Package org.apache.commons.math3.complex

Examples of org.apache.commons.math3.complex.Quaternion

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    @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);
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    @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);
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        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);
    }
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        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);
    }
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        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);
}
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        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(Math.sqrt(30), norm, 0);

        final double normSquareRef = Quaternion.multiply(q, q.getConjugate()).getScalarPart();
        Assert.assertEquals(Math.sqrt(normSquareRef), norm, 0);
    }
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    }

    @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);
    }
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        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();
    }
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    }

    @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));
    }
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    }

    @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));
 
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Related Classes of org.apache.commons.math3.complex.Quaternion

  • org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • org.apache.commons.math3.analysis.function.HarmonicOscillator
  • org.apache.commons.math3.analysis.function.Sin
  • org.apache.commons.math3.analysis.function.Sinc
  • org.apache.commons.math3.analysis.MultivariateFunction
  • org.apache.commons.math3.analysis.QuinticFunction
  • org.apache.commons.math3.analysis.solvers.BrentSolver
  • org.apache.commons.math3.analysis.UnivariateFunction
  • org.apache.commons.math3.complex.Complex
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