/* Copyright 2010-2011 Centre National d'Études Spatiales
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS 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.orekit.propagation.numerical;
  
  import java.util.IdentityHashMap;
  import java.util.Map;
  
  import org.hipparchus.analysis.differentiation.Gradient;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.forces.ForceModel;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.integration.AdditionalEquations;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.ParameterDriversList;
  
  /** Set of {@link AdditionalEquations additional equations} computing the partial derivatives
   * of the state (orbit) with respect to initial state and force models parameters.
   * <p>
   * This set of equations are automatically added to a {@link NumericalPropagator numerical propagator}
   * in order to compute partial derivatives of the orbit along with the orbit itself. This is
   * useful for example in orbit determination applications.
   * </p>
   * <p>
   * The partial derivatives with respect to initial state can be either dimension 6
   * (orbit only) or 7 (orbit and mass).
   * </p>
   * <p>
   * The partial derivatives with respect to force models parameters has a dimension
   * equal to the number of selected parameters. Parameters selection is implemented at
   * {@link ForceModel force models} level. Users must retrieve a {@link ParameterDriver
   * parameter driver} using {@link ForceModel#getParameterDriver(String)} and then
   * select it by calling {@link ParameterDriver#setSelected(boolean) setSelected(true)}.
   * </p>
   * <p>
   * If several force models provide different {@link ParameterDriver drivers} for the
   * same parameter name, selecting any of these drivers has the side effect of
   * selecting all the drivers for this shared parameter. In this case, the partial
   * derivatives will be the sum of the partial derivatives contributed by the
   * corresponding force models. This case typically arises for central attraction
   * coefficient, which has an influence on {@link org.orekit.forces.gravity.NewtonianAttraction
   * Newtonian attraction}, {@link org.orekit.forces.gravity.HolmesFeatherstoneAttractionModel
   * gravity field}, and {@link org.orekit.forces.gravity.Relativity relativity}.
   * </p>
   * @author V&eacute;ronique Pommier-Maurussane
   * @author Luc Maisonobe
   */
  public class PartialDerivativesEquations implements AdditionalEquations {
  
      /** Propagator computing state evolution. */
      private final NumericalPropagator propagator;
  
      /** Selected parameters for Jacobian computation. */
      private ParameterDriversList selected;
  
      /** Parameters map. */
      private Map<ParameterDriver, Integer> map;
  
      /** Name. */
      private final String name;
  
      /** Flag for Jacobian matrices initialization. */
      private boolean initialized;
  
      /** Simple constructor.
       * <p>
       * Upon construction, this set of equations is <em>automatically</em> added to
       * the propagator by calling its {@link
       * NumericalPropagator#addAdditionalEquations(AdditionalEquations)} method. So
       * there is no need to call this method explicitly for these equations.
       * </p>
       * @param name name of the partial derivatives equations
       * @param propagator the propagator that will handle the orbit propagation
       */
      public PartialDerivativesEquations(final String name, final NumericalPropagator propagator) {
          this.name                   = name;
          this.selected               = null;
          this.map                    = null;
          this.propagator             = propagator;
          this.initialized            = false;
          propagator.addAdditionalEquations(this);
      }
  
     /** {@inheritDoc} */
     public String getName() {
         return name;
     }
 
     /** Freeze the selected parameters from the force models.
      */
     private void freezeParametersSelection() {
         if (selected == null) {
 
             // first pass: gather all parameters, binding similar names together
             selected = new ParameterDriversList();
             for (final ForceModel provider : propagator.getAllForceModels()) {
                 for (final ParameterDriver driver : provider.getParametersDrivers()) {
                     selected.add(driver);
                 }
             }
 
             // second pass: now that shared parameter names are bound together,
             // their selections status have been synchronized, we can filter them
             selected.filter(true);
 
             // third pass: sort parameters lexicographically
             selected.sort();
 
             // fourth pass: set up a map between parameters drivers and matrices columns
             map = new IdentityHashMap<ParameterDriver, Integer>();
             int parameterIndex = 0;
             for (final ParameterDriver selectedDriver : selected.getDrivers()) {
                 for (final ForceModel provider : propagator.getAllForceModels()) {
                     for (final ParameterDriver driver : provider.getParametersDrivers()) {
                         if (driver.getName().equals(selectedDriver.getName())) {
                             map.put(driver, parameterIndex);
                         }
                     }
                 }
                 ++parameterIndex;
             }
 
