Example usage for org.apache.commons.math3.analysis.differentiation DerivativeStructure taylor

Introduction

In this page you can find the example usage for org.apache.commons.math3.analysis.differentiation DerivativeStructure taylor.

Prototype

public double taylor(final double... delta) 

Source Link

Document

Evaluate Taylor expansion a derivative structure.

Usage

From source file:org.orekit.bodies.OneAxisEllipsoidTest.java

@Test
public void testMovingGeodeticPoint() throws OrekitException {

    final OneAxisEllipsoid earth = new OneAxisEllipsoid(Constants.WGS84_EARTH_EQUATORIAL_RADIUS,
            Constants.WGS84_EARTH_FLATTENING, FramesFactory.getITRF(IERSConventions.IERS_2010, true));
    double lat0 = FastMath.toRadians(60.0);
    double lon0 = FastMath.toRadians(25.0);
    double alt0 = 100.0;
    double lat1 = 1.0e-3;
    double lon1 = -2.0e-3;
    double alt1 = 1.2;
    double lat2 = -1.0e-5;
    double lon2 = -3.0e-5;
    double alt2 = -0.01;
    final DerivativeStructure latDS = new DerivativeStructure(1, 2, lat0, lat1, lat2);
    final DerivativeStructure lonDS = new DerivativeStructure(1, 2, lon0, lon1, lon2);
    final DerivativeStructure altDS = new DerivativeStructure(1, 2, alt0, alt1, alt2);

    // direct computation of position, velocity and acceleration
    PVCoordinates pv = earth.transform(new FieldGeodeticPoint<DerivativeStructure>(latDS, lonDS, altDS));

    // finite differences computation
    FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(5, 0.1);
    UnivariateDifferentiableFunction fx = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            GeodeticPoint gp = new GeodeticPoint(latDS.taylor(dt), lonDS.taylor(dt), altDS.taylor(dt));
            return earth.transform(gp).getX();
        }// w w  w. j  a  v a 2  s.  c  o m
    });
    UnivariateDifferentiableFunction fy = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            GeodeticPoint gp = new GeodeticPoint(latDS.taylor(dt), lonDS.taylor(dt), altDS.taylor(dt));
            return earth.transform(gp).getY();
        }
    });
    UnivariateDifferentiableFunction fz = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            GeodeticPoint gp = new GeodeticPoint(latDS.taylor(dt), lonDS.taylor(dt), altDS.taylor(dt));
            return earth.transform(gp).getZ();
        }
    });
    DerivativeStructure dtZero = new DerivativeStructure(1, 2, 0, 0.0);
    DerivativeStructure xDS = fx.value(dtZero);
    DerivativeStructure yDS = fy.value(dtZero);
    DerivativeStructure zDS = fz.value(dtZero);
    Assert.assertEquals(xDS.getValue(), pv.getPosition().getX(), 2.0e-20 * FastMath.abs(xDS.getValue()));
    Assert.assertEquals(xDS.getPartialDerivative(1), pv.getVelocity().getX(),
            2.0e-12 * FastMath.abs(xDS.getPartialDerivative(1)));
    Assert.assertEquals(xDS.getPartialDerivative(2), pv.getAcceleration().getX(),
            2.0e-9 * FastMath.abs(xDS.getPartialDerivative(2)));
    Assert.assertEquals(yDS.getValue(), pv.getPosition().getY(), 2.0e-20 * FastMath.abs(yDS.getValue()));
    Assert.assertEquals(yDS.getPartialDerivative(1), pv.getVelocity().getY(),
            2.0e-12 * FastMath.abs(yDS.getPartialDerivative(1)));
    Assert.assertEquals(yDS.getPartialDerivative(2), pv.getAcceleration().getY(),
            2.0e-9 * FastMath.abs(yDS.getPartialDerivative(2)));
    Assert.assertEquals(zDS.getValue(), pv.getPosition().getZ(), 2.0e-20 * FastMath.abs(zDS.getValue()));
    Assert.assertEquals(zDS.getPartialDerivative(1), pv.getVelocity().getZ(),
            2.0e-12 * FastMath.abs(zDS.getPartialDerivative(1)));
    Assert.assertEquals(zDS.getPartialDerivative(2), pv.getAcceleration().getZ(),
            2.0e-9 * FastMath.abs(zDS.getPartialDerivative(2)));
}

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From source file:org.orekit.propagation.numerical.Jacobianizer.java

/** Shift a scalar.
 * @param nominal nominal scalar/* www.j av  a2  s  .c  o  m*/
 * @param index index of the variable with respect to which we shift
 * @param h shift step
 * @return shifted scalar
 */
private double shift(final DerivativeStructure nominal, final int index, final double h) {
    final double[] delta = new double[nominal.getFreeParameters()];
    delta[index] = h;
    return nominal.taylor(delta);
}

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