Major refactoring of types for algebra elements. Element type could differ from field type.

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

@@ -8,12 +8,12 @@ fun main(args: Array<String>) {
 
     val n = 6000
 
-    val structure = NdStructure(intArrayOf(n, n), DoubleBufferFactory) { 1.0 }
+    val structure = ndStructure(intArrayOf(n, n), DoubleBufferFactory) { 1.0 }
 
-    structure.map { it + 1 } // warm-up
+    structure.mapToBuffer { it + 1 } // warm-up
 
     val time1 = measureTimeMillis {
-        val res = structure.map { it + 1 }
+        val res = structure.mapToBuffer { it + 1 }
     }
     println("Structure mapping finished in $time1 millis")
 

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

@@ -104,7 +104,7 @@ abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matr
         val m = matrix.numCols
         val pivot = IntArray(matrix.numRows)
         //TODO fix performance
-        val lu: MutableNDStructure<T> = MutableNdStructure(intArrayOf(matrix.numRows, matrix.numCols), ::boxingMutableBuffer) { index: IntArray -> matrix[index[0], index[1]] }
+        val lu: MutableNDStructure<T> = mutableNdStructure(intArrayOf(matrix.numRows, matrix.numCols), ::boxingMutableBuffer) { index: IntArray -> matrix[index[0], index[1]] }
 
 
         with(matrix.context.ring) {

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

@@ -122,11 +122,11 @@ data class StructureMatrixSpace<T : Any, R : Ring<T>>(
 
     override fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> T): Matrix<T, R> {
         return if (rows == rowNum && columns == colNum) {
-            val structure = NdStructure(strides, bufferFactory) { initializer(it[0], it[1]) }
+            val structure = ndStructure(strides, bufferFactory) { initializer(it[0], it[1]) }
             StructureMatrix(this, structure)
         } else {
             val context = StructureMatrixSpace(rows, columns, ring, bufferFactory)
-            val structure = NdStructure(context.strides, bufferFactory) { initializer(it[0], it[1]) }
+            val structure = ndStructure(context.strides, bufferFactory) { initializer(it[0], it[1]) }
             StructureMatrix(context, structure)
         }
     }

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

@@ -16,13 +16,18 @@ interface VectorSpace<T : Any, S : Space<T>> : Space<Point<T>> {
 
     val space: S
 
-    fun produce(initializer: (Int) -> T): Vector<T, S>
+    fun produce(initializer: (Int) -> T): Point<T>
 
-    override val zero: Vector<T, S> get() = produce { space.zero }
+    /**
+     * Produce a space-element of this vector space for expressions
+     */
+    fun produceElement(initializer: (Int) -> T): Vector<T, S>
 
-    override fun add(a: Point<T>, b: Point<T>): Vector<T, S> = produce { with(space) { a[it] + b[it] } }
+    override val zero: Point<T> get() = produce { space.zero }
 
-    override fun multiply(a: Point<T>, k: Double): Vector<T, S> = produce { with(space) { a[it] * k } }
+    override fun add(a: Point<T>, b: Point<T>): Point<T> = produce { with(space) { a[it] + b[it] } }
+
+    override fun multiply(a: Point<T>, k: Double): Point<T> = produce { with(space) { a[it] * k } }
 
     //TODO add basis
 
@@ -53,7 +58,7 @@ interface VectorSpace<T : Any, S : Space<T>> : Space<Point<T>> {
 /**
  * A point coupled to the linear space
  */
-interface Vector<T : Any, S : Space<T>> : SpaceElement<Point<T>, VectorSpace<T, S>>, Point<T> {
+interface Vector<T : Any, S : Space<T>> : SpaceElement<Vector<T,S>, VectorSpace<T, S>>, Point<T> {
     override val size: Int get() = context.size
 
     override operator fun plus(b: Point<T>): Vector<T, S> = context.add(self, b)
@@ -65,11 +70,11 @@ interface Vector<T : Any, S : Space<T>> : SpaceElement<Point<T>, VectorSpace<T,
         /**
          * Create vector with custom field
          */
-        fun <T : Any, F : Space<T>> generic(size: Int, field: F, initializer: (Int) -> T) =
+        fun <T : Any, S : Space<T>> generic(size: Int, field: S, initializer: (Int) -> T): Vector<T, S> =
-                VectorSpace.buffered(size, field).produce(initializer)
+                VectorSpace.buffered(size, field).produceElement(initializer)
 
-        fun real(size: Int, initializer: (Int) -> Double) = VectorSpace.real(size).produce(initializer)
+        fun real(size: Int, initializer: (Int) -> Double): Vector<Double,DoubleField> = VectorSpace.real(size).produceElement(initializer)
-        fun ofReal(vararg elements: Double) = VectorSpace.real(elements.size).produce{elements[it]}
+        fun ofReal(vararg elements: Double): Vector<Double,DoubleField> = VectorSpace.real(elements.size).produceElement { elements[it] }
 
     }
 }
@@ -79,7 +84,8 @@ data class BufferVectorSpace<T : Any, S : Space<T>>(
         override val space: S,
         val bufferFactory: BufferFactory<T>
 ) : VectorSpace<T, S> {
-    override fun produce(initializer: (Int) -> T): Vector<T, S> = BufferVector(this, bufferFactory(size, initializer))
+    override fun produce(initializer: (Int) -> T) = bufferFactory(size, initializer)
+    override fun produceElement(initializer: (Int) -> T): Vector<T, S> = BufferVector(this, produce(initializer))
 }
 
 
@@ -95,7 +101,7 @@ data class BufferVector<T : Any, S : Space<T>>(override val context: VectorSpace
         return buffer[index]
     }
 
-    override val self: BufferVector<T, S> get() = this
+    override fun getSelf(): BufferVector<T, S
 
     override fun iterator(): Iterator<T> = (0 until size).map { buffer[it] }.iterator()
 

