/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
@file:Suppress("FunctionName", "NOTHING_TO_INLINE", "KotlinRedundantDiagnosticSuppress")
package space.kscience.kmath.functions
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.Ring
/**
* Returns the same degrees' description of the monomial, but without extra zero degrees on the end.
*/
internal fun List<UInt>.cleanUp() = subList(0, indexOfLast { it != 0U } + 1)
/**
* Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is.
*/
@PublishedApi
internal inline fun <C> NumberedPolynomialAsIs(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(coefs)
/**
* Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient".
* The collections will be transformed to map with [toMap] and then will be used as is.
*/
@PublishedApi
internal inline fun <C> NumberedPolynomialAsIs(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
/**
* Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature — term's coefficient".
* The array will be transformed to map with [toMap] and then will be used as is.
*/
@PublishedApi
internal inline fun <C> NumberedPolynomialAsIs(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
/**
* Constructs [NumberedPolynomial] with provided coefficients map [coefs]. The map is used as is.
*
* **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
* cause wrong computation result or even runtime error.**
*/
@DelicatePolynomialAPI
public inline fun <C> NumberedPolynomialWithoutCheck(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(coefs)
/**
* Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient".
* The collections will be transformed to map with [toMap] and then will be used as is.
*
* **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
* cause wrong computation result or even runtime error.**
*/
@DelicatePolynomialAPI
public inline fun <C> NumberedPolynomialWithoutCheck(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
/**
* Constructs [NumberedPolynomial] with provided array of [pairs] of pairs "term's signature — term's coefficient".
* The array will be transformed to map with [toMap] and then will be used as is.
*
* **Be sure you read description of [NumberedPolynomial.coefficients]. Otherwise, you may make a mistake that will
* cause wrong computation result or even runtime error.**
*/
@DelicatePolynomialAPI
public inline fun <C> NumberedPolynomialWithoutCheck(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial<C>(pairs.toMap())
/**
* Constructs [NumberedPolynomial] with provided coefficients map [coefs].
*
* [coefs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public fun <C> NumberedPolynomial(coefs: Map<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> =
NumberedPolynomialAsIs(
coefs.mapKeys({ key, _ -> key.cleanUp() }, add)
)
/**
* Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public fun <C> NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>, add: (C, C) -> C) : NumberedPolynomial<C> =
NumberedPolynomialAsIs(
pairs.associateBy({ it.first.cleanUp() }, { it.second }, add)
)
/**
* Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public fun <C> NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>, add: (C, C) -> C) : NumberedPolynomial<C> =
NumberedPolynomialAsIs(
pairs.asIterable().associateBy({ it.first.cleanUp() }, { it.second }, add)
)
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
/**
* Constructs [NumberedPolynomial] with provided coefficients map [coefs].
*
* [coefs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> A.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs, ::add)
/**
* Constructs [NumberedPolynomial] with provided coefficients map [coefs].
*
* [coefs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs) { left: C, right: C -> left + right }
/**
* Constructs [NumberedPolynomial] with provided coefficients map [coefs].
*
* [coefs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [coefs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(coefs: Map<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(coefs) { left: C, right: C -> left + right }
/**
* Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> A.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs, ::add)
/**
* Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs) { left: C, right: C -> left + right }
/**
* Constructs [NumberedPolynomial] with provided collection of [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*/
public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(pairs: Collection<Pair<List<UInt>, C>>) : NumberedPolynomial<C> = NumberedPolynomial(pairs) { left: C, right: C -> left + right }
/**
* Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> A.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs) { left: C, right: C -> left + right }
/**
* Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs) { left: C, right: C -> left + right }
/**
* Constructs [NumberedPolynomial] with provided array [pairs] of pairs "term's signature — term's coefficient".
*
* [pairs] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [pairs] keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*
* @see NumberedPolynomialWithoutCheck
*/
public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomial(vararg pairs: Pair<List<UInt>, C>) : NumberedPolynomial<C> = NumberedPolynomial(*pairs) { left: C, right: C -> left + right }
/**
* Converts [this] constant to [NumberedPolynomial].
*/
public inline fun <C> C.asNumberedPolynomial() : NumberedPolynomial<C> = NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this))
/**
* Marks DSL that allows to more simply create [NumberedPolynomial]s with good performance.
