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* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
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package org.apache.commons.math3.analysis.interpolation;
import java.util.Random;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.dfp.Dfp;
import org.apache.commons.math3.dfp.DfpField;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class FieldHermiteInterpolatorTest {
@Test
public void testZero() {
FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();
interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(0) });
for (int x = -10; x < 10; x++) {
BigFraction y = interpolator.value(new BigFraction(x))[0];
Assert.assertEquals(BigFraction.ZERO, y);
BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(x), 1);
Assert.assertEquals(BigFraction.ZERO, derivatives[0][0]);
Assert.assertEquals(BigFraction.ZERO, derivatives[1][0]);
}
}
@Test
public void testQuadratic() {
FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();
interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(2) });
interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(0) });
interpolator.addSamplePoint(new BigFraction(2), new BigFraction[] { new BigFraction(0) });
for (double x = -10; x < 10; x += 1.0) {
BigFraction y = interpolator.value(new BigFraction(x))[0];
Assert.assertEquals((x - 1) * (x - 2), y.doubleValue(), 1.0e-15);
BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(x), 3);
Assert.assertEquals((x - 1) * (x - 2), derivatives[0][0].doubleValue(), 1.0e-15);
Assert.assertEquals(2 * x - 3, derivatives[1][0].doubleValue(), 1.0e-15);
Assert.assertEquals(2, derivatives[2][0].doubleValue(), 1.0e-15);
Assert.assertEquals(0, derivatives[3][0].doubleValue(), 1.0e-15);
}
}
@Test
public void testMixedDerivatives() {
FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();
interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(1) }, new BigFraction[] { new BigFraction(2) });
interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(4) });
interpolator.addSamplePoint(new BigFraction(2), new BigFraction[] { new BigFraction(5) }, new BigFraction[] { new BigFraction(2) });
BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(0), 5);
Assert.assertEquals(new BigFraction( 1), derivatives[0][0]);
Assert.assertEquals(new BigFraction( 2), derivatives[1][0]);
Assert.assertEquals(new BigFraction( 8), derivatives[2][0]);
Assert.assertEquals(new BigFraction(-24), derivatives[3][0]);
Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
Assert.assertEquals(new BigFraction( 0), derivatives[5][0]);
derivatives = interpolator.derivatives(new BigFraction(1), 5);
Assert.assertEquals(new BigFraction( 4), derivatives[0][0]);
Assert.assertEquals(new BigFraction( 2), derivatives[1][0]);
Assert.assertEquals(new BigFraction( -4), derivatives[2][0]);
Assert.assertEquals(new BigFraction( 0), derivatives[3][0]);
Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
Assert.assertEquals(new BigFraction( 0), derivatives[5][0]);
derivatives = interpolator.derivatives(new BigFraction(2), 5);
Assert.assertEquals(new BigFraction( 5), derivatives[0][0]);
Assert.assertEquals(new BigFraction( 2), derivatives[1][0]);
Assert.assertEquals(new BigFraction( 8), derivatives[2][0]);
Assert.assertEquals(new BigFraction( 24), derivatives[3][0]);
Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
Assert.assertEquals(new BigFraction( 0), derivatives[5][0]);
}
@Test
public void testRandomPolynomialsValuesOnly() {
Random random = new Random(0x42b1e7dbd361a932l);
for (int i = 0; i < 100; ++i) {
int maxDegree = 0;
PolynomialFunction[] p = new PolynomialFunction[5];
for (int k = 0; k < p.length; ++k) {
int degree = random.nextInt(7);
p[k] = randomPolynomial(degree, random);
maxDegree = FastMath.max(maxDegree, degree);
}
DfpField field = new DfpField(30);
Dfp step = field.getOne().divide(field.newDfp(10));
FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<Dfp>();
for (int j = 0; j < 1 + maxDegree; ++j) {
Dfp x = field.newDfp(j).multiply(step);
Dfp[] values = new Dfp[p.length];
for (int k = 0; k < p.length; ++k) {
values[k] = field.newDfp(p[k].value(x.getReal()));
}
interpolator.addSamplePoint(x, values);
}
for (int j = 0; j < 20; ++j) {
Dfp x = field.newDfp(j).multiply(step);
Dfp[] values = interpolator.value(x);
Assert.assertEquals(p.length, values.length);
for (int k = 0; k < p.length; ++k) {
Assert.assertEquals(p[k].value(x.getReal()),
values[k].getReal(),
1.0e-8 * FastMath.abs(p[k].value(x.getReal())));
}
}
}
}
@Test
public void testRandomPolynomialsFirstDerivative() {
Random random = new Random(0x570803c982ca5d3bl);
for (int i = 0; i < 100; ++i) {