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

@@ -1,23 +1,6 @@
 package scientifik.kmath.operations
 
 
-/**
- * The generic mathematics elements which is able to store its context
- * @param T the self type of the element
- * @param S the type of mathematical context for this element
- */
-interface MathElement<T, S> {
-    /**
-     * Self value. Needed for static type checking.
-     */
-    val self: T
-
-    /**
-     * The context this element belongs to
-     */
-    val context: S
-}
-
 /**
  * A general interface representing linear context of some kind.
  * The context defines sum operation for its elements and multiplication by real value.
@@ -53,19 +36,8 @@ interface Space<T> {
 
     //TODO move to external extensions when they are available
     fun Iterable<T>.sum(): T = fold(zero) { left, right -> left + right }
-    fun Sequence<T>.sum(): T = fold(zero) { left, right -> left + right }
-}
 
-/**
+    fun Sequence<T>.sum(): T = fold(zero) { left, right -> left + right }
- * The element of linear context
- * @param T  self type of the element. Needed for static type checking
- * @param S the type of space
- */
-interface SpaceElement<T, S : Space<T>> : MathElement<T, S> {
-    operator fun plus(b: T): T = context.add(self, b)
-    operator fun minus(b: T): T = context.add(self, context.multiply(b, -1.0))
-    operator fun times(k: Number): T = context.multiply(self, k.toDouble())
-    operator fun div(k: Number): T = context.multiply(self, 1.0 / k.toDouble())
 }
 
 /**
@@ -86,15 +58,6 @@ interface Ring<T> : Space<T> {
 
 }
 
-/**
- * Ring element
- */
-interface RingElement<T, S : Ring<T>> : SpaceElement<T, S> {
-    override val context: S
-
-    operator fun times(b: T): T = context.multiply(self, b)
-}
-
 /**
  * Four operations algebra
  */
@@ -110,12 +73,3 @@ interface Field<T> : Ring<T> {
     operator fun T.minus(b: Number) = this.minus(b * one)
     operator fun Number.minus(b: T) = -b + this
 }
-
-/**
- * Field element
- */
-interface FieldElement<T, F : Field<T>> : RingElement<T, F> {
-    override val context: F
-
-    operator fun div(b: T): T = context.divide(self, b)
-}

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

@@ -0,0 +1,49 @@
+package scientifik.kmath.operations
+
+/**
+ * The generic mathematics elements which is able to store its context
+ * @param S the type of mathematical context for this element
+ */
+interface MathElement<S> {
+    /**
+     * The context this element belongs to
+     */
+    val context: S
+}
+
+/**
+ * The element of linear context
+ * @param T the type of space operation results
+ * @param I self type of the element. Needed for static type checking
+ * @param S the type of space
+ */
+interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement<S> {
+    /**
+     * Self value. Needed for static type checking.
+     */
+    fun unwrap(): T
+
+    fun T.wrap(): I
+
+    operator fun plus(b: T) = context.add(unwrap(), b).wrap()
+    operator fun minus(b: T) = context.add(unwrap(), context.multiply(b, -1.0)).wrap()
+    operator fun times(k: Number) = context.multiply(unwrap(), k.toDouble()).wrap()
+    operator fun div(k: Number) = context.multiply(unwrap(), 1.0 / k.toDouble()).wrap()
+}
+
+/**
+ * Ring element
+ */
+interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T, I, R> {
+    override val context: R
+    operator fun times(b: T) = context.multiply(unwrap(), b).wrap()
+}
+
+/**
+ * Field element
+ */
+interface FieldElement<T, I : FieldElement<T, I, F>, F : Field<T>> : RingElement<T, I, F> {
+    override val context: F
+
+    operator fun div(b: T) = context.divide(unwrap(), b).wrap()
+}

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

@@ -16,15 +16,18 @@ object ComplexField : Field<Complex> {
 
     override fun multiply(a: Complex, b: Complex): Complex = Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
 
-    override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
+    override fun divide(a: Complex, b: Complex): Complex {
+        val norm = b.square
+        return Complex((a.re * b.re + a.im * b.im) / norm, (a.re * b.im - a.im * b.re) / norm)
+    }
 
-    operator fun Double.plus(c: Complex) = this.toComplex() + c
+    operator fun Double.plus(c: Complex) = add(this.toComplex(), c)
 
-    operator fun Double.minus(c: Complex) = this.toComplex() - c
+    operator fun Double.minus(c: Complex) = add(this.toComplex(), -c)
 
     operator fun Complex.plus(d: Double) = d + this
 
-    operator fun Complex.minus(d: Double) = this - d.toComplex()
+    operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
 
     operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
 }
@@ -34,6 +37,7 @@ object ComplexField : Field<Complex> {
  */
 data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
     override val self: Complex get() = this
+
     override val context: ComplexField
         get() = ComplexField
 

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

@@ -12,42 +12,18 @@ interface ExtendedField<T : Any> :
         ExponentialOperations<T>
 
 
-/**
- * Field for real values
- */
-object RealField : ExtendedField<Real>, Norm<Real, Real> {
-    override val zero: Real = Real(0.0)
-    override fun add(a: Real, b: Real): Real = Real(a.value + b.value)
-    override val one: Real = Real(1.0)
-    override fun multiply(a: Real, b: Real): Real = Real(a.value * b.value)
-    override fun multiply(a: Real, k: Double): Real = Real(a.value * k)
-    override fun divide(a: Real, b: Real): Real = Real(a.value / b.value)
-
-    override fun sin(arg: Real): Real = Real(kotlin.math.sin(arg.value))
-    override fun cos(arg: Real): Real = Real(kotlin.math.cos(arg.value))
-
-    override fun power(arg: Real, pow: Double): Real = Real(arg.value.pow(pow))
-
-    override fun exp(arg: Real): Real = Real(kotlin.math.exp(arg.value))
-
-    override fun ln(arg: Real): Real = Real(kotlin.math.ln(arg.value))
-
-    override fun norm(arg: Real): Real = Real(kotlin.math.abs(arg.value))
-}
 
