1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.math3.analysis.interpolation; 18 19 import java.util.Random; 20 21 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure; 22 import org.apache.commons.math3.analysis.polynomials.PolynomialFunction; 23 import org.apache.commons.math3.exception.NoDataException; 24 import org.apache.commons.math3.util.FastMath; 25 import org.junit.Assert; 26 import org.junit.Test; 27 28 public class HermiteInterpolatorTest { 29 30 @Test testZero()31 public void testZero() { 32 HermiteInterpolator interpolator = new HermiteInterpolator(); 33 interpolator.addSamplePoint(0.0, new double[] { 0.0 }); 34 for (double x = -10; x < 10; x += 1.0) { 35 DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0]; 36 Assert.assertEquals(0.0, y.getValue(), 1.0e-15); 37 Assert.assertEquals(0.0, y.getPartialDerivative(1), 1.0e-15); 38 } 39 checkPolynomial(new PolynomialFunction(new double[] { 0.0 }), 40 interpolator.getPolynomials()[0]); 41 } 42 43 @Test testQuadratic()44 public void testQuadratic() { 45 HermiteInterpolator interpolator = new HermiteInterpolator(); 46 interpolator.addSamplePoint(0.0, new double[] { 2.0 }); 47 interpolator.addSamplePoint(1.0, new double[] { 0.0 }); 48 interpolator.addSamplePoint(2.0, new double[] { 0.0 }); 49 for (double x = -10; x < 10; x += 1.0) { 50 DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0]; 51 Assert.assertEquals((x - 1.0) * (x - 2.0), y.getValue(), 1.0e-15); 52 Assert.assertEquals(2 * x - 3.0, y.getPartialDerivative(1), 1.0e-15); 53 } 54 checkPolynomial(new PolynomialFunction(new double[] { 2.0, -3.0, 1.0 }), 55 interpolator.getPolynomials()[0]); 56 } 57 58 @Test testMixedDerivatives()59 public void testMixedDerivatives() { 60 HermiteInterpolator interpolator = new HermiteInterpolator(); 61 interpolator.addSamplePoint(0.0, new double[] { 1.0 }, new double[] { 2.0 }); 62 interpolator.addSamplePoint(1.0, new double[] { 4.0 }); 63 interpolator.addSamplePoint(2.0, new double[] { 5.0 }, new double[] { 2.0 }); 64 Assert.assertEquals(4, interpolator.getPolynomials()[0].degree()); 65 DerivativeStructure y0 = interpolator.value(new DerivativeStructure(1, 1, 0, 0.0))[0]; 66 Assert.assertEquals(1.0, y0.getValue(), 1.0e-15); 67 Assert.assertEquals(2.0, y0.getPartialDerivative(1), 1.0e-15); 68 Assert.assertEquals(4.0, interpolator.value(1.0)[0], 1.0e-15); 69 DerivativeStructure y2 = interpolator.value(new DerivativeStructure(1, 1, 0, 2.0))[0]; 70 Assert.assertEquals(5.0, y2.getValue(), 1.0e-15); 71 Assert.assertEquals(2.0, y2.getPartialDerivative(1), 1.0e-15); 72 checkPolynomial(new PolynomialFunction(new double[] { 1.0, 2.0, 4.0, -4.0, 1.0 }), 73 interpolator.getPolynomials()[0]); 74 } 75 76 @Test testRandomPolynomialsValuesOnly()77 public void testRandomPolynomialsValuesOnly() { 78 79 Random random = new Random(0x42b1e7dbd361a932l); 80 81 for (int i = 0; i < 100; ++i) { 82 83 int maxDegree = 0; 84 PolynomialFunction[] p = new PolynomialFunction[5]; 85 for (int k = 0; k < p.length; ++k) { 86 int degree = random.nextInt(7); 87 p[k] = randomPolynomial(degree, random); 88 maxDegree = FastMath.max(maxDegree, degree); 89 } 90 91 HermiteInterpolator interpolator = new