Merge to update docs and contributions #504
@ -5,8 +5,10 @@
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package space.kscience.kmath.functions
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.*
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import kotlin.contracts.*
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import kotlin.math.max
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// TODO: Docs
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@ -321,6 +323,251 @@ public inline fun <C, A : Ring<C>, R> A.labeledPolynomial(block: LabeledPolynomi
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//
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//// endregion
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//// region Algebraic derivative and antiderivative
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//// TODO
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//// endregion
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// region Algebraic derivative and antiderivative
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/**
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* Returns algebraic derivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
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algebra: A,
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variable: Variable,
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): LabeledPolynomial<C> = algebra {
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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if (variable !in degs) return@forEach
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put(
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buildMap {
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degs.forEach { (vari, deg) ->
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when {
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vari != variable -> put(vari, deg)
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deg > 1u -> put(vari, deg - 1u)
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}
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}
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},
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optimizedMultiply(c, degs[variable]!!)
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)
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}
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}
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)
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}
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/**
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* Returns algebraic derivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
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algebra: A,
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variables: Collection<Variable>,
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): LabeledPolynomial<C> = algebra {
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val cleanedVariables = variables.toSet()
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if (cleanedVariables.isEmpty()) return this@derivativeWithRespectTo
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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if (!degs.keys.containsAll(cleanedVariables)) return@forEach
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put(
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buildMap {
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degs.forEach { (vari, deg) ->
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when {
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vari !in cleanedVariables -> put(vari, deg)
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deg > 1u -> put(vari, deg - 1u)
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}
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}
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},
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cleanedVariables.fold(c) { acc, variable -> optimizedMultiply(acc, degs[variable]!!) }
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)
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}
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}
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)
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}
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/**
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* Returns algebraic derivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
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algebra: A,
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variable: Variable,
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order: UInt
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): LabeledPolynomial<C> = algebra {
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if (order == 0u) return this@nthDerivativeWithRespectTo
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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if (degs.getOrElse(variable) { 0u } < order) return@forEach
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put(
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buildMap {
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degs.forEach { (vari, deg) ->
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when {
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vari != variable -> put(vari, deg)
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deg > order -> put(vari, deg - order)
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}
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}
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},
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degs[variable]!!.let { deg ->
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(deg downTo deg - order + 1u)
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.fold(c) { acc, ord -> optimizedMultiply(acc, ord) }
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}
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)
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}
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}
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)
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}
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/**
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* Returns algebraic derivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
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algebra: A,
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variablesAndOrders: Map<Variable, UInt>,
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): LabeledPolynomial<C> = algebra {
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val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
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if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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if (filteredVariablesAndOrders.any { (variable, order) -> degs.getOrElse(variable) { 0u } < order }) return@forEach
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put(
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buildMap {
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degs.forEach { (vari, deg) ->
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if (vari !in filteredVariablesAndOrders) put(vari, deg)
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else {
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val order = filteredVariablesAndOrders[vari]!!
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if (deg > order) put(vari, deg - order)
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}
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}
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},
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filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
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degs[index]!!.let { deg ->
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(deg downTo deg - order + 1u)
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.fold(acc1) { acc2, ord -> optimizedMultiply(acc2, ord) }
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}
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}
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)
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}
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}
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)
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}
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/**
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* Returns algebraic antiderivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
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algebra: A,
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variable: Variable,
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): LabeledPolynomial<C> = algebra {
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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val newDegs = buildMap<Variable, UInt>(degs.size + 1) {
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put(variable, 1u)
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for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
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}
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put(
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newDegs,
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c / optimizedMultiply(one, newDegs[variable]!!)
