forked from kscience/kmath
Optimised existing substitution function. Prototyped substitution for RFs.
This commit is contained in:
Gleb Minaev
parent
86553e9f35
commit
ed2f14b68e
@ -50,24 +50,36 @@ public inline fun <C, A, R> A.scalablePolynomial(block: ScalablePolynomialSpace<
|
||||
}
|
||||
|
||||
@Suppress("NOTHING_TO_INLINE")
|
||||
internal inline fun <C> iadd(
|
||||
ring: Ring<C>,
|
||||
augend: MutableList<C>,
|
||||
addend: List<C>,
|
||||
degree: Int
|
||||
) = ring {
|
||||
for (deg in 0 .. degree) augend[deg] += addend[deg]
|
||||
internal inline fun <C> copyTo(
|
||||
origin: List<C>,
|
||||
originDegree: Int,
|
||||
target: MutableList<C>,
|
||||
) {
|
||||
for (deg in 0 .. originDegree) target[deg] = origin[deg]
|
||||
}
|
||||
|
||||
@Suppress("NOTHING_TO_INLINE")
|
||||
internal inline fun <C> addTo(
|
||||
internal inline fun <C> multiplyAddingToUpdater(
|
||||
ring: Ring<C>,
|
||||
augend: List<C>,
|
||||
addend: List<C>,
|
||||
degree: Int,
|
||||
target: MutableList<C>
|
||||
) = ring {
|
||||
for (deg in 0 .. degree) target[deg] = augend[deg] + addend[deg]
|
||||
multiplicand: MutableList<C>,
|
||||
multiplicandDegree: Int,
|
||||
multiplier: List<C>,
|
||||
multiplierDegree: Int,
|
||||
updater: MutableList<C>,
|
||||
zero: C,
|
||||
) {
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = multiplicand,
|
||||
multiplicandDegree = multiplicandDegree,
|
||||
multiplier = multiplier,
|
||||
multiplierDegree = multiplierDegree,
|
||||
target = updater
|
||||
)
|
||||
for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
|
||||
multiplicand[updateDeg] = updater[updateDeg]
|
||||
updater[updateDeg] = zero
|
||||
}
|
||||
}
|
||||
|
||||
@Suppress("NOTHING_TO_INLINE")
|
||||
@ -107,32 +119,29 @@ public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
|
||||
return result
|
||||
}
|
||||
|
||||
public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: Polynomial<C>) : Polynomial<C> = ring.polynomial {
|
||||
if (coefficients.isEmpty()) return zero
|
||||
public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: Polynomial<C>) : Polynomial<C> = ring {
|
||||
if (coefficients.isEmpty()) return Polynomial(emptyList())
|
||||
|
||||
val thisDegree = degree
|
||||
if (thisDegree == -1) return zero
|
||||
val argDegree = arg.degree
|
||||
val thisDegree = coefficients.indexOfLast { it != zero }
|
||||
if (thisDegree == -1) return Polynomial(emptyList())
|
||||
val argDegree = arg.coefficients.indexOfLast { it != zero }
|
||||
if (argDegree == -1) return coefficients[0].asPolynomial()
|
||||
val constantZero = constantZero
|
||||
val constantZero = zero
|
||||
val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
|
||||
val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
|
||||
var resultDegree = 0
|
||||
for (deg in thisDegree downTo 0) {
|
||||
resultCoefsUpdate[0] = coefficients[deg]
|
||||
multiplyAddingTo(
|
||||
ring=ring,
|
||||
multiplyAddingToUpdater(
|
||||
ring = ring,
|
||||
multiplicand = resultCoefs,
|
||||
multiplicandDegree = resultDegree,
|
||||
multiplier = arg.coefficients,
|
||||
multiplierDegree = argDegree,
|
||||
target = resultCoefsUpdate
|
||||
updater = resultCoefsUpdate,
|
||||
zero = constantZero
|
||||
)
|
||||
resultDegree += argDegree
|
||||
for (updateDeg in 0 .. resultDegree) {
|
||||
resultCoefs[updateDeg] = resultCoefsUpdate[updateDeg]
|
||||
resultCoefsUpdate[updateDeg] = constantZero
|
||||
}
|
||||
}
|
||||
return Polynomial<C>(resultCoefs)
|
||||
}
|
||||
|
||||
@ -5,9 +5,12 @@
|
||||
|
||||
package space.kscience.kmath.functions
|
||||
|
||||
import space.kscience.kmath.operations.Field
|
||||
import space.kscience.kmath.operations.Ring
|
||||
import space.kscience.kmath.operations.invoke
|
||||
import kotlin.contracts.InvocationKind
|
||||
import kotlin.contracts.contract
|
||||
import kotlin.math.max
|
||||
|
||||
|
||||
/**
|
||||
@ -24,6 +27,177 @@ public inline fun <C, A : Ring<C>, R> A.rationalFunction(block: RationalFunction
|
||||
return RationalFunctionSpace(this).block()
|
||||
}
|
||||
|
||||
/**
|
||||
* Evaluates the value of the given double polynomial for given double argument.
