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Feature: Polynomials and rational functions #469

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lounres merged 132 commits from feature/polynomials into dev 2022-07-28 18:04:06 +03:00
Conversation 19 Commits 132 Files Changed 51 +39 -46
2 changed files with 39 additions and 46 deletions
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81
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
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@ -50,7 +50,7 @@ public data class Polynomial<out C>(
*/ */
public val coefficients: List<C> public val coefficients: List<C>
) { ) {
override fun toString(): String = "ListPolynomial$coefficients" override fun toString(): String = "Polynomial$coefficients"
} }
/** /**
@ -63,7 +63,7 @@ public data class Polynomial<out C>(
*/ */
public open class PolynomialSpace<C, A>( public open class PolynomialSpace<C, A>(
/** /**
* Underlying ring of constants. Its operations on constants are inherited by local operations on constants. * Underlying ring of constants. Its operations on constants are used by local operations on constants and polynomials.
*/ */
public val ring: A, public val ring: A,
) : Ring<Polynomial<C>>, ScaleOperations<Polynomial<C>> where A : Ring<C>, A : ScaleOperations<C> { ) : Ring<Polynomial<C>>, ScaleOperations<Polynomial<C>> where A : Ring<C>, A : ScaleOperations<C> {
@ -191,61 +191,54 @@ public open class PolynomialSpace<C, A>(
/** /**
* Returns negation of the polynomial. * Returns negation of the polynomial.
*/ */
public override operator fun Polynomial<C>.unaryMinus(): Polynomial<C> = public override operator fun Polynomial<C>.unaryMinus(): Polynomial<C> = ring {
with(ring) { Polynomial(coefficients.map { -it })
Polynomial(coefficients.map { -it }) }
}
/** /**
* Returns sum of the polynomials. * Returns sum of the polynomials.
*/ */
public override operator fun Polynomial<C>.plus(other: Polynomial<C>): Polynomial<C> { public override operator fun Polynomial<C>.plus(other: Polynomial<C>): Polynomial<C> = ring {
with(ring) { val thisDegree = degree
val thisDegree = degree val otherDegree = other.degree
val otherDegree = other.degree return Polynomial(
return Polynomial( List(max(thisDegree, otherDegree) + 1) {
List(max(thisDegree, otherDegree) + 1) { when {
when { it > thisDegree -> other.coefficients[it]
it > thisDegree -> other.coefficients[it] it > otherDegree -> coefficients[it]
it > otherDegree -> coefficients[it] else -> coefficients[it] + other.coefficients[it]
else -> coefficients[it] + other.coefficients[it]
}
} }
) }
} )
} }
/** /**
* Returns difference of the polynomials. * Returns difference of the polynomials.
*/ */
public override operator fun Polynomial<C>.minus(other: Polynomial<C>): Polynomial<C> { public override operator fun Polynomial<C>.minus(other: Polynomial<C>): Polynomial<C> = ring {
with(ring) { val thisDegree = degree
val thisDegree = degree val otherDegree = other.degree
val otherDegree = other.degree return Polynomial(
return Polynomial( List(max(thisDegree, otherDegree) + 1) {
List(max(thisDegree, otherDegree) + 1) { when {
when { it > thisDegree -> -other.coefficients[it]
it > thisDegree -> -other.coefficients[it] it > otherDegree -> coefficients[it]
it > otherDegree -> coefficients[it] else -> coefficients[it] - other.coefficients[it]
else -> coefficients[it] - other.coefficients[it]
}
} }
) }
} )
} }
/** /**
* Returns product of the polynomials. * Returns product of the polynomials.
*/ */
public override operator fun Polynomial<C>.times(other: Polynomial<C>): Polynomial<C> { public override operator fun Polynomial<C>.times(other: Polynomial<C>): Polynomial<C> = ring {
with(ring) { val thisDegree = degree
val thisDegree = degree val otherDegree = other.degree
val otherDegree = other.degree return Polynomial(
return Polynomial( List(thisDegree + otherDegree + 1) { d ->
List(thisDegree + otherDegree + 1) { d -> (max(0, d - otherDegree)..min(thisDegree, d))
(max(0, d - otherDegree)..min(thisDegree, d)) .map { coefficients[it] * other.coefficients[d - it] }
.map { coefficients[it] * other.coefficients[d - it] } .reduce { acc, rational -> acc + rational }
.reduce { acc, rational -> acc + rational } }
} )
)
}
} }
/** /**

4
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/polynomialUtil.kt
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@ -91,7 +91,7 @@ public fun <C, A> Polynomial<C>.integrate(
public fun <C : Comparable<C>> Polynomial<C>.integrate( public fun <C : Comparable<C>> Polynomial<C>.integrate(
ring: Field<C>, ring: Field<C>,
range: ClosedRange<C>, range: ClosedRange<C>,
): C { ): C = ring {
val antiderivative = integrate(ring) val antiderivative = integrate(ring)
return ring { antiderivative.value(ring, range.endInclusive) - antiderivative.value(ring, range.start) } return antiderivative.value(ring, range.endInclusive) - antiderivative.value(ring, range.start)
} }