 /**
  * Real field element wrapping double.
  *
  * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
  */
-inline class Real(val value: Double) : FieldElement<Real, RealField> {
+inline class Real(val value: Double) : FieldElement<Double, Real, DoubleField> {
+    override fun unwrap(): Double = value
 
-    //values are dynamically calculated to save memory
+    override fun Double.wrap(): Real = Real(value)
-    override val self
-        get() = this
 
-    override val context
+    override val context get() = DoubleField
-        get() = RealField
 
     companion object {
 
@@ -79,11 +55,31 @@ object DoubleField : ExtendedField<Double>, Norm<Double, Double> {
 /**
  * A field for double without boxing. Does not produce appropriate field element
  */
-object IntField : Field<Int>{
+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 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
 }
+
+//interface FieldAdapter<T, R> : Field<R> {
+//
+//    val field: Field<T>
+//
+//    abstract fun T.evolve(): R
+//    abstract fun R.devolve(): T
+//
+//    override val zero get() = field.zero.evolve()
+//    override val one get() = field.zero.evolve()
+//
+//    override fun add(a: R, b: R): R = field.add(a.devolve(), b.devolve()).evolve()
+//
+//    override fun multiply(a: R, k: Double): R = field.multiply(a.devolve(), k).evolve()
+//
+//
+//    override fun multiply(a: R, b: R): R = field.multiply(a.devolve(), b.devolve()).evolve()
+//
+//    override fun divide(a: R, b: R): R = field.divide(a.devolve(), b.devolve()).evolve()
+//}

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

@@ -1,45 +1,65 @@
 package scientifik.kmath.structures
 
 import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.FieldElement
 
-open class BufferNDField<T, F : Field<T>>(final override val shape: IntArray, final override val field: F, val bufferFactory: BufferFactory<T>) : NDField<T, F> {
+open class BufferNDField<T, F : Field<T>>(final override val shape: IntArray, final override val field: F, val bufferFactory: BufferFactory<T>) : NDField<T, F, NDBuffer<T>> {
     val strides = DefaultStrides(shape)
 
-    override fun produce(initializer: F.(IntArray) -> T): BufferNDElement<T, F> {
+    override fun produce(initializer: F.(IntArray) -> T) =
-        return BufferNDElement(this, bufferFactory(strides.linearSize) { offset -> field.initializer(strides.index(offset)) })
+            BufferNDElement(this, bufferFactory(strides.linearSize) { offset -> field.initializer(strides.index(offset)) })
-    }
 
-    open fun produceBuffered(initializer: F.(Int) -> T) =
+    open fun NDBuffer<T>.map(transform: F.(T) -> T) =
-            BufferNDElement(this, bufferFactory(strides.linearSize) { offset -> field.initializer(offset) })
+            BufferNDElement(this@BufferNDField, bufferFactory(strides.linearSize) { offset -> field.transform(buffer[offset]) })
 
-//    override fun add(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
+    open fun NDBuffer<T>.mapIndexed(transform: F.(index: IntArray, T) -> T) =
-//        checkShape(a, b)
+            BufferNDElement(this@BufferNDField, bufferFactory(strides.linearSize) { offset -> field.transform(strides.index(offset), buffer[offset]) })
-//        return if (a is BufferNDElement<T, *> && b is BufferNDElement<T, *>) {
+
-//            BufferNDElement(this,bufferFactory(strides.linearSize){i-> field.run { a.buffer[i] + b.buffer[i]}})
+    open fun combine(a: NDBuffer<T>, b: NDBuffer<T>, transform: F.(T, T) -> T) =
-//        } else {
+            BufferNDElement(this, bufferFactory(strides.linearSize) { offset -> field.transform(a[offset], b[offset]) })
-//            produce { field.run { a[it] + b[it] } }
+
-//        }
+    /**
-//    }
+     * Convert any [NDStructure] to buffered structure using strides from this context.
-//
+     * If the structure is already [NDBuffer], conversion is free. If not, it could be expensive because iteration over indexes
-//    override fun NDStructure<T>.plus(b: Number): NDElement<T,F> {
+     */
-//        checkShape(this)
+    fun NDStructure<T>.toBuffer(): NDBuffer<T> =
-//        return if (this is BufferNDElement<T, *>) {
+            this as? NDBuffer<T> ?: produce { index -> get(index) }
-//            BufferNDElement(this@BufferNDField,bufferFactory(strides.linearSize){i-> field.run { this@plus.buffer[i] + b}})
+
-//        } else {
+    override val zero: NDBuffer<T> by lazy { produce { field.zero } }
-//            produce {index -> field.run { this@plus[index] + b } }
+
-//        }
+    override fun add(a: NDBuffer<T>, b: NDBuffer<T>): NDBuffer<T> = combine(a, b) { aValue, bValue -> add(aValue, bValue) }
-//    }
+
+    override fun multiply(a: NDBuffer<T>, k: Double): NDBuffer<T> = a.map { it * k }
+
+    override val one: NDBuffer<T> by lazy { produce { field.one } }
+
+    override fun multiply(a: NDBuffer<T>, b: NDBuffer<T>): NDBuffer<T> = combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
+
+    override fun divide(a: NDBuffer<T>, b: NDBuffer<T>): NDBuffer<T> = combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
 }
 
-class BufferNDElement<T, F : Field<T>>(override val context: BufferNDField<T, F>, val buffer: Buffer<T>) : NDElement<T, F> {
+class BufferNDElement<T, F : Field<T>>(override val context: BufferNDField<T, F>, override val buffer: Buffer<T>) :
+        NDBuffer<T>,
+        FieldElement<NDBuffer<T>, BufferNDElement<T, F>, BufferNDField<T, F>>,
+        NDElement<T, F> {
+
+    override val elementField: F get() = context.field
+
+    override fun unwrap(): NDBuffer<T> = this
+
+    override fun NDBuffer<T>.wrap(): BufferNDElement<T, F> = BufferNDElement(context, this.buffer)
+
+    override val strides get() = context.strides
 
