NDStructures redone

.gitignore

@@ -1,5 +1,5 @@
 .gradle
-/build/
+**/build/
 /.idea/
 
 # Avoid ignoring Gradle wrapper jar file (.jar files are usually ignored)

build.gradle

@@ -1,5 +1,5 @@
 buildscript {
-    ext.kotlin_version = '1.3.0-rc-146'
+    ext.kotlin_version = '1.3.0-rc-190'
 
     repositories {
         jcenter()

kmath-core/build.gradle

@@ -1,6 +1,6 @@
 plugins {
     id 'kotlin-multiplatform'// version '1.3.0-rc-116'
-    id "me.champeau.gradle.jmh" version "0.4.5"
+    id "me.champeau.gradle.jmh" version "0.4.7"
 }
 
 repositories {
@@ -8,9 +8,14 @@ repositories {
     mavenCentral()
 }
 
+dependencies{
+    jmh 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
+}
+
 kotlin {
     targets {
-        fromPreset(presets.jvm, 'jvm')
+        fromPreset(presets.jvmWithJava, 'jvm')
+        //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

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

@@ -1,18 +1,19 @@
 package scientifik.kmath.linear
 
-import scientifik.kmath.structures.MutableNDArray
+import scientifik.kmath.structures.MutableNDStructure
-import scientifik.kmath.structures.NDArray
+import scientifik.kmath.structures.NDStructure
-import scientifik.kmath.structures.NDArrays
+import scientifik.kmath.structures.genericNdStructure
+import scientifik.kmath.structures.get
 import kotlin.math.absoluteValue
 
 /**
- * Implementation copier from Apache common-maths
+ * Implementation based on Apache common-maths LU-decomposition
  */
 abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
 
     private val field get() = matrix.context.field
     /** Entries of LU decomposition.  */
-    internal val lu: NDArray<T>
+    internal val lu: NDStructure<T>
     /** Pivot permutation associated with LU decomposition.  */
     internal val pivot: IntArray
     /** Parity of the permutation associated with the LU decomposition.  */
@@ -85,26 +86,18 @@ abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
             }
         }
 
-//    /**
-//     * Get a solver for finding the A  X = B solution in exact linear
-//     * sense.
-//     * @return a solver
-//     */
-//    val solver: DecompositionSolver
-//        get() = Solver(lu, pivot, singular)
-
     /**
      * In-place transformation for [MutableNDArray], using given transformation for each element
      */
-    operator fun <T> MutableNDArray<T>.set(i: Int, j: Int, value: T) {
+    operator fun <T> MutableNDStructure<T>.set(i: Int, j: Int, value: T) {
-        this[listOf(i, j)] = value
+        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<NDArray<T>, IntArray> {
+    private fun calculateLU(): Pair<NDStructure<T>, IntArray> {
         if (matrix.rows != matrix.columns) {
             error("LU decomposition supports only square matrices")
         }
@@ -112,7 +105,7 @@ abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
         val m = matrix.columns
         val pivot = IntArray(matrix.rows)
         //TODO fix performance
-        val lu: MutableNDArray<T> = NDArrays.createMutable(matrix.context.field, listOf(matrix.rows, matrix.columns)) { index -> matrix[index[0], index[1]] }
+        val lu: MutableNDStructure<T> = genericNdStructure(intArrayOf(matrix.rows, matrix.columns)) { index -> matrix[index[0], index[1]] }
 
 
         with(matrix.context.field) {
@@ -203,44 +196,6 @@ class RealLUDecomposition(matrix: Matrix<Double>, private val singularityThresho
 /** Specialized solver.  */
 object RealLUSolver : LinearSolver<Double> {
 