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)
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}
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}
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)
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}
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/**
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* Returns algebraic antiderivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
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algebra: A,
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variables: Collection<Variable>,
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): LabeledPolynomial<C> = algebra {
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val cleanedVariables = variables.toSet()
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if (cleanedVariables.isEmpty()) return this@antiderivativeWithRespectTo
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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val newDegs = buildMap<Variable, UInt>(degs.size + 1) {
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for (variable in cleanedVariables) put(variable, 1u)
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for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
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}
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put(
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newDegs,
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cleanedVariables.fold(c) { acc, variable -> acc / optimizedMultiply(one, newDegs[variable]!!) }
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)
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}
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}
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)
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}
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/**
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* Returns algebraic derivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
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algebra: A,
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variable: Variable,
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order: UInt
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): LabeledPolynomial<C> = algebra {
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if (order == 0u) return this@nthAntiderivativeWithRespectTo
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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val newDegs = buildMap<Variable, UInt>(degs.size + 1) {
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put(variable, order)
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for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
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}
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put(
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newDegs,
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newDegs[variable]!!.let { deg ->
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(deg downTo deg - order + 1u)
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.fold(c) { acc, ord -> acc / optimizedMultiply(one, ord) }
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}
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)
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}
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}
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)
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}
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/**
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* Returns algebraic derivative of received polynomial.
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*/
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@UnstableKMathAPI
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public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo(
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algebra: A,
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variablesAndOrders: Map<Variable, UInt>,
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): LabeledPolynomial<C> = algebra {
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val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
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if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
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LabeledPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients
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.forEach { (degs, c) ->
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val newDegs = buildMap<Variable, UInt>(degs.size + 1) {
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for ((variable, order) in filteredVariablesAndOrders) put(variable, order)
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for ((vari, deg) in degs) put(vari, deg + getOrElse(vari) { 0u })
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}
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put(
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newDegs,
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filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
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newDegs[index]!!.let { deg ->
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(deg downTo deg - order + 1u)
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.fold(acc1) { acc2, ord -> acc2 / optimizedMultiply(one, ord) }
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}
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}
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)
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}
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}
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)
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}
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// endregion
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@ -4,7 +4,7 @@ import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.operations.*
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import kotlin.contracts.*
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import kotlin.jvm.JvmName
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import kotlin.math.max
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// TODO: Docs
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@ -382,70 +382,51 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
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): NumberedPolynomial<C> = algebra {
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NumberedPolynomial<C>(
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buildMap(coefficients.size) {
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coefficients.forEach { (degs, c) ->
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put(
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degs.mapIndexed { index, deg ->
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when {
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index != variable -> deg
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deg > 0u -> deg - 1u
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else -> return@forEach
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}
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},
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optimizedMultiply(c, degs.getOrElse(variable) { 1u }.toInt())
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)
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}
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coefficients
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.forEach { (degs, c) ->
|
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if (degs.size > variable) return@forEach
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put(
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degs.mapIndexed { index, deg ->
|
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when {
|
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index != variable -> deg
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deg > 0u -> deg - 1u
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else -> return@forEach
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}
|
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}.cleanUp(),
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optimizedMultiply(c, degs[variable])
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)
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||||
}
|
||||
}
|
||||
)
|
||||
}
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|
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/**
|
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* Returns algebraic derivative of received polynomial.
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*/ // TODO: This one does not work!!!
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
|
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algebra: A,
|
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variables: IntArray,
|
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): NumberedPolynomial<C> = algebra {
|
||||
NumberedPolynomial<C>(
|
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buildMap(coefficients.size) {
|
||||
coefficients.forEach { (degs, c) ->
|
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put(
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degs.mapIndexed { index, deg ->
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when {
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index !in variables -> deg
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deg > 0u -> deg - 1u
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else -> return@forEach
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||||
}
|
||||
},
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optimizedMultiply(c, variables.fold(1u) { acc, variable -> acc * degs.getOrElse(variable) { 1u } }.toInt())
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns algebraic derivative of received polynomial.
|
||||
*/ // TODO: This one does not work!!!
|
||||
*/
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
|
||||
algebra: A,
|
||||
variables: Collection<Int>,
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
val cleanedVariables = variables.toSet()
|
||||
if (cleanedVariables.isEmpty()) return this@derivativeWithRespectTo
|
||||
val maxRespectedVariable = cleanedVariables.maxOrNull()!!
