From 50a65524db2afbd03b298506661fa89a312fa986 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Thu, 3 May 2018 11:35:08 +0300
Subject: [PATCH] Conceptual design of linear algebra on the way

---
 .../kmath/structures/LinearAlgrebra.kt        | 45 +++++++++++++++++++
 .../scientifik/kmath/structures/NDArray.kt    | 11 ++---
 .../kmath/structures/RealNDArray.kt           |  1 +
 3 files changed, 52 insertions(+), 5 deletions(-)
 create mode 100644 common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt

diff --git a/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt b/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt
new file mode 100644
index 000000000..3de6d7560
--- /dev/null
+++ b/common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt
@@ -0,0 +1,45 @@
+package scientifik.kmath.structures
+
+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> {
+
+    abstract fun produce(initializer: (Int, Int) -> T): E
+
+    override val zero: E by lazy {
+        produce { _, _ -> field.zero }
+    }
+
+    override fun add(a: E, b: E): E {
+        return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
+    }
+
+    override fun multiply(a: E, k: Double): E {
+        //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 } }
+    }
+}
+
+/**
+ * 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.
+ */
+interface LinearObject<T> : SpaceElement<LinearObject<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>
+}
diff --git a/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt b/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt
index 7f27222cc..4e2458fff 100644
--- a/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt
+++ b/common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt
@@ -16,8 +16,9 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
      */
     abstract fun produce(initializer: (List<Int>) -> T): NDArray<T>
 
-    override val zero: NDArray<T>
-        get() = produce { this.field.zero }
+    override val zero: NDArray<T> by lazy {
+        produce { this.field.zero }
+    }
 
     private fun checkShape(vararg arrays: NDArray<T>) {
         arrays.forEach {
@@ -40,7 +41,7 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
      */
     override fun multiply(a: NDArray<T>, k: Double): NDArray<T> {
         checkShape(a)
-        return produce { with(field) {a[it] * k} }
+        return produce { with(field) { a[it] * k } }
     }
 
     override val one: NDArray<T>
@@ -51,7 +52,7 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
      */
     override fun multiply(a: NDArray<T>, b: NDArray<T>): NDArray<T> {
         checkShape(a)
-        return produce { with(field) {a[it] * b[it]} }
+        return produce { with(field) { a[it] * b[it] } }
     }
 
     /**
@@ -59,7 +60,7 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
      */
     override fun divide(a: NDArray<T>, b: NDArray<T>): NDArray<T> {
         checkShape(a)
-        return produce { with(field) {a[it] / b[it]} }
+        return produce { with(field) { a[it] / b[it] } }
     }
 }
 
diff --git a/jvm/src/main/kotlin/scientifik/kmath/structures/RealNDArray.kt b/jvm/src/main/kotlin/scientifik/kmath/structures/RealNDArray.kt
index 3be892ced..217e89033 100644
--- a/jvm/src/main/kotlin/scientifik/kmath/structures/RealNDArray.kt
+++ b/jvm/src/main/kotlin/scientifik/kmath/structures/RealNDArray.kt
@@ -35,6 +35,7 @@ private class RealNDField(shape: List<Int>) : NDField<Double>(shape, DoubleField
     override fun produce(initializer: (List<Int>) -> Double): NDArray<Double> {
         //TODO use sparse arrays for large capacities
         val buffer = DoubleBuffer.allocate(capacity)
+        //FIXME there could be performance degradation due to iteration procedure. Replace by straight iteration
         NDArray.iterateIndexes(shape).forEach {
             buffer.put(offset(it), initializer(it))
         }