Differentiation.java
/* Copyright 2002-2019 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (CS) under one or more
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* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
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*
* 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,
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package org.orekit.utils;
import org.hipparchus.analysis.UnivariateFunction;
import org.hipparchus.analysis.UnivariateVectorFunction;
import org.hipparchus.analysis.differentiation.DSFactory;
import org.hipparchus.analysis.differentiation.DerivativeStructure;
import org.hipparchus.analysis.differentiation.FiniteDifferencesDifferentiator;
import org.hipparchus.analysis.differentiation.UnivariateDifferentiableVectorFunction;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.orbits.Orbit;
import org.orekit.orbits.OrbitType;
import org.orekit.orbits.PositionAngle;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.numerical.NumericalPropagator;
/** Utility class for differentiating various kinds of functions.
* @author Luc Maisonobe
* @since 8.0
*/
public class Differentiation {
/** Factory for the DerivativeStructure instances. */
private static final DSFactory FACTORY = new DSFactory(1, 1);
/** Private constructor for utility class.
*/
private Differentiation() {
}
/** Differentiate a scalar function using finite differences.
* @param function function to differentiate
* @param nbPoints number of points used for finite differences
* @param step step for finite differences, in <em>physical</em> units
* @return scalar function evaluating to the derivative of the original function
* @since 9.3
*/
public static ParameterFunction differentiate(final ParameterFunction function,
final int nbPoints, final double step) {
return new ParameterFunction() {
/** Finite differences differentiator to use. */
private final FiniteDifferencesDifferentiator differentiator =
new FiniteDifferencesDifferentiator(nbPoints, step);
/** {@inheritDoc} */
@Override
public double value(final ParameterDriver driver) {
final UnivariateFunction uf = new UnivariateFunction() {
/** {@inheritDoc} */
@Override
public double value(final double value) {
final double saved = driver.getValue();
driver.setValue(value);
final double functionValue = function.value(driver);
driver.setValue(saved);
return functionValue;
}
};
final DerivativeStructure dsParam = FACTORY.variable(0, driver.getValue());
final DerivativeStructure dsValue = differentiator.differentiate(uf).value(dsParam);
return dsValue.getPartialDerivative(1);
}
};
}
/** Differentiate a vector function using finite differences.
* @param function function to differentiate
* @param provider attitude provider to use for modified states
* @param dimension dimension of the vector value of the function
* @param orbitType type used to map the orbit to a one dimensional array
* @param positionAngle type of the position angle used for orbit mapping to array
* @param dP user specified position error, used for step size computation for finite differences
* @param nbPoints number of points used for finite differences
* @return matrix function evaluating to the Jacobian of the original function
*/
public static StateJacobian differentiate(final StateFunction function, final int dimension,
final AttitudeProvider provider,
final OrbitType orbitType, final PositionAngle positionAngle,
final double dP, final int nbPoints) {
return new StateJacobian() {
@Override
public double[][] value(final SpacecraftState state) {
final double[] tolerances =
NumericalPropagator.tolerances(dP, state.getOrbit(), orbitType)[0];
final double[][] jacobian = new double[dimension][6];
for (int j = 0; j < 6; ++j) {
// compute partial derivatives with respect to state component j
final UnivariateVectorFunction componentJ =
new StateComponentFunction(j, function, provider, state,
orbitType, positionAngle);
final FiniteDifferencesDifferentiator differentiator =
new FiniteDifferencesDifferentiator(nbPoints, tolerances[j]);
final UnivariateDifferentiableVectorFunction differentiatedJ =
differentiator.differentiate(componentJ);
final DerivativeStructure[] c = differentiatedJ.value(FACTORY.variable(0, 0.0));
// populate the j-th column of the Jacobian
for (int i = 0; i < dimension; ++i) {
jacobian[i][j] = c[i].getPartialDerivative(1);
}
}
return jacobian;
}
};
}
/** Restriction of a {@link StateFunction} to a function of a single state component.
*/
private static class StateComponentFunction implements UnivariateVectorFunction {
/** Component index in the mapped orbit array. */
private final int index;
/** State-dependent function. */
private final StateFunction f;
/** Type used to map the orbit to a one dimensional array. */
private final OrbitType orbitType;
/** Tpe of the position angle used for orbit mapping to array. */
private final PositionAngle positionAngle;
/** Base state, of which only one component will change. */
private final SpacecraftState baseState;
/** Attitude provider to use for modified states. */
private final AttitudeProvider provider;
/** Simple constructor.
* @param index component index in the mapped orbit array
* @param f state-dependent function
* @param provider attitude provider to use for modified states
* @param baseState base state, of which only one component will change
* @param orbitType type used to map the orbit to a one dimensional array
* @param positionAngle type of the position angle used for orbit mapping to array
*/
StateComponentFunction(final int index, final StateFunction f,
final AttitudeProvider provider, final SpacecraftState baseState,
final OrbitType orbitType, final PositionAngle positionAngle) {
this.index = index;
this.f = f;
this.provider = provider;
this.orbitType = orbitType;
this.positionAngle = positionAngle;
this.baseState = baseState;
}
/** {@inheritDoc} */
@Override
public double[] value(final double x) {
final double[] array = new double[6];
final double[] arrayDot = new double[6];
orbitType.mapOrbitToArray(baseState.getOrbit(), positionAngle, array, arrayDot);
array[index] += x;
final Orbit orbit = orbitType.mapArrayToOrbit(array, arrayDot,
positionAngle,
baseState.getDate(),
baseState.getMu(),
baseState.getFrame());
final SpacecraftState state =
new SpacecraftState(orbit,
provider.getAttitude(orbit, orbit.getDate(), orbit.getFrame()),
baseState.getMass());
return f.value(state);
}
}
}