From af446d2d2c318a1395a7ecaa9dee6a6b789137e9 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Sun, 6 May 2018 22:45:27 +0300
Subject: [PATCH] Abstract linear algebra and real value array implementation.
 Not tested.

---
 .../kmath/structures/LinearAlgrebra.kt        | 110 +++++++++++++++---
 .../scientifik/kmath/structures/NDArray.kt    |   1 +
 2 files changed, 92 insertions(+), 19 deletions(-)

diff --git a/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt b/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt
index 3de6d7560..416a5d477 100644
--- a/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt
+++ b/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt
@@ -1,45 +1,117 @@
 package scientifik.kmath.structures
 
+import scientifik.kmath.operations.DoubleField
 import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.Space
 import scientifik.kmath.operations.SpaceElement
 
-abstract class LinearSpace<T, E : LinearObject<T>>(val rows: Int, val columns: Int, val field: Field<T>) : Space<E> {
+/**
+ * The space for linear elements. Supports scalar product alongside with standard linear operations.
+ */
+abstract class LinearSpace<T, V: LinearStructure<out T>>(val rows: Int, val columns: Int, val field: Field<T>) : Space<V> {
 
-    abstract fun produce(initializer: (Int, Int) -> T): E
+    /**
+     * Produce the element of this space
+     */
+    abstract fun produce(initializer: (Int, Int) -> T): V
 
-    override val zero: E by lazy {
+    /**
+     * Produce new linear space with given dimensions
+     */
+    abstract fun produceSpace(rows: Int, columns: Int): LinearSpace<T,V>
+
+    override val zero: V by lazy {
         produce { _, _ -> field.zero }
     }
 
-    override fun add(a: E, b: E): E {
+    override fun add(a: V, b: V): V {
         return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
     }
 
-    override fun multiply(a: E, k: Double): E {
+    override fun multiply(a: V, k: Double): V {
         //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
+     */
+    fun multiply(a: V, b: V): V {
+        if (a.columns != b.rows) {
+            //TODO replace by specific exception
+            throw RuntimeException("Dimension mismatch in vector dot product")
+        }
+        return produceSpace(a.rows, b.columns).produce { i, j ->
+            (0..a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
+        }
+    }
+
+    infix fun V.dot(b: V): V = multiply(this, b)
 }
 
 /**
- * An element of linear algebra with fixed dimension. The linear space allows linear operations on objects of the same dimensions.
- * Scalar product operations are performed outside space.
- *
- * @param T the type of linear object element type.
+ * A matrix-like structure that is not dependent on specific space implementation
  */
-interface LinearObject<T> : SpaceElement<LinearObject<T>> {
+interface LinearStructure<T> {
     val rows: Int
     val columns: Int
     operator fun get(i: Int, j: Int): T
 
-    /**
-     * Get a transposed object with switched dimensions
-     */
-    fun transpose(): LinearObject<T>
-
-    /**
-     * Perform scalar multiplication (dot) operation, checking dimensions. The argument object and result both could be outside initial space.
-     */
-    operator fun times(other: LinearObject<T>): LinearObject<T>
+    fun transpose(): LinearStructure<T> {
+        return object : LinearStructure<T> {
+            override val rows: Int = this@LinearStructure.columns
+            override val columns: Int = this@LinearStructure.rows
+            override fun get(i: Int, j: Int): T = this@LinearStructure.get(j, i)
+        }
+    }
 }
+
+class RealArraySpace(rows: Int, columns: Int) : LinearSpace<Double, RealArray>(rows, columns, DoubleField) {
+    override fun produce(initializer: (Int, Int) -> Double): RealArray {
+        return RealArray(this, initializer)
+    }
+
+    override fun produceSpace(rows: Int, columns: Int): LinearSpace<Double, RealArray> {
+        return RealArraySpace(rows, columns)
+    }
+}
+
+class RealArray(override val context: RealArraySpace, initializer: (Int, Int) -> Double): LinearStructure<Double>, SpaceElement<RealArray> {
+
+    val array: Array<Array<Double>> = Array(context.rows) { i -> Array(context.columns) { j -> initializer(i, j) } }
+
+    override val rows: Int = context.rows
+
+    override val columns: Int = context.columns
+
+    override fun get(i: Int, j: Int): Double {
+        return array[i][j]
+    }
+
+    override val self: RealArray = this
+}
+
+
+///**
+// * An element of linear algebra with fixed dimension. The linear space allows linear operations on objects of the same dimensions.
+// * Scalar product operations are performed outside space.
+// *
+// * @param E the type of linear object element type.
+// */
+//interface LinearObject<E> : SpaceElement<LinearObject<E>> {
+//    override val context: LinearSpace<>
+//
+//    val rows: Int
+//    val columns: Int
+//    operator fun get(i: Int, j: Int): E
+//
+//    /**
+//     * Get a transposed object with switched dimensions
+//     */
+//    fun transpose(): LinearObject<E>
+//
+//    /**
+//     * Perform scalar multiplication (dot) operation, checking dimensions. The argument object and result both could be outside initial space.
+//     */
+//    operator fun times(other: LinearObject<E>): LinearObject<E>
+//}
diff --git a/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt b/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt
index 4e2458fff..0005565c1 100644
--- a/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt
+++ b/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt
@@ -9,6 +9,7 @@ class ShapeMismatchException(val expected: List<Int>, val actual: List<Int>) : R
  * Field for n-dimensional arrays.
  * @param shape - the list of dimensions of the array
  * @param field - operations field defined on individual array element
+ * @param T the type of the element contained in NDArray
  */
 abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDArray<T>> {
     /**