Added some test of NumberedPolynomial utilities.

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/functions/NumberedPolynomialUtilTest.kt

@@ -0,0 +1,293 @@
+/*
+ * 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.test.misc.Rational
+import space.kscience.kmath.test.misc.RationalField
+import space.kscience.kmath.test.misc.assertContentEquals
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+
+class NumberedPolynomialUtilTest {
+    @Test
+    fun test_substitute_Double_Map() {
+        assertContentEquals(
+            mapOf(emptyList<UInt>() to 0.0),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 1.0,
+                listOf(1u) to -2.0,
+                listOf(2u) to 1.0,
+            ).substitute(mapOf(
+                0 to 1.0
+            )).coefficients,
+            0.001,
+            "test 1"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf()).coefficients,
+            0.001,
+            "test 2"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(0u, 2u) to 0.2700930201481795,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                0 to 0.0
+            )).coefficients,
+            0.001,
+            "test 3"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 1.433510890645169,
+                listOf(1u) to 0.6264844682514724,
+                listOf(2u) to 0.8405727903771333,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                1 to 0.8400458576651112
+            )).coefficients,
+            0.001,
+            "test 4"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 1.934530767358133,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                0 to 0.4846192734143442,
+                1 to 0.8400458576651112,
+            )).coefficients,
+            0.001,
+            "test 5"
+        )
+        assertContentEquals(
+            mapOf(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to 0.8597048543814783,
+                listOf(1u) to 0.22997637465889875,
+                listOf(2u) to 0.32675302591924016,
+                listOf(0u, 1u) to 0.4561746111587508,
+                listOf(1u, 1u) to 0.5304946210170756,
+                listOf(2u, 1u) to 0.6244313712888998,
+                listOf(0u, 2u) to 0.2700930201481795,
+                listOf(1u, 2u) to -0.06962351375204712,
+                listOf(2u, 2u) to -0.015206988092131501,
+            ).substitute(mapOf(
+                5 to 0.9211194782050933
+            )).coefficients,
+            0.001,
+            "test 6"
+        )
+    }
+    @Test
+    fun test_substitute_Constant() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(0)
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(1),
+                listOf(1u) to Rational(-2),
+                listOf(2u) to Rational(1)
+            ).substitute(RationalField, mapOf(
+                0 to Rational(1)
+            )),
+            "test 1"
+        )
+        // 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
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(143, 150)
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(-3, 2),
+                listOf(1u) to Rational(8, 6),
+                listOf(2u) to Rational(14, 6),
+                listOf(0u, 1u) to Rational(-3, 1),
+                listOf(1u, 1u) to Rational(-19, 2),
+                listOf(2u, 1u) to Rational(9, 4),
+                listOf(0u, 2u) to Rational(5, 5),
+                listOf(1u, 2u) to Rational(18, 9),
+                listOf(2u, 2u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf(
+                0 to Rational(-2, 5),
+                1 to Rational(12, 9),
+            )),
+            "test 2"
+        )
+        // 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
+        assertEquals(
+            NumberedPolynomialAsIs(
+            listOf<UInt>() to Rational(47639065216, 2562890625)
+            ),
+            NumberedPolynomialAsIs(
+                listOf(8u) to Rational(-3, 2),
+                listOf(7u, 1u) to Rational(8, 6),
+                listOf(6u, 2u) to Rational(14, 6),
+                listOf(5u, 3u) to Rational(-3, 1),
+                listOf(4u, 4u) to Rational(-19, 2),
+                listOf(3u, 5u) to Rational(9, 4),
+                listOf(2u, 6u) to Rational(5, 5),