-//
-//    /** {@inheritDoc}  */
-//    override fun solve(b: RealVector): RealVector {
-//        val m = pivot.size
-//        if (b.getDimension() != m) {
-//            throw DimensionMismatchException(b.getDimension(), m)
-//        }
-//        if (singular) {
-//            throw SingularMatrixException()
-//        }
-//
-//        val bp = DoubleArray(m)
-//
-//        // Apply permutations to b
-//        for (row in 0 until m) {
-//            bp[row] = b.getEntry(pivot[row])
-//        }
-//
-//        // Solve LY = b
-//        for (col in 0 until m) {
-//            val bpCol = bp[col]
-//            for (i in col + 1 until m) {
-//                bp[i] -= bpCol * lu[i][col]
-//            }
-//        }
-//
-//        // Solve UX = Y
-//        for (col in m - 1 downTo 0) {
-//            bp[col] /= lu[col][col]
-//            val bpCol = bp[col]
-//            for (i in 0 until col) {
-//                bp[i] -= bpCol * lu[i][col]
-//            }
-//        }
-//
-//        return ArrayRealVector(bp, false)
-//    }
-
 
     fun decompose(mat: Matrix<Double>, threshold: Double = 1e-11): RealLUDecomposition = RealLUDecomposition(mat, threshold)
 

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

@@ -4,10 +4,10 @@ import scientifik.kmath.operations.DoubleField
 import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.Space
 import scientifik.kmath.operations.SpaceElement
+import scientifik.kmath.structures.GenericNDField
 import scientifik.kmath.structures.NDArray
-import scientifik.kmath.structures.NDArrays.createFactory
+import scientifik.kmath.structures.NDField
-import scientifik.kmath.structures.NDFieldFactory
+import scientifik.kmath.structures.get
-import scientifik.kmath.structures.realNDFieldFactory
 
 /**
  * The space for linear elements. Supports scalar product alongside with standard linear operations.
@@ -193,6 +193,11 @@ interface Vector<T : Any> : SpaceElement<Vector<T>, VectorSpace<T>> {
     }
 }
 
+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.
@@ -201,11 +206,11 @@ class ArrayMatrixSpace<T : Any>(
         rows: Int,
         columns: Int,
         field: Field<T>,
-        val ndFactory: NDFieldFactory<T> = createFactory(field)
+        val ndFactory: NDFieldFactory<T> = genericNDFieldFactory(field)
 ) : MatrixSpace<T>(rows, columns, field) {
 
     val ndField by lazy {
-        ndFactory(listOf(rows, columns))
+        ndFactory(intArrayOf(rows, columns))
     }
 
     override fun produce(initializer: (Int, Int) -> T): Matrix<T> = ArrayMatrix(this, initializer)
@@ -218,10 +223,10 @@ class ArrayMatrixSpace<T : Any>(
 class ArrayVectorSpace<T : Any>(
         size: Int,
         field: Field<T>,
-        val ndFactory: NDFieldFactory<T> = createFactory(field)
+        val ndFactory: NDFieldFactory<T> = genericNDFieldFactory(field)
 ) : VectorSpace<T>(size, field) {
     val ndField by lazy {
-        ndFactory(listOf(size))
+        ndFactory(intArrayOf(size))
     }
 
     override fun produce(initializer: (Int) -> T): Vector<T> = ArrayVector(this, initializer)
@@ -306,6 +311,6 @@ 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, j -> get(i) }
+    return Matrix.of(size, 1, context.field) { i, _ -> get(i) }
 }
 