*
* For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as
* ```
* Int.algebra {
* val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
* 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 +
* (-6) { 1 inPowerOf 1u } // (-6) x_1^1
* }
* }
* ```
* @usesMathJax
*/
@DslMarker
@UnstableKMathAPI
internal annotation class NumberedPolynomialConstructorDSL1
/**
* Builder of [NumberedPolynomial] signature. It should be used as an implicit context for lambdas that describe term signature.
*/
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL1
public class DSL1NumberedPolynomialTermSignatureBuilder {
/**
* Signature storage. Any declaration of any variable's power updates the storage by increasing corresponding value.
* Afterward the storage will be used as a resulting signature.
*/
private val signature: MutableList<UInt> = ArrayList()
/**
* Builds the resulting signature.
*
* In fact, it just returns [signature] as regular signature of type `List<UInt>`.
*/
@PublishedApi
internal fun build(): List<UInt> = signature
/**
* Declares power of variable #[this] of degree [deg].
*
* Declaring another power of the same variable will increase its degree by received degree.
*/
public infix fun Int.inPowerOf(deg: UInt) {
if (deg == 0u) return
val index = this
if (index > signature.lastIndex) {
signature.addAll(List(index - signature.lastIndex - 1) { 0u })
signature.add(deg)
} else {
signature[index] += deg
}
}
/**
* Declares power of variable #[this] of degree [deg].
*
* Declaring another power of the same variable will increase its degree by received degree.
*/
public inline infix fun Int.pow(deg: UInt): Unit = this inPowerOf deg
/**
* Declares power of variable #[this] of degree [deg].
*
* Declaring another power of the same variable will increase its degree by received degree.
*/
public inline infix fun Int.`in`(deg: UInt): Unit = this inPowerOf deg
/**
* Declares power of variable #[this] of degree [deg].
*
* Declaring another power of the same variable will increase its degree by received degree.
*/
public inline infix fun Int.of(deg: UInt): Unit = this inPowerOf deg
}
/**
* Builder of [NumberedPolynomial]. It should be used as an implicit context for lambdas that describe [NumberedPolynomial].
*/
@UnstableKMathAPI
@NumberedPolynomialConstructorDSL1
public class DSL1NumberedPolynomialBuilder<C>(
/**
* Summation operation that will be used to sum coefficients of monomials of same signatures.
*/
private val add: (C, C) -> C,
/**
* Initial capacity of coefficients map.
*/
initialCapacity: Int? = null
) {
/**
* Coefficients storage. Any declaration of any monomial updates the storage.
* Afterward the storage will be used as a resulting coefficients map.
*/
private val coefficients: MutableMap<List<UInt>, C> = if (initialCapacity != null) LinkedHashMap(initialCapacity) else LinkedHashMap()
/**
* Builds the resulting coefficients map.
*
* In fact, it just returns [coefficients] as regular coefficients map of type `Map<List<UInt>, C>`.
*/
@PublishedApi
internal fun build(): NumberedPolynomial<C> = NumberedPolynomial<C>(coefficients)
/**
* Declares monomial with [this] coefficient and provided [signature].
*
* Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
* coefficients is zero at any moment the monomial won't be removed but will be left as it is.
*/
public infix fun C.with(signature: List<UInt>) {
coefficients.putOrChange(signature, this@with, add)
}
/**
* Declares monomial with [this] coefficient and signature constructed by [block].
*
* Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
* coefficients is zero at any moment the monomial won't be removed but will be left as it is.
*/
public inline infix fun C.with(noinline block: DSL1NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit = this.invoke(block)
/**
* Declares monomial with [this] coefficient and signature constructed by [block].
*
* Declaring another monomial with the same signature will add [this] coefficient to existing one. If the sum of such
* coefficients is zero at any moment the monomial won't be removed but will be left as it is.
*/
public inline operator fun C.invoke(block: DSL1NumberedPolynomialTermSignatureBuilder.() -> Unit): Unit =
this with DSL1NumberedPolynomialTermSignatureBuilder().apply(block).build()
}
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
///**
// * Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of constants.
// *
// * For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as
// * ```
// * Int.algebra {
// * val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
// * 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 +
// * (-6) { 1 inPowerOf 1u } // (-6) x_1^1
// * }
// * }
// * ```
// * @usesMathJax
// */
// FIXME: For now this fabric does not let next two fabrics work. (See KT-52803.) Possible feature solutions:
// 1. `LowPriorityInOverloadResolution` becomes public. Then it should be applied to this function.
