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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
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math4.geometry.euclidean.threed;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.text.NumberFormat;
import java.util.Locale;
import org.apache.commons.math4.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.MathArithmeticException;
import org.apache.commons.math4.geometry.euclidean.threed.FieldVector3D;
import org.apache.commons.math4.geometry.euclidean.threed.Cartesian3D;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.numbers.core.Precision;
import org.junit.Assert;
import org.junit.Test;
public class FieldVector3DTest {
@Test
public void testConstructors() throws DimensionMismatchException {
double cosAlpha = 1 / 2.0;
double sinAlpha = FastMath.sqrt(3) / 2.0;
double cosDelta = FastMath.sqrt(2) / 2.0;
double sinDelta = -FastMath.sqrt(2) / 2.0;
FieldVector3D<DerivativeStructure> u = new FieldVector3D<>(2,
new FieldVector3D<>(new DerivativeStructure(2, 1, 0, FastMath.PI / 3),
new DerivativeStructure(2, 1, 1, -FastMath.PI / 4)));
checkVector(u, 2 * cosAlpha * cosDelta, 2 * sinAlpha * cosDelta, 2 * sinDelta);
Assert.assertEquals(-2 * sinAlpha * cosDelta, u.getX().getPartialDerivative(1, 0), 1.0e-12);
Assert.assertEquals(+2 * cosAlpha * cosDelta, u.getY().getPartialDerivative(1, 0), 1.0e-12);
Assert.assertEquals(0, u.getZ().getPartialDerivative(1, 0), 1.0e-12);
Assert.assertEquals(-2 * cosAlpha * sinDelta, u.getX().getPartialDerivative(0, 1), 1.0e-12);
Assert.assertEquals(-2 * sinAlpha * sinDelta, u.getY().getPartialDerivative(0, 1), 1.0e-12);
Assert.assertEquals(2 * cosDelta, u.getZ().getPartialDerivative(0, 1), 1.0e-12);
checkVector(new FieldVector3D<>(2, createVector(1, 0, 0, 3)),
2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
createVector(1, 0, 0, 4)),
2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
new Cartesian3D(1, 0, 0)),
2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
checkVector(new FieldVector3D<>(2, createVector(1, 0, 0, 3),
-3, createVector(0, 0, -1, 3)),
2, 0, 3, -1, 0, 0, 0, -1, 0, 0, 0, -1);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
createVector(1, 0, 0, 4),
new DerivativeStructure(4, 1, 3, -3.0),
createVector(0, 0, -1, 4)),
2, 0, 3, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, -1);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
new Cartesian3D(1, 0, 0),
new DerivativeStructure(4, 1, 3, -3.0),
new Cartesian3D(0, 0, -1)),
2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1);
checkVector(new FieldVector3D<>(2, createVector(1, 0, 0, 3),
5, createVector(0, 1, 0, 3),
-3, createVector(0, 0, -1, 3)),
2, 5, 3, 4, 0, 0, 0, 4, 0, 0, 0, 4);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
createVector(1, 0, 0, 4),
new DerivativeStructure(4, 1, 3, 5.0),
createVector(0, 1, 0, 4),
new DerivativeStructure(4, 1, 3, -3.0),
createVector(0, 0, -1, 4)),
2, 5, 3, 4, 0, 0, 1, 0, 4, 0, 1, 0, 0, 4, -1);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
new Cartesian3D(1, 0, 0),
new DerivativeStructure(4, 1, 3, 5.0),
new Cartesian3D(0, 1, 0),
new DerivativeStructure(4, 1, 3, -3.0),
new Cartesian3D(0, 0, -1)),
2, 5, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1);
checkVector(new FieldVector3D<>(2, createVector(1, 0, 0, 3),
5, createVector(0, 1, 0, 3),
5, createVector(0, -1, 0, 3),
-3, createVector(0, 0, -1, 3)),
2, 0, 3, 9, 0, 0, 0, 9, 0, 0, 0, 9);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
createVector(1, 0, 0, 4),
new DerivativeStructure(4, 1, 3, 5.0),
createVector(0, 1, 0, 4),
new DerivativeStructure(4, 1, 3, 5.0),
createVector(0, -1, 0, 4),
new DerivativeStructure(4, 1, 3, -3.0),
createVector(0, 0, -1, 4)),
2, 0, 3, 9, 0, 0, 1, 0, 9, 0, 0, 0, 0, 9, -1);
checkVector(new FieldVector3D<>(new DerivativeStructure(4, 1, 3, 2.0),
new Cartesian3D(1, 0, 0),
new DerivativeStructure(4, 1, 3, 5.0),
new Cartesian3D(0, 1, 0),
new DerivativeStructure(4, 1, 3, 5.0),
new Cartesian3D(0, -1, 0),
new DerivativeStructure(4, 1, 3, -3.0),
new Cartesian3D(0, 0, -1)),
2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1);