-    override val self: NDStructure<T> get() = this
     override val shape: IntArray get() = context.shape
 
-    override fun get(index: IntArray): T = buffer[context.strides.offset(index)]
+    override fun get(index: IntArray): T = buffer[strides.offset(index)]
 
-    override fun elements(): Sequence<Pair<IntArray, T>> = context.strides.indices().map { it to get(it) }
+    override fun elements(): Sequence<Pair<IntArray, T>> = strides.indices().map { it to get(it) }
 
+    override fun map(action: F.(T) -> T): BufferNDElement<T, F> = context.run { map(action) }
+
+    override fun mapIndexed(transform: F.(index: IntArray, T) -> T): BufferNDElement<T, F> = context.run { mapIndexed(transform) }
 }
 
 
@@ -47,7 +67,7 @@ class BufferNDElement<T, F : Field<T>>(override val context: BufferNDField<T, F>
  * Element by element application of any operation on elements to the whole array. Just like in numpy
  */
 operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferNDElement<T, F>) =
-        ndElement.context.produceBuffered { i -> invoke(ndElement.buffer[i]) }
+        ndElement.context.run { ndElement.map { invoke(it) } }
 
 /* plus and minus */
 
@@ -55,24 +75,24 @@ operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferNDE
  * Summation operation for [BufferNDElement] and single element
  */
 operator fun <T : Any, F : Field<T>> BufferNDElement<T, F>.plus(arg: T) =
-        context.produceBuffered { i -> buffer[i] + arg }
+        context.run { map { it + arg } }
 
 /**
  * Subtraction operation between [BufferNDElement] and single element
  */
-operator fun <T: Any, F : Field<T>> BufferNDElement<T, F>.minus(arg: T) =
+operator fun <T : Any, F : Field<T>> BufferNDElement<T, F>.minus(arg: T) =
-        context.produceBuffered { i -> buffer[i] - arg }
+        context.run { map { it - arg } }
 
 /* prod and div */
 
 /**
  * Product operation for [BufferNDElement] and single element
  */
-operator fun <T: Any, F : Field<T>> BufferNDElement<T, F>.times(arg: T) =
+operator fun <T : Any, F : Field<T>> BufferNDElement<T, F>.times(arg: T) =
-        context.produceBuffered { i -> buffer[i] * arg }
+        context.run { map { it * arg } }
 
 /**
  * Division operation between [BufferNDElement] and single element
  */
-operator fun <T: Any, F : Field<T>> BufferNDElement<T, F>.div(arg: T) =
+operator fun <T : Any, F : Field<T>> BufferNDElement<T, F>.div(arg: T) =
-        context.produceBuffered { i -> buffer[i] / arg }
+        context.run { map { it / arg } }

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

@@ -6,40 +6,40 @@ import scientifik.kmath.operations.PowerOperations
 import scientifik.kmath.operations.TrigonometricOperations
 
 
-interface ExtendedNDField<T : Any, F : ExtendedField<T>> :
+interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<out T>> :
-        NDField<T, F>,
+        NDField<T, F, N>,
-        TrigonometricOperations<NDStructure<T>>,
+        TrigonometricOperations<N>,
-        PowerOperations<NDStructure<T>>,
+        PowerOperations<N>,
-        ExponentialOperations<NDStructure<T>>
+        ExponentialOperations<N>
 
 
 /**
  * NDField that supports [ExtendedField] operations on its elements
  */
-inline class ExtendedNDFieldWrapper<T : Any, F : ExtendedField<T>>(private val ndField: NDField<T, F>) : ExtendedNDField<T, F> {
+class ExtendedNDFieldWrapper<T : Any, F : ExtendedField<T>, N : NDStructure<out T>>(private val ndField: NDField<T, F, N>) : ExtendedNDField<T, F, N>, NDField<T,F,N> by ndField {
 
     override val shape: IntArray get() = ndField.shape
     override val field: F get() = ndField.field
 
-    override fun produce(initializer: F.(IntArray) -> T): NDElement<T, F> = ndField.produce(initializer)
+    override fun produce(initializer: F.(IntArray) -> T) = ndField.produce(initializer)
 
-    override fun power(arg: NDStructure<T>, pow: Double): NDElement<T, F> {
+    override fun power(arg: N, pow: Double): N {
         return produce { with(field) { power(arg[it], pow) } }
     }
 
-    override fun exp(arg: NDStructure<T>): NDElement<T, F> {
+    override fun exp(arg: N): N {
         return produce { with(field) { exp(arg[it]) } }
     }
 
-    override fun ln(arg: NDStructure<T>): NDElement<T, F> {
+    override fun ln(arg: N): N {
         return produce { with(field) { ln(arg[it]) } }
     }
 
-    override fun sin(arg: NDStructure<T>): NDElement<T, F> {
+    override fun sin(arg: N): N {
         return produce { with(field) { sin(arg[it]) } }
     }
 
-    override fun cos(arg: NDStructure<T>): NDElement<T, F> {
+    override fun cos(arg: N): N {
         return produce { with(field) { cos(arg[it]) } }
     }
 }

