Example usage for org.apache.commons.math3.analysis.differentiation FiniteDifferencesDifferentiator FiniteDifferencesDifferentiator

Introduction

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

Prototype

public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize)
        throws NotPositiveException, NumberIsTooSmallException 

Source Link

Document

Build a differentiator with number of points and step size when independent variable is unbounded.

Usage

From source file:com.bwc.ora.models.Lrp.java

/**
 * Get the local maximums from a collection of Points.
 *
 * @param lrpSeries/*from  ww  w  .  j  a va  2s .co  m*/
 * @param seriesTitle
 * @return
 */
public static XYSeries getMaximumsWithHiddenPeaks(XYSeries lrpSeries, String seriesTitle) {
    XYSeries maxPoints = new XYSeries(seriesTitle);

    //convert to x and y coordinate arrays
    double[][] xyline = lrpSeries.toArray();

    //use a spline interpolator to converts points into an equation
    UnivariateInterpolator interpolator = new SplineInterpolator();
    UnivariateFunction function = interpolator.interpolate(xyline[0], xyline[1]);

    // create a differentiator using 5 points and 0.01 step
    FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(5, 0.01);

    // create a new function that computes both the value and the derivatives
    // using DerivativeStructure
    UnivariateDifferentiableFunction completeF = differentiator.differentiate(function);

    // now we can compute the value and its derivatives
    // here we decided to display up to second order derivatives,
    // because we feed completeF with order 2 DerivativeStructure instances
    //find local minima in second derivative, these indicate the peaks (and hidden peaks)
    //of the input
    for (double x = xyline[0][0] + 1; x < xyline[0][xyline[0].length - 1] - 1; x += 0.5) {
        DerivativeStructure xDSc = new DerivativeStructure(1, 2, 0, x);
        DerivativeStructure xDSl = new DerivativeStructure(1, 2, 0, x - 0.5);
        DerivativeStructure xDSr = new DerivativeStructure(1, 2, 0, x + 0.5);
        DerivativeStructure yDSc = completeF.value(xDSc);
        DerivativeStructure yDSl = completeF.value(xDSl);
        DerivativeStructure yDSr = completeF.value(xDSr);
        double c2d = yDSc.getPartialDerivative(2);
        if (c2d < yDSl.getPartialDerivative(2) && c2d < yDSr.getPartialDerivative(2)) {
            maxPoints.add((int) Math.round(x), yDSc.getValue());
        }
    }

    return maxPoints;
}

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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();
        }//from w ww  . ja  v  a  2 s.  com
    });
    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.orbits.KeplerianParametersTest.java

@Test
public void testKeplerianDerivatives() {
    final KeplerianOrbit o = new KeplerianOrbit(new PVCoordinates(new Vector3D(-4947831., -3765382., -3708221.),
            new Vector3D(-2079., 5291., -7842.)), FramesFactory.getEME2000(), date, 3.9860047e14);
    final Vector3D p = o.getPVCoordinates().getPosition();
    final Vector3D v = o.getPVCoordinates().getVelocity();
    final Vector3D a = o.getPVCoordinates().getAcceleration();

    // check that despite we did not provide acceleration, it got recomputed
    Assert.assertEquals(7.605422, a.getNorm(), 1.0e-6);

    FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(8, 0.1);

    // check velocity is the derivative of position
    double vx = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getPosition().getX();
        }/*from   ww w . j  a v  a  2  s .  com*/
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(o.getPVCoordinates().getVelocity().getX(), vx, 3.0e-12 * v.getNorm());
    double vy = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getPosition().getY();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(o.getPVCoordinates().getVelocity().getY(), vy, 3.0e-12 * v.getNorm());
    double vz = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getPosition().getZ();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(o.getPVCoordinates().getVelocity().getZ(), vz, 3.0e-12 * v.getNorm());

    // check acceleration is the derivative of velocity
    double ax = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getVelocity().getX();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(o.getPVCoordinates().getAcceleration().getX(), ax, 3.0e-12 * a.getNorm());
    double ay = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getVelocity().getY();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(o.getPVCoordinates().getAcceleration().getY(), ay, 3.0e-12 * a.getNorm());
    double az = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getVelocity().getZ();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(o.getPVCoordinates().getAcceleration().getZ(), az, 3.0e-12 * a.getNorm());