checkVector(new FieldVector3D<>(new DerivativeStructure[] {
new DerivativeStructure(3, 1, 2, 2),
new DerivativeStructure(3, 1, 1, 5),
new DerivativeStructure(3, 1, 0, -3)
}),
2, 5, -3, 0, 0, 1, 0, 1, 0, 1, 0, 0);
}
@Test
public void testEquals() {
FieldVector3D<DerivativeStructure> u1 = createVector(1, 2, 3, 3);
FieldVector3D<DerivativeStructure> v = createVector(1, 2, 3 + 10 * Precision.EPSILON, 3);
Assert.assertTrue(u1.equals(u1));
Assert.assertTrue(u1.equals(new FieldVector3D<>(new DerivativeStructure(3, 1, 0, 1.0),
new DerivativeStructure(3, 1, 1, 2.0),
new DerivativeStructure(3, 1, 2, 3.0))));
Assert.assertFalse(u1.equals(new FieldVector3D<>(new DerivativeStructure(3, 1, 1.0),
new DerivativeStructure(3, 1, 1, 2.0),
new DerivativeStructure(3, 1, 2, 3.0))));
Assert.assertFalse(u1.equals(new FieldVector3D<>(new DerivativeStructure(3, 1, 0, 1.0),
new DerivativeStructure(3, 1, 2.0),
new DerivativeStructure(3, 1, 2, 3.0))));
Assert.assertFalse(u1.equals(new FieldVector3D<>(new DerivativeStructure(3, 1, 0, 1.0),
new DerivativeStructure(3, 1, 1, 2.0),
new DerivativeStructure(3, 1, 3.0))));
Assert.assertFalse(u1.equals(v));
Assert.assertFalse(u1.equals(u1.toVector3D()));
Assert.assertTrue(createVector(0, Double.NaN, 0, 3).equals(createVector(0, 0, Double.NaN, 3)));
}
@Test
public void testHash() {
Assert.assertEquals(createVector(0, Double.NaN, 0, 3).hashCode(), createVector(0, 0, Double.NaN, 3).hashCode());
FieldVector3D<DerivativeStructure> u = createVector(1, 2, 3, 3);
FieldVector3D<DerivativeStructure> v = createVector(1, 2, 3 + 10 * Precision.EPSILON, 3);
Assert.assertTrue(u.hashCode() != v.hashCode());
}
@Test
public void testInfinite() {
Assert.assertTrue(createVector(1, 1, Double.NEGATIVE_INFINITY, 3).isInfinite());
Assert.assertTrue(createVector(1, Double.NEGATIVE_INFINITY, 1, 3).isInfinite());
Assert.assertTrue(createVector(Double.NEGATIVE_INFINITY, 1, 1, 3).isInfinite());
Assert.assertFalse(createVector(1, 1, 2, 3).isInfinite());
Assert.assertFalse(createVector(1, Double.NaN, Double.NEGATIVE_INFINITY, 3).isInfinite());
}
@Test
public void testNaN() {
Assert.assertTrue(createVector(1, 1, Double.NaN, 3).isNaN());
Assert.assertTrue(createVector(1, Double.NaN, 1, 3).isNaN());
Assert.assertTrue(createVector(Double.NaN, 1, 1, 3).isNaN());
Assert.assertFalse(createVector(1, 1, 2, 3).isNaN());
Assert.assertFalse(createVector(1, 1, Double.NEGATIVE_INFINITY, 3).isNaN());
}
@Test
public void testToString() {
Assert.assertEquals("{3; 2; 1}", createVector(3, 2, 1, 3).toString());
NumberFormat format = new DecimalFormat("0.000", new DecimalFormatSymbols(Locale.US));
Assert.assertEquals("{3.000; 2.000; 1.000}", createVector(3, 2, 1, 3).toString(format));
}
@Test(expected=DimensionMismatchException.class)
public void testWrongDimension() throws DimensionMismatchException {
new FieldVector3D<>(new DerivativeStructure[] {
new DerivativeStructure(3, 1, 0, 2),
new DerivativeStructure(3, 1, 0, 5)
});
}
@Test
public void testCoordinates() {
FieldVector3D<DerivativeStructure> v = createVector(1, 2, 3, 3);
Assert.assertTrue(FastMath.abs(v.getX().getReal() - 1) < 1.0e-12);
Assert.assertTrue(FastMath.abs(v.getY().getReal() - 2) < 1.0e-12);
Assert.assertTrue(FastMath.abs(v.getZ().getReal() - 3) < 1.0e-12);
DerivativeStructure[] coordinates = v.toArray();
Assert.assertTrue(FastMath.abs(coordinates[0].getReal() - 1) < 1.0e-12);
Assert.assertTrue(FastMath.abs(coordinates[1].getReal() - 2) < 1.0e-12);
Assert.assertTrue(FastMath.abs(coordinates[2].getReal() - 3) < 1.0e-12);
}
@Test
public void testNorm1() {
Assert.assertEquals( 0.0, createVector(0, 0, 0, 3).getNorm1().getReal(), 0);
Assert.assertEquals( 6.0, createVector(1, -2, 3, 3).getNorm1().getReal(), 0);
Assert.assertEquals( 1.0, createVector(1, -2, 3, 3).getNorm1().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals(-1.0, createVector(1, -2, 3, 3).getNorm1().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 1.0, createVector(1, -2, 3, 3).getNorm1().getPartialDerivative(0, 0, 1), 0);
}
@Test
public void testNorm() {
double r = FastMath.sqrt(14);
Assert.assertEquals(0.0, createVector(0, 0, 0, 3).getNorm().getReal(), 0);
