README.md

@@ -1,2 +1,31 @@
-# kmath
-Kotlin mathematics extensions library
+# KMath
+Kotlin MATHematics library is intended as a kotlin based analog of numpy python library. Contrary to `numpy`
+and `scipy` it is modular and has a lightweight core.
+
+## Features
+
+* **Algebra**
+    * Mathematical operation entities like rings, spaces and fields with (**TODO** add example to wiki) 
+    * Basic linear algebra operations (summs products, etc) backed by `Space` API.
+    * [In progress] advanced linear algebra operations like matrix inversions.
+* **Array-like structures** Full support of numpy-like ndarray including mixed ariphmetic operations and function operations
+on arrays and numbers just like it works in python (with benefit of static type checking).
+
+## Multi-platform support
+KMath is developed as a multi-platform library, which means that most of interfaces are declared in common module.
+Implementation is also done in common module wherever it is possible. In some cases features are delegated to 
+platform even if they could be done in common module because of platform performance optimization.
+
+## Performance
+The calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve 
+both performance and flexibility. We expect to firstly focus on creating convenient universal API and then work on 
+increasing performance for specific cases. We expect the worst KMath performance still be better than natural python,
+but worse than optimized native/scipy (mostly due to boxing operations on primitive numbers). The best performance 
+of optimized parts should be better than scipy.
+
+## Releases
+The project is currently in pre-release stage. Work builds could be obtained with 
+[![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath). 
+
+## Contributing
+The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.

build.gradle

@@ -1,5 +1,5 @@
 buildscript {
-    ext.kotlin_version = '1.2.41'
+    ext.kotlin_version = '1.2.60'
 
     repositories {
         mavenCentral()

kmath-common/src/main/kotlin/scientifik/kmath/operations/Algebra.kt

@@ -1,5 +1,16 @@
 package scientifik.kmath.operations
 
+
+/**
+ * The generic mathematics elements which is able to store its context
+ */
+interface MathElement<T, S>{
+    /**
+     * 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.
@@ -37,23 +48,20 @@ interface Space<T> {
 
 /**
  * The element of linear context
- * @param S self type of the element. Needed for static type checking
+ * @param T  self type of the element. Needed for static type checking
+ * @param S the type of space
  */
-interface SpaceElement<S : SpaceElement<S>> {
-    /**
-     * The context this element belongs to
-     */
-    val context: Space<S>
+interface SpaceElement<T, S : Space<T>>: MathElement<T,S> {
 
     /**
      * Self value. Needed for static type checking. Needed to avoid type erasure on JVM.
      */
-    val self: S
+    val self: T
 
-    operator fun plus(b: S): S = context.add(self, b)
-    operator fun minus(b: S): S = context.add(self, context.multiply(b, -1.0))
-    operator fun times(k: Number): S = context.multiply(self, k.toDouble())
-    operator fun div(k: Number): S = context.multiply(self, 1.0 / k.toDouble())
+    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())
 }
 
 /**
@@ -77,10 +85,10 @@ interface Ring<T> : Space<T> {
 /**
  * Ring element
  */
-interface RingElement<S : RingElement<S>> : SpaceElement<S> {
-    override val context: Ring<S>
+interface RingElement<T, S : Ring<T>> : SpaceElement<T, S> {
+    override val context: S
 
-    operator fun times(b: S): S = context.multiply(self, b)
+    operator fun times(b: T): T = context.multiply(self, b)
 }
 
 /**
@@ -96,8 +104,8 @@ interface Field<T> : Ring<T> {
 /**
  * Field element
  */
-interface FieldElement<S : FieldElement<S>> : RingElement<S> {
-    override val context: Field<S>
+interface FieldElement<T, S : Field<T>> : RingElement<T, S> {
+    override val context: S
 
-    operator fun div(b: S): S = context.divide(self, b)
+    operator fun div(b: T): T = context.divide(self, b)
 }

kmath-common/src/main/kotlin/scientifik/kmath/operations/Fields.kt

@@ -1,23 +1,39 @@
 package scientifik.kmath.operations
 
+import kotlin.math.pow
 import kotlin.math.sqrt
 
 /**
  * Field for real values
  */
-object RealField : Field<Real> {
+object RealField : Field<Real>, TrigonometricOperations<Real>, PowerOperations<Real>, ExponentialOperations<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))
 }
 
