| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * 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 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math3.complex; |
| |
| import java.util.Random; |
| import org.apache.commons.math3.complex.Quaternion; |
| import org.apache.commons.math3.exception.DimensionMismatchException; |
| import org.apache.commons.math3.exception.ZeroException; |
| import org.apache.commons.math3.geometry.euclidean.threed.Rotation; |
| import org.apache.commons.math3.geometry.euclidean.threed.RotationConvention; |
| import org.apache.commons.math3.geometry.euclidean.threed.Vector3D; |
| import org.apache.commons.math3.util.FastMath; |
| import org.junit.Test; |
| import org.junit.Assert; |
| |
| public class QuaternionTest { |
| /** Epsilon for double comparison. */ |
| private static final double EPS = Math.ulp(1d); |
| /** Epsilon for double comparison. */ |
| private static final double COMPARISON_EPS = 1e-14; |
| |
| @Test |
| public final void testAccessors1() { |
| final double q0 = 2; |
| final double q1 = 5.4; |
| final double q2 = 17; |
| final double q3 = 0.0005; |
| final Quaternion q = new Quaternion(q0, q1, q2, q3); |
| |
| Assert.assertEquals(q0, q.getQ0(), 0); |
| Assert.assertEquals(q1, q.getQ1(), 0); |
| Assert.assertEquals(q2, q.getQ2(), 0); |
| Assert.assertEquals(q3, q.getQ3(), 0); |
| } |
| |
| @Test |
| public final void testAccessors2() { |
| final double q0 = 2; |
| final double q1 = 5.4; |
| final double q2 = 17; |
| final double q3 = 0.0005; |
| final Quaternion q = new Quaternion(q0, q1, q2, q3); |
| |
| final double sP = q.getScalarPart(); |
| final double[] vP = q.getVectorPart(); |
| |
| Assert.assertEquals(q0, sP, 0); |
| Assert.assertEquals(q1, vP[0], 0); |
| Assert.assertEquals(q2, vP[1], 0); |
| Assert.assertEquals(q3, vP[2], 0); |
| } |
| |
| @Test |
| public final void testAccessors3() { |
| final double q0 = 2; |
| final double q1 = 5.4; |
| final double q2 = 17; |
| final double q3 = 0.0005; |
| final Quaternion q = new Quaternion(q0, new double[] { q1, q2, q3 }); |
| |
| final double sP = q.getScalarPart(); |
| final double[] vP = q.getVectorPart(); |
| |
| Assert.assertEquals(q0, sP, 0); |
| Assert.assertEquals(q1, vP[0], 0); |
| Assert.assertEquals(q2, vP[1], 0); |
| Assert.assertEquals(q3, vP[2], 0); |
| } |
| |
| @Test(expected=DimensionMismatchException.class) |
| public void testWrongDimension() { |
| new Quaternion(new double[] { 1, 2 }); |
| } |
| |
| @Test |
| public final void testConjugate() { |
| final double q0 = 2; |
| final double q1 = 5.4; |
| final double q2 = 17; |
| final double q3 = 0.0005; |
| final Quaternion q = new Quaternion(q0, q1, q2, q3); |
| |
| final Quaternion qConjugate = q.getConjugate(); |
| |
| Assert.assertEquals(q0, qConjugate.getQ0(), 0); |
| Assert.assertEquals(-q1, qConjugate.getQ1(), 0); |
| Assert.assertEquals(-q2, qConjugate.getQ2(), 0); |
| Assert.assertEquals(-q3, qConjugate.getQ3(), 0); |
| } |
| |
| @Test |
| public final void testProductQuaternionQuaternion() { |
| |
| // Case : analytic test case |
| |
| final Quaternion qA = new Quaternion(1, 0.5, -3, 4); |
| final Quaternion qB = new Quaternion(6, 2, 1, -9); |
| final Quaternion qResult = Quaternion.multiply(qA, qB); |
| |
| Assert.assertEquals(44, qResult.getQ0(), EPS); |
