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Feature: Polynomials and rational functions #469

Merged
lounres merged 132 commits from feature/polynomials into dev 2022-07-28 18:04:06 +03:00
Conversation 19 Commits 132 Files Changed 51 +104 -15
3 changed files with 104 additions and 15 deletions
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6
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
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@ -369,14 +369,14 @@ public open class PolynomialSpace<C, A : Ring<C>>(
*/
public override fun Polynomial<C>.isOne(): Boolean =
with(coefficients) {
isNotEmpty() && withIndex().any { (index, c) -> if (index == 0) c.isOne() else c.isZero() }
isNotEmpty() && withIndex().all { (index, c) -> if (index == 0) c.isOne() else c.isZero() }
}
/**
* Check if the instant is minus unit polynomial.
*/
public override fun Polynomial<C>.isMinusOne(): Boolean =
with(coefficients) {
isNotEmpty() && withIndex().any { (index, c) -> if (index == 0) c.isMinusOne() else c.isZero() }
isNotEmpty() && withIndex().all { (index, c) -> if (index == 0) c.isMinusOne() else c.isZero() }
}
/**
@ -415,7 +415,7 @@ public open class PolynomialSpace<C, A : Ring<C>>(
with(coefficients) {
when {
isEmpty() -> constantZero
degree > 0 -> null
withIndex().any { (index, c) -> index == 0 || c.isZero() } -> null
else -> first()
}
}

