Feature: Polynomials and rational functions #469
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.functions
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import space.kscience.kmath.test.misc.Rational
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import space.kscience.kmath.test.misc.RationalField
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import space.kscience.kmath.test.misc.assertContentEquals
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import kotlin.test.Test
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import kotlin.test.assertEquals
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class NumberedPolynomialUtilTest {
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@Test
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fun test_substitute_Double_Map() {
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assertContentEquals(
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mapOf(emptyList<UInt>() to 0.0),
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NumberedPolynomialAsIs(
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listOf<UInt>() to 1.0,
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listOf(1u) to -2.0,
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listOf(2u) to 1.0,
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).substitute(mapOf(
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0 to 1.0
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)).coefficients,
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0.001,
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"test 1"
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)
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assertContentEquals(
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mapOf(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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).substitute(mapOf()).coefficients,
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0.001,
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"test 2"
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)
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assertContentEquals(
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mapOf(
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listOf<UInt>() to 0.8597048543814783,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(0u, 2u) to 0.2700930201481795,
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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).substitute(mapOf(
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0 to 0.0
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)).coefficients,
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0.001,
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"test 3"
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)
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assertContentEquals(
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mapOf(
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listOf<UInt>() to 1.433510890645169,
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listOf(1u) to 0.6264844682514724,
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listOf(2u) to 0.8405727903771333,
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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).substitute(mapOf(
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1 to 0.8400458576651112
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)).coefficients,
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0.001,
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"test 4"
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)
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assertContentEquals(
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mapOf(
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listOf<UInt>() to 1.934530767358133,
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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).substitute(mapOf(
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0 to 0.4846192734143442,
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1 to 0.8400458576651112,
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)).coefficients,
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0.001,
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"test 5"
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)
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assertContentEquals(
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mapOf(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to 0.8597048543814783,
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listOf(1u) to 0.22997637465889875,
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listOf(2u) to 0.32675302591924016,
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listOf(0u, 1u) to 0.4561746111587508,
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listOf(1u, 1u) to 0.5304946210170756,
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listOf(2u, 1u) to 0.6244313712888998,
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listOf(0u, 2u) to 0.2700930201481795,
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listOf(1u, 2u) to -0.06962351375204712,
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listOf(2u, 2u) to -0.015206988092131501,
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).substitute(mapOf(
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5 to 0.9211194782050933
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)).coefficients,
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0.001,
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"test 6"
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)
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}
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@Test
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fun test_substitute_Constant() {
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assertEquals(
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(0)
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(1),
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listOf(1u) to Rational(-2),
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listOf(2u) to Rational(1)
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).substitute(RationalField, mapOf(
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0 to Rational(1)
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)),
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"test 1"
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)
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// https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9
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assertEquals(
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(143, 150)
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(-3, 2),
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listOf(1u) to Rational(8, 6),
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listOf(2u) to Rational(14, 6),
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listOf(0u, 1u) to Rational(-3, 1),
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listOf(1u, 1u) to Rational(-19, 2),
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listOf(2u, 1u) to Rational(9, 4),
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listOf(0u, 2u) to Rational(5, 5),
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listOf(1u, 2u) to Rational(18, 9),
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listOf(2u, 2u) to Rational(5, 2),
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).substitute(RationalField, mapOf(
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0 to Rational(-2, 5),
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1 to Rational(12, 9),
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)),
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"test 2"
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)
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// https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9
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assertEquals(
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(47639065216, 2562890625)
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),
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NumberedPolynomialAsIs(
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listOf(8u) to Rational(-3, 2),
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listOf(7u, 1u) to Rational(8, 6),
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listOf(6u, 2u) to Rational(14, 6),