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

@@ -1,112 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.Field
-
-
-/**
- * A generic buffer for both primitives and objects
- */
-interface Buffer<T> {
-    operator fun get(index: Int): T
-    operator fun set(index: Int, value: T)
-
-    /**
-     * A shallow copy of the buffer
-     */
-    fun copy(): Buffer<T>
-}
-
-/**
- * Generic implementation of NDField based on continuous buffer
- */
-abstract class BufferNDField<T>(shape: List<Int>, field: Field<T>) : NDField<T>(shape, field) {
-
-    /**
-     * Strides for memory access
-     */
-    private val strides: List<Int> by lazy {
-        ArrayList<Int>(shape.size).apply {
-            var current = 1
-            add(1)
-            shape.forEach {
-                current *= it
-                add(current)
-            }
-        }
-    }
-
-    protected fun offset(index: List<Int>): Int {
-        return index.mapIndexed { i, value ->
-            if (value < 0 || value >= shape[i]) {
-                throw RuntimeException("Index out of shape bounds: ($i,$value)")
-            }
-            value * strides[i]
-        }.sum()
-    }
-
-    //TODO introduce a fast way to calculate index of the next element?
-    protected fun index(offset: Int): List<Int> {
-        return sequence {
-            var current = offset
-            var strideIndex = strides.size - 2
-            while (strideIndex >= 0) {
-                yield(current / strides[strideIndex])
-                current %= strides[strideIndex]
-                strideIndex--
-            }
-        }.toList().reversed()
-    }
-
-    private val capacity: Int
-        get() = strides[shape.size]
-
-
-    protected abstract fun createBuffer(capacity: Int, initializer: (Int) -> T): Buffer<T>
-
-    override fun produce(initializer: (List<Int>) -> T): NDArray<T> {
-        val buffer = createBuffer(capacity) { initializer(index(it)) }
-        return BufferNDArray(this, buffer)
-    }
-
-    /**
-     * Produce mutable NDArray instance
-     */
-    fun produceMutable(initializer: (List<Int>) -> T): MutableNDArray<T> {
-        val buffer = createBuffer(capacity) { initializer(index(it)) }
-        return MutableBufferedNDArray(this, buffer)
-    }
-
-
-    private open class BufferNDArray<T>(override val context: BufferNDField<T>, val data: Buffer<T>) : NDArray<T> {
-
-        override fun get(vararg index: Int): T {
-            return data[context.offset(index.asList())]
-        }
-
-        override fun equals(other: Any?): Boolean {
-            if (this === other) return true
-            if (other !is BufferNDArray<*>) return false
-
-            if (context != other.context) return false
-            if (data != other.data) return false
-
-            return true
-        }
-
-        override fun hashCode(): Int {
-            var result = context.hashCode()
-            result = 31 * result + data.hashCode()
-            return result
-        }
-
-        override val self: NDArray<T> get() = this
-    }
-
-    private class MutableBufferedNDArray<T>(context: BufferNDField<T>, data: Buffer<T>): BufferNDArray<T>(context,data), MutableNDArray<T>{
-        override operator fun set(index: List<Int>, value: T){
-            data[context.offset(index)] = value
-        }
-    }
-}
-
-

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

@@ -0,0 +1,74 @@
+package scientifik.kmath.structures
+
+
+/**
+ * A generic linear buffer for both primitives and objects
+ */
+interface Buffer<T> {
+
+    val size: Int
+
+    operator fun get(index: Int): T
+
+    /**
+     * A shallow copy of the buffer
+     */
+    fun copy(): Buffer<T>
+}
+
+interface MutableBuffer<T> : Buffer<T> {
+    operator fun set(index: Int, value: T)
+
+    /**
+     * A shallow copy of the buffer
+     */
+    override fun copy(): MutableBuffer<T>
+}
+
+inline class ListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T> {
+
+    override val size: Int
+        get() = list.size
+
+    override fun get(index: Int): T = list[index]
+
+    override fun set(index: Int, value: T) {
+        list[index] = value
+    }
+
+    override fun copy(): MutableBuffer<T> = ListBuffer(ArrayList(list))
+}
+
+class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
+    override val size: Int
+        get() = array.size
+
+    override fun get(index: Int): T = array[index]
+
+    override fun set(index: Int, value: T) {
+        array[index] = value
+    }
+
+    override fun copy(): MutableBuffer<T> = ArrayBuffer(array.copyOf())
+}
+
+class DoubleBuffer(private val array: DoubleArray) : MutableBuffer<Double> {
+    override val size: Int
+        get() = array.size
+
+    override fun get(index: Int): Double = array[index]
+
+    override fun set(index: Int, value: Double) {
+        array[index] = value
+    }
+
+    override fun copy(): MutableBuffer<Double> = DoubleBuffer(array.copyOf())
+}
+
+inline fun <reified T : Any> buffer(size: Int, noinline initializer: (Int) -> T): Buffer<T> {
+    return ArrayBuffer(Array(size, initializer))
+}
+
+inline fun <reified T : Any> mutableBuffer(size: Int, noinline initializer: (Int) -> T): MutableBuffer<T> {
+    return ArrayBuffer(Array(size, initializer))
+}