| Assert.assertEquals(28, qResult.getQ1(), EPS); |
| Assert.assertEquals(-4.5, qResult.getQ2(), EPS); |
| Assert.assertEquals(21.5, qResult.getQ3(), EPS); |
| |
| // comparison with the result given by the formula : |
| // qResult = (scalarA * scalarB - vectorA . vectorB) + (scalarA * vectorB + scalarB * vectorA + vectorA ^ |
| // vectorB) |
| |
| final Vector3D vectorA = new Vector3D(qA.getVectorPart()); |
| final Vector3D vectorB = new Vector3D(qB.getVectorPart()); |
| final Vector3D vectorResult = new Vector3D(qResult.getVectorPart()); |
| |
| final double scalarPartRef = qA.getScalarPart() * qB.getScalarPart() - Vector3D.dotProduct(vectorA, vectorB); |
| |
| Assert.assertEquals(scalarPartRef, qResult.getScalarPart(), EPS); |
| |
| final Vector3D vectorPartRef = ((vectorA.scalarMultiply(qB.getScalarPart())).add(vectorB.scalarMultiply(qA |
| .getScalarPart()))).add(Vector3D.crossProduct(vectorA, vectorB)); |
| final double norm = (vectorResult.subtract(vectorPartRef)).getNorm(); |
| |
| Assert.assertEquals(0, norm, EPS); |
| |
| // Conjugate of the product of two quaternions and product of their conjugates : |
| // Conj(qA * qB) = Conj(qB) * Conj(qA) |
| |
| final Quaternion conjugateOfProduct = qB.getConjugate().multiply(qA.getConjugate()); |
| final Quaternion productOfConjugate = (qA.multiply(qB)).getConjugate(); |
| |
| Assert.assertEquals(conjugateOfProduct.getQ0(), productOfConjugate.getQ0(), EPS); |
| Assert.assertEquals(conjugateOfProduct.getQ1(), productOfConjugate.getQ1(), EPS); |
| Assert.assertEquals(conjugateOfProduct.getQ2(), productOfConjugate.getQ2(), EPS); |
| Assert.assertEquals(conjugateOfProduct.getQ3(), productOfConjugate.getQ3(), EPS); |
| } |
| |
| @Test |
| public final void testProductQuaternionVector() { |
| |
| // Case : Product between a vector and a quaternion : QxV |
| |
| final Quaternion quaternion = new Quaternion(4, 7, -1, 2); |
| final double[] vector = {2.0, 1.0, 3.0}; |
| final Quaternion qResultQxV = Quaternion.multiply(quaternion, new Quaternion(vector)); |
| |
| Assert.assertEquals(-19, qResultQxV.getQ0(), EPS); |
| Assert.assertEquals(3, qResultQxV.getQ1(), EPS); |
| Assert.assertEquals(-13, qResultQxV.getQ2(), EPS); |
| Assert.assertEquals(21, qResultQxV.getQ3(), EPS); |
| |
| // comparison with the result given by the formula : |
| // qResult = (- vectorQ . vector) + (scalarQ * vector + vectorQ ^ vector) |
| |
| final double[] vectorQ = quaternion.getVectorPart(); |
| final double[] vectorResultQxV = qResultQxV.getVectorPart(); |
| |
| final double scalarPartRefQxV = -Vector3D.dotProduct(new Vector3D(vectorQ), new Vector3D(vector)); |
| Assert.assertEquals(scalarPartRefQxV, qResultQxV.getScalarPart(), EPS); |
| |
| final Vector3D vectorPartRefQxV = (new Vector3D(vector).scalarMultiply(quaternion.getScalarPart())).add(Vector3D |
| .crossProduct(new Vector3D(vectorQ), new Vector3D(vector))); |
| final double normQxV = (new Vector3D(vectorResultQxV).subtract(vectorPartRefQxV)).getNorm(); |
| Assert.assertEquals(0, normQxV, EPS); |
| |
| // Case : Product between a vector and a quaternion : VxQ |
| |
| final Quaternion qResultVxQ = Quaternion.multiply(new Quaternion(vector), quaternion); |
| |
| Assert.assertEquals(-19, qResultVxQ.getQ0(), EPS); |
| Assert.assertEquals(13, qResultVxQ.getQ1(), EPS); |