 /**
- * Real field element wrapping double
+ * Real field element wrapping double.
+ *
+ * TODO could be replaced by inline class in kotlin 1.3 if it would allow to avoid boxing
  */
-class Real(val value: Double) : FieldElement<Real>, Number() {
+class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
+    /*
+     * The class uses composition instead of inheritance since Double is final
+     */
+
     override fun toByte(): Byte = value.toByte()
     override fun toChar(): Char = value.toChar()
     override fun toDouble(): Double = value
@@ -29,8 +45,10 @@ class Real(val value: Double) : FieldElement<Real>, Number() {
     //values are dynamically calculated to save memory
     override val self
         get() = this
+
     override val context
         get() = RealField
+
 }
 
 /**
@@ -54,10 +72,9 @@ object ComplexField : Field<Complex> {
 /**
  * Complex number class
  */
-data class Complex(val re: Double, val im: Double) : FieldElement<Complex> {
-    override val self: Complex
-        get() = this
-    override val context: 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
 
     /**
@@ -72,15 +89,15 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex> {
     val module: Double
         get() = sqrt(square)
 
-
-    //TODO is it convenient?
-    operator fun not() = conjugate
 }
 
+/**
+ * A field for double without boxing. Does not produce appropriate field element
+ */
 object DoubleField : Field<Double> {
     override val zero: Double = 0.0
     override fun add(a: Double, b: Double): Double = a + b
-    override fun multiply(a: Double, b: Double): Double = a * b
+    override fun multiply(a: Double, @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE") b: Double): Double = a * b
     override val one: Double = 1.0
     override fun divide(a: Double, b: Double): Double = a / b
 }

kmath-common/src/main/kotlin/scientifik/kmath/operations/OptionalOperations.kt

@@ -0,0 +1,48 @@
+package scientifik.kmath.operations
+
+
+/* Trigonometric operations */
+
+/**
+ * A container for trigonometric operations for specific type. Trigonometric operations are limited to fields.
+ *
+ * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
+ * It also allows to override behavior for optional operations
+ *
+ */
+interface TrigonometricOperations<T>: Field<T> {
+    fun sin(arg: T): T
+    fun cos(arg: T): T
+
+    fun tg(arg: T): T = sin(arg) / cos(arg)
+
+    fun ctg(arg: T): T = cos(arg) / sin(arg)
+}
+
+fun <T : FieldElement<T, out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
+fun <T : FieldElement<T, out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
+fun <T : FieldElement<T, out TrigonometricOperations<T>>> tg(arg: T): T = arg.context.tg(arg)
+fun <T : FieldElement<T, out TrigonometricOperations<T>>> ctg(arg: T): T = arg.context.ctg(arg)
+
+/* Power and roots */
+
+/**
+ * A context extension to include power operations like square roots, etc
+ */
+interface PowerOperations<T> {
+    fun power(arg: T, pow: Double): T
+}
+
+infix fun <T : MathElement<T, out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
+fun <T : MathElement<T, out PowerOperations<T>>> sqrt(arg: T): T = arg pow 0.5
+fun <T : MathElement<T, out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
+
+/* Exponential */
+
+interface ExponentialOperations<T>{
+    fun exp(arg: T): T
+    fun ln(arg: T): T
+}
+
+fun <T: MathElement<T, out ExponentialOperations<T>>> exp(arg:T): T = arg.context.exp(arg)
+fun <T: MathElement<T, out ExponentialOperations<T>>> ln(arg:T): T = arg.context.ln(arg)