|
||||
*/
|
||||
public fun RationalFunction<Double>.substitute(arg: Double): Double =
|
||||
numerator.substitute(arg) / denominator.substitute(arg)
|
||||
|
||||
/**
|
||||
* Evaluates the value of the given polynomial for given argument.
|
||||
*
|
||||
* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
|
||||
*/
|
||||
public fun <C> RationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
|
||||
numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns numerator (polynomial) of rational function gotten by substitution rational function [arg] to the polynomial instance.
|
||||
* More concrete, if [arg] is a fraction `f(x)/g(x)` and the receiving instance is `p(x)`, then
|
||||
* ```
|
||||
* p(f/g) * g^deg(p)
|
||||
* ```
|
||||
* is returned.
|
||||
*
|
||||
* Used in [Polynomial.substitute] and [RationalFunction.substitute] for performance optimisation.
|
||||
*/ // TODO: Дописать
|
||||
internal fun <C> Polynomial<C>.substituteRationalFunctionTakeNumerator(ring: Ring<C>, arg: RationalFunction<C>): Polynomial<C> = ring {
|
||||
if (coefficients.isEmpty()) return Polynomial(emptyList())
|
||||
|
||||
val thisDegree = coefficients.indexOfLast { it != zero }
|
||||
if (thisDegree == -1) return Polynomial(emptyList())
|
||||
val thisDegreeLog2 = 31 - thisDegree.countLeadingZeroBits()
|
||||
val numeratorDegree = arg.numerator.coefficients.indexOfLast { it != zero }
|
||||
val denominatorDegree = arg.denominator.coefficients.indexOfLast { it != zero }
|
||||
val argDegree = max(numeratorDegree, denominatorDegree)
|
||||
val constantZero = zero
|
||||
val powersOf2 = buildList<Int>(thisDegreeLog2 + 1) {
|
||||
var result = 1
|
||||
for (exp in 0 .. thisDegreeLog2) {
|
||||
add(result)
|
||||
result = result shl 1
|
||||
}
|
||||
}
|
||||
val hashes = powersOf2.runningReduce { acc, i -> acc + i }
|
||||
val numeratorPowers = buildList<List<C>>(thisDegreeLog2 + 1) {
|
||||
add(arg.numerator.coefficients)
|
||||
repeat(thisDegreeLog2) {
|
||||
val next = MutableList<C>(powersOf2[it + 1] * numeratorDegree + 1) { constantZero }
|
||||
add(next)
|
||||
val last = last()
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = last,
|
||||
multiplicandDegree = powersOf2[it] * numeratorDegree + 1,
|
||||
multiplier = last,
|
||||
multiplierDegree = powersOf2[it] * numeratorDegree + 1,
|
||||
target = next,
|
||||
)
|
||||
}
|
||||
}
|
||||
val denominatorPowers = buildList<List<C>>(thisDegreeLog2 + 1) {
|
||||
add(arg.denominator.coefficients)
|
||||
repeat(thisDegreeLog2) {
|
||||
val next = MutableList<C>(powersOf2[it + 1] * denominatorDegree + 1) { constantZero }
|
||||
add(next)
|
||||
val last = last()
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = last,
|
||||
multiplicandDegree = powersOf2[it] * denominatorDegree + 1,
|
||||
multiplier = last,
|
||||
multiplierDegree = powersOf2[it] * denominatorDegree + 1,
|
||||
target = next,
|
||||
)
|
||||
}
|
||||
}
|
||||
val levelResultCoefsPool = buildList<MutableList<C>>(thisDegreeLog2 + 1) {
|
||||
repeat(thisDegreeLog2 + 1) {
|
||||
add(MutableList(hashes[it] * argDegree) { constantZero })
|
||||
}
|
||||
}
|
||||
val edgedMultiplier = MutableList<C>(0) { TODO() }
|
||||
val edgedMultiplierUpdater = MutableList<C>(0) { TODO() }
|
||||
|
||||
fun MutableList<C>.reset() {
|
||||
for (i in indices) set(i, constantZero)
|
