+            }
+        }
+        jvmTest {
+            dependencies {
+                implementation 'org.jetbrains.kotlin:kotlin-test'
+                implementation 'org.jetbrains.kotlin:kotlin-test-junit'
+            }
+        }
+        jsMain {
+            dependencies {
+                implementation 'org.jetbrains.kotlin:kotlin-stdlib-js'
+            }
+        }
+        jsTest {
+            dependencies {
+                implementation 'org.jetbrains.kotlin:kotlin-test-js'
+            }
+        }
+//        mingwMain {
+//        }
+//        mingwTest {
+//        }
+    }
+}

kmath-jmh/build.gradle

@@ -4,12 +4,7 @@ plugins {
     id "me.champeau.gradle.jmh" version "0.4.7"
 }
 
-repositories {
-    maven { url = 'http://dl.bintray.com/kotlin/kotlin-eap' }
-    mavenCentral()
-}
-
 dependencies {
-    implementation project(':kmath-core')
+    compile project(':kmath-core')
-    jmh 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
+    //jmh project(':kmath-core')
 }

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

@@ -4,8 +4,7 @@ import org.openjdk.jmh.annotations.*
 import java.nio.IntBuffer
 
 
-@Fork(1)
+@Warmup(iterations = 1)
-@Warmup(iterations = 2)
 @Measurement(iterations = 5)
 @State(Scope.Benchmark)
 open class ArrayBenchmark {
@@ -30,7 +29,6 @@ open class ArrayBenchmark {
         for (i in 1..10000) {
             res += array[10000 - i]
         }
-        print(res)
     }
 
     @Benchmark
@@ -39,7 +37,6 @@ open class ArrayBenchmark {
         for (i in 1..10000) {
             res += arrayBuffer.get(10000 - i)
         }
-        print(res)
     }
 
     @Benchmark
@@ -48,6 +45,5 @@ open class ArrayBenchmark {
         for (i in 1..10000) {
             res += nativeBuffer.get(10000 - i)
         }
-        print(res)
     }
 }

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

@@ -0,0 +1,38 @@
+package scientifik.kmath.structures
+
+import org.openjdk.jmh.annotations.*
+import scientifik.kmath.operations.Complex
+
+@Warmup(iterations = 1)
+@Measurement(iterations = 5)
+@State(Scope.Benchmark)
+open class BufferBenchmark {
+
+    @Benchmark
+    fun genericDoubleBufferReadWrite() {
+        val buffer = Double.createBuffer(size)
+        (0 until size).forEach {
+            buffer[it] = it.toDouble()
+        }
+
+        (0 until size).forEach {
+            buffer[it]
+        }
+    }
+
+    @Benchmark
+    fun complexBufferReadWrite() {
+        val buffer = Complex.createBuffer(size/2)
+        (0 until size/2).forEach {
+            buffer[it] = Complex(it.toDouble(), -it.toDouble())
+        }
+
+        (0 until size/2).forEach {
+            buffer[it]
+        }
+    }
+
+    companion object {
+        const val size = 1000
+    }
+}

settings.gradle

@@ -1,13 +0,0 @@
-pluginManagement {
-    repositories {
-        mavenCentral()
-        maven { url = 'https://plugins.gradle.org/m2/' }
-    }
-}
-
-enableFeaturePreview('GRADLE_METADATA')
-
-rootProject.name = 'kmath'
-include ':kmath-core'
-include ':kmath-jmh'
-

settings.gradle.kts

@@ -0,0 +1,16 @@
+pluginManagement {
+    repositories {
+        mavenCentral()
+        maven("https://plugins.gradle.org/m2/")
+    }
+}
+
+//enableFeaturePreview("GRADLE_METADATA")
+
+rootProject.name = "kmath"
+include(
+        ":kmath-core",
+        ":kmath-io",
+        ":kmath-coroutines",
+        ":kmath-jmh"
+)