Assert.assertEquals(r, createVector(1, 2, 3, 3).getNorm().getReal(), 1.0e-12);
Assert.assertEquals( 1.0 / r, createVector(1, 2, 3, 3).getNorm().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals( 2.0 / r, createVector(1, 2, 3, 3).getNorm().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 3.0 / r, createVector(1, 2, 3, 3).getNorm().getPartialDerivative(0, 0, 1), 0);
}
@Test
public void testNormSq() {
Assert.assertEquals(0.0, createVector(0, 0, 0, 3).getNormSq().getReal(), 0);
Assert.assertEquals(14, createVector(1, 2, 3, 3).getNormSq().getReal(), 1.0e-12);
Assert.assertEquals( 2, createVector(1, 2, 3, 3).getNormSq().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals( 4, createVector(1, 2, 3, 3).getNormSq().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 6, createVector(1, 2, 3, 3).getNormSq().getPartialDerivative(0, 0, 1), 0);
}
@Test
public void testNormInf() {
Assert.assertEquals( 0.0, createVector(0, 0, 0, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 3.0, createVector(1, -2, 3, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 0.0, createVector(1, -2, 3, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals( 0.0, createVector(1, -2, 3, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 1.0, createVector(1, -2, 3, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
Assert.assertEquals( 3.0, createVector(2, -1, 3, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 0.0, createVector(2, -1, 3, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals( 0.0, createVector(2, -1, 3, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 1.0, createVector(2, -1, 3, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
Assert.assertEquals( 3.0, createVector(1, -3, 2, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 0.0, createVector(1, -3, 2, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals(-1.0, createVector(1, -3, 2, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 0.0, createVector(1, -3, 2, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
Assert.assertEquals( 3.0, createVector(2, -3, 1, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 0.0, createVector(2, -3, 1, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals(-1.0, createVector(2, -3, 1, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 0.0, createVector(2, -3, 1, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
Assert.assertEquals( 3.0, createVector(3, -1, 2, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 1.0, createVector(3, -1, 2, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals( 0.0, createVector(3, -1, 2, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 0.0, createVector(3, -1, 2, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
Assert.assertEquals( 3.0, createVector(3, -2, 1, 3).getNormInf().getReal(), 0);
Assert.assertEquals( 1.0, createVector(3, -2, 1, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
Assert.assertEquals( 0.0, createVector(3, -2, 1, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
Assert.assertEquals( 0.0, createVector(3, -2, 1, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
}
@Test
public void testDistance1() {
FieldVector3D<DerivativeStructure> v1 = createVector(1, -2, 3, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(-4, 2, 0, 3);
Assert.assertEquals(0.0, FieldVector3D.distance1(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
DerivativeStructure distance = FieldVector3D.distance1(v1, v2);
Assert.assertEquals(12.0, distance.getReal(), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
distance = FieldVector3D.distance1(v1, new Cartesian3D(-4, 2, 0));
Assert.assertEquals(12.0, distance.getReal(), 1.0e-12);
Assert.assertEquals( 1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(-1, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals( 1, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
distance = FieldVector3D.distance1(new Cartesian3D(-4, 2, 0), v1);
Assert.assertEquals(12.0, distance.getReal(), 1.0e-12);
Assert.assertEquals( 1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(-1, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals( 1, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