         }
     }
 
     /** Get the selected parameters, in Jacobian matrix column order.
      * <p>
      * The force models parameters for which partial derivatives are desired,
      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
      * before this method is called, so the proper list is returned.
      * </p>
      * @return selected parameters, in Jacobian matrix column order which
      * is lexicographic order
      */
     public ParameterDriversList getSelectedParameters() {
         freezeParametersSelection();
         return selected;
     }
 
     /** Set the initial value of the Jacobian with respect to state and parameter.
      * <p>
      * This method is equivalent to call {@link #setInitialJacobians(SpacecraftState,
      * double[][], double[][])} with dYdY0 set to the identity matrix and dYdP set
      * to a zero matrix.
      * </p>
      * <p>
      * The force models parameters for which partial derivatives are desired,
      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
      * before this method is called, so proper matrices dimensions are used.
      * </p>
      * @param s0 initial state
      * @return state with initial Jacobians added
      * @see #getSelectedParameters()
      * @since 9.0
      */
     public SpacecraftState setInitialJacobians(final SpacecraftState s0) {
         freezeParametersSelection();
         final int stateDimension = 6;
         final double[][] dYdY0 = new double[stateDimension][stateDimension];
         final double[][] dYdP  = new double[stateDimension][selected.getNbParams()];
         for (int i = 0; i < stateDimension; ++i) {
             dYdY0[i][i] = 1.0;
         }
         return setInitialJacobians(s0, dYdY0, dYdP);
     }
 
     /** Set the initial value of the Jacobian with respect to state and parameter.
      * <p>
      * The returned state must be added to the propagator (it is not done
      * automatically, as the user may need to add more states to it).
      * </p>
      * <p>
      * The force models parameters for which partial derivatives are desired,
      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
      * before this method is called, and the {@code dY1dP} matrix dimension <em>must</em>
      * be consistent with the selection.
      * </p>
      * @param s1 current state
      * @param dY1dY0 Jacobian of current state at time t₁ with respect
      * to state at some previous time t₀ (must be 6x6)
      * @param dY1dP Jacobian of current state at time t₁ with respect
      * to parameters (may be null if no parameters are selected)
      * @return state with initial Jacobians added
      * @see #getSelectedParameters()
      */
     public SpacecraftState setInitialJacobians(final SpacecraftState s1,
                                                final double[][] dY1dY0, final double[][] dY1dP) {
 
         freezeParametersSelection();
 
         // Check dimensions
         final int stateDim = dY1dY0.length;
         if (stateDim != 6 || stateDim != dY1dY0[0].length) {
             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_6X6,
                                       stateDim, dY1dY0[0].length);
         }
         if (dY1dP != null && stateDim != dY1dP.length) {
             throw new OrekitException(OrekitMessages.STATE_AND_PARAMETERS_JACOBIANS_ROWS_MISMATCH,
                                       stateDim, dY1dP.length);
         }
         if (dY1dP == null && selected.getNbParams() != 0 ||
             dY1dP != null && selected.getNbParams() != dY1dP[0].length) {
             throw new OrekitException(new OrekitException(OrekitMessages.INITIAL_MATRIX_AND_PARAMETERS_NUMBER_MISMATCH,
                                                           dY1dP == null ? 0 : dY1dP[0].length, selected.getNbParams()));
         }
 
         // store the matrices as a single dimension array
         initialized = true;
         final JacobiansMapper mapper = getMapper();
         final double[] p = new double[mapper.getAdditionalStateDimension()];
         mapper.setInitialJacobians(s1, dY1dY0, dY1dP, p);
 
         // set value in propagator
         return s1.addAdditionalState(name, p);
 