| Assert.assertEquals(21, qResultVxQ.getQ2(), EPS); |
| Assert.assertEquals(3, qResultVxQ.getQ3(), EPS); |
| |
| final double[] vectorResultVxQ = qResultVxQ.getVectorPart(); |
| |
| // comparison with the result given by the formula : |
| // qResult = (- vector . vectorQ) + (scalarQ * vector + vector ^ vectorQ) |
| |
| final double scalarPartRefVxQ = -Vector3D.dotProduct(new Vector3D(vectorQ), new Vector3D(vector)); |
| Assert.assertEquals(scalarPartRefVxQ, qResultVxQ.getScalarPart(), EPS); |
| |
| final Vector3D vectorPartRefVxQ = (new Vector3D(vector).scalarMultiply(quaternion.getScalarPart())).add(Vector3D |
| .crossProduct(new Vector3D(vector), new Vector3D(vectorQ))); |
| final double normVxQ = (new Vector3D(vectorResultVxQ).subtract(vectorPartRefVxQ)).getNorm(); |
| Assert.assertEquals(0, normVxQ, EPS); |
| } |
| |
| @Test |
| public final void testDotProductQuaternionQuaternion() { |
| // expected output |
| final double expected = -6.; |
| // inputs |
| final Quaternion q1 = new Quaternion(1, 2, 2, 1); |
| final Quaternion q2 = new Quaternion(3, -2, -1, -3); |
| |
| final double actual1 = Quaternion.dotProduct(q1, q2); |
| final double actual2 = q1.dotProduct(q2); |
| |
| Assert.assertEquals(expected, actual1, EPS); |
| Assert.assertEquals(expected, actual2, EPS); |
| } |
| |
| @Test |
| public final void testScalarMultiplyDouble() { |
| // expected outputs |
| final double w = 1.6; |
| final double x = -4.8; |
| final double y = 11.20; |
| final double z = 2.56; |
| // inputs |
| final Quaternion q1 = new Quaternion(0.5, -1.5, 3.5, 0.8); |
| final double a = 3.2; |
| |
| final Quaternion q = q1.multiply(a); |
| |
| Assert.assertEquals(w, q.getQ0(), COMPARISON_EPS); |
| Assert.assertEquals(x, q.getQ1(), COMPARISON_EPS); |
| Assert.assertEquals(y, q.getQ2(), COMPARISON_EPS); |
| Assert.assertEquals(z, q.getQ3(), COMPARISON_EPS); |
| } |
| |
| @Test |
| public final void testAddQuaternionQuaternion() { |
| // expected outputs |
| final double w = 4; |
| final double x = -1; |
| final double y = 2; |
| final double z = -4; |
| // inputs |
| final Quaternion q1 = new Quaternion(1., 2., -2., -1.); |
| final Quaternion q2 = new Quaternion(3., -3., 4., -3.); |
| |
| final Quaternion qa = Quaternion.add(q1, q2); |
| final Quaternion qb = q1.add(q2); |
| |
| Assert.assertEquals(w, qa.getQ0(), EPS); |
| Assert.assertEquals(x, qa.getQ1(), EPS); |
| Assert.assertEquals(y, qa.getQ2(), EPS); |
| Assert.assertEquals(z, qa.getQ3(), EPS); |
| |
| Assert.assertEquals(w, qb.getQ0(), EPS); |
| Assert.assertEquals(x, qb.getQ1(), EPS); |
| Assert.assertEquals(y, qb.getQ2(), EPS); |
| Assert.assertEquals(z, qb.getQ3(), EPS); |
| } |
| |
| @Test |
| public final void testSubtractQuaternionQuaternion() { |
| // expected outputs |
| final double w = -2.; |
| final double x = 5.; |
| final double y = -6.; |
| final double z = 2.; |
| // inputs |
| final Quaternion q1 = new Quaternion(1., 2., -2., -1.); |
| final Quaternion q2 = new Quaternion(3., -3., 4., -3.); |
| |
| final Quaternion qa = Quaternion.subtract(q1, q2); |
| final Quaternion qb = q1.subtract(q2); |
| |
| Assert.assertEquals(w, qa.getQ0(), EPS); |
| Assert.assertEquals(x, qa.getQ1(), EPS); |
| Assert.assertEquals(y, qa.getQ2(), EPS); |
| Assert.assertEquals(z, qa.getQ3(), EPS); |
