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* http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math4.analysis.interpolation;
import java.util.Random;
import org.apache.commons.math4.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math4.analysis.interpolation.HermiteInterpolator;
import org.apache.commons.math4.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.exception.NoDataException;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class HermiteInterpolatorTest {
@Test
public void testZero() {
HermiteInterpolator interpolator = new HermiteInterpolator();
interpolator.addSamplePoint(0.0, new double[] { 0.0 });
for (double x = -10; x < 10; x += 1.0) {
DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
Assert.assertEquals(0.0, y.getValue(), 1.0e-15);
Assert.assertEquals(0.0, y.getPartialDerivative(1), 1.0e-15);
}
checkPolynomial(new PolynomialFunction(new double[] { 0.0 }),
interpolator.getPolynomials()[0]);
}
@Test
public void testQuadratic() {
HermiteInterpolator interpolator = new HermiteInterpolator();
interpolator.addSamplePoint(0.0, new double[] { 2.0 });
interpolator.addSamplePoint(1.0, new double[] { 0.0 });
interpolator.addSamplePoint(2.0, new double[] { 0.0 });
for (double x = -10; x < 10; x += 1.0) {
DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
Assert.assertEquals((x - 1.0) * (x - 2.0), y.getValue(), 1.0e-15);
Assert.assertEquals(2 * x - 3.0, y.getPartialDerivative(1), 1.0e-15);
}
checkPolynomial(new PolynomialFunction(new double[] { 2.0, -3.0, 1.0 }),
interpolator.getPolynomials()[0]);
}
@Test
public void testMixedDerivatives() {
HermiteInterpolator interpolator = new HermiteInterpolator();
interpolator.addSamplePoint(0.0, new double[] { 1.0 }, new double[] { 2.0 });
interpolator.addSamplePoint(1.0, new double[] { 4.0 });
interpolator.addSamplePoint(2.0, new double[] { 5.0 }, new double[] { 2.0 });
Assert.assertEquals(4, interpolator.getPolynomials()[0].degree());
DerivativeStructure y0 = interpolator.value(new DerivativeStructure(1, 1, 0, 0.0))[0];
Assert.assertEquals(1.0, y0.getValue(), 1.0e-15);
Assert.assertEquals(2.0, y0.getPartialDerivative(1), 1.0e-15);
Assert.assertEquals(4.0, interpolator.value(1.0)[0], 1.0e-15);
DerivativeStructure y2 = interpolator.value(new DerivativeStructure(1, 1, 0, 2.0))[0];
Assert.assertEquals(5.0, y2.getValue(), 1.0e-15);
Assert.assertEquals(2.0, y2.getPartialDerivative(1), 1.0e-15);
checkPolynomial(new PolynomialFunction(new double[] { 1.0, 2.0, 4.0, -4.0, 1.0 }),
interpolator.getPolynomials()[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);
}
HermiteInterpolator interpolator = new HermiteInterpolator();
for (int j = 0; j < 1 + maxDegree; ++j) {
double x = 0.1 * j;
double[] values = new double[p.length];
for (int k = 0; k < p.length; ++k) {
values[k] = p[k].value(x);
}
interpolator.addSamplePoint(x, values);
}
for (double x = 0; x < 2; x += 0.1) {
double[] values = interpolator.value(x);
Assert.assertEquals(p.length, values.length);
for (int k = 0; k < p.length; ++k) {
Assert.assertEquals(p[k].value(x), values[k], 1.0e-8 * FastMath.abs(p[k].value(x)));
}
}
PolynomialFunction[] result = interpolator.getPolynomials();
for (int k = 0; k < p.length; ++k) {
checkPolynomial(p[k], result[k]);
}
}
}
@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);
}
HermiteInterpolator interpolator = new HermiteInterpolator();
for (int j = 0; j < 1 + maxDegree / 2; ++j) {
double x = 0.1 * j;
double[] values = new double[p.length];
double[] derivatives = new double[p.length];
for (int k = 0; k < p.length; ++k) {
values[k] = p[k].value(x);
derivatives[k] = pPrime[k].value(x);
}
interpolator.addSamplePoint(x, values, derivatives);
}
for (double x = 0; x < 2; x += 0.1) {