kmath-common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt

@@ -0,0 +1,144 @@
+package scientifik.kmath.structures
+
+import scientifik.kmath.operations.DoubleField
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.SpaceElement
+
+/**
+ * The space for linear elements. Supports scalar product alongside with standard linear operations.
+ * @param T type of individual element of the vector or matrix
+ * @param V the type of vector space element
+ */
+abstract class LinearSpace<T : Any, V : LinearStructure<out T>>(val rows: Int, val columns: Int, val field: Field<T>) : Space<V> {
+
+    /**
+     * Produce the element of this space
+     */
+    abstract fun produce(initializer: (Int, Int) -> T): V
+
+    /**
+     * 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: V, b: V): V {
+        return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
+    }
+
+    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.rows != b.columns) {
+            //TODO replace by specific exception
+            error("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)
+}
+
+/**
+ * A matrix-like structure that is not dependent on specific space implementation
+ */
+interface LinearStructure<T : Any> {
+    val rows: Int
+    val columns: Int
+
+    operator fun get(i: Int, j: Int): 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)
+        }
+    }
+}
+
+interface Vector<T : Any> : LinearStructure<T> {
+    override val columns: Int
+        get() = 1
+
+    operator fun get(i: Int) = get(i, 0)
+}
+
+
+/**
+ * DoubleArray-based implementation of vector space
+ */
+class ArraySpace<T : Any>(rows: Int, columns: Int, field: Field<T>) : LinearSpace<T, LinearStructure<out T>>(rows, columns, field) {
+
+    override fun produce(initializer: (Int, Int) -> T): LinearStructure<T> = ArrayMatrix<T>(this, initializer)
+
+
+    override fun produceSpace(rows: Int, columns: Int): LinearSpace<T, LinearStructure<out T>> {
+        return ArraySpace(rows, columns, field)
+    }
+}
+
+/**
+ * Member of [ArraySpace] which wraps 2-D array
+ */
+class ArrayMatrix<T : Any>(override val context: ArraySpace<T>, initializer: (Int, Int) -> T) : LinearStructure<T>, SpaceElement<LinearStructure<out T>, ArraySpace<T>> {
+
+    val list: List<List<T>> = (0 until rows).map { i -> (0 until columns).map { j -> initializer(i, j) } }
+
+    override val rows: Int get() = context.rows
+
+    override val columns: Int get() = context.columns
+
+    override fun get(i: Int, j: Int): T {
+        return list[i][j]
+    }
+
+    override val self: ArrayMatrix<T> get() = this
+}
+
+
+class ArrayVector<T : Any>(override val context: ArraySpace<T>, initializer: (Int) -> T) : Vector<T>, SpaceElement<LinearStructure<out T>, ArraySpace<T>> {
+
+    init {
+        if (context.columns != 1) {
+            error("Vector must have single column")
+        }
+    }
+
+    val list: List<T> = (0 until context.rows).map(initializer)
+
+
+    override val rows: Int get() = context.rows
+
+    override val columns: Int = 1
+
+    override fun get(i: Int, j: Int): T {
+        return list[i]
+    }
+
+    override val self: ArrayVector<T> get() = this
+
+}
+
+fun <T : Any> vector(size: Int, field: Field<T>, initializer: (Int) -> T) = ArrayVector(ArraySpace(size, 1, field), initializer)
+//TODO replace by primitive array version
+fun realVector(size: Int, initializer: (Int) -> Double) = vector(size, DoubleField, initializer)
+
+fun <T : Any> Array<T>.asVector(field: Field<T>) = vector(size, field) { this[it] }
+//TODO add inferred field from field element
+fun DoubleArray.asVector() = realVector(this.size) { this[it] }
+
+fun <T : Any> matrix(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) = ArrayMatrix<T>(ArraySpace(rows, columns, field), initializer)
+fun realMatrix(rows: Int, columns: Int, initializer: (Int, Int) -> Double) = matrix(rows, columns, DoubleField, initializer)

kmath-common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt

@@ -3,22 +3,32 @@ package scientifik.kmath.structures
 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()
 
 /**
  * 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>> {
+
     /**
      * 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>
 
-    override val zero: NDArray<T>
-        get() = produce { this.field.zero }
+    override val zero: NDArray<T> by lazy {
+        produce { this.field.zero }
+    }
 
+    /**
+     * Check the shape of given NDArray and throw exception if it does not coincide with shape of the field
+     */
     private fun checkShape(vararg arrays: NDArray<T>) {
         arrays.forEach {
             if (shape != it.shape) {
@@ -64,13 +74,13 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
 }
 
 
-interface NDArray<T> : FieldElement<NDArray<T>>, Iterable<Pair<List<Int>, T>> {
+interface NDArray<T> : FieldElement<NDArray<T>, NDField<T>> {
 
     /**
      * The list of dimensions of this NDArray
      */
     val shape: List<Int>
-        get() = (context as NDField<T>).shape
+        get() = context.shape
 
     /**
      * The number of dimentsions for this array
@@ -87,14 +97,14 @@ interface NDArray<T> : FieldElement<NDArray<T>>, Iterable<Pair<List<Int>, T>> {
         return get(*index.toIntArray())
     }
 
-    override operator fun iterator(): Iterator<Pair<List<Int>, T>> {
+    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 as NDField<T>).produce { action(it, this[it]) }
+    fun transform(action: (List<Int>, T) -> T): NDArray<T> = context.produce { action(it, this[it]) }
 
     companion object {
         /**
@@ -115,6 +125,79 @@ interface NDArray<T> : FieldElement<NDArray<T>>, Iterable<Pair<List<Int>, T>> {
     }
 }
 