    // check jerk is the derivative of acceleration
    final double r2 = p.getNormSq();
    final double r = FastMath.sqrt(r2);
    Vector3D keplerianJerk = new Vector3D(-3 * Vector3D.dotProduct(p, v) / r2, a, -a.getNorm() / r, v);
    double jx = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getAcceleration().getX();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(keplerianJerk.getX(), jx, 3.0e-12 * keplerianJerk.getNorm());
    double jy = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getAcceleration().getY();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(keplerianJerk.getY(), jy, 3.0e-12 * keplerianJerk.getNorm());
    double jz = differentiator.differentiate(new UnivariateFunction() {
        public double value(double dt) {
            return o.shiftedBy(dt).getPVCoordinates().getAcceleration().getZ();
        }
    }).value(new DerivativeStructure(1, 1, 0, 0.0)).getPartialDerivative(1);
    Assert.assertEquals(keplerianJerk.getZ(), jz, 3.0e-12 * keplerianJerk.getNorm());

}

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From source file:org.orekit.utils.FieldPVCoordinatesTest.java

@Test
public void testNormalize() {
    RandomGenerator generator = new Well19937a(0x7ede9376e4e1ab5al);
    FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(5, 1.0e-3);
    for (int i = 0; i < 200; ++i) {
        final FieldPVCoordinates<DerivativeStructure> pv = randomPVCoordinates(generator, 1e6, 1e3, 1.0);
        DerivativeStructure x = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return pv.shiftedBy(t).getPosition().normalize().getX().getValue();
            }/*from   w  w  w  . j  a  v a  2 s.co m*/
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        DerivativeStructure y = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return pv.shiftedBy(t).getPosition().normalize().getY().getValue();
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        DerivativeStructure z = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return pv.shiftedBy(t).getPosition().normalize().getZ().getValue();
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        FieldPVCoordinates<DerivativeStructure> normalized = pv.normalize();
        Assert.assertEquals(x.getValue(), normalized.getPosition().getX().getValue(), 1.0e-16);
        Assert.assertEquals(y.getValue(), normalized.getPosition().getY().getValue(), 1.0e-16);
        Assert.assertEquals(z.getValue(), normalized.getPosition().getZ().getValue(), 1.0e-16);
        Assert.assertEquals(x.getPartialDerivative(1), normalized.getVelocity().getX().getValue(), 3.0e-13);
        Assert.assertEquals(y.getPartialDerivative(1), normalized.getVelocity().getY().getValue(), 3.0e-13);
        Assert.assertEquals(z.getPartialDerivative(1), normalized.getVelocity().getZ().getValue(), 3.0e-13);
        Assert.assertEquals(x.getPartialDerivative(2), normalized.getAcceleration().getX().getValue(), 6.0e-10);
        Assert.assertEquals(y.getPartialDerivative(2), normalized.getAcceleration().getY().getValue(), 6.0e-10);
        Assert.assertEquals(z.getPartialDerivative(2), normalized.getAcceleration().getZ().getValue(), 6.0e-10);
    }
}

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From source file:org.orekit.utils.IERSConventionsTest.java

private void checkDerivative(final TimeFunction<DerivativeStructure> function, final AbsoluteDate date,
        final double span, final double sampleStep, final double h, final double tolerance) {

    UnivariateDifferentiableFunction differentiated = new FiniteDifferencesDifferentiator(4, h)
            .differentiate(new UnivariateFunction() {
                @Override//  w  ww  .  ja v  a 2s.co m
                public double value(final double dt) {
                    return function.value(date.shiftedBy(dt)).getValue();
                }
            });

    for (double dt = 0; dt < span; dt += sampleStep) {
        DerivativeStructure yRef = differentiated.value(new DerivativeStructure(1, 1, 0, dt));
        DerivativeStructure y = function.value(date.shiftedBy(dt));
        Assert.assertEquals(yRef.getPartialDerivative(1), y.getPartialDerivative(1), tolerance);
    }

}

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From source file:org.orekit.utils.PVCoordinatesTest.java

