Optional math operations.
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@ -1,5 +1,16 @@
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package scientifik.kmath.operations
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/**
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* The generic mathematics elements which is able to store its context
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*/
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interface MathElement<T, S>{
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/**
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* The context this element belongs to
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*/
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val context: S
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}
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/**
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* A general interface representing linear context of some kind.
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* The context defines sum operation for its elements and multiplication by real value.
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@ -37,23 +48,20 @@ interface Space<T> {
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/**
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* The element of linear context
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* @param S self type of the element. Needed for static type checking
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* @param T self type of the element. Needed for static type checking
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* @param S the type of space
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*/
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interface SpaceElement<S : SpaceElement<S>> {
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/**
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* The context this element belongs to
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*/
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val context: Space<S>
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interface SpaceElement<T, S : Space<T>>: MathElement<T,S> {
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/**
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* Self value. Needed for static type checking. Needed to avoid type erasure on JVM.
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*/
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val self: S
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val self: T
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operator fun plus(b: S): S = context.add(self, b)
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operator fun minus(b: S): S = context.add(self, context.multiply(b, -1.0))
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operator fun times(k: Number): S = context.multiply(self, k.toDouble())
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operator fun div(k: Number): S = context.multiply(self, 1.0 / k.toDouble())
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operator fun plus(b: T): T = context.add(self, b)
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operator fun minus(b: T): T = context.add(self, context.multiply(b, -1.0))
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operator fun times(k: Number): T = context.multiply(self, k.toDouble())
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operator fun div(k: Number): T = context.multiply(self, 1.0 / k.toDouble())
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}
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/**
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@ -77,10 +85,10 @@ interface Ring<T> : Space<T> {
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/**
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* Ring element
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*/
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interface RingElement<S : RingElement<S>> : SpaceElement<S> {
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override val context: Ring<S>
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interface RingElement<T, S : Ring<T>> : SpaceElement<T, S> {
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override val context: S
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operator fun times(b: S): S = context.multiply(self, b)
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operator fun times(b: T): T = context.multiply(self, b)
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}
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/**
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@ -96,8 +104,8 @@ interface Field<T> : Ring<T> {
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/**
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* Field element
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*/
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interface FieldElement<S : FieldElement<S>> : RingElement<S> {
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override val context: Field<S>
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interface FieldElement<T, S : Field<T>> : RingElement<T, S> {
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override val context: S
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operator fun div(b: S): S = context.divide(self, b)
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operator fun div(b: T): T = context.divide(self, b)
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}
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@ -1,23 +1,39 @@
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package scientifik.kmath.operations
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import kotlin.math.pow
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import kotlin.math.sqrt
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/**
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* Field for real values
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*/
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object RealField : Field<Real> {
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object RealField : Field<Real>, TrigonometricOperations<Real>, PowerOperations<Real>, ExponentialOperations<Real> {
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override val zero: Real = Real(0.0)
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override fun add(a: Real, b: Real): Real = Real(a.value + b.value)
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override val one: Real = Real(1.0)
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override fun multiply(a: Real, b: Real): Real = Real(a.value * b.value)
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override fun multiply(a: Real, k: Double): Real = Real(a.value * k)
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override fun divide(a: Real, b: Real): Real = Real(a.value / b.value)
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override fun sin(arg: Real): Real = Real(kotlin.math.sin(arg.value))
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override fun cos(arg: Real): Real = Real(kotlin.math.cos(arg.value))
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override fun power(arg: Real, pow: Double): Real = Real(arg.value.pow(pow))
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override fun exp(arg: Real): Real = Real(kotlin.math.exp(arg.value))
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override fun ln(arg: Real): Real = Real(kotlin.math.ln(arg.value))
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}
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/**
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* Real field element wrapping double
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* Real field element wrapping double.
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*
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* TODO could be replaced by inline class in kotlin 1.3 if it would allow to avoid boxing
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*/
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class Real(val value: Double) : FieldElement<Real>, Number() {
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class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
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/*
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* The class uses composition instead of inheritance since Double is final
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*/
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override fun toByte(): Byte = value.toByte()
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override fun toChar(): Char = value.toChar()
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override fun toDouble(): Double = value
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@ -29,8 +45,10 @@ class Real(val value: Double) : FieldElement<Real>, Number() {
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//values are dynamically calculated to save memory
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override val self
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get() = this
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override val context
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get() = RealField
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}
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/**
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@ -54,10 +72,9 @@ object ComplexField : Field<Complex> {
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/**
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* Complex number class
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*/
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data class Complex(val re: Double, val im: Double) : FieldElement<Complex> {
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override val self: Complex
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get() = this
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override val context: Field<Complex>
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data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
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override val self: Complex get() = this
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override val context: ComplexField
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get() = ComplexField
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/**
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@ -72,15 +89,15 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex> {
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val module: Double
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get() = sqrt(square)
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//TODO is it convenient?
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operator fun not() = conjugate
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}
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/**
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* A field for double without boxing. Does not produce appropriate field element
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*/
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object DoubleField : Field<Double> {
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override val zero: Double = 0.0
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override fun add(a: Double, b: Double): Double = a + b
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override fun multiply(a: Double, b: Double): Double = a * b
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override fun multiply(a: Double, @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE") b: Double): Double = a * b
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override val one: Double = 1.0
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override fun divide(a: Double, b: Double): Double = a / b
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}
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package scientifik.kmath.operations
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/* Trigonometric operations */
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/**
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* A container for trigonometric operations for specific type. Trigonometric operations are limited to fields.
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*
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* The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
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* It also allows to override behavior for optional operations
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*
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*/
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interface TrigonometricOperations<T>: Field<T> {
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fun sin(arg: T): T
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fun cos(arg: T): T
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fun tg(arg: T): T = sin(arg) / cos(arg)
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fun ctg(arg: T): T = cos(arg) / sin(arg)
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}
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fun <T : FieldElement<T, out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
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fun <T : FieldElement<T, out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
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fun <T : FieldElement<T, out TrigonometricOperations<T>>> tg(arg: T): T = arg.context.tg(arg)
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fun <T : FieldElement<T, out TrigonometricOperations<T>>> ctg(arg: T): T = arg.context.ctg(arg)
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/* Power and roots */
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/**
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* A context extension to include power operations like square roots, etc
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*/
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interface PowerOperations<T> {
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fun power(arg: T, pow: Double): T
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}
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infix fun <T : MathElement<T, out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
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fun <T : MathElement<T, out PowerOperations<T>>> sqrt(arg: T): T = arg pow 0.5
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fun <T : MathElement<T, out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
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/* Exponential */
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interface ExponentialOperations<T>{
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fun exp(arg: T): T
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fun ln(arg: T): T
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}
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fun <T: MathElement<T, out ExponentialOperations<T>>> exp(arg:T): T = arg.context.exp(arg)
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fun <T: MathElement<T, out ExponentialOperations<T>>> ln(arg:T): T = arg.context.ln(arg)
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package scientifik.kmath.operations
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import kotlin.test.Test
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import kotlin.test.assertEquals
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class RealFieldTest {
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@Test
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fun testSqrt() {
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val sqrt = with(RealField) {
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sqrt(25 * one)
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}
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assertEquals(5.0, sqrt.toDouble())
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}
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}
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