Dev #194
@ -2,7 +2,7 @@
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## [Unreleased]
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### Added
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- Better trigonometric and hyperbolic functions for `AutoDiffField` (https://github.com/mipt-npm/kmath/pull/140).
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### Changed
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### Deprecated
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@ -10,7 +10,7 @@
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### Removed
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### Fixed
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- `symbol` method in `MstExtendedField` (https://github.com/mipt-npm/kmath/pull/140)
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### Security
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## [0.1.4]
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@ -44,7 +44,9 @@ object MstSpace : Space<MST>, NumericAlgebra<MST> {
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* @author Alexander Nozik
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*/
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object MstRing : Ring<MST>, NumericAlgebra<MST> {
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override val zero: MST = number(0.0)
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override val zero: MST
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get() = MstSpace.zero
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override val one: MST = number(1.0)
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override fun number(value: Number): MST = MstSpace.number(value)
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@ -67,8 +69,11 @@ object MstRing : Ring<MST>, NumericAlgebra<MST> {
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* @author Alexander Nozik
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*/
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object MstField : Field<MST> {
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override val zero: MST = number(0.0)
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override val one: MST = number(1.0)
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override val zero: MST
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get() = MstRing.zero
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override val one: MST
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get() = MstRing.one
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override fun symbol(value: String): MST = MstRing.symbol(value)
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override fun number(value: Number): MST = MstRing.number(value)
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@ -89,14 +94,25 @@ object MstField : Field<MST> {
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* @author Iaroslav Postovalov
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*/
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object MstExtendedField : ExtendedField<MST> {
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override val zero: MST = number(0.0)
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override val one: MST = number(1.0)
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override val zero: MST
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get() = MstField.zero
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override val one: MST
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get() = MstField.one
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override fun symbol(value: String): MST = MstField.symbol(value)
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override fun sin(arg: MST): MST = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg)
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override fun cos(arg: MST): MST = unaryOperation(TrigonometricOperations.COS_OPERATION, arg)
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override fun tan(arg: MST): MST = unaryOperation(TrigonometricOperations.TAN_OPERATION, arg)
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override fun asin(arg: MST): MST = unaryOperation(TrigonometricOperations.ASIN_OPERATION, arg)
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override fun acos(arg: MST): MST = unaryOperation(TrigonometricOperations.ACOS_OPERATION, arg)
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override fun atan(arg: MST): MST = unaryOperation(TrigonometricOperations.ATAN_OPERATION, arg)
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override fun sinh(arg: MST): MST = unaryOperation(HyperbolicOperations.SINH_OPERATION, arg)
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override fun cosh(arg: MST): MST = unaryOperation(HyperbolicOperations.COSH_OPERATION, arg)
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override fun tanh(arg: MST): MST = unaryOperation(HyperbolicOperations.TANH_OPERATION, arg)
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override fun asinh(arg: MST): MST = unaryOperation(HyperbolicOperations.ASINH_OPERATION, arg)
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override fun acosh(arg: MST): MST = unaryOperation(HyperbolicOperations.ACOSH_OPERATION, arg)
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override fun atanh(arg: MST): MST = unaryOperation(HyperbolicOperations.ATANH_OPERATION, arg)
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override fun add(a: MST, b: MST): MST = MstField.add(a, b)
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override fun multiply(a: MST, k: Number): MST = MstField.multiply(a, k)
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override fun multiply(a: MST, b: MST): MST = MstField.multiply(a, b)
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@ -65,7 +65,6 @@ inline fun <T : Any, F : Field<T>> F.deriv(body: AutoDiffField<T, F>.() -> Varia
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}
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}
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abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> {
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abstract val context: F
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@ -152,7 +151,6 @@ internal class AutoDiffContext<T : Any, F : Field<T>>(override val context: F) :
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// Basic math (+, -, *, /)
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override fun add(a: Variable<T>, b: Variable<T>): Variable<T> = derive(variable { a.value + b.value }) { z ->
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a.d += z.d
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b.d += z.d
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@ -173,38 +171,66 @@ internal class AutoDiffContext<T : Any, F : Field<T>>(override val context: F) :
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}
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}
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// Extensions for differentiation of various basic mathematical functions
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// x ^ 2
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fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: Variable<T>): Variable<T> =
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derive(variable { x.value * x.value }) { z -> x.d += z.d * 2 * x.value }
