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17 package org.apache.commons.math4.legacy.analysis.interpolation;
18
19 import java.util.Random;
20
21 import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunction;
22 import org.apache.commons.math4.legacy.core.dfp.Dfp;
23 import org.apache.commons.math4.legacy.core.dfp.DfpField;
24 import org.apache.commons.math4.legacy.linear.Dfp25;
25 import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
26 import org.apache.commons.math4.legacy.exception.NoDataException;
27 import org.apache.commons.math4.core.jdkmath.JdkMath;
28 import org.junit.Assert;
29 import org.junit.Test;
30
31 public class FieldHermiteInterpolatorTest {
32
33 @Test
34 public void testZero() {
35 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
36 interpolator.addSamplePoint(Dfp25.of(0), new Dfp[] { Dfp25.of(0) });
37 for (int x = -10; x < 10; x++) {
38 Dfp y = interpolator.value(Dfp25.of(x))[0];
39 Assert.assertEquals(Dfp25.ZERO, y);
40 Dfp[][] derivatives = interpolator.derivatives(Dfp25.of(x), 1);
41 Assert.assertEquals(Dfp25.ZERO, derivatives[0][0]);
42 Assert.assertEquals(Dfp25.ZERO, derivatives[1][0]);
43 }
44 }
45
46 @Test
47 public void testQuadratic() {
48 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
49 interpolator.addSamplePoint(Dfp25.of(0), new Dfp[] { Dfp25.of(2) });
50 interpolator.addSamplePoint(Dfp25.of(1), new Dfp[] { Dfp25.of(0) });
51 interpolator.addSamplePoint(Dfp25.of(2), new Dfp[] { Dfp25.of(0) });
52 for (double x = -10; x < 10; x += 1.0) {
53 Dfp y = interpolator.value(Dfp25.of(x))[0];
54 Assert.assertEquals((x - 1) * (x - 2), y.toDouble(), 1.0e-15);
55 Dfp[][] derivatives = interpolator.derivatives(Dfp25.of(x), 3);
56 Assert.assertEquals((x - 1) * (x - 2), derivatives[0][0].toDouble(), 1.0e-15);
57 Assert.assertEquals(2 * x - 3, derivatives[1][0].toDouble(), 1.0e-15);
58 Assert.assertEquals(2, derivatives[2][0].toDouble(), 1.0e-15);
59 Assert.assertEquals(0, derivatives[3][0].toDouble(), 1.0e-15);
60 }
61 }
62
63 @Test
64 public void testMixedDerivatives() {
65 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
66 interpolator.addSamplePoint(Dfp25.of(0), new Dfp[] { Dfp25.of(1) }, new Dfp[] { Dfp25.of(2) });
67 interpolator.addSamplePoint(Dfp25.of(1), new Dfp[] { Dfp25.of(4) });
68 interpolator.addSamplePoint(Dfp25.of(2), new Dfp[] { Dfp25.of(5) }, new Dfp[] { Dfp25.of(2) });
69 Dfp[][] derivatives = interpolator.derivatives(Dfp25.of(0), 5);
70 Assert.assertEquals(Dfp25.of( 1), derivatives[0][0]);
71 Assert.assertEquals(Dfp25.of( 2), derivatives[1][0]);
72 Assert.assertEquals(Dfp25.of( 8), derivatives[2][0]);
73 Assert.assertEquals(Dfp25.of(-24), derivatives[3][0]);
74 Assert.assertEquals(Dfp25.of( 24), derivatives[4][0]);
75 Assert.assertEquals(Dfp25.of( 0), derivatives[5][0]);
76 derivatives = interpolator.derivatives(Dfp25.of(1), 5);
77 Assert.assertEquals(Dfp25.of( 4), derivatives[0][0]);
78 Assert.assertEquals(Dfp25.of( 2), derivatives[1][0]);
79 Assert.assertEquals(Dfp25.of( -4), derivatives[2][0]);
80 Assert.assertEquals(Dfp25.of( 0), derivatives[3][0]);
81 Assert.assertEquals(Dfp25.of( 24), derivatives[4][0]);
82 Assert.assertEquals(Dfp25.of( 0), derivatives[5][0]);