}
@Test
public void testDistance() {
FieldVector3D<DerivativeStructure> v1 = createVector(1, -2, 3, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(-4, 2, 0, 3);
Assert.assertEquals(0.0, FieldVector3D.distance(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
DerivativeStructure distance = FieldVector3D.distance(v1, v2);
Assert.assertEquals(FastMath.sqrt(50), distance.getReal(), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
distance = FieldVector3D.distance(v1, new Cartesian3D(-4, 2, 0));
Assert.assertEquals(FastMath.sqrt(50), distance.getReal(), 1.0e-12);
Assert.assertEquals( 5 / FastMath.sqrt(50), distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(-4 / FastMath.sqrt(50), distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals( 3 / FastMath.sqrt(50), distance.getPartialDerivative(0, 0, 1), 1.0e-12);
distance = FieldVector3D.distance(new Cartesian3D(-4, 2, 0), v1);
Assert.assertEquals(FastMath.sqrt(50), distance.getReal(), 1.0e-12);
Assert.assertEquals( 5 / FastMath.sqrt(50), distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(-4 / FastMath.sqrt(50), distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals( 3 / FastMath.sqrt(50), distance.getPartialDerivative(0, 0, 1), 1.0e-12);
}
@Test
public void testDistanceSq() {
FieldVector3D<DerivativeStructure> v1 = createVector(1, -2, 3, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(-4, 2, 0, 3);
Assert.assertEquals(0.0, FieldVector3D.distanceSq(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
DerivativeStructure distanceSq = FieldVector3D.distanceSq(v1, v2);
Assert.assertEquals(50.0, distanceSq.getReal(), 1.0e-12);
Assert.assertEquals(0, distanceSq.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(0, distanceSq.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(0, distanceSq.getPartialDerivative(0, 0, 1), 1.0e-12);
distanceSq = FieldVector3D.distanceSq(v1, new Cartesian3D(-4, 2, 0));
Assert.assertEquals(50.0, distanceSq.getReal(), 1.0e-12);
Assert.assertEquals(10, distanceSq.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(-8, distanceSq.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals( 6, distanceSq.getPartialDerivative(0, 0, 1), 1.0e-12);
distanceSq = FieldVector3D.distanceSq(new Cartesian3D(-4, 2, 0), v1);
Assert.assertEquals(50.0, distanceSq.getReal(), 1.0e-12);
Assert.assertEquals(10, distanceSq.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(-8, distanceSq.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals( 6, distanceSq.getPartialDerivative(0, 0, 1), 1.0e-12);
}
@Test
public void testDistanceInf() {
FieldVector3D<DerivativeStructure> v1 = createVector(1, -2, 3, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(-4, 2, 0, 3);
Assert.assertEquals(0.0, FieldVector3D.distanceInf(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
DerivativeStructure distance = FieldVector3D.distanceInf(v1, v2);
Assert.assertEquals(5.0, distance.getReal(), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
distance = FieldVector3D.distanceInf(v1, new Cartesian3D(-4, 2, 0));
Assert.assertEquals(5.0, distance.getReal(), 1.0e-12);
Assert.assertEquals(1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
distance = FieldVector3D.distanceInf(new Cartesian3D(-4, 2, 0), v1);
Assert.assertEquals(5.0, distance.getReal(), 1.0e-12);
Assert.assertEquals(1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
Assert.assertEquals(v1.subtract(v2).getNormInf().getReal(), FieldVector3D.distanceInf(v1, v2).getReal(), 1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector( 1, -2, 3, 3), createVector(-4, 2, 0, 3)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector( 1, 3, -2, 3), createVector(-4, 0, 2, 3)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(-2, 1, 3, 3), createVector( 2, -4, 0, 3)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(-2, 3, 1, 3), createVector( 2, 0, -4, 3)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(3, -2, 1, 3), createVector(0, 2, -4, 3)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(3, 1, -2, 3), createVector(0, -4, 2, 3)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector( 1, -2, 3, 3), new Cartesian3D(-4, 2, 0)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector( 1, 3, -2, 3), new Cartesian3D(-4, 0, 2)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(-2, 1, 3, 3), new Cartesian3D( 2, -4, 0)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(-2, 3, 1, 3), new Cartesian3D( 2, 0, -4)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(3, -2, 1, 3), new Cartesian3D(0, 2, -4)).getReal(),