86
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/PolynomialTest.kt
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@ -5,10 +5,8 @@
package space.kscience.kmath.functions
import space.kscience.kmath.operations.algebra
import space.kscience.kmath.test.misc.*
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.*
class PolynomialTest {
@ -393,6 +391,21 @@ class PolynomialTest {
}
}
@Test
fun test_Polynomial_unaryMinus() {
RationalField.polynomial {
assertEquals(
Polynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7)),
-Polynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7)),
"test 1"
)
assertEquals(
Polynomial(Rational(-5, 9), Rational(8, 9), Rational(8, 7), Rational(0), Rational(0)),
-Polynomial(Rational(5, 9), Rational(-8, 9), Rational(-8, 7), Rational(0), Rational(0)),
"test 2"
)
}
}
@Test
fun test_Polynomial_Polynomial_plus() {
RationalField.polynomial {
// (5/9 - 8/9 x - 8/7 x^2) + (-5/7 + 5/1 x + 5/8 x^2) ?= -10/63 + 37/9 x - 29/56 x^2
@ -459,17 +472,66 @@ class PolynomialTest {
}
}
@Test
fun simple_polynomial_test() {
val polynomial : Polynomial<Double>
Double.algebra.scalablePolynomial {
val x = Polynomial(listOf(0.0, 1.0))
polynomial = x * x - 2 * x + 1
fun test_Polynomial_Polynomial_times() {
IntModuloRing(35).polynomial {
// (1 + x + x^2) * (1 - x + x^2) ?= 1 + x^2 + x^4
assertEquals(
Polynomial(1, 0, 1, 0, 1),
Polynomial(1, -1, 1) * Polynomial(1, 1, 1),
"test 1"
)
// Spoiler: 5 * 7 = 0
assertEquals(
Polynomial(),
Polynomial(5, -25, 10) * Polynomial(21, 14, -7),
"test 2"
)
}
assertEquals(0.0, polynomial.substitute(1.0), 0.001)
}
@Test
fun testIntegration() {
val polynomial = Polynomial(1.0, -2.0, 1.0)
assertEquals(0.0, polynomial.substitute(1.0), 0.001)
fun test_Polynomial_isZero() {
RationalField.polynomial {
assertTrue("test 1") { Polynomial<Rational>().isZero() }
assertTrue("test 2") { Polynomial<Rational>(Rational(0)).isZero() }
assertTrue("test 3") { Polynomial<Rational>(Rational(0), Rational(0)).isZero() }
assertTrue("test 4") { Polynomial<Rational>(Rational(0), Rational(0), Rational(0)).isZero() }
assertFalse("test 5") { Polynomial<Rational>(Rational(3, 5)).isZero() }
assertFalse("test 6") { Polynomial<Rational>(Rational(3, 5), Rational(0)).isZero() }
assertFalse("test 7") { Polynomial<Rational>(Rational(0), Rational(3, 5), Rational(0)).isZero() }
}
}
@Test
fun test_Polynomial_isOne() {
RationalField.polynomial {
assertFalse("test 1") { Polynomial<Rational>().isOne() }
assertFalse("test 2") { Polynomial(Rational(0)).isOne() }
assertFalse("test 3") { Polynomial(Rational(0), Rational(0)).isOne() }
assertFalse("test 4") { Polynomial(Rational(0), Rational(0), Rational(0)).isOne() }
assertFalse("test 5") { Polynomial(Rational(3, 5)).isOne() }
assertTrue("test 6") { Polynomial(Rational(5, 5)).isOne() }
assertFalse("test 7") { Polynomial(Rational(3, 5), Rational(0)).isOne() }
assertTrue("test 8") { Polynomial(Rational(3, 3), Rational(0)).isOne() }
assertFalse("test 9") { Polynomial(Rational(0), Rational(3, 5), Rational(0)).isOne() }
assertFalse("test 10") { Polynomial(Rational(0), Rational(5, 5), Rational(0)).isOne() }
assertFalse("test 11") { Polynomial(Rational(1), Rational(3, 5), Rational(0)).isOne() }
assertFalse("test 12") { Polynomial(Rational(1), Rational(5, 5), Rational(0)).isOne() }
}
}
@Test
fun test_Polynomial_isMinusOne() {
RationalField.polynomial {
assertFalse("test 1") { Polynomial<Rational>().isMinusOne() }
assertFalse("test 2") { Polynomial(Rational(0)).isMinusOne() }
assertFalse("test 3") { Polynomial(Rational(0), Rational(0)).isMinusOne() }
assertFalse("test 4") { Polynomial(Rational(0), Rational(0), Rational(0)).isMinusOne() }
assertFalse("test 5") { Polynomial(Rational(3, 5)).isMinusOne() }
assertTrue("test 6") { Polynomial(Rational(-5, 5)).isMinusOne() }
assertFalse("test 7") { Polynomial(Rational(3, 5), Rational(0)).isMinusOne() }
assertTrue("test 8") { Polynomial(Rational(-3, 3), Rational(0)).isMinusOne() }
assertFalse("test 9") { Polynomial(Rational(0), Rational(3, 5), Rational(0)).isMinusOne() }
assertFalse("test 10") { Polynomial(Rational(0), Rational(5, -5), Rational(0)).isMinusOne() }
assertFalse("test 11") { Polynomial(Rational(-1), Rational(3, 5), Rational(0)).isMinusOne() }
assertFalse("test 12") { Polynomial(Rational(-1), Rational(5, -5), Rational(0)).isMinusOne() }
}
}
}

27
kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/PolynomialUtilTest.kt Normal file
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@ -0,0 +1,27 @@
/*
* 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.
*/
package space.kscience.kmath.functions
import space.kscience.kmath.operations.algebra
import kotlin.test.Test
import kotlin.test.assertEquals
class PolynomialUtilTest {
@Test
fun simple_polynomial_test() {
val polynomial : Polynomial<Double>
Double.algebra.scalablePolynomial {
val x = Polynomial(listOf(0.0, 1.0))
polynomial = x * x - 2 * x + 1
}
assertEquals(0.0, polynomial.substitute(1.0), 0.001)
}
@Test
fun testIntegration() {
val polynomial = Polynomial(1.0, -2.0, 1.0)
assertEquals(0.0, polynomial.substitute(1.0), 0.001)
}
}