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

@@ -0,0 +1,126 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.DoubleField
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.FieldElement
+
+
+interface NDElement<T, F : Field<T>> : NDStructure<T> {
+    val elementField: F
+
+    fun mapIndexed(transform: F.(index: IntArray, T) -> T): NDElement<T, F>
+    fun map(action: F.(T) -> T) = mapIndexed { _, value -> action(value) }
+}
+
+
+object NDElements {
+    /**
+     * Create a optimized NDArray of doubles
+     */
+    fun real(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }) =
+            NDField.real(shape).produce(initializer)
+
+
+    fun real1D(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }) =
+            real(intArrayOf(dim)) { initializer(it[0]) }
+
+
+    fun real2D(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }) =
+            real(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
+
+    fun real3D(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }) =
+            real(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
+
+
+    /**
+     * Simple boxing NDArray
+     */
+    fun <T : Any, F : Field<T>> generic(shape: IntArray, field: F, initializer: F.(IntArray) -> T): GenericNDElement<T, F> {
+        val ndField = GenericNDField(shape, field)
+        val structure = ndStructure(shape) { index -> field.initializer(index) }
+        return GenericNDElement(ndField, structure)
+    }
+
+    inline fun <reified T : Any, F : Field<T>> inline(shape: IntArray, field: F, noinline initializer: F.(IntArray) -> T): GenericNDElement<T, F> {
+        val ndField = GenericNDField(shape, field)
+        val structure = ndStructure(shape, ::inlineBuffer) { index -> field.initializer(index) }
+        return GenericNDElement(ndField, structure)
+    }
+}
+
+
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy
+ */
+operator fun <T, F : Field<T>> Function1<T, T>.invoke(ndElement: NDElement<T, F>) = ndElement.map { value -> this@invoke(value) }
+
+/* plus and minus */
+
+/**
+ * Summation operation for [NDElements] and single element
+ */
+operator fun <T, F : Field<T>> NDElement<T, F>.plus(arg: T): NDElement<T, F> = this.map { value -> elementField.run { arg + value } }
+
+/**
+ * Subtraction operation between [NDElements] and single element
+ */
+operator fun <T, F : Field<T>> NDElement<T, F>.minus(arg: T): NDElement<T, F> = this.map { value -> elementField.run { arg - value } }
+
+/* prod and div */
+
+/**
+ * Product operation for [NDElements] and single element
+ */
+operator fun <T, F : Field<T>> NDElement<T, F>.times(arg: T): NDElement<T, F> = this.map { value -> elementField.run { arg * value } }
+
+/**
+ * Division operation between [NDElements] and single element
+ */
+operator fun <T, F : Field<T>> NDElement<T, F>.div(arg: T): NDElement<T, F> = this.map { value -> elementField.run { arg / value } }
+
+
+//    /**
+//     * Reverse sum operation
+//     */
+//    operator fun T.plus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@plus + arg[index] }
+//    }
+//
+//    /**
+//     * Reverse minus operation
+//     */
+//    operator fun T.minus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@minus - arg[index] }
+//    }
+//
+//    /**
+//     * Reverse product operation
+//     */
+//    operator fun T.times(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@times * arg[index] }
+//    }
+//
+//    /**
+//     * Reverse division operation
+//     */
+//    operator fun T.div(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
+//        field.run { this@div / arg[index] }
+//    }
+
+
+/**
+ *  Read-only [NDStructure] coupled to the context.
+ */
+class GenericNDElement<T, F : Field<T>>(override val context: NDField<T, F, NDStructure<T>>, private val structure: NDStructure<T>) :
+        NDStructure<T> by structure,
+        NDElement<T, F>,
+        FieldElement<NDStructure<T>, GenericNDElement<T, F>, NDField<T, F, NDStructure<T>>> {
+    override val elementField: F get() = context.field
+
+    override fun unwrap(): NDStructure<T> = structure
+
+    override fun NDStructure<T>.wrap() = GenericNDElement(context, this)
+
+    override fun mapIndexed(transform: F.(index: IntArray, T) -> T) =
+            ndStructure(context.shape) { index: IntArray -> context.field.transform(index, get(index)) }.wrap()
+}

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

@@ -1,8 +1,6 @@
 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
@@ -13,27 +11,19 @@ class ShapeMismatchException(val expected: IntArray, val actual: IntArray) : Run
  * Field for n-dimensional arrays.
  * @param shape - the list of dimensions of the array
  * @param field - operations field defined on individual array element
- * @param T the type of the element contained in NDArray
+ * @param T - the type of the element contained in ND structure
+ * @param F - field over structure elements
+ * @param R - actual nd-element type of this field
  */
-interface NDField<T, F : Field<T>> : Field<NDStructure<T>> {
+interface NDField<T, F : Field<T>, N : NDStructure<out T>> : Field<N> {
 
     val shape: IntArray
     val field: F
 
-    /**
-     * Create new instance of NDArray using field shape and given initializer
-     * The producer takes list of indices as argument and returns contained value
-     */
-    fun produce(initializer: F.(IntArray) -> T): NDElement<T, F>
-
-    override val zero: NDElement<T, F> get() = produce { zero }
-
-    override val one: NDElement<T, F> get() = produce { one }
-
     /**
      * Check the shape of given NDArray and throw exception if it does not coincide with shape of the field
      */
-    fun checkShape(vararg elements: NDStructure<T>) {
+    fun checkShape(vararg elements: N) {
         elements.forEach {
             if (!shape.contentEquals(it.shape)) {
                 throw ShapeMismatchException(shape, it.shape)
@@ -41,37 +31,8 @@ interface NDField<T, F : Field<T>> : Field<NDStructure<T>> {
         }
     }
 
-    /**
+    fun produce(initializer: F.(IntArray) -> T): N
-     * Element-by-element addition
-     */
-    override fun add(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
-        checkShape(a, b)
-        return produce { field.run { a[it] + b[it] } }
-    }
 
-    /**
-     * Multiply all elements by cinstant
-     */
-    override fun multiply(a: NDStructure<T>, k: Double): NDElement<T, F> {
-        checkShape(a)
-        return produce { field.run { a[it] * k } }
-    }
-
-    /**
-     * Element-by-element multiplication
-     */
-    override fun multiply(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
-        checkShape(a)
-        return produce { field.run { a[it] * b[it] } }
-    }
-
-    /**
-     * Element-by-element division
-     */
-    override fun divide(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
-        checkShape(a)
-        return produce { field.run { a[it] / b[it] } }
-    }
 
     companion object {
         /**
@@ -82,7 +43,7 @@ interface NDField<T, F : Field<T>> : Field<NDStructure<T>> {
         /**
          * Create a nd-field with boxing generic buffer
          */
-        fun <T : Any, F : Field<T>> generic(shape: IntArray, field: F) = BufferNDField(shape, field, ::boxingBuffer)
+        fun <T : Any, F : Field<T>> generic(shape: IntArray, field: F) = GenericNDField(shape, field)
 
