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Added utilities. Rewrote polynomial-in-polynomial substitution

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Gleb Minaev 2022-03-17 16:28:41 +03:00
parent d63c4acf10
commit 86553e9f35
1 changed files with 46 additions and 9 deletions
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55
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/polynomialUtil.kt
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@ -49,6 +49,41 @@ public inline fun <C, A, R> A.scalablePolynomial(block: ScalablePolynomialSpace<
return ScalablePolynomialSpace(this).block()
}
@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]
}
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> addTo(
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]
}
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingTo(
ring: Ring<C>,
multiplicand: List<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
target: MutableList<C>
) = ring {
for (d in 0 .. multiplicandDegree + multiplierDegree)
for (k in max(0, d - multiplierDegree)..min(multiplicandDegree, d))
target[d] += multiplicand[k] * multiplier[d - k]
}
// TODO: May be apply Horner's method too?
/**
* Evaluates the value of the given double polynomial for given double argument.
@ -80,19 +115,21 @@ public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: Polynomial<C>) : Pol
val argDegree = arg.degree
if (argDegree == -1) return coefficients[0].asPolynomial()
val constantZero = constantZero
val resultCoefs: MutableList<C> = MutableList(thisDegree + argDegree + 1) { constantZero }
val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree + argDegree + 1) { constantZero }
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]
for (updateDeg in 0 .. resultDegree + argDegree) {
var newC = resultCoefsUpdate[updateDeg]
for (deg1 in max(0, updateDeg - argDegree)..min(resultDegree, updateDeg))
newC += resultCoefs[deg1] * arg.coefficients[updateDeg - deg1]
resultCoefsUpdate[updateDeg] = newC
}
multiplyAddingTo(
ring=ring,
multiplicand = resultCoefs,
multiplicandDegree = resultDegree,
multiplier = arg.coefficients,
multiplierDegree = argDegree,
target = resultCoefsUpdate
)
resultDegree += argDegree
for (updateDeg in 0 .. resultDegree + argDegree) {
for (updateDeg in 0 .. resultDegree) {
resultCoefs[updateDeg] = resultCoefsUpdate[updateDeg]
resultCoefsUpdate[updateDeg] = constantZero
}