     }
 
     /** Get a mapper between two-dimensional Jacobians and one-dimensional additional state.
      * @return a mapper between two-dimensional Jacobians and one-dimensional additional state,
      * with the same name as the instance
      * @see #setInitialJacobians(SpacecraftState)
      * @see #setInitialJacobians(SpacecraftState, double[][], double[][])
      */
     public JacobiansMapper getMapper() {
         if (!initialized) {
             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_INITIALIZED);
         }
         return new JacobiansMapper(name, selected,
                                    propagator.getOrbitType(),
                                    propagator.getPositionAngleType());
     }
 
     /** {@inheritDoc} */
     public double[] computeDerivatives(final SpacecraftState s, final double[] pDot) {
 
         // initialize acceleration Jacobians to zero
         final int paramDim = selected.getNbParams();
         final int dim = 3;
         final double[][] dAccdParam = new double[dim][paramDim];
         final double[][] dAccdPos   = new double[dim][dim];
         final double[][] dAccdVel   = new double[dim][dim];
 
         final NumericalGradientConverter fullConverter    = new NumericalGradientConverter(s, 6, propagator.getAttitudeProvider());
         final NumericalGradientConverter posOnlyConverter = new NumericalGradientConverter(s, 3, propagator.getAttitudeProvider());
 
         // compute acceleration Jacobians, finishing with the largest force: Newtonian attraction
         for (final ForceModel forceModel : propagator.getAllForceModels()) {
 
             final NumericalGradientConverter converter = forceModel.dependsOnPositionOnly() ? posOnlyConverter : fullConverter;
             final FieldSpacecraftState<Gradient> dsState = converter.getState(forceModel);
             final Gradient[] parameters = converter.getParameters(dsState, forceModel);
 
             final FieldVector3D<Gradient> acceleration = forceModel.acceleration(dsState, parameters);
             final double[] derivativesX = acceleration.getX().getGradient();
             final double[] derivativesY = acceleration.getY().getGradient();
             final double[] derivativesZ = acceleration.getZ().getGradient();
 
             // update Jacobians with respect to state
             addToRow(derivativesX, 0, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
             addToRow(derivativesY, 1, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
             addToRow(derivativesZ, 2, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
 
             int index = converter.getFreeStateParameters();
             for (ParameterDriver driver : forceModel.getParametersDrivers()) {
                 if (driver.isSelected()) {
                     final int parameterIndex = map.get(driver);
                     dAccdParam[0][parameterIndex] += derivativesX[index];
                     dAccdParam[1][parameterIndex] += derivativesY[index];
                     dAccdParam[2][parameterIndex] += derivativesZ[index];
                     ++index;
                 }
             }
 
         }
 
         // the variational equations of the complete state Jacobian matrix have the following form:
 
         // [        |        ]   [                 |                  ]   [     |     ]
         // [  Adot  |  Bdot  ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [  A  |  B  ]
         // [        |        ]   [                 |                  ]   [     |     ]
         // ---------+---------   ------------------+------------------- * ------+------
         // [        |        ]   [                 |                  ]   [     |     ]
         // [  Cdot  |  Ddot  ] = [    dAcc/dPos    |     dAcc/dVel    ]   [  C  |  D  ]
         // [        |        ]   [                 |                  ]   [     |     ]
 
         // The A, B, C and D sub-matrices and their derivatives (Adot ...) are 3x3 matrices
 
         // The expanded multiplication above can be rewritten to take into account
         // the fixed values found in the sub-matrices in the left factor. This leads to:
 
         //     [ Adot ] = [ C ]
         //     [ Bdot ] = [ D ]
         //     [ Cdot ] = [ dAcc/dPos ] * [ A ] + [ dAcc/dVel ] * [ C ]
         //     [ Ddot ] = [ dAcc/dPos ] * [ B ] + [ dAcc/dVel ] * [ D ]
 
         // The following loops compute these expressions taking care of the mapping of the
         // (A, B, C, D) matrices into the single dimension array p and of the mapping of the
         // (Adot, Bdot, Cdot, Ddot) matrices into the single dimension array pDot.
 