+                listOf(1u, 7u) to Rational(18, 9),
+                listOf(0u, 8u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf(
+                0 to Rational(-2, 5),
+                1 to Rational(12, 9),
+            )),
+            "test 3"
+        )
+        // 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
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf(8u) to Rational(-3, 2),
+                listOf(7u, 1u) to Rational(8, 6),
+                listOf(6u, 2u) to Rational(14, 6),
+                listOf(5u, 3u) to Rational(-3, 1),
+                listOf(4u, 4u) to Rational(-19, 2),
+                listOf(3u, 5u) to Rational(9, 4),
+                listOf(2u, 6u) to Rational(5, 5),
+                listOf(1u, 7u) to Rational(18, 9),
+                listOf(0u, 8u) to Rational(5, 2),
+            ),
+            NumberedPolynomialAsIs(
+                listOf(8u) to Rational(-3, 2),
+                listOf(7u, 1u) to Rational(8, 6),
+                listOf(6u, 2u) to Rational(14, 6),
+                listOf(5u, 3u) to Rational(-3, 1),
+                listOf(4u, 4u) to Rational(-19, 2),
+                listOf(3u, 5u) to Rational(9, 4),
+                listOf(2u, 6u) to Rational(5, 5),
+                listOf(1u, 7u) to Rational(18, 9),
+                listOf(0u, 8u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf<Int, Rational>()),
+            "test 4"
+        )
+    }
+    @Test
+    fun test_substitute_Polynomial() {
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(0)
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(1),
+                listOf(1u) to Rational(-2),
+                listOf(2u) to Rational(1)
+            ).substitute(RationalField, mapOf(
+                0 to NumberedPolynomialAsIs(
+                    listOf<UInt>() to Rational(1)
+                )
+            )),
+            "test 1"
+        )
+        // 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
+        assertEquals(
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(-3, 2),
+                listOf(0u, 1u) to Rational(-92, 21),
+                listOf(0u, 2u) to Rational(-2627, 2352),
+                listOf(0u, 3u) to Rational(4565, 3136),
+                listOf(0u, 4u) to Rational(605, 1568),
+                listOf(1u) to Rational(-20, 3),
+                listOf(1u, 1u) to Rational(1445, 21),
+                listOf(1u, 2u) to Rational(-13145, 392),
+                listOf(1u, 3u) to Rational(-3025, 196),
+                listOf(2u) to Rational(175, 3),
+                listOf(2u, 1u) to Rational(2475, 28),
+                listOf(2u, 2u) to Rational(15125, 98),
+                listOf(3u) to Rational(0),
+                listOf(3u, 1u) to Rational(0),
+                listOf(4u) to Rational(0),
+            ),
+            NumberedPolynomialAsIs(
+                listOf<UInt>() to Rational(-3, 2),
+                listOf(1u) to Rational(8, 6),
+                listOf(2u) to Rational(14, 6),
+                listOf(0u, 1u) to Rational(-3, 1),
+                listOf(1u, 1u) to Rational(-19, 2),
+                listOf(2u, 1u) to Rational(9, 4),
+                listOf(0u, 2u) to Rational(5, 5),
+                listOf(1u, 2u) to Rational(18, 9),
+                listOf(2u, 2u) to Rational(5, 2),
+            ).substitute(RationalField, mapOf(
+                0 to NumberedPolynomialAsIs(
+                    listOf(1u) to Rational(-5, 1),
+                    listOf(0u, 1u) to Rational(2, 8),
+                ),
+                1 to NumberedPolynomialAsIs(
+                    listOf(1u) to Rational(0, 5),
+                    listOf(0u, 1u) to Rational(11, 7),
+                ),
+            )),
+            "test 2"
+        )
+    }
+}

kmath-functions/src/commonTest/kotlin/space/kscience/kmath/test/misc/assertion.kt

@@ -0,0 +1,14 @@
+/*
+ * 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.test.misc
+
+import kotlin.test.assertEquals
+
+
+fun <T> assertContentEquals(expected: Map<T, Double>, actual: Map<T, Double>, absoluteTolerance: Double, message: String? = null) {
+    assertEquals(expected.keys, actual.keys, message)
+    for ((key, expectedValue) in expected) assertEquals(expectedValue, actual[key]!!, absoluteTolerance, message)
+}