         /**
          * Create a most suitable implementation for nd-field using reified class
@@ -92,123 +53,43 @@ interface NDField<T, F : Field<T>> : Field<NDStructure<T>> {
 }
 
 
-interface NDElement<T, F : Field<T>> : FieldElement<NDStructure<T>, NDField<T, F>>, NDStructure<T> {
+class GenericNDField<T : Any, F : Field<T>>(override val shape: IntArray, override val field: F, val bufferFactory: BufferFactory<T> = ::boxingBuffer) : NDField<T, F, NDStructure<T>> {
-    companion object {
+    override fun produce(initializer: F.(IntArray) -> T): NDStructure<T> = ndStructure(shape, bufferFactory) { field.initializer(it) }
-        /**
-         * Create a platform-optimized NDArray of doubles
-         */
-        fun real(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
-            return NDField.real(shape).produce(initializer)
-        }
 
-        fun real1D(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
+    override val zero: NDStructure<T>  by lazy { produce { zero } }
-            return real(intArrayOf(dim)) { initializer(it[0]) }
-        }
 
-        fun real2D(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
+    override val one: NDStructure<T> by lazy { produce { one } }
-            return real(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
-        }
 
-        fun real3D(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
-            return real(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
-        }
-
-//        inline fun real(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> {
-//            val field = NDField.real(shape)
-//            return GenericNDElement(field, field.run(block))
-//        }
 
     /**
-         * Simple boxing NDArray
+     * Element-by-element addition
      */
-        fun <T : Any, F : Field<T>> generic(shape: IntArray, field: F, initializer: F.(IntArray) -> T): NDElement<T, F> {
+    override fun add(a: NDStructure<T>, b: NDStructure<T>): NDStructure<T> {
-            return NDField.generic(shape, field).produce(initializer)
+        checkShape(a, b)
+        return produce { field.run { a[it] + b[it] } }
     }
 
-        inline fun <reified T : Any, F : Field<T>> inline(shape: IntArray, field: F, noinline initializer: F.(IntArray) -> T): NDElement<T, F> {
+    /**
-            return NDField.inline(shape, field).produce(initializer)
+     * Multiply all elements by cinstant
+     */
+    override fun multiply(a: NDStructure<T>, k: Double): NDStructure<T> {
+        checkShape(a)
+        return produce { field.run { a[it] * k } }
     }
+
+    /**
+     * Element-by-element multiplication
+     */
+    override fun multiply(a: NDStructure<T>, b: NDStructure<T>): NDStructure<T> {
+        checkShape(a)
+        return produce { field.run { a[it] * b[it] } }
+    }
+
+    /**
+     * Element-by-element division
+     */
+    override fun divide(a: NDStructure<T>, b: NDStructure<T>): NDStructure<T> {
+        checkShape(a)
+        return produce { field.run { a[it] / b[it] } }
     }
 }
-
-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)) }
-
-
-/**
- * Element by element application of any operation on elements to the whole array. Just like in numpy
- */
-operator fun <T, F : Field<T>> Function1<T, T>.invoke(ndElement: NDElement<T, F>): NDElement<T, F> = ndElement.transform { value -> this@invoke(value) }
-
-/* plus and minus */
-
-/**
- * Summation operation for [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.plus(arg: T): NDElement<T, F> = transform { value ->
-    context.field.run { arg + value }
-}
-
-/**
- * Subtraction operation between [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.minus(arg: T): NDElement<T, F> = transform { value ->
-    context.field.run { arg - value }
-}
-
-/* prod and div */
-
-/**
- * Product operation for [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.times(arg: T): NDElement<T, F> = transform { value ->
-    context.field.run { arg * value }
-}
-
-/**
- * Division operation between [NDElement] and single element
- */
-operator fun <T, F : Field<T>> NDElement<T, F>.div(arg: T): NDElement<T, F> = transform { value ->
-    context.field.run { arg / value }
-}
-
-
-//    /**
-//     * Reverse sum operation
-//     */
-//    operator fun T.plus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@plus + arg[index] }
-//    }
-//
-//    /**
-//     * Reverse minus operation
-//     */
-//    operator fun T.minus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@minus - arg[index] }
-//    }
-//
-//    /**
-//     * Reverse product operation
-//     */
-//    operator fun T.times(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@times * arg[index] }
-//    }
-//
-//    /**
-//     * Reverse division operation
-//     */
-//    operator fun T.div(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@div / arg[index] }
-//    }
-
-class GenericNDField<T : Any, F : Field<T>>(override val shape: IntArray, override val field: F) : NDField<T, F> {
-    override fun produce(initializer: F.(IntArray) -> T): NDElement<T, F> = GenericNDElement(this, produceStructure(initializer))
-    private inline fun produceStructure(crossinline initializer: F.(IntArray) -> T): NDStructure<T> = NdStructure(shape, ::boxingBuffer) { field.initializer(it) }
-}
-
-/**
- *  Read-only [NDStructure] coupled to the context.
- */
-class GenericNDElement<T, F : Field<T>>(override val context: NDField<T, F>, private val structure: NDStructure<T>) : NDElement<T, F>, NDStructure<T> by structure {
-    override val self: NDElement<T, F> get() = this
-}

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

@@ -112,26 +112,24 @@ class DefaultStrides private constructor(override val shape: IntArray) : Strides
     }
 }
 
-abstract class GenericNDStructure<T, B : Buffer<T>> : NDStructure<T> {
+interface NDBuffer<T> : NDStructure<T> {
-    abstract val buffer: B
+    val buffer: Buffer<T>
-    abstract val strides: Strides
+    val strides: Strides
 
     override fun get(index: IntArray): T = buffer[strides.offset(index)]
 
-    override val shape: IntArray
+    override val shape: IntArray get() = strides.shape
-        get() = strides.shape
 
-    override fun elements() =
+    override fun elements() = strides.indices().map { it to this[it] }
-            strides.indices().map { it to this[it] }
 }
 