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// x ^ 1/2
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: Variable<T>): Variable<T> =
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derive(variable { sqrt(x.value) }) { z -> x.d += z.d * 0.5 / z.value }
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// x ^ y (const)
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Double): Variable<T> =
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derive(variable { power(x.value, y) }) { z -> x.d += z.d * y * power(x.value, y - 1) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Int): Variable<T> = pow(x, y.toDouble())
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Int): Variable<T> =
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pow(x, y.toDouble())
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// exp(x)
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: Variable<T>): Variable<T> =
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derive(variable { exp(x.value) }) { z -> x.d += z.d * z.value }
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// ln(x)
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: Variable<T>): Variable<T> =
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derive(variable { ln(x.value) }) { z -> x.d += z.d / x.value }
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// x ^ y (any)
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Variable<T>): Variable<T> =
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exp(y * ln(x))
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// sin(x)
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: Variable<T>): Variable<T> =
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derive(variable { sin(x.value) }) { z -> x.d += z.d * cos(x.value) }
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// cos(x)
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: Variable<T>): Variable<T> =
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derive(variable { cos(x.value) }) { z -> x.d -= z.d * sin(x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tan(x: Variable<T>): Variable<T> =
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derive(variable { tan(x.value) }) { z ->
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val c = cos(x.value)
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x.d += z.d / (c * c)
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}
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asin(x: Variable<T>): Variable<T> =
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derive(variable { asin(x.value) }) { z -> x.d += z.d / sqrt(one - x.value * x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acos(x: Variable<T>): Variable<T> =
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derive(variable { acos(x.value) }) { z -> x.d -= z.d / sqrt(one - x.value * x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atan(x: Variable<T>): Variable<T> =
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derive(variable { atan(x.value) }) { z -> x.d += z.d / (one + x.value * x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sinh(x: Variable<T>): Variable<T> =
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derive(variable { sin(x.value) }) { z -> x.d += z.d * cosh(x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cosh(x: Variable<T>): Variable<T> =
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derive(variable { cos(x.value) }) { z -> x.d += z.d * sinh(x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tanh(x: Variable<T>): Variable<T> =
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derive(variable { tan(x.value) }) { z ->
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val c = cosh(x.value)
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x.d += z.d / (c * c)
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}
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asinh(x: Variable<T>): Variable<T> =
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derive(variable { asinh(x.value) }) { z -> x.d += z.d / sqrt(one + x.value * x.value) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acosh(x: Variable<T>): Variable<T> =
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derive(variable { acosh(x.value) }) { z -> x.d += z.d / (sqrt((x.value - one) * (x.value + one))) }
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fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atanh(x: Variable<T>): Variable<T> =
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derive(variable { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) }
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@ -3,19 +3,19 @@ package scientifik.kmath.misc
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import scientifik.kmath.operations.RealField
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import scientifik.kmath.structures.asBuffer
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import kotlin.math.PI
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import kotlin.math.pow
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import kotlin.math.sqrt
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertTrue
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class AutoDiffTest {
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fun Variable(int: Int): Variable<Double> = Variable(int.toDouble())
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fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>): DerivationResult<Double> =
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inline fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>): DerivationResult<Double> =
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RealField.deriv(body)
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@Test
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fun testPlusX2() {
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val x = Variable(3) // diff w.r.t this x at 3
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val x = Variable(3.0) // diff w.r.t this x at 3
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val y = deriv { x + x }
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assertEquals(6.0, y.value) // y = x + x = 6
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assertEquals(2.0, y.deriv(x)) // dy/dx = 2
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@ -24,8 +24,8 @@ class AutoDiffTest {
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@Test
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fun testPlus() {
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// two variables
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val x = Variable(2)
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val y = Variable(3)
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val x = Variable(2.0)
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val y = Variable(3.0)
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val z = deriv { x + y }
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assertEquals(5.0, z.value) // z = x + y = 5
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assertEquals(1.0, z.deriv(x)) // dz/dx = 1
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@ -35,8 +35,8 @@ class AutoDiffTest {
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@Test
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fun testMinus() {
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// two variables