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

@@ -1,72 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.Field
-
-typealias NDFieldFactory<T> = (shape: List<Int>) -> NDField<T>
-
-/**
- * The factory class for fast platform-dependent implementation of NDField of doubles
- */
-expect val realNDFieldFactory: NDFieldFactory<Double>
-
-
-class SimpleNDField<T : Any>(field: Field<T>, shape: List<Int>) : BufferNDField<T>(shape, field) {
-    override fun createBuffer(capacity: Int, initializer: (Int) -> T): Buffer<T> {
-        val array = ArrayList<T>(capacity)
-        (0 until capacity).forEach {
-            array.add(initializer(it))
-        }
-
-        return BufferOfObjects(array)
-    }
-
-    private class BufferOfObjects<T>(val array: ArrayList<T>) : Buffer<T> {
-        override fun get(index: Int): T = array[index]
-
-        override fun set(index: Int, value: T) {
-            array[index] = value
-        }
-
-        override fun copy(): Buffer<T> = BufferOfObjects(ArrayList(array))
-    }
-}
-
-object NDArrays {
-    /**
-     * Create a platform-optimized NDArray of doubles
-     */
-    fun realNDArray(shape: List<Int>, initializer: (List<Int>) -> Double = { 0.0 }): NDArray<Double> {
-        return realNDFieldFactory(shape).produce(initializer)
-    }
-
-    fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDArray<Double> {
-        return realNDArray(listOf(dim)) { initializer(it[0]) }
-    }
-
-    fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDArray<Double> {
-        return realNDArray(listOf(dim1, dim2)) { initializer(it[0], it[1]) }
-    }
-
-    fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDArray<Double> {
-        return realNDArray(listOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
-    }
-
-    /**
-     * Simple boxing NDField
-     */
-    fun <T : Any> createFactory(field: Field<T>): NDFieldFactory<T> = { shape -> SimpleNDField(field, shape) }
-
-    /**
-     * Simple boxing NDArray
-     */
-    fun <T : Any> create(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): NDArray<T> {
-        return SimpleNDField(field, shape).produce { initializer(it) }
-    }
-
-    /**
-     * Mutable boxing NDArray
-     */
-    fun <T : Any> createMutable(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): MutableNDArray<T> {
-        return SimpleNDField(field, shape).produceMutable { initializer(it) }
-    }
-}

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

@@ -1,12 +1,13 @@
 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: List<Int>, val actual: List<Int>) : RuntimeException()
+class ShapeMismatchException(val expected: IntArray, val actual: IntArray) : RuntimeException()
 
 /**
  * Field for n-dimensional arrays.
@@ -14,13 +15,15 @@ class ShapeMismatchException(val expected: List<Int>, val actual: List<Int>) : R
  * @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: List<Int>, val field: Field<T>) : Field<NDArray<T>> {
+abstract class NDField<T>(val shape: IntArray, val field: Field<T>) : Field<NDArray<T>> {
+
+    abstract fun produceStructure(initializer: (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
      */
-    abstract fun produce(initializer: (List<Int>) -> T): NDArray<T>
+    fun produce(initializer: (IntArray) -> T): NDArray<T> = NDArray(this, produceStructure(initializer))
 
     override val zero: NDArray<T> by lazy {
         produce { this.field.zero }
@@ -31,7 +34,7 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
      */
     private fun checkShape(vararg arrays: NDArray<T>) {
         arrays.forEach {
-            if (shape != it.shape) {
+            if (!shape.contentEquals(it.shape)) {
                 throw ShapeMismatchException(shape, it.shape)
             }
         }
@@ -71,76 +74,44 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
         checkShape(a)
         return produce { with(field) { a[it] / b[it] } }
     }
+
+    /**
+     * Reverse sum operation
+     */
+    operator fun <T> T.plus(arg: NDArray<T>): NDArray<T> = arg + this
+
+    /**
+     * Reverse minus operation
+     */
+    operator fun <T> T.minus(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
+        with(arg.context.field) {
+            this@minus - value
+        }
     }
 
     /**
- * Many-dimensional array
+     * Reverse product operation
      */
-interface NDArray<T> : FieldElement<NDArray<T>, NDField<T>> {
+    operator fun <T> T.times(arg: NDArray<T>): NDArray<T> = arg * this
 