1.0e-12);
Assert.assertEquals(5.0,
FieldVector3D.distanceInf(createVector(3, 1, -2, 3), new Cartesian3D(0, -4, 2)).getReal(),
1.0e-12);
}
@Test
public void testSubtract() {
FieldVector3D<DerivativeStructure> v1 = createVector(1, 2, 3, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(-3, -2, -1, 3);
v1 = v1.subtract(v2);
checkVector(v1, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0);
checkVector(v2.subtract(v1), -7, -6, -5, 1, 0, 0, 0, 1, 0, 0, 0, 1);
checkVector(v2.subtract(new Cartesian3D(4, 4, 4)), -7, -6, -5, 1, 0, 0, 0, 1, 0, 0, 0, 1);
checkVector(v2.subtract(3, v1), -15, -14, -13, 1, 0, 0, 0, 1, 0, 0, 0, 1);
checkVector(v2.subtract(3, new Cartesian3D(4, 4, 4)), -15, -14, -13, 1, 0, 0, 0, 1, 0, 0, 0, 1);
checkVector(v2.subtract(new DerivativeStructure(3, 1, 2, 3), new Cartesian3D(4, 4, 4)),
-15, -14, -13, 1, 0, -4, 0, 1, -4, 0, 0, -3);
checkVector(createVector(1, 2, 3, 4).subtract(new DerivativeStructure(4, 1, 3, 5.0),
createVector(3, -2, 1, 4)),
-14, 12, -2,
-4, 0, 0, -3,
0, -4, 0, 2,
0, 0, -4, -1);
}
@Test
public void testAdd() {
FieldVector3D<DerivativeStructure> v1 = createVector(1, 2, 3, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(-3, -2, -1, 3);
v1 = v1.add(v2);
checkVector(v1, -2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2);
checkVector(v2.add(v1), -5, -2, 1, 3, 0, 0, 0, 3, 0, 0, 0, 3);
checkVector(v2.add(new Cartesian3D(-2, 0, 2)), -5, -2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1);
checkVector(v2.add(3, v1), -9, -2, 5, 7, 0, 0, 0, 7, 0, 0, 0, 7);
checkVector(v2.add(3, new Cartesian3D(-2, 0, 2)), -9, -2, 5, 1, 0, 0, 0, 1, 0, 0, 0, 1);
checkVector(v2.add(new DerivativeStructure(3, 1, 2, 3), new Cartesian3D(-2, 0, 2)),
-9, -2, 5, 1, 0, -2, 0, 1, 0, 0, 0, 3);
checkVector(createVector(1, 2, 3, 4).add(new DerivativeStructure(4, 1, 3, 5.0),
createVector(3, -2, 1, 4)),
16, -8, 8,
6, 0, 0, 3,
0, 6, 0, -2,
0, 0, 6, 1);
}
@Test
public void testScalarProduct() {
FieldVector3D<DerivativeStructure> v = createVector(1, 2, 3, 3);
v = v.scalarMultiply(3);
checkVector(v, 3, 6, 9);
checkVector(v.scalarMultiply(0.5), 1.5, 3, 4.5);
}
@Test
public void testVectorialProducts() {
FieldVector3D<DerivativeStructure> v1 = createVector(2, 1, -4, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(3, 1, -1, 3);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v2).getReal() - 11) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v2.toVector3D()).getReal() - 11) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1.toVector3D(), v2).getReal() - 11) < 1.0e-12);
FieldVector3D<DerivativeStructure> v3 = FieldVector3D.crossProduct(v1, v2);
checkVector(v3, 3, -10, -1);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v3).getReal()) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v2, v3).getReal()) < 1.0e-12);
v3 = FieldVector3D.crossProduct(v1, v2.toVector3D());
checkVector(v3, 3, -10, -1);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v3).getReal()) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v2, v3).getReal()) < 1.0e-12);
v3 = FieldVector3D.crossProduct(v1.toVector3D(), v2);
checkVector(v3, 3, -10, -1);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v3).getReal()) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v2, v3).getReal()) < 1.0e-12);
}
@Test
public void testCrossProductCancellation() {
FieldVector3D<DerivativeStructure> v1 = createVector(9070467121.0, 4535233560.0, 1, 3);
FieldVector3D<DerivativeStructure> v2 = createVector(9070467123.0, 4535233561.0, 1, 3);
checkVector(FieldVector3D.crossProduct(v1, v2), -1, 2, 1);
double scale = FastMath.scalb(1.0, 100);