||||
}
|
||||
|
||||
fun processLevel(level: Int, start: Int, end: Int) : List<C> {
|
||||
val levelResultCoefs = levelResultCoefsPool[level + 1]
|
||||
|
||||
if (level == -1) {
|
||||
levelResultCoefs[0] = coefficients[start]
|
||||
} else {
|
||||
levelResultCoefs.reset()
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = processLevel(level = level - 1, start = start, end = (start + end) / 2),
|
||||
multiplicandDegree = hashes[level] * argDegree,
|
||||
multiplier = denominatorPowers[level],
|
||||
multiplierDegree = powersOf2[level] * denominatorDegree,
|
||||
target = levelResultCoefs
|
||||
)
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = processLevel(level = level - 1, start = (start + end) / 2, end = end),
|
||||
multiplicandDegree = hashes[level] * argDegree,
|
||||
multiplier = numeratorPowers[level],
|
||||
multiplierDegree = powersOf2[level] * numeratorDegree,
|
||||
target = levelResultCoefs
|
||||
)
|
||||
}
|
||||
|
||||
return levelResultCoefs
|
||||
}
|
||||
|
||||
fun processLevelEdged(level: Int, start: Int, end: Int) : List<C> {
|
||||
val levelResultCoefs = levelResultCoefsPool[level + 1]
|
||||
|
||||
if (level == -1) {
|
||||
levelResultCoefs[0] = coefficients[start]
|
||||
} else {
|
||||
val levelsPowerOf2 = powersOf2[level]
|
||||
if (end - start >= levelsPowerOf2) {
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = processLevelEdged(level = level - 1, start = start + levelsPowerOf2, end = end),
|
||||
multiplicandDegree = hashes[level] * argDegree, // TODO: Ввести переменную
|
||||
multiplier = numeratorPowers[level],
|
||||
multiplierDegree = powersOf2[level] * numeratorDegree,
|
||||
target = levelResultCoefs
|
||||
)
|
||||
multiplyAddingTo(
|
||||
ring = ring,
|
||||
multiplicand = processLevel(level = level - 1, start = start, end = start + levelsPowerOf2),
|
||||
multiplicandDegree = hashes[level] * argDegree,
|
||||
multiplier = edgedMultiplier,
|
||||
multiplierDegree = max((hashes[level] and thisDegree) - powersOf2[level] + 1, 0) * denominatorDegree, // TODO: Ввести переменную
|
||||
target = levelResultCoefs
|
||||
)
|
||||
if (level != thisDegreeLog2) {
|
||||
multiplyAddingToUpdater(
|
||||
ring = ring,
|
||||
multiplicand = edgedMultiplier,
|
||||
multiplicandDegree = max((hashes[level] and thisDegree) - powersOf2[level] + 1, 0) * denominatorDegree, // TODO: Ввести переменную
|
||||
multiplier = denominatorPowers[level],
|
||||
multiplierDegree = powersOf2[level] * denominatorDegree,
|
||||
updater = edgedMultiplierUpdater,
|
||||
zero = constantZero
|
||||
)
|
||||
}
|
||||
} else {
|
||||
copyTo(
|
||||
origin = processLevelEdged(level = level - 1, start = start + levelsPowerOf2, end = end),
|
||||
originDegree = hashes[level] * argDegree, // TODO: Ввести переменную
|
||||
target = levelResultCoefs
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
return levelResultCoefs
|
||||
}
|
||||
|
||||
return Polynomial(
|
||||
processLevelEdged(
|
||||
level = thisDegreeLog2,
|
||||
start = 0,
|
||||
end = thisDegree + 1
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
//operator fun <T: Field<T>> RationalFunction<T>.invoke(arg: T): T = numerator(arg) / denominator(arg)
|
||||
//
|
||||
//fun <T: Field<T>> RationalFunction<T>.reduced(): RationalFunction<T> =
|
||||
|
||||
Loading…
Reference in New Issue
Block a user