int maxDegree = 0;
PolynomialFunction[] p = new PolynomialFunction[5];
PolynomialFunction[] pPrime = new PolynomialFunction[5];
for (int k = 0; k < p.length; ++k) {
int degree = random.nextInt(7);
p[k] = randomPolynomial(degree, random);
pPrime[k] = p[k].polynomialDerivative();
maxDegree = FastMath.max(maxDegree, degree);
}
DfpField field = new DfpField(30);
Dfp step = field.getOne().divide(field.newDfp(10));
FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<Dfp>();
for (int j = 0; j < 1 + maxDegree / 2; ++j) {
Dfp x = field.newDfp(j).multiply(step);
Dfp[] values = new Dfp[p.length];
Dfp[] derivatives = new Dfp[p.length];
for (int k = 0; k < p.length; ++k) {
values[k] = field.newDfp(p[k].value(x.getReal()));
derivatives[k] = field.newDfp(pPrime[k].value(x.getReal()));
}
interpolator.addSamplePoint(x, values, derivatives);
}
Dfp h = step.divide(field.newDfp(100000));
for (int j = 0; j < 20; ++j) {
Dfp x = field.newDfp(j).multiply(step);
Dfp[] y = interpolator.value(x);
Dfp[] yP = interpolator.value(x.add(h));
Dfp[] yM = interpolator.value(x.subtract(h));
Assert.assertEquals(p.length, y.length);
for (int k = 0; k < p.length; ++k) {
Assert.assertEquals(p[k].value(x.getReal()),
y[k].getReal(),
1.0e-8 * FastMath.abs(p[k].value(x.getReal())));
Assert.assertEquals(pPrime[k].value(x.getReal()),
yP[k].subtract(yM[k]).divide(h.multiply(2)).getReal(),
4.0e-8 * FastMath.abs(p[k].value(x.getReal())));
}
}
}
}
@Test
public void testSine() {
DfpField field = new DfpField(30);
FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<Dfp>();
for (Dfp x = field.getZero(); x.getReal() < FastMath.PI; x = x.add(0.5)) {
interpolator.addSamplePoint(x, new Dfp[] { x.sin() });
}
for (Dfp x = field.newDfp(0.1); x.getReal() < 2.9; x = x.add(0.01)) {
Dfp y = interpolator.value(x)[0];
Assert.assertEquals( x.sin().getReal(), y.getReal(), 3.5e-5);
}
}
@Test
public void testSquareRoot() {
DfpField field = new DfpField(30);
FieldHermiteInterpolator<Dfp> interpolator = new FieldHermiteInterpolator<Dfp>();
for (Dfp x = field.getOne(); x.getReal() < 3.6; x = x.add(0.5)) {
interpolator.addSamplePoint(x, new Dfp[] { x.sqrt() });
}
for (Dfp x = field.newDfp(1.1); x.getReal() < 3.5; x = x.add(0.01)) {
Dfp y = interpolator.value(x)[0];
Assert.assertEquals(x.sqrt().getReal(), y.getReal(), 1.5e-4);
}
}
@Test
public void testWikipedia() {
// this test corresponds to the example from Wikipedia page:
// http://en.wikipedia.org/wiki/Hermite_interpolation
FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();
interpolator.addSamplePoint(new BigFraction(-1),
new BigFraction[] { new BigFraction( 2) },
new BigFraction[] { new BigFraction(-8) },
new BigFraction[] { new BigFraction(56) });
interpolator.addSamplePoint(new BigFraction( 0),
new BigFraction[] { new BigFraction( 1) },
new BigFraction[] { new BigFraction( 0) },
new BigFraction[] { new BigFraction( 0) });
interpolator.addSamplePoint(new BigFraction( 1),
new BigFraction[] { new BigFraction( 2) },
new BigFraction[] { new BigFraction( 8) },
new BigFraction[] { new BigFraction(56) });
for (BigFraction x = new BigFraction(-1); x.doubleValue() <= 1.0; x = x.add(new BigFraction(1, 8))) {
BigFraction y = interpolator.value(x)[0];
BigFraction x2 = x.multiply(x);
BigFraction x4 = x2.multiply(x2);
BigFraction x8 = x4.multiply(x4);
Assert.assertEquals(x8.add(new BigFraction(1)), y);
}
}
@Test
public void testOnePointParabola() {
FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();
interpolator.addSamplePoint(new BigFraction(0),
new BigFraction[] { new BigFraction(1) },
new BigFraction[] { new BigFraction(1) },
new BigFraction[] { new BigFraction(2) });
for (BigFraction x = new BigFraction(-1); x.doubleValue() <= 1.0; x = x.add(new BigFraction(1, 8))) {
BigFraction y = interpolator.value(x)[0];
Assert.assertEquals(BigFraction.ONE.add(x.multiply(BigFraction.ONE.add(x))), y);
}
}
private PolynomialFunction randomPolynomial(int degree, Random random) {
double[] coeff = new double[ 1 + degree];
for (int j = 0; j < degree; ++j) {
coeff[j] = random.nextDouble();
}
return new PolynomialFunction(coeff);
}
@Test(expected=NoDataException.class)
public void testEmptySampleValue() {
new FieldHermiteInterpolator<BigFraction>().value(BigFraction.ZERO);
}
@Test(expected=NoDataException.class)
public void testEmptySampleDerivative() {
new FieldHermiteInterpolator<BigFraction>().derivatives(BigFraction.ZERO, 1);
}
@Test(expected=IllegalArgumentException.class)
public void testDuplicatedAbscissa() {
FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();
interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(0) });
interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(1) });
}
}