     /**
-     * The list of dimensions of this NDArray
+     * Reverse division operation
      */
-    val shape: List<Int>
+    operator fun <T> T.div(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
-        get() = context.shape
+        with(arg.context.field) {
-
+            this@div / value
-    /**
-     * The number of dimentsions for this array
-     */
-    val dimension: Int
-        get() = shape.size
-
-    /**
-     * Get the element with given indexes. If number of indexes is different from {@link dimension}, throws exception.
-     */
-    operator fun get(vararg index: Int): T
-
-    operator fun get(index: List<Int>): T {
-        return get(*index.toIntArray())
-    }
-
-    operator fun iterator(): Iterator<Pair<List<Int>, T>> {
-        return iterateIndexes(shape).map { Pair(it, this[it]) }.iterator()
-    }
-
-    /**
-     * Generate new NDArray, using given transformation for each element
-     */
-    fun transform(action: (List<Int>, T) -> T): NDArray<T> = context.produce { action(it, this[it]) }
-
-    companion object {
-        /**
-         * Iterate over all indexes in the nd-shape
-         */
-        fun iterateIndexes(shape: List<Int>): Sequence<List<Int>> {
-            return if (shape.size == 1) {
-                (0 until shape[0]).asSequence().map { listOf(it) }
-            } else {
-                val tailShape = ArrayList(shape).apply { removeAt(0) }
-                val tailSequence: List<List<Int>> = iterateIndexes(tailShape).toList()
-                (0 until shape[0]).asSequence().map { firstIndex ->
-                    //adding first element to each of provided index lists
-                    tailSequence.map { listOf(firstIndex) + it }.asSequence()
-                }.flatten()
-            }
         }
     }
 }
 
 /**
- * In-place mutable [NDArray]
+ * NDStructure coupled to the context. Emulates Python ndarray
  */
-interface MutableNDArray<T> : NDArray<T> {
+data class NDArray<T>(override val context: NDField<T>, private val structure: NDStructure<T>) : FieldElement<NDArray<T>, NDField<T>>, NDStructure<T> by structure {
-    operator fun set(index: List<Int>, value: T)
+    override val self: NDArray<T>
-}
+        get() = this
 
-/**
+    fun transform(action: (IntArray, T) -> T): NDArray<T> = context.produce { action(it, get(*it)) }
- * In-place transformation for [MutableNDArray], using given transformation for each element
- */
-fun <T> MutableNDArray<T>.transformInPlace(action: (List<Int>, T) -> T) {
-    for ((index, oldValue) in this) {
-        this[index] = action(index, oldValue)
-    }
 }
 
 /**
@@ -159,11 +130,6 @@ operator fun <T> NDArray<T>.plus(arg: T): NDArray<T> = transform { _, value ->
     }
 }
 
-/**
- * Reverse sum operation
- */
-operator fun <T> T.plus(arg: NDArray<T>): NDArray<T> = arg + this
-
 /**
  * Subtraction operation between [NDArray] and single element
  */
@@ -173,15 +139,6 @@ operator fun <T> NDArray<T>.minus(arg: T): NDArray<T> = transform { _, value ->
     }
 }
 
-/**
- * Reverse minus operation
- */
-operator fun <T> T.minus(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
-    with(arg.context.field) {
-        this@minus - value
-    }
-}
-
 /* prod and div */
 
 /**
@@ -193,11 +150,6 @@ operator fun <T> NDArray<T>.times(arg: T): NDArray<T> = transform { _, value ->
     }
 }
 
-/**
- * Reverse product operation
- */
-operator fun <T> T.times(arg: NDArray<T>): NDArray<T> = arg * this
-
 /**
  * Division operation between [NDArray] and single element
  */
@@ -207,12 +159,41 @@ operator fun <T> NDArray<T>.div(arg: T): NDArray<T> = transform { _, value ->
     }
 }
 
-/**
+class GenericNDField<T : Any>(shape: IntArray, field: Field<T>) : NDField<T>(shape, field) {
- * Reverse division operation
+    override fun produceStructure(initializer: (IntArray) -> T): NDStructure<T> = genericNdStructure(shape, initializer)
- */
-operator fun <T> T.div(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
-    with(arg.context.field) {
-        this@div / value
-    }
 }
 
