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Java example source code file (JacobianMatrices.java)

This example Java source code file (JacobianMatrices.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

dimensionmismatchexception, expandablestatefulode, firstorderdifferentialequations, jacobianmatrices, jacobianssecondaryequations, mainstatejacobianprovider, mainstatejacobianwrapper, maxcountexceededexception, mismatchedequations, parameterconfiguration, parameterizedode, parameterjacobianprovider, reflection, string, unknownparameterexception, util

The JacobianMatrices.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF 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.apache.commons.math3.ode;

import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.util.LocalizedFormats;

/**
 * This class defines a set of {@link SecondaryEquations secondary equations} to
 * compute the Jacobian matrices with respect to the initial state vector and, if
 * any, to some parameters of the primary ODE set.
 * <p>
 * It is intended to be packed into an {@link ExpandableStatefulODE}
 * in conjunction with a primary set of ODE, which may be:
 * <ul>
 * <li>a {@link FirstOrderDifferentialEquations}
 * <li>a {@link MainStateJacobianProvider}
 * </ul>
 * In order to compute Jacobian matrices with respect to some parameters of the
 * primary ODE set, the following parameter Jacobian providers may be set:
 * <ul>
 * <li>a {@link ParameterJacobianProvider}
 * <li>a {@link ParameterizedODE}
 * </ul>
 * </p>
 *
 * @see ExpandableStatefulODE
 * @see FirstOrderDifferentialEquations
 * @see MainStateJacobianProvider
 * @see ParameterJacobianProvider
 * @see ParameterizedODE
 *
 * @since 3.0
 */
public class JacobianMatrices {

    /** Expandable first order differential equation. */
    private ExpandableStatefulODE efode;

    /** Index of the instance in the expandable set. */
    private int index;

    /** FODE with exact primary Jacobian computation skill. */
    private MainStateJacobianProvider jode;

    /** FODE without exact parameter Jacobian computation skill. */
    private ParameterizedODE pode;

    /** Main state vector dimension. */
    private int stateDim;

    /** Selected parameters for parameter Jacobian computation. */
    private ParameterConfiguration[] selectedParameters;

    /** FODE with exact parameter Jacobian computation skill. */
    private List<ParameterJacobianProvider> jacobianProviders;

    /** Parameters dimension. */
    private int paramDim;

    /** Boolean for selected parameters consistency. */
    private boolean dirtyParameter;

    /** State and parameters Jacobian matrices in a row. */
    private double[] matricesData;

    /** Simple constructor for a secondary equations set computing Jacobian matrices.
     * <p>
     * Parameters must belong to the supported ones given by {@link
     * Parameterizable#getParametersNames()}, so the primary set of differential
     * equations must be {@link Parameterizable}.
     * </p>
     * <p>Note that each selection clears the previous selected parameters.

* * @param fode the primary first order differential equations set to extend * @param hY step used for finite difference computation with respect to state vector * @param parameters parameters to consider for Jacobian matrices processing * (may be null if parameters Jacobians is not desired) * @exception DimensionMismatchException if there is a dimension mismatch between * the steps array {@code hY} and the equation dimension */ public JacobianMatrices(final FirstOrderDifferentialEquations fode, final double[] hY, final String... parameters) throws DimensionMismatchException { this(new MainStateJacobianWrapper(fode, hY), parameters); } /** Simple constructor for a secondary equations set computing Jacobian matrices. * <p> * Parameters must belong to the supported ones given by {@link * Parameterizable#getParametersNames()}, so the primary set of differential * equations must be {@link Parameterizable}. * </p> * <p>Note that each selection clears the previous selected parameters.