| |
| Assert.assertEquals(w, qb.getQ0(), EPS); |
| Assert.assertEquals(x, qb.getQ1(), EPS); |
| Assert.assertEquals(y, qb.getQ2(), EPS); |
| Assert.assertEquals(z, qb.getQ3(), EPS); |
| } |
| |
| @Test |
| public final void testNorm() { |
| |
| final double q0 = 2; |
| final double q1 = 1; |
| final double q2 = -4; |
| final double q3 = 3; |
| final Quaternion q = new Quaternion(q0, q1, q2, q3); |
| |
| final double norm = q.getNorm(); |
| |
| Assert.assertEquals(FastMath.sqrt(30), norm, 0); |
| |
| final double normSquareRef = Quaternion.multiply(q, q.getConjugate()).getScalarPart(); |
| Assert.assertEquals(FastMath.sqrt(normSquareRef), norm, 0); |
| } |
| |
| @Test |
| public final void testNormalize() { |
| |
| final Quaternion q = new Quaternion(2, 1, -4, -2); |
| |
| final Quaternion versor = q.normalize(); |
| |
| Assert.assertEquals(2.0 / 5.0, versor.getQ0(), 0); |
| Assert.assertEquals(1.0 / 5.0, versor.getQ1(), 0); |
| Assert.assertEquals(-4.0 / 5.0, versor.getQ2(), 0); |
| Assert.assertEquals(-2.0 / 5.0, versor.getQ3(), 0); |
| |
| Assert.assertEquals(1, versor.getNorm(), 0); |
| } |
| |
| @Test(expected=ZeroException.class) |
| public final void testNormalizeFail() { |
| final Quaternion zeroQ = new Quaternion(0, 0, 0, 0); |
| zeroQ.normalize(); |
| } |
| |
| @Test |
| public final void testObjectEquals() { |
| final double one = 1; |
| final Quaternion q1 = new Quaternion(one, one, one, one); |
| Assert.assertTrue(q1.equals(q1)); |
| |
| final Quaternion q2 = new Quaternion(one, one, one, one); |
| Assert.assertTrue(q2.equals(q1)); |
| |
| final Quaternion q3 = new Quaternion(one, FastMath.nextUp(one), one, one); |
| Assert.assertFalse(q3.equals(q1)); |
| } |
| |
| @Test |
| public final void testQuaternionEquals() { |
| final double inc = 1e-5; |
| final Quaternion q1 = new Quaternion(2, 1, -4, -2); |
| final Quaternion q2 = new Quaternion(q1.getQ0() + inc, q1.getQ1(), q1.getQ2(), q1.getQ3()); |
| final Quaternion q3 = new Quaternion(q1.getQ0(), q1.getQ1() + inc, q1.getQ2(), q1.getQ3()); |
| final Quaternion q4 = new Quaternion(q1.getQ0(), q1.getQ1(), q1.getQ2() + inc, q1.getQ3()); |
| final Quaternion q5 = new Quaternion(q1.getQ0(), q1.getQ1(), q1.getQ2(), q1.getQ3() + inc); |
| |
| Assert.assertFalse(q1.equals(q2, 0.9 * inc)); |
| Assert.assertFalse(q1.equals(q3, 0.9 * inc)); |
| Assert.assertFalse(q1.equals(q4, 0.9 * inc)); |
| Assert.assertFalse(q1.equals(q5, 0.9 * inc)); |
| |
| Assert.assertTrue(q1.equals(q2, 1.1 * inc)); |
| Assert.assertTrue(q1.equals(q3, 1.1 * inc)); |
| Assert.assertTrue(q1.equals(q4, 1.1 * inc)); |
| Assert.assertTrue(q1.equals(q5, 1.1 * inc)); |
| } |
| |
| @Test |
| public final void testQuaternionEquals2() { |
| final Quaternion q1 = new Quaternion(1, 4, 2, 3); |
| final double gap = 1e-5; |
| final Quaternion q2 = new Quaternion(1 + gap, 4 + gap, 2 + gap, 3 + gap); |
| |
| Assert.assertTrue(q1.equals(q2, 10 * gap)); |
| Assert.assertFalse(q1.equals(q2, gap)); |
| Assert.assertFalse(q1.equals(q2, gap / 10)); |
| } |
| |
| @Test |
| public final void testIsUnitQuaternion() { |
| final Random r = new Random(48); |
| final int numberOfTrials = 1000; |
| for (int i = 0; i < numberOfTrials; i++) { |
| final Quaternion q1 = new Quaternion(r.nextDouble(), r.nextDouble(), r.nextDouble(), r.nextDouble()); |