+//typealias NDFieldFactory<T> = (IntArray)->NDField<T>
+
+object NDArrays {
+    /**
+     * Create a platform-optimized NDArray of doubles
+     */
+    fun realNDArray(shape: IntArray, initializer: (IntArray) -> Double = { 0.0 }): NDArray<Double> {
+        return GenericNDField(shape, DoubleField).produce(initializer)
+    }
+
+    fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDArray<Double> {
+        return realNDArray(intArrayOf(dim)) { initializer(it[0]) }
+    }
+
+    fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDArray<Double> {
+        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> {
+        return realNDArray(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
+    }
+
+//    /**
+//     * Simple boxing NDField
+//     */
+//    fun <T : Any> fieldFactory(field: Field<T>): NDFieldFactory<T> = { shape -> GenericNDField(shape, field) }
+
+    /**
+     * Simple boxing NDArray
+     */
+    fun <T : Any> create(field: Field<T>, shape: IntArray, initializer: (IntArray) -> T): NDArray<T> {
+        return GenericNDField(shape, field).produce { initializer(it) }
+    }
+}

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

@@ -0,0 +1,174 @@
+package scientifik.kmath.structures
+
+
+interface NDStructure<T> : Iterable<Pair<IntArray, T>> {
+
+    val shape: IntArray
+
+    val dimension
+        get() = shape.size
+
+    operator fun get(index: IntArray): T
+}
+
+operator fun <T> NDStructure<T>.get(vararg index: Int): T = get(index)
+
+interface MutableNDStructure<T> : NDStructure<T> {
+    operator fun set(index: IntArray, value: T)
+}
+
+fun <T> MutableNDStructure<T>.transformInPlace(action: (IntArray, T) -> T) {
+    for ((index, oldValue) in this) {
+        this[index] = action(index, oldValue)
+    }
+}
+
+/**
+ * A way to convert ND index to linear one and back
+ */
+interface Strides {
+    /**
+     * Shape of NDstructure
+     */
+    val shape: IntArray
+
+    /**
+     * Array strides
+     */
+    val strides: List<Int>
+
+    /**
+     * Get linear index from multidimensional index
+     */
+    fun offset(index: IntArray): Int
+
+    /**
+     * Get multidimensional from linear
+     */
+    fun index(offset: Int): IntArray
+
+    val linearSize: Int
+
+    /**
+     * Iterate over ND indices in a natural order
+     */
+    fun indices(): Sequence<IntArray> {
+        //TODO introduce a fast way to calculate index of the next element?
+        return (0 until linearSize).asSequence().map { index(it) }
+    }
+}
+
+class DefaultStrides(override val shape: IntArray) : Strides {
+    /**
+     * Strides for memory access
+     */
+    override val strides by lazy {
+        sequence {
+            var current = 1
+            yield(1)
+            shape.forEach {
+                current *= it
+                yield(current)
+            }
+        }.toList()
+    }
+
+    override fun offset(index: IntArray): Int {
+        return index.mapIndexed { i, value ->
+            if (value < 0 || value >= shape[i]) {
+                throw RuntimeException("Index out of shape bounds: ($i,$value)")
+            }
+            value * strides[i]
+        }.sum()
+    }
+
+    override fun index(offset: Int): IntArray {
+        return sequence {
+            var current = offset
+            var strideIndex = strides.size - 2
+            while (strideIndex >= 0) {
+                yield(current / strides[strideIndex])
+                current %= strides[strideIndex]
+                strideIndex--
+            }
+        }.toList().reversed().toIntArray()
+    }
+
+    override val linearSize: Int
+        get() = strides[shape.size]
+}
+
+abstract class GenericNDStructure<T, B : Buffer<T>> : NDStructure<T> {
+    protected abstract val buffer: B
+    protected abstract val strides: Strides
+
+    override fun get(index: IntArray): T = buffer[strides.offset(index)]
+
+    override val shape: IntArray
+        get() = strides.shape
+
+    override fun iterator(): Iterator<Pair<IntArray, T>> =
+            strides.indices().map { it to this[it] }.iterator()
+}
+
+/**
+ * Boxing generic [NDStructure]
+ */
+class BufferNDStructure<T>(
+        override val strides: Strides,
+        override val buffer: Buffer<T>
+) : GenericNDStructure<T, Buffer<T>>() {
+
+    init {
+        if (strides.linearSize != buffer.size) {
+            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
+        }
+    }
+}
+
+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)
+
+
+/**
+ * Mutable ND buffer based on linear [Buffer]
+ */
+class MutableBufferNDStructure<T>(
+        override val strides: Strides,
+        override val buffer: MutableBuffer<T>
+) : GenericNDStructure<T, MutableBuffer<T>>(), MutableNDStructure<T> {
+
+    init {
+        if (strides.linearSize != buffer.size) {
+            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
+        }
+    }
+
+    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 = ListBuffer<T>(sequence.toMutableList())
+    return MutableBufferNDStructure(strides, buffer)
+}