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients.forEach { (degs, c) ->
|
||||
put(
|
||||
degs.mapIndexed { index, deg ->
|
||||
when {
|
||||
index !in variables -> deg
|
||||
deg > 0u -> deg - 1u
|
||||
else -> return@forEach
|
||||
}
|
||||
},
|
||||
optimizedMultiply(c, variables.fold(1u) { acc, variable -> acc * degs.getOrElse(variable) { 1u } }.toInt())
|
||||
)
|
||||
}
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
if (degs.size > maxRespectedVariable) return@forEach
|
||||
put(
|
||||
degs.mapIndexed { index, deg ->
|
||||
when {
|
||||
index !in cleanedVariables -> deg
|
||||
deg > 0u -> deg - 1u
|
||||
else -> return@forEach
|
||||
}
|
||||
}.cleanUp(),
|
||||
cleanedVariables.fold(c) { acc, variable -> optimizedMultiply(acc, degs[variable]) }
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
@ -459,24 +440,60 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
|
||||
variable: Int,
|
||||
order: UInt
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
if (order == 0u) return this@nthDerivativeWithRespectTo
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients.forEach { (degs, c) ->
|
||||
put(
|
||||
degs.mapIndexed { index, deg ->
|
||||
when {
|
||||
index != variable -> deg
|
||||
deg >= order -> deg - order
|
||||
else -> return@forEach
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
if (degs.size > variable) return@forEach
|
||||
put(
|
||||
degs.mapIndexed { index, deg ->
|
||||
when {
|
||||
index != variable -> deg
|
||||
deg >= order -> deg - order
|
||||
else -> return@forEach
|
||||
}
|
||||
}.cleanUp(),
|
||||
degs[variable].let { deg ->
|
||||
(deg downTo deg - order + 1u)
|
||||
.fold(c) { acc, ord -> optimizedMultiply(acc, ord) }
|
||||
}
|
||||
},
|
||||
degs.getOrElse(variable) { 1u }.toInt().let {
|
||||
(0u until order).fold(c) { acc, ord ->
|
||||
optimizedMultiply(acc, ord.toInt())
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns algebraic derivative of received polynomial.
|
||||
*/
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
|
||||
algebra: A,
|
||||
variablesAndOrders: Map<Int, UInt>,
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
|
||||
if (filteredVariablesAndOrders.isEmpty()) return this@nthDerivativeWithRespectTo
|
||||
val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
if (degs.size > maxRespectedVariable) return@forEach
|
||||
put(
|
||||
degs.mapIndexed { index, deg ->
|
||||
if (index !in filteredVariablesAndOrders) return@mapIndexed deg
|
||||
val order = filteredVariablesAndOrders[index]!!
|
||||
if (deg >= order) deg - order else return@forEach
|
||||
}.cleanUp(),
|
||||
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
|
||||
degs[index].let { deg ->
|
||||
(deg downTo deg - order + 1u)
|
||||
.fold(acc1) { acc2, ord -> optimizedMultiply(acc2, ord) }
|
||||
}
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
@ -491,52 +508,92 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients.forEach { (degs, c) ->
|
||||
put(
|
||||
degs.mapIndexed { index, deg -> if(index != variable) deg else deg + 1u },
|
||||
c / optimizedMultiply(one, degs.getOrElse(variable) { 1u }.toInt())
|
||||
)
|
||||
}
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
put(
|
||||
List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u },
|
||||
c / optimizedMultiply(one, degs[variable])
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns algebraic antiderivative of received polynomial.
|
||||
*/ // TODO: This one does not work!!!