FieldVector3D<DerivativeStructure> big1 = new FieldVector3D<>(scale, v1);
FieldVector3D<DerivativeStructure> small2 = new FieldVector3D<>(1 / scale, v2);
checkVector(FieldVector3D.crossProduct(big1, small2), -1, 2, 1);
}
@Test
public void testAngular() {
Assert.assertEquals(0, createVector(1, 0, 0, 3).getAlpha().getReal(), 1.0e-10);
Assert.assertEquals(0, createVector(1, 0, 0, 3).getDelta().getReal(), 1.0e-10);
Assert.assertEquals(FastMath.PI / 2, createVector(0, 1, 0, 3).getAlpha().getReal(), 1.0e-10);
Assert.assertEquals(0, createVector(0, 1, 0, 3).getDelta().getReal(), 1.0e-10);
Assert.assertEquals(FastMath.PI / 2, createVector(0, 0, 1, 3).getDelta().getReal(), 1.0e-10);
FieldVector3D<DerivativeStructure> u = createVector(-1, 1, -1, 3);
Assert.assertEquals(3 * FastMath.PI /4, u.getAlpha().getReal(), 1.0e-10);
Assert.assertEquals(-1.0 / FastMath.sqrt(3), u.getDelta().sin().getReal(), 1.0e-10);
}
@Test
public void testAngularSeparation() throws MathArithmeticException {
FieldVector3D<DerivativeStructure> v1 = createVector(2, -1, 4, 3);
FieldVector3D<DerivativeStructure> k = v1.normalize();
FieldVector3D<DerivativeStructure> i = k.orthogonal();
FieldVector3D<DerivativeStructure> v2 = k.scalarMultiply(FastMath.cos(1.2)).add(i.scalarMultiply(FastMath.sin(1.2)));
Assert.assertTrue(FastMath.abs(FieldVector3D.angle(v1, v2).getReal() - 1.2) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.angle(v1, v2.toVector3D()).getReal() - 1.2) < 1.0e-12);
Assert.assertTrue(FastMath.abs(FieldVector3D.angle(v1.toVector3D(), v2).getReal() - 1.2) < 1.0e-12);
try {
FieldVector3D.angle(v1, Cartesian3D.ZERO);
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException mae) {
// expected
}
Assert.assertEquals(0.0, FieldVector3D.angle(v1, v1.toVector3D()).getReal(), 1.0e-15);
Assert.assertEquals(FastMath.PI, FieldVector3D.angle(v1, v1.negate().toVector3D()).getReal(), 1.0e-15);
}
@Test
public void testNormalize() throws MathArithmeticException {
Assert.assertEquals(1.0, createVector(5, -4, 2, 3).normalize().getNorm().getReal(), 1.0e-12);
try {
createVector(0, 0, 0, 3).normalize();
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException ae) {
// expected behavior
}
}
@Test
public void testNegate() {
checkVector(createVector(0.1, 2.5, 1.3, 3).negate(),
-0.1, -2.5, -1.3, -1, 0, 0, 0, -1, 0, 0, 0, -1);
}
@Test
public void testOrthogonal() throws MathArithmeticException {
FieldVector3D<DerivativeStructure> v1 = createVector(0.1, 2.5, 1.3, 3);
Assert.assertEquals(0.0, FieldVector3D.dotProduct(v1, v1.orthogonal()).getReal(), 1.0e-12);
FieldVector3D<DerivativeStructure> v2 = createVector(2.3, -0.003, 7.6, 3);
Assert.assertEquals(0.0, FieldVector3D.dotProduct(v2, v2.orthogonal()).getReal(), 1.0e-12);
FieldVector3D<DerivativeStructure> v3 = createVector(-1.7, 1.4, 0.2, 3);
Assert.assertEquals(0.0, FieldVector3D.dotProduct(v3, v3.orthogonal()).getReal(), 1.0e-12);
FieldVector3D<DerivativeStructure> v4 = createVector(4.2, 0.1, -1.8, 3);
Assert.assertEquals(0.0, FieldVector3D.dotProduct(v4, v4.orthogonal()).getReal(), 1.0e-12);
try {
createVector(0, 0, 0, 3).orthogonal();
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException ae) {
// expected behavior
}
}
@Test
public void testAngle() throws MathArithmeticException {
Assert.assertEquals(0.22572612855273393616,
FieldVector3D.angle(createVector(1, 2, 3, 3), createVector(4, 5, 6, 3)).getReal(),
1.0e-12);
Assert.assertEquals(7.98595620686106654517199e-8,
FieldVector3D.angle(createVector(1, 2, 3, 3), createVector(2, 4, 6.000001, 3)).getReal(),
1.0e-12);
Assert.assertEquals(3.14159257373023116985197793156,
FieldVector3D.angle(createVector(1, 2, 3, 3), createVector(-2, -4, -6.000001, 3)).getReal(),
1.0e-12);
try {
FieldVector3D.angle(createVector(0, 0, 0, 3), createVector(1, 0, 0, 3));
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException ae) {
// expected behavior
}
}
@Test
public void testAccurateDotProduct() {
// the following two vectors are nearly but not exactly orthogonal
// naive dot product (i.e. computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z
// leads to a result of 0.0, instead of the correct -1.855129...