HermiteInterpolator(); 92 for (int j = 0; j < 1 + maxDegree; ++j) { 93 double x = 0.1 * j; 94 double[] values = new double[p.length]; 95 for (int k = 0; k < p.length; ++k) { 96 values[k] = p[k].value(x); 97 } 98 interpolator.addSamplePoint(x, values); 99 } 100 101 for (double x = 0; x < 2; x += 0.1) { 102 double[] values = interpolator.value(x); 103 Assert.assertEquals(p.length, values.length); 104 for (int k = 0; k < p.length; ++k) { 105 Assert.assertEquals(p[k].value(x), values[k], 1.0e-8 * FastMath.abs(p[k].value(x))); 106 } 107 } 108 109 PolynomialFunction[] result = interpolator.getPolynomials(); 110 for (int k = 0; k < p.length; ++k) { 111 checkPolynomial(p[k], result[k]); 112 } 113 114 } 115 } 116 117 @Test testRandomPolynomialsFirstDerivative()118 public void testRandomPolynomialsFirstDerivative() { 119 120 Random random = new Random(0x570803c982ca5d3bl); 121 122 for (int i = 0; i < 100; ++i) { 123 124 int maxDegree = 0; 125 PolynomialFunction[] p = new PolynomialFunction[5]; 126 PolynomialFunction[] pPrime = new PolynomialFunction[5]; 127 for (int k = 0; k < p.length; ++k) { 128 int degree = random.nextInt(7); 129 p[k] = randomPolynomial(degree, random); 130 pPrime[k] = p[k].polynomialDerivative(); 131 maxDegree = FastMath.max(maxDegree, degree); 132 } 133 134 HermiteInterpolator interpolator = new HermiteInterpolator(); 135 for (int j = 0; j < 1 + maxDegree / 2; ++j) { 136 double x = 0.1 * j; 137 double[] values = new double[p.length]; 138 double[] derivatives = new double[p.length]; 139 for (int k = 0; k < p.length; ++k) { 140 values[k] = p[k].value(x); 141 derivatives[k] = pPrime[k].value(x); 142 } 143 interpolator.addSamplePoint(x, values, derivatives); 144 } 145 146 for (double x = 0; x < 2; x += 0.1) { 147 DerivativeStructure[] y = interpolator.value(new DerivativeStructure(1, 1, 0, x)); 148 Assert.assertEquals(p.length, y.length); 149 for (int k = 0; k < p.length; ++k) { 150 Assert.assertEquals(p[k].value(x), y[k].getValue(), 1.0e-8 * FastMath.abs(p[k].value(x))); 151 Assert.assertEquals(pPrime[k].value(x), y[k].getPartialDerivative(1), 4.0e-8 * FastMath.abs(p[k].value(x))); 152 } 153 } 154 155 PolynomialFunction[] result = interpolator.getPolynomials(); 156 for (int k = 0; k < p.length; ++k) { 157 checkPolynomial(p[k], result[k]); 158 } 159 160 } 161 } 162 163 @Test testSine()164 public void testSine() { 165 HermiteInterpolator interpolator = new HermiteInterpolator(); 166 for (double x = 0; x < FastMath.PI; x += 0.5) { 167 interpolator.addSamplePoint(x, new double[] { FastMath.sin(x) }); 168 } 169 for (double x = 0.1; x <= 2.9; x += 0.01) { 170 DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 2, 0, x))[0]; 171 Assert.assertEquals( FastMath.sin(x), y.getValue(), 3.5e-5); 172 Assert.assertEquals( FastMath.cos(x), y.getPartialDerivative(1), 1.3e-4); 173 Assert.assertEquals(-FastMath.sin(x), y.getPartialDerivative(2), 2.9e-3); 174 } 175 } 176 177 @Test testSquareRoot()178 public void testSquareRoot() { 179 HermiteInterpolator interpolator = new HermiteInterpolator(); 180 for (double x = 1.0; x < 3.6; x += 0.5) { 181 interpolator.addSamplePoint(x, new double[] { FastMath.sqrt(x) }); 182 } 183 for (double x = 1.1; x < 3.5; x += 0.01) { 184 DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0]; 185 Assert.assertEquals(FastMath.sqrt(x), y.getValue(), 1.5e-4); 186 Assert.assertEquals(0.5 / FastMath.sqrt(x), y.getPartialDerivative(1), 8.5e-4); 187 } 188 } 189 190 @Test testWikipedia()191 public void testWikipedia() { 192 // this test corresponds to the example from Wikipedia page: 193 // http://en.wikipedia.org/wiki/Hermite_interpolation 194 HermiteInterpolator interpolator = new HermiteInterpolator(); 195 interpolator.addSamplePoint(-1, new double[] { 2 }, new double[] { -8 }, new double[] { 56 }); 196 interpolator.addSamplePoint( 0, new double[] { 1 }, new double[] { 0 }, new double[] { 0 }); 197 interpolator.addSamplePoint( 1, new double[] { 2 }, new double[] { 8 }, new double[] { 56 }); 198 for (double x = -1.0; x <= 1.0; x += 0.125) { 199 DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0]; 200 double x2 = x * x; 201 double x4 = x2 * x2; 202 double x8 = x4 * x4; 203 Assert.assertEquals(x8 + 1, y.getValue(), 1.0e-15); 204 Assert.assertEquals(8 * x4 * x2 * x, y.getPartialDerivative(1), 1.0e-15); 205 } 206 checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 0, 0, 0, 0, 0, 0, 1 }), 207 interpolator.getPolynomials()[0]); 208 } 209 210 @Test testOnePointParabola()211 public void testOnePointParabola() { 212 HermiteInterpolator interpolator = new HermiteInterpolator(); 213 interpolator.addSamplePoint(0, new double[] { 1 }, new double[] { 1 }, new double[] { 2 }); 214 for (double x = -1.0; x <= 1.0; x += 0.125) { 215 DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0]; 216 Assert.assertEquals(1 + x * (1 + x), y.getValue(), 1.0e-15); 217 Assert.assertEquals(1 + 2 * x, y.getPartialDerivative(1), 1.0e-15); 218 } 219 checkPolynomial(new PolynomialFunction(new double[] { 1, 1, 1 }), 220 interpolator.getPolynomials()[0]); 221 } 222 randomPolynomial(int degree, Random random)223 private PolynomialFunction randomPolynomial(int degree, Random random) { 224 double[] coeff = new double[ 1 + degree]; 225 for (int j = 0; j < degree; ++j) { 226 coeff[j] = random.nextDouble(); 227 } 228 return new PolynomialFunction(coeff); 229 } 230 231 @Test(expected=NoDataException.class) testEmptySample()232 public void testEmptySample() { 233 new HermiteInterpolator().value(0.0); 234 } 235 236 @Test(expected=IllegalArgumentException.class) testDuplicatedAbscissa()237 public void testDuplicatedAbscissa() { 238 HermiteInterpolator interpolator = new HermiteInterpolator(); 239 interpolator.addSamplePoint(1.0, new double[] { 0.0 }); 240 interpolator.addSamplePoint(1.0, new double[] { 1.0 }); 241 } 242 checkPolynomial(PolynomialFunction expected, PolynomialFunction result)243 private void checkPolynomial(PolynomialFunction expected, PolynomialFunction result) { 244 Assert.assertTrue(result.degree() >= expected.degree()); 245 double[] cE = expected.getCoefficients(); 246 double[] cR = result.getCoefficients(); 247 for (int i = 0; i < cE.length; ++i) { 248 Assert.assertEquals(cE[i], cR[i], 1.0e-8 * FastMath.abs(cE[i])); 249 } 250 for (int i = cE.length; i < cR.length; ++i) { 251 Assert.assertEquals(0.0, cR[i], 1.0e-9); 252 } 253 } 254 255 } 256 257