DerivativeStructure[] y = interpolator.value(new DerivativeStructure(1, 1, 0, x));
Assert.assertEquals(p.length, y.length);
for (int k = 0; k < p.length; ++k) {
Assert.assertEquals(p[k].value(x), y[k].getValue(), 1.0e-8 * FastMath.abs(p[k].value(x)));
Assert.assertEquals(pPrime[k].value(x), y[k].getPartialDerivative(1), 4.0e-8 * FastMath.abs(p[k].value(x)));
}
}
PolynomialFunction[] result = interpolator.getPolynomials();
for (int k = 0; k < p.length; ++k) {
checkPolynomial(p[k], result[k]);
}
}
}
@Test
public void testSine() {
HermiteInterpolator interpolator = new HermiteInterpolator();
for (double x = 0; x < FastMath.PI; x += 0.5) {
interpolator.addSamplePoint(x, new double[] { FastMath.sin(x) });
}
for (double x = 0.1; x <= 2.9; x += 0.01) {
DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 2, 0, x))[0];
Assert.assertEquals( FastMath.sin(x), y.getValue(), 3.5e-5);
Assert.assertEquals( FastMath.cos(x), y.getPartialDerivative(1), 1.3e-4);
Assert.assertEquals(-FastMath.sin(x), y.getPartialDerivative(2), 2.9e-3);
}
}
@Test
public void testSquareRoot() {
HermiteInterpolator interpolator = new HermiteInterpolator();
for (double x = 1.0; x < 3.6; x += 0.5) {
interpolator.addSamplePoint(x, new double[] { FastMath.sqrt(x) });
}
for (double x = 1.1; x < 3.5; x += 0.01) {
DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
Assert.assertEquals(FastMath.sqrt(x), y.getValue(), 1.5e-4);
Assert.assertEquals(0.5 / FastMath.sqrt(x), y.getPartialDerivative(1), 8.5e-4);
}
}
@Test
public void testWikipedia() {
// this test corresponds to the example from Wikipedia page:
// http://en.wikipedia.org/wiki/Hermite_interpolation
HermiteInterpolator interpolator = new HermiteInterpolator();
interpolator.addSamplePoint(-1, new double[] { 2 }, new double[] { -8 }, new double[] { 56 });
interpolator.addSamplePoint( 0, new double[] { 1 }, new double[] { 0 }, new double[] { 0 });
interpolator.addSamplePoint( 1, new double[] { 2 }, new double[] { 8 }, new double[] { 56 });
for (double x = -1.0; x <= 1.0; x += 0.125) {
DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
double x2 = x * x;
double x4 = x2 * x2;
double x8 = x4 * x4;
Assert.assertEquals(x8 + 1, y.getValue(), 1.0e-15);
Assert.assertEquals(8 * x4 * x2 * x, y.getPartialDerivative(1), 1.0e-15);
}
checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 0, 0, 0, 0, 0, 0, 1 }),
interpolator.getPolynomials()[0]);
}
@Test
public void testOnePointParabola() {
HermiteInterpolator interpolator = new HermiteInterpolator();
interpolator.addSamplePoint(0, new double[] { 1 }, new double[] { 1 }, new double[] { 2 });
for (double x = -1.0; x <= 1.0; x += 0.125) {
DerivativeStructure y = interpolator.value(new DerivativeStructure(1, 1, 0, x))[0];
Assert.assertEquals(1 + x * (1 + x), y.getValue(), 1.0e-15);
Assert.assertEquals(1 + 2 * x, y.getPartialDerivative(1), 1.0e-15);
}
checkPolynomial(new PolynomialFunction(new double[] { 1, 1, 1 }),
interpolator.getPolynomials()[0]);
}
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 testEmptySample() {
new HermiteInterpolator().value(0.0);
}
@Test(expected=MathIllegalArgumentException.class)
public void testDuplicatedAbscissa() {
HermiteInterpolator interpolator = new HermiteInterpolator();
interpolator.addSamplePoint(1.0, new double[] { 0.0 });
interpolator.addSamplePoint(1.0, new double[] { 1.0 });
}
private void checkPolynomial(PolynomialFunction expected, PolynomialFunction result) {
Assert.assertTrue(result.degree() >= expected.degree());
double[] cE = expected.getCoefficients();
double[] cR = result.getCoefficients();
for (int i = 0; i < cE.length; ++i) {
Assert.assertEquals(cE[i], cR[i], 1.0e-8 * FastMath.abs(cE[i]));
}
for (int i = cE.length; i < cR.length; ++i) {
Assert.assertEquals(0.0, cR[i], 1.0e-9);
}
}
}