FieldVector3D<DerivativeStructure> u1 = createVector(-1321008684645961.0 / 268435456.0,
-5774608829631843.0 / 268435456.0,
-7645843051051357.0 / 8589934592.0, 3);
FieldVector3D<DerivativeStructure> u2 = createVector(-5712344449280879.0 / 2097152.0,
-4550117129121957.0 / 2097152.0,
8846951984510141.0 / 131072.0, 3);
DerivativeStructure sNaive = u1.getX().multiply(u2.getX()).add(u1.getY().multiply(u2.getY())).add(u1.getZ().multiply(u2.getZ()));
DerivativeStructure sAccurate = FieldVector3D.dotProduct(u1, u2);
Assert.assertEquals(0.0, sNaive.getReal(), 1.0e-30);
Assert.assertEquals(-2088690039198397.0 / 1125899906842624.0, sAccurate.getReal(), 1.0e-15);
}
@Test
public void testDotProduct() {
// we compare accurate versus naive dot product implementations
// on regular vectors (i.e. not extreme cases like in the previous test)
UniformRandomProvider random = RandomSource.create(RandomSource.WELL_1024_A, 553267312521321237l);
for (int i = 0; i < 10000; ++i) {
double ux = 10000 * random.nextDouble();
double uy = 10000 * random.nextDouble();
double uz = 10000 * random.nextDouble();
double vx = 10000 * random.nextDouble();
double vy = 10000 * random.nextDouble();
double vz = 10000 * random.nextDouble();
double sNaive = ux * vx + uy * vy + uz * vz;
FieldVector3D<DerivativeStructure> uds = createVector(ux, uy, uz, 3);
FieldVector3D<DerivativeStructure> vds = createVector(vx, vy, vz, 3);
Cartesian3D v = new Cartesian3D(vx, vy, vz);
DerivativeStructure sAccurate = FieldVector3D.dotProduct(uds, vds);
Assert.assertEquals(sNaive, sAccurate.getReal(), 2.5e-16 * sNaive);
Assert.assertEquals(ux + vx, sAccurate.getPartialDerivative(1, 0, 0), 2.5e-16 * sNaive);
Assert.assertEquals(uy + vy, sAccurate.getPartialDerivative(0, 1, 0), 2.5e-16 * sNaive);
Assert.assertEquals(uz + vz, sAccurate.getPartialDerivative(0, 0, 1), 2.5e-16 * sNaive);
sAccurate = FieldVector3D.dotProduct(uds, v);
Assert.assertEquals(sNaive, sAccurate.getReal(), 2.5e-16 * sNaive);
Assert.assertEquals(vx, sAccurate.getPartialDerivative(1, 0, 0), 2.5e-16 * sNaive);
Assert.assertEquals(vy, sAccurate.getPartialDerivative(0, 1, 0), 2.5e-16 * sNaive);
Assert.assertEquals(vz, sAccurate.getPartialDerivative(0, 0, 1), 2.5e-16 * sNaive);
}
}
@Test
public void testAccurateCrossProduct() {
// the vectors u1 and u2 are nearly but not exactly anti-parallel
// (7.31e-16 degrees from 180 degrees) naive cross product (i.e.
// computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z
// leads to a result of [0.0009765, -0.0001220, -0.0039062],
// instead of the correct [0.0006913, -0.0001254, -0.0007909]
final FieldVector3D<DerivativeStructure> u1 = createVector(-1321008684645961.0 / 268435456.0,
-5774608829631843.0 / 268435456.0,
-7645843051051357.0 / 8589934592.0, 3);
final FieldVector3D<DerivativeStructure> u2 = createVector( 1796571811118507.0 / 2147483648.0,
7853468008299307.0 / 2147483648.0,
2599586637357461.0 / 17179869184.0, 3);
final FieldVector3D<DerivativeStructure> u3 = createVector(12753243807587107.0 / 18446744073709551616.0,
-2313766922703915.0 / 18446744073709551616.0,
-227970081415313.0 / 288230376151711744.0, 3);
FieldVector3D<DerivativeStructure> cNaive = new FieldVector3D<>(u1.getY().multiply(u2.getZ()).subtract(u1.getZ().multiply(u2.getY())),
u1.getZ().multiply(u2.getX()).subtract(u1.getX().multiply(u2.getZ())),
u1.getX().multiply(u2.getY()).subtract(u1.getY().multiply(u2.getX())));
FieldVector3D<DerivativeStructure> cAccurate = FieldVector3D.crossProduct(u1, u2);
Assert.assertTrue(FieldVector3D.distance(u3, cNaive).getReal() > 2.9 * u3.getNorm().getReal());
Assert.assertEquals(0.0, FieldVector3D.distance(u3, cAccurate).getReal(), 1.0e-30 * cAccurate.getNorm().getReal());
}
@Test
public void testCrossProduct() {
// we compare accurate versus naive cross product implementations
// on regular vectors (i.e. not extreme cases like in the previous test)