83 derivatives = interpolator.derivatives(Dfp25.of(2), 5);
84 Assert.assertEquals(Dfp25.of( 5), derivatives[0][0]);
85 Assert.assertEquals(Dfp25.of( 2), derivatives[1][0]);
86 Assert.assertEquals(Dfp25.of( 8), derivatives[2][0]);
87 Assert.assertEquals(Dfp25.of( 24), derivatives[3][0]);
88 Assert.assertEquals(Dfp25.of( 24), derivatives[4][0]);
89 Assert.assertEquals(Dfp25.of( 0), derivatives[5][0]);
90 }
91
92 @Test
93 public void testRandomPolynomialsValuesOnly() {
94
95 Random random = new Random(0x42b1e7dbd361a932L);
96
97 for (int i = 0; i < 100; ++i) {
98
99 int maxDegree = 0;
100 PolynomialFunction[] p = new PolynomialFunction[5];
101 for (int k = 0; k < p.length; ++k) {
102 int degree = random.nextInt(7);
103 p[k] = randomPolynomial(degree, random);
104 maxDegree = JdkMath.max(maxDegree, degree);
105 }
106
107 DfpField field = new DfpField(30);
108 Dfp step = field.getOne().divide(field.newDfp(10));
109 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
110 for (int j = 0; j < 1 + maxDegree; ++j) {
111 Dfp x = field.newDfp(j).multiply(step);
112 Dfp[] values = new Dfp[p.length];
113 for (int k = 0; k < p.length; ++k) {
114 values[k] = field.newDfp(p[k].value(x.getReal()));
115 }
116 interpolator.addSamplePoint(x, values);
117 }
118
119 for (int j = 0; j < 20; ++j) {
120 Dfp x = field.newDfp(j).multiply(step);
121 Dfp[] values = interpolator.value(x);
122 Assert.assertEquals(p.length, values.length);
123 for (int k = 0; k < p.length; ++k) {
124 Assert.assertEquals(p[k].value(x.getReal()),
125 values[k].getReal(),
126 1.0e-8 * JdkMath.abs(p[k].value(x.getReal())));
127 }
128 }
129 }
130 }
131
132 @Test
133 public void testRandomPolynomialsFirstDerivative() {
134
135 Random random = new Random(0x570803c982ca5d3bL);
136
137 for (int i = 0; i < 100; ++i) {
138
139 int maxDegree = 0;
140 PolynomialFunction[] p = new PolynomialFunction[5];
141 PolynomialFunction[] pPrime = new PolynomialFunction[5];
142 for (int k = 0; k < p.length; ++k) {
143 int degree = random.nextInt(7);
144 p[k] = randomPolynomial(degree, random);
145 pPrime[k] = p[k].polynomialDerivative();
146 maxDegree = JdkMath.max(maxDegree, degree);
147 }
148
149 DfpField field = new DfpField(30);
150 Dfp step = field.getOne().divide(field.newDfp(10));
151 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
152 for (int j = 0; j < 1 + maxDegree / 2; ++j) {
153 Dfp x = field.newDfp(j).multiply(step);
154 Dfp[] values = new Dfp[p.length];
155 Dfp[] derivatives = new Dfp[p.length];
156 for (int k = 0; k < p.length; ++k) {
157 values[k] = field.newDfp(p[k].value(x.getReal()));
158 derivatives[k] = field.newDfp(pPrime[k].value(x.getReal()));
159 }
160 interpolator.addSamplePoint(x, values, derivatives);
161 }
162
163 Dfp h = step.divide(field.newDfp(100000));
164 for (int j = 0; j < 20; ++j) {
165 Dfp x = field.newDfp(j).multiply(step);
166 Dfp[] y = interpolator.value(x);
167 Dfp[] yP = interpolator.value(x.add(h));
168 Dfp[] yM = interpolator.value(x.subtract(h));
169 Assert.assertEquals(p.length, y.length);
170 for (int k = 0; k < p.length; ++k) {
171 Assert.assertEquals(p[k].value(x.getReal()),
172 y[k].getReal(),
173 1.0e-8 * JdkMath.abs(p[k].value(x.getReal())));
174 Assert.assertEquals(pPrime[k].value(x.getReal()),