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val x = Variable(7)
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val y = Variable(3)
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val x = Variable(7.0)
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val y = Variable(3.0)
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val z = deriv { x - y }
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assertEquals(4.0, z.value) // z = x - y = 4
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assertEquals(1.0, z.deriv(x)) // dz/dx = 1
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@ -45,7 +45,7 @@ class AutoDiffTest {
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@Test
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fun testMulX2() {
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val x = Variable(3) // diff w.r.t this x at 3
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val x = Variable(3.0) // diff w.r.t this x at 3
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val y = deriv { x * x }
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assertEquals(9.0, y.value) // y = x * x = 9
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assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
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@ -53,7 +53,7 @@ class AutoDiffTest {
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@Test
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fun testSqr() {
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val x = Variable(3)
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val x = Variable(3.0)
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val y = deriv { sqr(x) }
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assertEquals(9.0, y.value) // y = x ^ 2 = 9
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assertEquals(6.0, y.deriv(x)) // dy/dx = 2 * x = 7
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@ -61,7 +61,7 @@ class AutoDiffTest {
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@Test
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fun testSqrSqr() {
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val x = Variable(2)
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val x = Variable(2.0)
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val y = deriv { sqr(sqr(x)) }
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assertEquals(16.0, y.value) // y = x ^ 4 = 16
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assertEquals(32.0, y.deriv(x)) // dy/dx = 4 * x^3 = 32
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@ -69,7 +69,7 @@ class AutoDiffTest {
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@Test
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fun testX3() {
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val x = Variable(2) // diff w.r.t this x at 2
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val x = Variable(2.0) // diff w.r.t this x at 2
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val y = deriv { x * x * x }
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assertEquals(8.0, y.value) // y = x * x * x = 8
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assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x * x = 12
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@ -77,8 +77,8 @@ class AutoDiffTest {
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@Test
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fun testDiv() {
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val x = Variable(5)
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val y = Variable(2)
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val x = Variable(5.0)
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val y = Variable(2.0)
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val z = deriv { x / y }
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assertEquals(2.5, z.value) // z = x / y = 2.5
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assertEquals(0.5, z.deriv(x)) // dz/dx = 1 / y = 0.5
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@ -87,7 +87,7 @@ class AutoDiffTest {
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@Test
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fun testPow3() {
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val x = Variable(2) // diff w.r.t this x at 2
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val x = Variable(2.0) // diff w.r.t this x at 2
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val y = deriv { pow(x, 3) }
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assertEquals(8.0, y.value) // y = x ^ 3 = 8
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assertEquals(12.0, y.deriv(x)) // dy/dx = 3 * x ^ 2 = 12
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@ -95,8 +95,8 @@ class AutoDiffTest {
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@Test
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fun testPowFull() {
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val x = Variable(2)
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val y = Variable(3)
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val x = Variable(2.0)
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val y = Variable(3.0)
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val z = deriv { pow(x, y) }
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assertApprox(8.0, z.value) // z = x ^ y = 8
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assertApprox(12.0, z.deriv(x)) // dz/dx = y * x ^ (y - 1) = 12
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@ -105,7 +105,7 @@ class AutoDiffTest {
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@Test
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fun testFromPaper() {
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val x = Variable(3)
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val x = Variable(3.0)
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val y = deriv { 2 * x + x * x * x }
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assertEquals(33.0, y.value) // y = 2 * x + x * x * x = 33
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assertEquals(29.0, y.deriv(x)) // dy/dx = 2 + 3 * x * x = 29
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@ -113,9 +113,9 @@ class AutoDiffTest {
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@Test
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fun testInnerVariable() {
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val x = Variable(1)
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val x = Variable(1.0)
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val y = deriv {
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Variable(1) * x
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Variable(1.0) * x
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}
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assertEquals(1.0, y.value) // y = x ^ n = 1
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assertEquals(1.0, y.deriv(x)) // dy/dx = n * x ^ (n - 1) = n - 1
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@ -124,9 +124,9 @@ class AutoDiffTest {
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@Test
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fun testLongChain() {
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val n = 10_000
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val x = Variable(1)