UniformRandomProvider random = RandomSource.create(RandomSource.WELL_1024_A, 885362227452043214l);
for (int i = 0; i < 10000; ++i) {
double ux = random.nextDouble();
double uy = random.nextDouble();
double uz = random.nextDouble();
double vx = random.nextDouble();
double vy = random.nextDouble();
double vz = random.nextDouble();
Cartesian3D cNaive = new Cartesian3D(uy * vz - uz * vy, uz * vx - ux * vz, ux * vy - uy * vx);
FieldVector3D<DerivativeStructure> uds = createVector(ux, uy, uz, 3);
FieldVector3D<DerivativeStructure> vds = createVector(vx, vy, vz, 3);
Cartesian3D v = new Cartesian3D(vx, vy, vz);
checkVector(FieldVector3D.crossProduct(uds, vds),
cNaive.getX(), cNaive.getY(), cNaive.getZ(),
0, vz - uz, uy - vy,
uz - vz, 0, vx - ux,
vy - uy, ux - vx, 0);
checkVector(FieldVector3D.crossProduct(uds, v),
cNaive.getX(), cNaive.getY(), cNaive.getZ(),
0, vz, -vy,
-vz, 0, vx,
vy, -vx, 0);
}
}
private FieldVector3D<DerivativeStructure> createVector(double x, double y, double z, int params) {
return new FieldVector3D<>(new DerivativeStructure(params, 1, 0, x),
new DerivativeStructure(params, 1, 1, y),
new DerivativeStructure(params, 1, 2, z));
}
private void checkVector(FieldVector3D<DerivativeStructure> v, double x, double y, double z) {
Assert.assertEquals(x, v.getX().getReal(), 1.0e-12);
Assert.assertEquals(y, v.getY().getReal(), 1.0e-12);
Assert.assertEquals(z, v.getZ().getReal(), 1.0e-12);
}
private void checkVector(FieldVector3D<DerivativeStructure> v, double x, double y, double z,
double dxdx, double dxdy, double dxdz,
double dydx, double dydy, double dydz,
double dzdx, double dzdy, double dzdz) {
Assert.assertEquals(x, v.getX().getReal(), 1.0e-12);
Assert.assertEquals(y, v.getY().getReal(), 1.0e-12);
Assert.assertEquals(z, v.getZ().getReal(), 1.0e-12);
Assert.assertEquals(dxdx, v.getX().getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(dxdy, v.getX().getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(dxdz, v.getX().getPartialDerivative(0, 0, 1), 1.0e-12);
Assert.assertEquals(dydx, v.getY().getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(dydy, v.getY().getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(dydz, v.getY().getPartialDerivative(0, 0, 1), 1.0e-12);
Assert.assertEquals(dzdx, v.getZ().getPartialDerivative(1, 0, 0), 1.0e-12);
Assert.assertEquals(dzdy, v.getZ().getPartialDerivative(0, 1, 0), 1.0e-12);
Assert.assertEquals(dzdz, v.getZ().getPartialDerivative(0, 0, 1), 1.0e-12);
}
private void checkVector(FieldVector3D<DerivativeStructure> v, double x, double y, double z,
double dxdx, double dxdy, double dxdz, double dxdt,
double dydx, double dydy, double dydz, double dydt,
double dzdx, double dzdy, double dzdz, double dzdt) {
Assert.assertEquals(x, v.getX().getReal(), 1.0e-12);
Assert.assertEquals(y, v.getY().getReal(), 1.0e-12);
Assert.assertEquals(z, v.getZ().getReal(), 1.0e-12);
Assert.assertEquals(dxdx, v.getX().getPartialDerivative(1, 0, 0, 0), 1.0e-12);
Assert.assertEquals(dxdy, v.getX().getPartialDerivative(0, 1, 0, 0), 1.0e-12);
Assert.assertEquals(dxdz, v.getX().getPartialDerivative(0, 0, 1, 0), 1.0e-12);
Assert.assertEquals(dxdt, v.getX().getPartialDerivative(0, 0, 0, 1), 1.0e-12);
Assert.assertEquals(dydx, v.getY().getPartialDerivative(1, 0, 0, 0), 1.0e-12);
Assert.assertEquals(dydy, v.getY().getPartialDerivative(0, 1, 0, 0), 1.0e-12);
Assert.assertEquals(dydz, v.getY().getPartialDerivative(0, 0, 1, 0), 1.0e-12);
Assert.assertEquals(dydt, v.getY().getPartialDerivative(0, 0, 0, 1), 1.0e-12);
Assert.assertEquals(dzdx, v.getZ().getPartialDerivative(1, 0, 0, 0), 1.0e-12);
Assert.assertEquals(dzdy, v.getZ().getPartialDerivative(0, 1, 0, 0), 1.0e-12);
Assert.assertEquals(dzdz, v.getZ().getPartialDerivative(0, 0, 1, 0), 1.0e-12);
Assert.assertEquals(dzdt, v.getZ().getPartialDerivative(0, 0, 0, 1), 1.0e-12);
}
}