         // copy C and E into Adot and Bdot
         final int stateDim = 6;
         final double[] p = s.getAdditionalState(getName());
         System.arraycopy(p, dim * stateDim, pDot, 0, dim * stateDim);
 
         // compute Cdot and Ddot
         for (int i = 0; i < dim; ++i) {
             final double[] dAdPi = dAccdPos[i];
             final double[] dAdVi = dAccdVel[i];
             for (int j = 0; j < stateDim; ++j) {
                 pDot[(dim + i) * stateDim + j] =
                     dAdPi[0] * p[j]                + dAdPi[1] * p[j +     stateDim] + dAdPi[2] * p[j + 2 * stateDim] +
                     dAdVi[0] * p[j + 3 * stateDim] + dAdVi[1] * p[j + 4 * stateDim] + dAdVi[2] * p[j + 5 * stateDim];
             }
         }
 
         for (int k = 0; k < paramDim; ++k) {
             // the variational equations of the parameters Jacobian matrix are computed
             // one column at a time, they have the following form:
             // [      ]   [                 |                  ]   [   ]   [                  ]
             // [ Edot ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [ E ]   [  dVel/dParam = 0 ]
             // [      ]   [                 |                  ]   [   ]   [                  ]
             // --------   ------------------+------------------- * ----- + --------------------
             // [      ]   [                 |                  ]   [   ]   [                  ]
             // [ Fdot ] = [    dAcc/dPos    |     dAcc/dVel    ]   [ F ]   [    dAcc/dParam   ]
             // [      ]   [                 |                  ]   [   ]   [                  ]
 
             // The E and F sub-columns and their derivatives (Edot, Fdot) are 3 elements columns.
 
             // The expanded multiplication and addition above can be rewritten to take into
             // account the fixed values found in the sub-matrices in the left factor. This leads to:
 
             //     [ Edot ] = [ F ]
             //     [ Fdot ] = [ dAcc/dPos ] * [ E ] + [ dAcc/dVel ] * [ F ] + [ dAcc/dParam ]
 
             // The following loops compute these expressions taking care of the mapping of the
             // (E, F) columns into the single dimension array p and of the mapping of the
             // (Edot, Fdot) columns into the single dimension array pDot.
 
             // copy F into Edot
             final int columnTop = stateDim * stateDim + k;
             pDot[columnTop]                = p[columnTop + 3 * paramDim];
             pDot[columnTop +     paramDim] = p[columnTop + 4 * paramDim];
             pDot[columnTop + 2 * paramDim] = p[columnTop + 5 * paramDim];
 
             // compute Fdot
             for (int i = 0; i < dim; ++i) {
                 final double[] dAdPi = dAccdPos[i];
                 final double[] dAdVi = dAccdVel[i];
                 pDot[columnTop + (dim + i) * paramDim] =
                     dAccdParam[i][k] +
                     dAdPi[0] * p[columnTop]                + dAdPi[1] * p[columnTop +     paramDim] + dAdPi[2] * p[columnTop + 2 * paramDim] +
                     dAdVi[0] * p[columnTop + 3 * paramDim] + dAdVi[1] * p[columnTop + 4 * paramDim] + dAdVi[2] * p[columnTop + 5 * paramDim];
             }
 
         }
 
         // these equations have no effect on the main state itself
         return null;
 
     }
 
     /** Get the flag for the initialization of the state jacobian.
      * @return true if the state jacobian is initialized
      * @since 10.2
      */
     public boolean isInitialize() {
         return initialized;
     }
 
     /** Fill Jacobians rows.
      * @param derivatives derivatives of a component of acceleration (along either x, y or z)
      * @param index component index (0 for x, 1 for y, 2 for z)
      * @param freeStateParameters number of free parameters, either 3 (position),
      * 6 (position-velocity) or 7 (position-velocity-mass)
      * @param dAccdPos Jacobian of acceleration with respect to spacecraft position
      * @param dAccdVel Jacobian of acceleration with respect to spacecraft velocity
      */
     private void addToRow(final double[] derivatives, final int index, final int freeStateParameters,
                           final double[][] dAccdPos, final double[][] dAccdVel) {
 
         for (int i = 0; i < 3; ++i) {
             dAccdPos[index][i] += derivatives[i];
         }
         if (freeStateParameters > 3) {
             for (int i = 0; i < 3; ++i) {
                 dAccdVel[index][i] += derivatives[i + 3];
             }
         }
 
     }
 
 }