 /**
  * Boxing generic [NDStructure]
  */
-class BufferNDStructure<T>(
+data class BufferNDStructure<T>(
         override val strides: Strides,
         override val buffer: Buffer<T>
-) : GenericNDStructure<T, Buffer<T>>() {
+) : NDBuffer<T> {
 
     init {
         if (strides.linearSize != buffer.size) {
@@ -158,7 +156,7 @@ class BufferNDStructure<T>(
 /**
  * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [BufferNDStructure]
  */
-inline fun <T, reified R : Any> NDStructure<T>.map(factory: BufferFactory<R> = ::inlineBuffer, crossinline transform: (T) -> R): BufferNDStructure<R> {
+inline fun <T, reified R : Any> NDStructure<T>.mapToBuffer(factory: BufferFactory<R> = ::inlineBuffer, crossinline transform: (T) -> R): BufferNDStructure<R> {
     return if (this is BufferNDStructure<T>) {
         BufferNDStructure(this.strides, factory.invoke(strides.linearSize) { transform(buffer[it]) })
     } else {
@@ -172,8 +170,7 @@ inline fun <T, reified R : Any> NDStructure<T>.map(factory: BufferFactory<R> = :
  *
  * Strides should be reused if possible
  */
-@Suppress("FunctionName")
+fun <T> ndStructure(strides: Strides, bufferFactory: BufferFactory<T> = ::boxingBuffer, initializer: (IntArray) -> T) =
-fun <T : Any> NdStructure(strides: Strides, bufferFactory: BufferFactory<T>, initializer: (IntArray) -> T) =
         BufferNDStructure(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
 
 /**
@@ -182,9 +179,8 @@ fun <T : Any> NdStructure(strides: Strides, bufferFactory: BufferFactory<T>, ini
 inline fun <reified T : Any> inlineNDStructure(strides: Strides, crossinline initializer: (IntArray) -> T) =
         BufferNDStructure(strides, inlineBuffer(strides.linearSize) { i -> initializer(strides.index(i)) })
 
-@Suppress("FunctionName")
+fun <T> ndStructure(shape: IntArray, bufferFactory: BufferFactory<T> = ::boxingBuffer, initializer: (IntArray) -> T) =
-fun <T : Any> NdStructure(shape: IntArray, bufferFactory: BufferFactory<T>, initializer: (IntArray) -> T) =
+        ndStructure(DefaultStrides(shape), bufferFactory, initializer)
-        NdStructure(DefaultStrides(shape), bufferFactory, initializer)
 
 inline fun <reified T : Any> inlineNdStructure(shape: IntArray, crossinline initializer: (IntArray) -> T) =
         inlineNDStructure(DefaultStrides(shape), initializer)
@@ -195,7 +191,7 @@ inline fun <reified T : Any> inlineNdStructure(shape: IntArray, crossinline init
 class MutableBufferNDStructure<T>(
         override val strides: Strides,
         override val buffer: MutableBuffer<T>
-) : GenericNDStructure<T, MutableBuffer<T>>(), MutableNDStructure<T> {
+) : NDBuffer<T>, MutableNDStructure<T> {
 
     init {
         if (strides.linearSize != buffer.size) {
@@ -209,16 +205,14 @@ class MutableBufferNDStructure<T>(
 /**
  * The same as [inlineNDStructure], but mutable
  */
-@Suppress("FunctionName")
+fun <T : Any> mutableNdStructure(strides: Strides, bufferFactory: MutableBufferFactory<T> = ::boxingMutableBuffer, initializer: (IntArray) -> T) =
-fun <T : Any> MutableNdStructure(strides: Strides, bufferFactory: MutableBufferFactory<T>, initializer: (IntArray) -> T) =
         MutableBufferNDStructure(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
 
 inline fun <reified T : Any> inlineMutableNdStructure(strides: Strides, crossinline initializer: (IntArray) -> T) =
         MutableBufferNDStructure(strides, inlineMutableBuffer(strides.linearSize) { i -> initializer(strides.index(i)) })
 
-@Suppress("FunctionName")
+fun <T : Any> mutableNdStructure(shape: IntArray, bufferFactory: MutableBufferFactory<T> = ::boxingMutableBuffer, initializer: (IntArray) -> T) =
-fun <T : Any> MutableNdStructure(shape: IntArray, bufferFactory: MutableBufferFactory<T>, initializer: (IntArray) -> T) =
+        mutableNdStructure(DefaultStrides(shape), bufferFactory, initializer)
-        MutableNdStructure(DefaultStrides(shape), bufferFactory, initializer)
 
 inline fun <reified T : Any> inlineMutableNdStructure(shape: IntArray, crossinline initializer: (IntArray) -> T) =
         inlineMutableNdStructure(DefaultStrides(shape), initializer)

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

@@ -4,20 +4,17 @@ import scientifik.kmath.operations.DoubleField
 
 typealias RealNDElement = BufferNDElement<Double, DoubleField>
 
-class RealNDField(shape: IntArray) : BufferNDField<Double, DoubleField>(shape, DoubleField, DoubleBufferFactory), ExtendedNDField<Double, DoubleField> {
+class RealNDField(shape: IntArray) :
+        BufferNDField<Double, DoubleField>(shape, DoubleField, DoubleBufferFactory),
+        ExtendedNDField<Double, DoubleField, NDBuffer<Double>> {
 
     /**
      * Inline map an NDStructure to
      */
-    private inline fun NDStructure<Double>.mapInline(crossinline operation: DoubleField.(Double) -> Double): RealNDElement {
+    private inline fun NDBuffer<Double>.mapInline(crossinline operation: DoubleField.(Double) -> Double): RealNDElement {
-        return if (this is BufferNDElement<Double, *>) {
         val array = DoubleArray(strides.linearSize) { offset -> DoubleField.operation(buffer[offset]) }
-            BufferNDElement(this@RealNDField, DoubleBuffer(array))
+        return BufferNDElement(this@RealNDField, DoubleBuffer(array))
-        } else {
-            produce { index -> DoubleField.operation(get(index)) }
     }
-    }
-
 