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy
+ */
+operator fun <T> Function1<T, T>.invoke(ndArray: NDArray<T>): NDArray<T> = ndArray.transform { _, value -> this(value) }
+
+/* plus and minus */
+
+/**
+ * Summation operation for [NDArray] and single element
+ */
+operator fun <T> NDArray<T>.plus(arg: T): NDArray<T> = transform { _, value ->
+    with(context.field){
+        arg + value
+    }
+}
+
+/**
+ * Reverse sum operation
+ */
+operator fun <T> T.plus(arg: NDArray<T>): NDArray<T> = arg + this
+
+/**
+ * Subtraction operation between [NDArray] and single element
+ */
+operator fun <T> NDArray<T>.minus(arg: T): NDArray<T> = transform  { _, value ->
+    with(context.field){
+        arg - 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 */
+
+/**
+ * Product operation for [NDArray] and single element
+ */
+operator fun <T> NDArray<T>.times(arg: T): NDArray<T> = transform { _, value ->
+    with(context.field){
+        arg * value
+    }
+}
+
+/**
+ * Reverse product operation
+ */
+operator fun <T> T.times(arg: NDArray<T>): NDArray<T> = arg * this
+
+/**
+ * Division operation between [NDArray] and single element
+ */
+operator fun <T> NDArray<T>.div(arg: T): NDArray<T> = transform  { _, value ->
+    with(context.field){
+        arg / value
+    }
+}
+
+/**
+ * Reverse division operation
+ */
+operator fun <T> T.div(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
+    with(arg.context.field){
+        this@div/ value
+    }
+}
+
 /**
  * Create a platform-specific NDArray of doubles
  */

kmath-common/src/test/kotlin/scientifik/kmath/operations/RealFieldTest.kt

@@ -0,0 +1,14 @@
+package scientifik.kmath.operations
+
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class RealFieldTest {
+    @Test
+    fun testSqrt() {
+        val sqrt = with(RealField) {
+            sqrt(25 * one)
+        }
+        assertEquals(5.0, sqrt.toDouble())
+    }
+}

kmath-jvm/build.gradle

@@ -5,7 +5,7 @@ repositories {
 }
 
 dependencies {
-    expectedBy project(":common")
+    expectedBy project(":kmath-common")
     compile "org.jetbrains.kotlin:kotlin-stdlib-jdk8:$kotlin_version"
     testCompile "junit:junit:4.12"
     testCompile "org.jetbrains.kotlin:kotlin-test-junit:$kotlin_version"

kmath-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))
         }
@@ -68,7 +69,7 @@ private class RealNDField(shape: List<Int>) : NDField<Double>(shape, DoubleField
         //TODO generate fixed hash code for quick comparison?
 
 
-        override val self: NDArray<Double> = this
+        override val self: NDArray<Double> get() = this
     }
 }
 

kmath-jvm/src/test/kotlin/scientifik/kmath/structures/ArrayMatrixTest.kt

@@ -0,0 +1,26 @@
+package scientifik.kmath.structures
+
+import org.junit.Assert.assertEquals
+import org.junit.Test
+
+class ArrayMatrixTest {
+
+    @Test
+    fun testSum() {
+        val vector1 = realVector(5) { it.toDouble() }
+        val vector2 = realVector(5) { 5 - it.toDouble() }
+        val sum = vector1 + vector2
+        assertEquals(5.0, sum[2, 0], 0.1)
+    }
+
+    @Test
+    fun testDot() {
+        val vector1 = realVector(5) { it.toDouble() }
+        val vector2 = realVector(5) { 5 - it.toDouble() }
+        val product = with(vector1.context) {
+            vector1 dot (vector2.transpose())
+        }
+
+        assertEquals(10.0, product[1, 0], 0.1)
+    }
+}

kmath-jvm/src/test/kotlin/scientifik/kmath/structures/RealNDFieldTest.kt

@@ -1,6 +1,7 @@
 package scientifik.kmath.structures
 
 import org.junit.Assert.assertEquals
+import kotlin.math.pow
 import kotlin.test.Test
 
 class RealNDFieldTest {
@@ -31,4 +32,11 @@ class RealNDFieldTest {
             }
         }
     }
+
+    @Test
+    fun testExternalFunction() {
+        val function: (Double) -> Double = { x -> x.pow(2) + 2 * x + 1 }
+        val result = function(array1) + 1.0
+        assertEquals(10.0, result[1,1],0.01)
+    }
 }

settings.gradle

@@ -1,4 +1,4 @@
 rootProject.name = 'kmath'
-include 'common'
-include 'jvm'
+include 'kmath-common'
+include 'kmath-jvm'