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

@@ -7,15 +7,15 @@ class ArrayMatrixTest {
 
     @Test
     fun testSum() {
-        val vector1 = realVector(5) { it.toDouble() }
+        val vector1 = Vector.ofReal(5) { it.toDouble() }
-        val vector2 = realVector(5) { 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 = realVector(5) { it.toDouble() }
+        val vector = Vector.ofReal(5) { it.toDouble() }
         val matrix = vector.toMatrix()
         assertEquals(4.0, matrix[4, 0])
     }
@@ -23,8 +23,8 @@ class ArrayMatrixTest {
 
     @Test
     fun testDot() {
-        val vector1 = realVector(5) { it.toDouble() }
+        val vector1 = Vector.ofReal(5) { it.toDouble() }
-        val vector2 = realVector(5) { 5 - it.toDouble() }
+        val vector2 = Vector.ofReal(5) { 5 - it.toDouble() }
         val product = vector1.toMatrix() dot (vector2.toMatrix().transpose())
 
 

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

@@ -6,10 +6,10 @@ import kotlin.test.Test
 import kotlin.test.assertEquals
 
 
-class SimpleNDFieldTest{
+class GenericNDFieldTest{
     @Test
     fun testStrides(){
-        val ndArray = create(DoubleField, listOf(10,10)){(it[0]+it[1]).toDouble()}
+        val ndArray = create(DoubleField, intArrayOf(10,10)){(it[0]+it[1]).toDouble()}
         assertEquals(ndArray[5,5], 10.0)
     }
 

kmath-core/src/jmh/kotlin/scietifik/kmath/structures/ArrayBenchmark.kt

@@ -1,12 +1,11 @@
 package scietifik.kmath.structures
 
-import org.openjdk.jmh.annotations.*
 import java.nio.IntBuffer
 
 
 @Fork(1)
 @Warmup(iterations = 2)
-@Measurement(iterations = 50)
+@Measurement(iterations = 5)
 @State(Scope.Benchmark)
 open class ArrayBenchmark {
 

kmath-core/src/jsMain/kotlin/scientifik/kmath/structures/_NDArrays.kt

@@ -1,8 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.DoubleField
-
-/**
- * Using boxing implementation for js
- */
-actual val realNDFieldFactory: NDFieldFactory<Double> = NDArrays.createFactory(DoubleField)

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

@@ -1,26 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.DoubleField
-import java.nio.DoubleBuffer
-
-private class RealNDField(shape: List<Int>) : BufferNDField<Double>(shape, DoubleField) {
-    override fun createBuffer(capacity: Int, initializer: (Int) -> Double): Buffer<Double> {
-        val array = DoubleArray(capacity, initializer)
-        val buffer = DoubleBuffer.wrap(array)
-        return BufferOfDoubles(buffer)
-    }
-
-    private class BufferOfDoubles(val buffer: DoubleBuffer): Buffer<Double>{
-        override fun get(index: Int): Double = buffer.get(index)
-
-        override fun set(index: Int, value: Double) {
-            buffer.put(index, value)
-        }
-
-        override fun copy(): Buffer<Double> {
-            return BufferOfDoubles(buffer)
-        }
-    }
-}
-
-actual val realNDFieldFactory: NDFieldFactory<Double> = { shape -> RealNDField(shape) }