175 yP[k].subtract(yM[k]).divide(h.multiply(2)).getReal(),
176 4.0e-8 * JdkMath.abs(p[k].value(x.getReal())));
177 }
178 }
179 }
180 }
181
182 @Test
183 public void testSine() {
184 DfpField field = new DfpField(30);
185 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
186 for (Dfp x = field.getZero(); x.getReal() < JdkMath.PI; x = x.add(0.5)) {
187 interpolator.addSamplePoint(x, new Dfp[] { x.sin() });
188 }
189 for (Dfp x = field.newDfp(0.1); x.getReal() < 2.9; x = x.add(0.01)) {
190 Dfp y = interpolator.value(x)[0];
191 Assert.assertEquals( x.sin().getReal(), y.getReal(), 3.5e-5);
192 }
193 }
194
195 @Test
196 public void testSquareRoot() {
197 DfpField field = new DfpField(30);
198 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
199 for (Dfp x = field.getOne(); x.getReal() < 3.6; x = x.add(0.5)) {
200 interpolator.addSamplePoint(x, new Dfp[] { x.sqrt() });
201 }
202 for (Dfp x = field.newDfp(1.1); x.getReal() < 3.5; x = x.add(0.01)) {
203 Dfp y = interpolator.value(x)[0];
204 Assert.assertEquals(x.sqrt().getReal(), y.getReal(), 1.5e-4);
205 }
206 }
207
208 @Test
209 public void testWikipedia() {
210
211
212 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
213 interpolator.addSamplePoint(Dfp25.of(-1),
214 new Dfp[] { Dfp25.of( 2) },
215 new Dfp[] { Dfp25.of(-8) },
216 new Dfp[] { Dfp25.of(56) });
217 interpolator.addSamplePoint(Dfp25.of( 0),
218 new Dfp[] { Dfp25.of( 1) },
219 new Dfp[] { Dfp25.of( 0) },
220 new Dfp[] { Dfp25.of( 0) });
221 interpolator.addSamplePoint(Dfp25.of( 1),
222 new Dfp[] { Dfp25.of( 2) },
223 new Dfp[] { Dfp25.of( 8) },
224 new Dfp[] { Dfp25.of(56) });
225 for (Dfp x = Dfp25.of(-1); x.toDouble() <= 1.0; x = x.add(Dfp25.of(1, 8))) {
226 Dfp y = interpolator.value(x)[0];
227 Dfp x2 = x.multiply(x);
228 Dfp x4 = x2.multiply(x2);
229 Dfp x8 = x4.multiply(x4);
230 Assert.assertEquals(x8.add(Dfp25.of(1)), y);
231 }
232 }
233
234 @Test
235 public void testOnePointParabola() {
236 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
237 interpolator.addSamplePoint(Dfp25.of(0),
238 new Dfp[] { Dfp25.of(1) },
239 new Dfp[] { Dfp25.of(1) },
240 new Dfp[] { Dfp25.of(2) });
241 for (Dfp x = Dfp25.of(-1); x.toDouble() <= 1.0; x = x.add(Dfp25.of(1, 8))) {
242 Dfp y = interpolator.value(x)[0];
243 Assert.assertEquals(Dfp25.ONE.add(x.multiply(Dfp25.ONE.add(x))), y);
244 }
245 }
246
247 private PolynomialFunction randomPolynomial(int degree, Random random) {
248 double[] coeff = new double[ 1 + degree];
249 for (int j = 0; j < degree; ++j) {
250 coeff[j] = random.nextDouble();
251 }
252 return new PolynomialFunction(coeff);
253 }
254
255 @Test(expected=NoDataException.class)
256 public void testEmptySampleValue() {
257 new FieldHermiteInterpolator<Dfp>().value(Dfp25.ZERO);
258 }
259
260 @Test(expected=NoDataException.class)
261 public void testEmptySampleDerivative() {
262 new FieldHermiteInterpolator<Dfp>().derivatives(Dfp25.ZERO, 1);
263 }
264
265 @Test(expected=MathIllegalArgumentException.class)
266 public void testDuplicatedAbscissa() {
267 FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<>();
268 interpolator.addSamplePoint(Dfp25.of(1), new Dfp[] { Dfp25.of(0) });
269 interpolator.addSamplePoint(Dfp25.of(1), new Dfp[] { Dfp25.of(1) });
270 }
271 }
272