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listOf(5u, 3u) to Rational(-3, 1),
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listOf(4u, 4u) to Rational(-19, 2),
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listOf(3u, 5u) to Rational(9, 4),
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listOf(2u, 6u) to Rational(5, 5),
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listOf(1u, 7u) to Rational(18, 9),
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listOf(0u, 8u) to Rational(5, 2),
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).substitute(RationalField, mapOf(
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0 to Rational(-2, 5),
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1 to Rational(12, 9),
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)),
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"test 3"
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)
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// https://www.wolframalpha.com/input?i=%28%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2%29+p%5E8+where+x+%3D+q%2Fp%2C+y+%3D+x%5E3%2C+p+%3D+-2%2F5%2C+q+%3D+12%2F9
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assertEquals(
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NumberedPolynomialAsIs(
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listOf(8u) to Rational(-3, 2),
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listOf(7u, 1u) to Rational(8, 6),
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listOf(6u, 2u) to Rational(14, 6),
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listOf(5u, 3u) to Rational(-3, 1),
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listOf(4u, 4u) to Rational(-19, 2),
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listOf(3u, 5u) to Rational(9, 4),
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listOf(2u, 6u) to Rational(5, 5),
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listOf(1u, 7u) to Rational(18, 9),
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listOf(0u, 8u) to Rational(5, 2),
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),
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NumberedPolynomialAsIs(
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listOf(8u) to Rational(-3, 2),
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listOf(7u, 1u) to Rational(8, 6),
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listOf(6u, 2u) to Rational(14, 6),
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listOf(5u, 3u) to Rational(-3, 1),
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listOf(4u, 4u) to Rational(-19, 2),
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listOf(3u, 5u) to Rational(9, 4),
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listOf(2u, 6u) to Rational(5, 5),
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listOf(1u, 7u) to Rational(18, 9),
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listOf(0u, 8u) to Rational(5, 2),
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).substitute(RationalField, mapOf<Int, Rational>()),
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"test 4"
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)
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}
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@Test
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fun test_substitute_Polynomial() {
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assertEquals(
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(0)
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(1),
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listOf(1u) to Rational(-2),
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listOf(2u) to Rational(1)
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).substitute(RationalField, mapOf(
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0 to NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(1)
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)
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)),
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"test 1"
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)
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// https://www.wolframalpha.com/input?i=%28-3%2F2+%2B+8%2F6+x+%2B+14%2F6+x%5E2%29+%2B+%28-3%2F1+%2B+-19%2F2+x+%2B+9%2F4+x%5E2%29+y+%2B+%285%2F5+%2B+18%2F9+x+%2B+5%2F2+x%5E2%29+y%5E2+where+x+%3D+-2%2F5%2C+y+%3D+12%2F9
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assertEquals(
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(-3, 2),
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listOf(0u, 1u) to Rational(-92, 21),
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listOf(0u, 2u) to Rational(-2627, 2352),
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listOf(0u, 3u) to Rational(4565, 3136),
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listOf(0u, 4u) to Rational(605, 1568),
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listOf(1u) to Rational(-20, 3),
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listOf(1u, 1u) to Rational(1445, 21),
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listOf(1u, 2u) to Rational(-13145, 392),
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listOf(1u, 3u) to Rational(-3025, 196),
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listOf(2u) to Rational(175, 3),
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listOf(2u, 1u) to Rational(2475, 28),
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listOf(2u, 2u) to Rational(15125, 98),
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listOf(3u) to Rational(0),
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listOf(3u, 1u) to Rational(0),
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listOf(4u) to Rational(0),
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),
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NumberedPolynomialAsIs(
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listOf<UInt>() to Rational(-3, 2),
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listOf(1u) to Rational(8, 6),
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listOf(2u) to Rational(14, 6),
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listOf(0u, 1u) to Rational(-3, 1),
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listOf(1u, 1u) to Rational(-19, 2),
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listOf(2u, 1u) to Rational(9, 4),
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listOf(0u, 2u) to Rational(5, 5),
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listOf(1u, 2u) to Rational(18, 9),
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listOf(2u, 2u) to Rational(5, 2),
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).substitute(RationalField, mapOf(
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0 to NumberedPolynomialAsIs(
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listOf(1u) to Rational(-5, 1),
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listOf(0u, 1u) to Rational(2, 8),
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),
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1 to NumberedPolynomialAsIs(
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listOf(1u) to Rational(0, 5),
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listOf(0u, 1u) to Rational(11, 7),
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),
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)),
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"test 2"
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)
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}
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}
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@ -0,0 +1,14 @@
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/*
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* 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.
|
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*/
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package space.kscience.kmath.test.misc
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import kotlin.test.assertEquals
|
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fun <T> assertContentEquals(expected: Map<T, Double>, actual: Map<T, Double>, absoluteTolerance: Double, message: String? = null) {
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assertEquals(expected.keys, actual.keys, message)
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for ((key, expectedValue) in expected) assertEquals(expectedValue, actual[key]!!, absoluteTolerance, message)
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}
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Block a user