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val x = Variable(1.0)
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val y = deriv {
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var res = Variable(1)
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var res = Variable(1.0)
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for (i in 1..n) res *= x
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res
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}
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@ -136,7 +136,7 @@ class AutoDiffTest {
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@Test
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fun testExample() {
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val x = Variable(2)
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val x = Variable(2.0)
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val y = deriv { sqr(x) + 5 * x + 3 }
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assertEquals(17.0, y.value) // the value of result (y)
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assertEquals(9.0, y.deriv(x)) // dy/dx
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@ -144,7 +144,7 @@ class AutoDiffTest {
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@Test
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fun testSqrt() {
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val x = Variable(16)
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val x = Variable(16.0)
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val y = deriv { sqrt(x) }
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assertEquals(4.0, y.value) // y = x ^ 1/2 = 4
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assertEquals(1.0 / 8, y.deriv(x)) // dy/dx = 1/2 / x ^ 1/4 = 1/8
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@ -152,18 +152,98 @@ class AutoDiffTest {
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@Test
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fun testSin() {
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val x = Variable(PI / 6)
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val x = Variable(PI / 6.0)
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val y = deriv { sin(x) }
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assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5
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assertApprox(kotlin.math.sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(PI/6) = sqrt(3)/2
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assertApprox(0.5, y.value) // y = sin(PI/6) = 0.5
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assertApprox(sqrt(3.0) / 2, y.deriv(x)) // dy/dx = cos(pi/6) = sqrt(3)/2
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}
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@Test
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fun testCos() {
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val x = Variable(PI / 6)
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val y = deriv { cos(x) }
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assertApprox(kotlin.math.sqrt(3.0) / 2, y.value) // y = cos(PI/6) = sqrt(3)/2
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assertApprox(-0.5, y.deriv(x)) // dy/dx = -sin(PI/6) = -0.5
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assertApprox(sqrt(3.0) / 2, y.value) //y = cos(pi/6) = sqrt(3)/2
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assertApprox(-0.5, y.deriv(x)) // dy/dx = -sin(pi/6) = -0.5
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}
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@Test
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fun testTan() {
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val x = Variable(PI / 6)
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val y = deriv { tan(x) }
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assertApprox(1.0 / sqrt(3.0), y.value) // y = tan(pi/6) = 1/sqrt(3)
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assertApprox(4.0 / 3.0, y.deriv(x)) // dy/dx = sec(pi/6)^2 = 4/3
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}
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@Test
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fun testAsin() {
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val x = Variable(PI / 6)
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val y = deriv { asin(x) }
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assertApprox(kotlin.math.asin(PI / 6.0), y.value) // y = asin(pi/6)
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assertApprox(6.0 / sqrt(36 - PI * PI), y.deriv(x)) // dy/dx = 6/sqrt(36-pi^2)
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}
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@Test
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fun testAcos() {
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val x = Variable(PI / 6)
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val y = deriv { acos(x) }
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assertApprox(kotlin.math.acos(PI / 6.0), y.value) // y = acos(pi/6)
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assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.deriv(x)) // dy/dx = -6/sqrt(36-pi^2)
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}
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@Test
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fun testAtan() {
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val x = Variable(PI / 6)
|
||||
val y = deriv { atan(x) }
|
||||
assertApprox(kotlin.math.atan(PI / 6.0), y.value) // y = atan(pi/6)
|
||||
assertApprox(36.0 / (36.0 + PI * PI), y.deriv(x)) // dy/dx = 36/(36+pi^2)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testSinh() {
|
||||
val x = Variable(0.0)
|
||||
val y = deriv { sinh(x) }
|
||||
assertApprox(kotlin.math.sinh(0.0), y.value) // y = sinh(0)
|
||||
assertApprox(kotlin.math.cosh(0.0), y.deriv(x)) // dy/dx = cosh(0)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCosh() {
|
||||
val x = Variable(0.0)
|
||||
val y = deriv { cosh(x) }
|
||||
assertApprox(1.0, y.value) //y = cosh(0)
|
||||
assertApprox(0.0, y.deriv(x)) // dy/dx = sinh(0)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testTanh() {
|
||||
val x = Variable(PI / 6)
|
||||
val y = deriv { tanh(x) }
|
||||
assertApprox(1.0 / sqrt(3.0), y.value) // y = tanh(pi/6)
|
||||
assertApprox(1.0 / kotlin.math.cosh(PI / 6.0).pow(2), y.deriv(x)) // dy/dx = sech(pi/6)^2
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testAsinh() {
|
||||
val x = Variable(PI / 6)
|
||||
val y = deriv { asinh(x) }
|
||||
assertApprox(kotlin.math.asinh(PI / 6.0), y.value) // y = asinh(pi/6)
|
||||
assertApprox(6.0 / sqrt(36 + PI * PI), y.deriv(x)) // dy/dx = 6/sqrt(pi^2+36)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testAcosh() {
|
||||
val x = Variable(PI / 6)
|
||||
val y = deriv { acosh(x) }
|
||||
assertApprox(kotlin.math.acosh(PI / 6.0), y.value) // y = acosh(pi/6)
|
||||
assertApprox(-6.0 / sqrt(36.0 - PI * PI), y.deriv(x)) // dy/dx = -6/sqrt(36-pi^2)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testAtanh() {
|
||||
val x = Variable(PI / 6.0)
|
||||
val y = deriv { atanh(x) }
|
||||
assertApprox(kotlin.math.atanh(PI / 6.0), y.value) // y = atanh(pi/6)
|
||||
assertApprox(-36.0 / (PI * PI - 36.0), y.deriv(x)) // dy/dx = -36/(pi^2-36)
|
||||
}
|
||||
|
||||
@Test
|
||||
|
||||
Loading…
Reference in New Issue
Block a user