     @Suppress("OVERRIDE_BY_INLINE")
     override inline fun produce(initializer: DoubleField.(IntArray) -> Double): RealNDElement {
@@ -25,23 +22,23 @@ class RealNDField(shape: IntArray) : BufferNDField<Double, DoubleField>(shape, D
         return BufferNDElement(this, DoubleBuffer(array))
     }
 
-    override fun power(arg: NDStructure<Double>, pow: Double) = arg.mapInline { power(it, pow) }
+    override fun power(arg: NDBuffer<Double>, pow: Double) = arg.mapInline { power(it, pow) }
 
-    override fun exp(arg: NDStructure<Double>) = arg.mapInline { exp(it) }
+    override fun exp(arg: NDBuffer<Double>) = arg.mapInline { exp(it) }
 
-    override fun ln(arg: NDStructure<Double>) = arg.mapInline { ln(it) }
+    override fun ln(arg: NDBuffer<Double>) = arg.mapInline { ln(it) }
 
-    override fun sin(arg: NDStructure<Double>) = arg.mapInline { sin(it) }
+    override fun sin(arg: NDBuffer<Double>) = arg.mapInline { sin(it) }
 
-    override fun cos(arg: NDStructure<Double>) = arg.mapInline { cos(it) }
+    override fun cos(arg: NDBuffer<Double>) = arg.mapInline { cos(it) }
 
-    override fun NDStructure<Double>.times(k: Number) = mapInline { value -> value * k.toDouble() }
+    override fun NDBuffer<Double>.times(k: Number) = mapInline { value -> value * k.toDouble() }
 
-    override fun NDStructure<Double>.div(k: Number) = mapInline { value -> value / k.toDouble() }
+    override fun NDBuffer<Double>.div(k: Number) = mapInline { value -> value / k.toDouble() }
 
-    override fun Number.times(b: NDStructure<Double>) = b * this
+    override fun Number.times(b: NDBuffer<Double>) = b * this
 
-    override fun Number.div(b: NDStructure<Double>) = b * (1.0 / this.toDouble())
+    override fun Number.div(b: NDBuffer<Double>) = b * (1.0 / this.toDouble())
 }
 
 /**

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

@@ -7,7 +7,7 @@ import kotlin.test.assertEquals
 class NDFieldTest {
     @Test
     fun testStrides() {
-        val ndArray = NDElement.real(intArrayOf(10, 10)) { (it[0] + it[1]).toDouble() }
+        val ndArray = NDElements.real(intArrayOf(10, 10)) { (it[0] + it[1]).toDouble() }
         assertEquals(ndArray[5, 5], 10.0)
     }
 }

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

@@ -1,7 +1,6 @@
 package scientifik.kmath.structures
 
 import scientifik.kmath.operations.Norm
-import scientifik.kmath.structures.NDElement.Companion.real2D
 import kotlin.math.abs
 import kotlin.math.pow
 import kotlin.test.Test

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

@@ -5,7 +5,7 @@ import scientifik.kmath.operations.Field
 
 class LazyNDField<T, F : Field<T>>(shape: IntArray, field: F, val scope: CoroutineScope = GlobalScope) : BufferNDField<T, F>(shape,field, ::boxingBuffer) {
 
-    override fun add(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
+    override fun add(a: NDStructure<T>, b: NDStructure<T>): NDElements<T, F> {
         return LazyNDStructure(this) { index ->
             val aDeferred = a.deferred(index)
             val bDeferred = b.deferred(index)
@@ -13,11 +13,11 @@ class LazyNDField<T, F : Field<T>>(shape: IntArray, field: F, val scope: Corouti
         }
     }
 
-    override fun multiply(a: NDStructure<T>, k: Double): NDElement<T, F> {
+    override fun multiply(a: NDStructure<T>, k: Double): NDElements<T, F> {
         return LazyNDStructure(this) { index -> a.await(index) * k }
     }
 
-    override fun multiply(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
+    override fun multiply(a: NDStructure<T>, b: NDStructure<T>): NDElements<T, F> {
         return LazyNDStructure(this) { index ->
             val aDeferred = a.deferred(index)
             val bDeferred = b.deferred(index)
@@ -25,7 +25,7 @@ class LazyNDField<T, F : Field<T>>(shape: IntArray, field: F, val scope: Corouti
         }
     }
 
-    override fun divide(a: NDStructure<T>, b: NDStructure<T>): NDElement<T, F> {
+    override fun divide(a: NDStructure<T>, b: NDStructure<T>): NDElements<T, F> {
         return LazyNDStructure(this) { index ->
             val aDeferred = a.deferred(index)
             val bDeferred = b.deferred(index)
@@ -34,8 +34,8 @@ class LazyNDField<T, F : Field<T>>(shape: IntArray, field: F, val scope: Corouti
     }
 }
 
-class LazyNDStructure<T, F : Field<T>>(override val context: LazyNDField<T, F>, val function: suspend F.(IntArray) -> T) : NDElement<T, F>, NDStructure<T> {
+class LazyNDStructure<T, F : Field<T>>(override val context: LazyNDField<T, F>, val function: suspend F.(IntArray) -> T) : NDElements<T, F>, NDStructure<T> {
-    override val self: NDElement<T, F> get() = this
+    override val self: NDElements<T, F> get() = this
     override val shape: IntArray get() = context.shape
 
     private val cache = HashMap<IntArray, Deferred<T>>()
@@ -58,7 +58,7 @@ fun <T> NDStructure<T>.deferred(index: IntArray) = if (this is LazyNDStructure<T
 
 suspend fun <T> NDStructure<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> {
+fun <T, F : Field<T>> NDElements<T, F>.lazy(scope: CoroutineScope = GlobalScope): LazyNDStructure<T, F> {
     return if (this is LazyNDStructure<T, F>) {
         this
     } else {