| final Quaternion q2 = q1.normalize(); |
| Assert.assertTrue(q2.isUnitQuaternion(COMPARISON_EPS)); |
| } |
| |
| final Quaternion q = new Quaternion(1, 1, 1, 1); |
| Assert.assertFalse(q.isUnitQuaternion(COMPARISON_EPS)); |
| } |
| |
| @Test |
| public final void testIsPureQuaternion() { |
| final Quaternion q1 = new Quaternion(0, 5, 4, 8); |
| Assert.assertTrue(q1.isPureQuaternion(EPS)); |
| |
| final Quaternion q2 = new Quaternion(0 - EPS, 5, 4, 8); |
| Assert.assertTrue(q2.isPureQuaternion(EPS)); |
| |
| final Quaternion q3 = new Quaternion(0 - 1.1 * EPS, 5, 4, 8); |
| Assert.assertFalse(q3.isPureQuaternion(EPS)); |
| |
| final Random r = new Random(48); |
| final double[] v = {r.nextDouble(), r.nextDouble(), r.nextDouble()}; |
| final Quaternion q4 = new Quaternion(v); |
| Assert.assertTrue(q4.isPureQuaternion(0)); |
| |
| final Quaternion q5 = new Quaternion(0, v); |
| Assert.assertTrue(q5.isPureQuaternion(0)); |
| } |
| |
| @Test |
| public final void testPolarForm() { |
| final Random r = new Random(48); |
| final int numberOfTrials = 1000; |
| for (int i = 0; i < numberOfTrials; i++) { |
| final Quaternion q = new Quaternion(2 * (r.nextDouble() - 0.5), 2 * (r.nextDouble() - 0.5), |
| 2 * (r.nextDouble() - 0.5), 2 * (r.nextDouble() - 0.5)); |
| final Quaternion qP = q.getPositivePolarForm(); |
| |
| Assert.assertTrue(qP.isUnitQuaternion(COMPARISON_EPS)); |
| Assert.assertTrue(qP.getQ0() >= 0); |
| |
| final Rotation rot = new Rotation(q.getQ0(), q.getQ1(), q.getQ2(), q.getQ3(), true); |
| final Rotation rotP = new Rotation(qP.getQ0(), qP.getQ1(), qP.getQ2(), qP.getQ3(), true); |
| |
| Assert.assertEquals(rot.getAngle(), rotP.getAngle(), COMPARISON_EPS); |
| Assert.assertEquals(rot.getAxis(RotationConvention.VECTOR_OPERATOR).getX(), |
| rot.getAxis(RotationConvention.VECTOR_OPERATOR).getX(), |
| COMPARISON_EPS); |
| Assert.assertEquals(rot.getAxis(RotationConvention.VECTOR_OPERATOR).getY(), |
| rot.getAxis(RotationConvention.VECTOR_OPERATOR).getY(), |
| COMPARISON_EPS); |
| Assert.assertEquals(rot.getAxis(RotationConvention.VECTOR_OPERATOR).getZ(), |
| rot.getAxis(RotationConvention.VECTOR_OPERATOR).getZ(), |
| COMPARISON_EPS); |
| } |
| } |
| |
| @Test |
| public final void testGetInverse() { |
| final Quaternion q = new Quaternion(1.5, 4, 2, -2.5); |
| |
| final Quaternion inverseQ = q.getInverse(); |
| Assert.assertEquals(1.5 / 28.5, inverseQ.getQ0(), 0); |
| Assert.assertEquals(-4.0 / 28.5, inverseQ.getQ1(), 0); |
| Assert.assertEquals(-2.0 / 28.5, inverseQ.getQ2(), 0); |
| Assert.assertEquals(2.5 / 28.5, inverseQ.getQ3(), 0); |
| |
| final Quaternion product = Quaternion.multiply(inverseQ, q); |
| Assert.assertEquals(1, product.getQ0(), EPS); |
| Assert.assertEquals(0, product.getQ1(), EPS); |
| Assert.assertEquals(0, product.getQ2(), EPS); |
| Assert.assertEquals(0, product.getQ3(), EPS); |
| |
| final Quaternion qNul = new Quaternion(0, 0, 0, 0); |
| try { |
| final Quaternion inverseQNul = qNul.getInverse(); |
| Assert.fail("expecting ZeroException but got : " + inverseQNul); |
| } catch (ZeroException ex) { |
| // expected |
| } |
| } |
| |
| @Test |
| public final void testToString() { |
| final Quaternion q = new Quaternion(1, 2, 3, 4); |
| Assert.assertTrue(q.toString().equals("[1.0 2.0 3.0 4.0]")); |
| } |
| } |