// 2. Union types are implemented. Then all three functions should be rewritten
// as one with single union type as a (context) receiver.
//@UnstableKMathAPI
//public inline fun <C, A: Ring<C>> A.NumberedPolynomialDSL1(initialCapacity: Int? = null, block: NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = NumberedPolynomialBuilder(::add, initialCapacity).apply(block).build()
/**
* Creates [NumberedPolynomial] with lambda [block] in context of [this] ring of [NumberedPolynomial]s.
*
* For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as
* ```
* Int.algebra {
* val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
* 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 +
* (-6) { 1 inPowerOf 1u } // (-6) x_1^1
* }
* }
* ```
* @usesMathJax
*/
@UnstableKMathAPI
public inline fun <C, A: Ring<C>> NumberedPolynomialSpace<C, A>.NumberedPolynomialDSL1(initialCapacity: Int? = null, block: DSL1NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = DSL1NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
/**
* Creates [NumberedPolynomial] with lambda [block] in context of [this] field of [NumberedRationalFunction]s.
*
* For example, polynomial \(5 x_0^2 x_2^3 - 6 x_1\) can be described as
* ```
* Int.algebra {
* val numberedPolynomial : NumberedPolynomial<Int> = NumberedPolynomial {
* 5 { 0 inPowerOf 2u; 2 inPowerOf 3u } // 5 x_0^2 x_2^3 +
* (-6) { 1 inPowerOf 1u } // (-6) x_1^1
* }
* }
* ```
* @usesMathJax
*/
@UnstableKMathAPI
public inline fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedPolynomialDSL1(initialCapacity: Int? = null, block: DSL1NumberedPolynomialBuilder<C>.() -> Unit) : NumberedPolynomial<C> = DSL1NumberedPolynomialBuilder({ left: C, right: C -> left + right }, initialCapacity).apply(block).build()
// Waiting for context receivers :( FIXME: Replace with context receivers when they will be available
/**
* Constructs [NumberedRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients].
*
* The maps will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*/
public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients),
NumberedPolynomial(denominatorCoefficients)
)
/**
* Constructs [NumberedRationalFunction] with provided coefficients maps [numeratorCoefficients] and [denominatorCoefficients].
*
* The maps will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. the maps' keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*/
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>, denominatorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients),
NumberedPolynomial(denominatorCoefficients)
)
/**
* Constructs [NumberedRationalFunction] with provided [numerator] and unit denominator.
*/
public fun <C, A: Ring<C>> A.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(numerator, NumberedPolynomial(mapOf(emptyList<UInt>() to one)))
/**
* Constructs [NumberedRationalFunction] with provided [numerator] and unit denominator.
*/
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numerator: NumberedPolynomial<C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(numerator, polynomialOne)
/**
* Constructs [NumberedRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit
* denominator.
*
* [numeratorCoefficients] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*/
public fun <C, A: Ring<C>> NumberedRationalFunctionSpace<C, A>.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients),
polynomialOne
)
/**
* Constructs [NumberedRationalFunction] with provided coefficients map [numeratorCoefficients] for numerator and unit
* denominator.
*
* [numeratorCoefficients] will be "cleaned up":
* 1. Zeros at the ends of terms' signatures (e.g. [numeratorCoefficients]'s keys) will be removed. (See [cleanUp].)
* 1. Terms that happen to have the same signature will be summed up.
* 1. New map will be formed of resulting terms.
*/
public fun <C, A: Ring<C>> A.NumberedRationalFunction(numeratorCoefficients: Map<List<UInt>, C>): NumberedRationalFunction<C> =
NumberedRationalFunction<C>(
NumberedPolynomial(numeratorCoefficients),
NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to one))
)
///**
// * Converts [this] constant to [NumberedRationalFunction].
// */
//context(A)
//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> =
// NumberedRationalFunction(
// NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this)),
// NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to one))
// )
///**
// * Converts [this] constant to [NumberedRationalFunction].
// */
//context(NumberedRationalFunctionSpace<C, A>)
//public fun <C, A: Ring<C>> C.asNumberedRationalFunction() : NumberedRationalFunction<C> =
// NumberedRationalFunction(
// NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to this)),
// NumberedPolynomialAsIs(mapOf(emptyList<UInt>() to constantOne))
// )