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
|
||||
algebra: A,
|
||||
variables: IntArray,
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients.forEach { (degs, c) ->
|
||||
put(
|
||||
degs.mapIndexed { index, deg -> if(index !in variables) deg else deg + 1u },
|
||||
c / optimizedMultiply(one, variables.fold(1u) { acc, variable -> acc * degs.getOrElse(variable) { 1u } }.toInt())
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns algebraic antiderivative of received polynomial.
|
||||
*/ // TODO: This one does not work!!!
|
||||
*/
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
|
||||
algebra: A,
|
||||
variables: Collection<Int>,
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
val cleanedVariables = variables.toSet()
|
||||
if (cleanedVariables.isEmpty()) return this@antiderivativeWithRespectTo
|
||||
val maxRespectedVariable = cleanedVariables.maxOrNull()!!
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients.forEach { (degs, c) ->
|
||||
put(
|
||||
degs.mapIndexed { index, deg -> if(index !in variables) deg else deg + 1u },
|
||||
c / optimizedMultiply(one, variables.fold(1u) { acc, variable -> acc * degs.getOrElse(variable) { 1u } }.toInt())
|
||||
)
|
||||
}
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
put(
|
||||
List(max(maxRespectedVariable + 1, degs.size)) { if (it !in variables) degs[it] else degs[it] + 1u },
|
||||
cleanedVariables.fold(c) { acc, variable -> acc / optimizedMultiply(one, degs[variable]) }
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns algebraic derivative of received polynomial.
|
||||
*/
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
|
||||
algebra: A,
|
||||
variable: Int,
|
||||
order: UInt
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
if (order == 0u) return this@nthAntiderivativeWithRespectTo
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
put(
|
||||
List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order },
|
||||
degs[variable].let { deg ->
|
||||
(deg downTo deg - order + 1u)
|
||||
.fold(c) { acc, ord -> acc / optimizedMultiply(one, ord) }
|
||||
}
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns algebraic derivative of received polynomial.
|
||||
*/
|
||||
@UnstableKMathAPI
|
||||
public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectTo(
|
||||
algebra: A,
|
||||
variablesAndOrders: Map<Int, UInt>,
|
||||
): NumberedPolynomial<C> = algebra {
|
||||
val filteredVariablesAndOrders = variablesAndOrders.filterValues { it != 0u }
|
||||
if (filteredVariablesAndOrders.isEmpty()) return this@nthAntiderivativeWithRespectTo
|
||||
val maxRespectedVariable = filteredVariablesAndOrders.keys.maxOrNull()!!
|
||||
NumberedPolynomial<C>(
|
||||
buildMap(coefficients.size) {
|
||||
coefficients
|
||||
.forEach { (degs, c) ->
|
||||
put(
|
||||
List(max(maxRespectedVariable + 1, degs.size)) { degs[it] + filteredVariablesAndOrders.getOrElse(it) { 0u } },
|
||||
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
|
||||
degs[index].let { deg ->
|
||||
(deg downTo deg - order + 1u)
|
||||
.fold(acc1) { acc2, ord -> acc2 / optimizedMultiply(one, ord) }
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
}
|
||||
)
|
||||
}
|
||||
|
||||
@ -138,7 +138,7 @@ public fun <C, A> Polynomial<C>.nthDerivative(
|
||||
algebra: A,
|
||||
order: UInt,
|
||||
): Polynomial<C> where A : Ring<C>, A : NumericAlgebra<C> = algebra {
|
||||
Polynomial(coefficients.drop(order.toInt()).mapIndexed { index, c -> (1..order.toInt()).fold(c) { acc, i -> acc * number(index + i) } })
|
||||
Polynomial(coefficients.drop(order.toInt()).mapIndexed { index, c -> (index + 1..index + order.toInt()).fold(c) { acc, i -> acc * number(i) } })
|
||||
}
|
||||
|
||||
/**
|
||||
|
||||
Loading…
Reference in New Issue
Block a user