doc/contexts.md

@@ -36,7 +36,7 @@ fun ComplexOperations.doSomethingWithComplex(c1: Complex, c2: Complex, c3: Compl
 ComplexOperations.doComethingWithComplex(c1,c2,c3)
 ```
 
-In fact, whole parts of proram could run in a mathematical context or even multiple nested contexts. 
+In fact, whole parts of program could run in a mathematical context or even multiple nested contexts. 
 
 In `kmath` contexts are responsible not only for operations, but also for raw object creation and advanced features.
 

doc/operations.md

@@ -0,0 +1,38 @@
+## Spaces and fields
+
+An obvious first choice of mathematical objects to implement in context-oriented style are algebra elements like spaces,
+rings and fields. Those are located in a `scientifik.kmath.operations.Algebra.kt` file. Alongside algebric context
+themselves, the file includes definitions for algebra elements such as `FieldElement`. A `FieldElement` object
+stores a reference to the `Field` which contains a additive and multiplicative operations for it, meaning
+it has one fixed context attached to it and does not require explicit external context. So those `MathElements` could be
+operated without context:
+```kotlin
+val c1 = Complex(1.0, 2.0)
+val c2 = ComplexField.i
+val c3 = c1 + c2
+```
+`ComplexField` also features special operations to mix complex numbers with real numbers like:
+```kotlin
+val c1 = Complex(1.0,2.0)
+val c2 = ComplexField.run{ c1 - 1.0} //returns [re:0.0, im: 2.0]
+val c3 = ComplexField.run{ c1 - i*2.0}
+```
+
+**Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
+that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for news.
+
+## Nested fields
+
+Algebra contexts allow to create more complex structures. For example, it is possible to create a `Matrix` from complex
+elements like this:
+```kotlin
+val element = NDElements.create(field = ComplexField, shape = intArrayOf(2,2)){index: IntArray ->
+    Complex(index[0] - index[1], index[0] + index[1])
+}
+```
+The `element` in this example is a member of `Field` of 2-d structures, each element of which is a member of its own
+`ComplexField`. The important thing is that one does not need to create a special nd-structure to hold complex
+numbers and implements operations on it, one need just to provide a field for its elements.
+
+**Note**: Fields themselves do not solve problem of JVM boxing, but it is possible to solve with special contexts like
+`BufferSpec`. This feature is in development phase.

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

@@ -18,6 +18,15 @@ object ComplexField : Field<Complex> {
 
     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
 
+    operator fun Double.plus(c: Complex) = this.toComplex() + c
+
+    operator fun Double.minus(c: Complex) = this.toComplex() - c
+
+    operator fun Complex.plus(d: Double) = d + this
+
+    operator fun Complex.minus(d: Double) = this - d.toComplex()
+
+    operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
 }
 
 /**
@@ -46,13 +55,3 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Compl
 }
 
 fun Double.toComplex() = Complex(this, 0.0)
-
-operator fun Double.plus(c: Complex) = this.toComplex() + c
-
-operator fun Double.minus(c: Complex) = this.toComplex() - c
-
-operator fun Complex.plus(d: Double) = d + this
-
-operator fun Complex.minus(d: Double) = this - d.toComplex()
-
-operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)

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

@@ -173,27 +173,27 @@ class GenericNDField<T : Any, F : Field<T>>(shape: IntArray, field: F) : NDField
 
 //typealias NDFieldFactory<T> = (IntArray)->NDField<T>
 
-object NDArrays {
+object NDElements {
     /**
      * Create a platform-optimized NDArray of doubles
      */
-    fun realNDArray(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
+    fun realNDElement(shape: IntArray, initializer: DoubleField.(IntArray) -> Double = { 0.0 }): NDElement<Double, DoubleField> {
         return ExtendedNDField(shape, DoubleField).produce(initializer)
     }
 
-    fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
-        return realNDArray(intArrayOf(dim)) { initializer(it[0]) }
+    fun real1DElement(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDElement<Double, DoubleField> {
+        return realNDElement(intArrayOf(dim)) { initializer(it[0]) }
     }
 
-    fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
-        return realNDArray(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
+    fun real2DElement(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDElement<Double, DoubleField> {
+        return realNDElement(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
     }
 
-    fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
-        return realNDArray(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
+    fun real3DElement(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDElement<Double, DoubleField> {
+        return realNDElement(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
     }
 
-    inline fun produceReal(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> {
+    inline fun real(shape: IntArray, block: ExtendedNDField<Double, DoubleField>.() -> NDStructure<Double>): NDElement<Double, DoubleField> {
         val field = ExtendedNDField(shape, DoubleField)
         return NDStructureElement(field, field.run(block))
     }

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

@@ -1,7 +1,7 @@
 package scientifik.kmath.structures
 
 import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.structures.NDArrays.create
+import scientifik.kmath.structures.NDElements.create
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

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

@@ -1,16 +1,16 @@
 package scientifik.kmath.structures
 
 import scientifik.kmath.operations.Norm
-import scientifik.kmath.structures.NDArrays.produceReal
-import scientifik.kmath.structures.NDArrays.real2DArray
+import scientifik.kmath.structures.NDElements.real
+import scientifik.kmath.structures.NDElements.real2DElement
 import kotlin.math.abs
 import kotlin.math.pow
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
 class NumberNDFieldTest {
-    val array1 = real2DArray(3, 3) { i, j -> (i + j).toDouble() }
-    val array2 = real2DArray(3, 3) { i, j -> (i - j).toDouble() }
+    val array1 = real2DElement(3, 3) { i, j -> (i + j).toDouble() }
+    val array2 = real2DElement(3, 3) { i, j -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
@@ -27,7 +27,7 @@ class NumberNDFieldTest {
     @Test
     fun testGeneration() {
 
-        val array = real2DArray(3, 3) { i, j -> (i * 10 + j).toDouble() }
+        val array = real2DElement(3, 3) { i, j -> (i * 10 + j).toDouble() }
 
         for (i in 0..2) {
             for (j in 0..2) {
@@ -64,7 +64,7 @@ class NumberNDFieldTest {
 
     @Test
     fun testInternalContext() {
-        produceReal(array1.shape) {
+        real(array1.shape) {
             with(L2Norm) {
                 1 + norm(array1) + exp(array2)
             }

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

@@ -9,7 +9,7 @@ class LazyNDFieldTest {
     @Test
     fun testLazyStructure() {
         var counter = 0
-        val regularStructure = NDArrays.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] }
+        val regularStructure = NDElements.create(IntField, intArrayOf(2, 2, 2)) { it[0] + it[1] - it[2] }
         val result = (regularStructure.lazy() + 2).transform {
             counter++
             it * it