@Test
public void testNormalize() {
    RandomGenerator generator = new Well19937a(0xb2011ffd25412067l);
    FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(5, 1.0e-3);
    for (int i = 0; i < 200; ++i) {
        final PVCoordinates pv = randomPVCoordinates(generator, 1e6, 1e3, 1.0);
        DerivativeStructure x = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return pv.shiftedBy(t).getPosition().normalize().getX();
            }//from w w w  .  j  av  a  2  s. com
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        DerivativeStructure y = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return pv.shiftedBy(t).getPosition().normalize().getY();
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        DerivativeStructure z = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return pv.shiftedBy(t).getPosition().normalize().getZ();
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        PVCoordinates normalized = pv.normalize();
        Assert.assertEquals(x.getValue(), normalized.getPosition().getX(), 1.0e-16);
        Assert.assertEquals(y.getValue(), normalized.getPosition().getY(), 1.0e-16);
        Assert.assertEquals(z.getValue(), normalized.getPosition().getZ(), 1.0e-16);
        Assert.assertEquals(x.getPartialDerivative(1), normalized.getVelocity().getX(), 3.0e-13);
        Assert.assertEquals(y.getPartialDerivative(1), normalized.getVelocity().getY(), 3.0e-13);
        Assert.assertEquals(z.getPartialDerivative(1), normalized.getVelocity().getZ(), 3.0e-13);
        Assert.assertEquals(x.getPartialDerivative(2), normalized.getAcceleration().getX(), 6.0e-10);
        Assert.assertEquals(y.getPartialDerivative(2), normalized.getAcceleration().getY(), 6.0e-10);
        Assert.assertEquals(z.getPartialDerivative(2), normalized.getAcceleration().getZ(), 6.0e-10);
    }
}

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From source file:org.orekit.utils.PVCoordinatesTest.java

@Test
public void testCrossProduct() {
    RandomGenerator generator = new Well19937a(0x85c592b3be733d23l);
    FiniteDifferencesDifferentiator differentiator = new FiniteDifferencesDifferentiator(5, 1.0e-3);
    for (int i = 0; i < 200; ++i) {
        final PVCoordinates pv1 = randomPVCoordinates(generator, 1.0, 1.0, 1.0);
        final PVCoordinates pv2 = randomPVCoordinates(generator, 1.0, 1.0, 1.0);
        DerivativeStructure x = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return Vector3D.crossProduct(pv1.shiftedBy(t).getPosition(), pv2.shiftedBy(t).getPosition())
                        .getX();/*w w w.  j a va 2 s . co m*/
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        DerivativeStructure y = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return Vector3D.crossProduct(pv1.shiftedBy(t).getPosition(), pv2.shiftedBy(t).getPosition())
                        .getY();
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        DerivativeStructure z = differentiator.differentiate(new UnivariateFunction() {
            public double value(double t) {
                return Vector3D.crossProduct(pv1.shiftedBy(t).getPosition(), pv2.shiftedBy(t).getPosition())
                        .getZ();
            }
        }).value(new DerivativeStructure(1, 2, 0, 0.0));
        PVCoordinates product = PVCoordinates.crossProduct(pv1, pv2);
        Assert.assertEquals(x.getValue(), product.getPosition().getX(), 1.0e-16);
        Assert.assertEquals(y.getValue(), product.getPosition().getY(), 1.0e-16);
        Assert.assertEquals(z.getValue(), product.getPosition().getZ(), 1.0e-16);
        Assert.assertEquals(x.getPartialDerivative(1), product.getVelocity().getX(), 9.0e-10);
        Assert.assertEquals(y.getPartialDerivative(1), product.getVelocity().getY(), 9.0e-10);
        Assert.assertEquals(z.getPartialDerivative(1), product.getVelocity().getZ(), 9.0e-10);
        Assert.assertEquals(x.getPartialDerivative(2), product.getAcceleration().getX(), 3.0e-9);
        Assert.assertEquals(y.getPartialDerivative(2), product.getAcceleration().getY(), 3.0e-9);
        Assert.assertEquals(z.getPartialDerivative(2), product.getAcceleration().getZ(), 3.0e-9);
    }
}

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