* * @param jode the primary first order differential equations set to extend * @param parameters parameters to consider for Jacobian matrices processing * (may be null if parameters Jacobians is not desired) */ public JacobianMatrices(final MainStateJacobianProvider jode, final String... parameters) { this.efode = null; this.index = -1; this.jode = jode; this.pode = null; this.stateDim = jode.getDimension(); if (parameters == null) { selectedParameters = null; paramDim = 0; } else { this.selectedParameters = new ParameterConfiguration[parameters.length]; for (int i = 0; i < parameters.length; ++i) { selectedParameters[i] = new ParameterConfiguration(parameters[i], Double.NaN); } paramDim = parameters.length; } this.dirtyParameter = false; this.jacobianProviders = new ArrayList<ParameterJacobianProvider>(); // set the default initial state Jacobian to the identity // and the default initial parameters Jacobian to the null matrix matricesData = new double[(stateDim + paramDim) * stateDim]; for (int i = 0; i < stateDim; ++i) { matricesData[i * (stateDim + 1)] = 1.0; } } /** Register the variational equations for the Jacobians matrices to the expandable set. * @param expandable expandable set into which variational equations should be registered * @throws DimensionMismatchException if the dimension of the partial state does not * match the selected equations set dimension * @exception MismatchedEquations if the primary set of the expandable set does * not match the one used to build the instance * @see ExpandableStatefulODE#addSecondaryEquations(SecondaryEquations) */ public void registerVariationalEquations(final ExpandableStatefulODE expandable) throws DimensionMismatchException, MismatchedEquations { // safety checks final FirstOrderDifferentialEquations ode = (jode instanceof MainStateJacobianWrapper) ? ((MainStateJacobianWrapper) jode).ode : jode; if (expandable.getPrimary() != ode) { throw new MismatchedEquations(); } efode = expandable; index = efode.addSecondaryEquations(new JacobiansSecondaryEquations()); efode.setSecondaryState(index, matricesData); } /** Add a parameter Jacobian provider. * @param provider the parameter Jacobian provider to compute exactly the parameter Jacobian matrix */ public void addParameterJacobianProvider(final ParameterJacobianProvider provider) { jacobianProviders.add(provider); } /** Set a parameter Jacobian provider. * @param parameterizedOde the parameterized ODE to compute the parameter Jacobian matrix using finite differences */ public void setParameterizedODE(final ParameterizedODE parameterizedOde) { this.pode = parameterizedOde; dirtyParameter = true; } /** Set the step associated to a parameter in order to compute by finite * difference the Jacobian matrix. * <p> * Needed if and only if the primary ODE set is a {@link ParameterizedODE}. * </p> * <p> * Given a non zero parameter value pval for the parameter, a reasonable value * for such a step is {@code pval * FastMath.sqrt(Precision.EPSILON)}. * </p> * <p> * A zero value for such a step doesn't enable to compute the parameter Jacobian matrix. * </p> * @param parameter parameter to consider for Jacobian processing * @param hP step for Jacobian finite difference computation w.r.t. the specified parameter * @see ParameterizedODE * @exception UnknownParameterException if the parameter is not supported */ public void setParameterStep(final String parameter, final double hP) throws UnknownParameterException { for (ParameterConfiguration param: selectedParameters) { if (parameter.equals(param.getParameterName())) { param.setHP(hP); dirtyParameter = true; return; } } throw new UnknownParameterException(parameter); } /** Set the initial value of the Jacobian matrix with respect to state. * <p> * If this method is not called, the initial value of the Jacobian * matrix with respect to state is set to identity. * </p> * @param dYdY0 initial Jacobian matrix w.r.t. state * @exception DimensionMismatchException if matrix dimensions are incorrect */ public void setInitialMainStateJacobian(final double[][] dYdY0) throws DimensionMismatchException { // Check dimensions checkDimension(stateDim, dYdY0); checkDimension(stateDim, dYdY0[0]); // store the matrix in row major order as a single dimension array int i = 0; for (final double[] row : dYdY0) { System.arraycopy(row, 0, matricesData, i, stateDim); i += stateDim; } if (efode != null) { efode.setSecondaryState(index, matricesData); } } /** Set the initial value of a column of the Jacobian matrix with respect to one parameter. * <p> * If this method is not called for some parameter, the initial value of * the column of the Jacobian matrix with respect to this parameter is set to zero. * </p> * @param pName parameter name * @param dYdP initial Jacobian column vector with respect to the parameter * @exception UnknownParameterException if a parameter is not supported * @throws DimensionMismatchException if the column vector does not match state dimension */ public void setInitialParameterJacobian(final String pName, final double[] dYdP) throws UnknownParameterException, DimensionMismatchException { // Check dimensions checkDimension(stateDim, dYdP); // store the column in a global single dimension array int i = stateDim * stateDim; for (ParameterConfiguration param: selectedParameters) { if (pName.equals(param.getParameterName())) { System.arraycopy(dYdP, 0, matricesData, i, stateDim); if (efode != null) { efode.setSecondaryState(index, matricesData); } return; } i += stateDim; } throw new UnknownParameterException(pName); } /** Get the current value of the Jacobian matrix with respect to state. * @param dYdY0 current Jacobian matrix with respect to state. */ public void getCurrentMainSetJacobian(final double[][] dYdY0) { // get current state for this set of equations from the expandable fode double[] p = efode.getSecondaryState(index); int j = 0; for (int i = 0; i < stateDim; i++) { System.arraycopy(p, j, dYdY0[i], 0, stateDim); j += stateDim; } } /** Get the current value of the Jacobian matrix with respect to one parameter. * @param pName name of the parameter for the computed Jacobian matrix * @param dYdP current Jacobian matrix with respect to the named parameter */ public void getCurrentParameterJacobian(String pName, final double[] dYdP) { // get current state for this set of equations from the expandable fode double[] p = efode.getSecondaryState(index); int i = stateDim * stateDim; for (ParameterConfiguration param: selectedParameters) { if (param.getParameterName().equals(pName)) { System.arraycopy(p, i, dYdP, 0, stateDim); return; } i += stateDim; } } /** Check array dimensions. * @param expected expected dimension * @param array (may be null if expected is 0) * @throws DimensionMismatchException if the array dimension does not match the expected one */ private void checkDimension(final int expected, final Object array) throws DimensionMismatchException { int arrayDimension = (array == null) ? 0 : Array.getLength(array); if (arrayDimension != expected) { throw new DimensionMismatchException(arrayDimension, expected); } } /** Local implementation of secondary equations. * <p> * This class is an inner class to ensure proper scheduling of calls * by forcing the use of {@link JacobianMatrices#registerVariationalEquations(ExpandableStatefulODE)}. * </p> */ private class JacobiansSecondaryEquations implements SecondaryEquations { /** {@inheritDoc} */ public int getDimension() { return stateDim * (stateDim + paramDim); } /** {@inheritDoc} */ public void computeDerivatives(final double t, final double[] y, final double[] yDot, final double[] z, final double[] zDot) throws MaxCountExceededException, DimensionMismatchException { // Lazy initialization if (dirtyParameter && (paramDim != 0)) { jacobianProviders.add(new ParameterJacobianWrapper(jode, pode, selectedParameters)); dirtyParameter = false; } // variational equations: // from d[dy/dt]/dy0 and d[dy/dt]/dp to d[dy/dy0]/dt and d[dy/dp]/dt // compute Jacobian matrix with respect to primary state double[][] dFdY = new double[stateDim][stateDim]; jode.computeMainStateJacobian(t, y, yDot, dFdY); // Dispatch Jacobian matrix in the compound secondary state vector for (int i = 0; i < stateDim; ++i) { final double[] dFdYi = dFdY[i]; for (int j = 0; j < stateDim; ++j) { double s = 0; final int startIndex = j; int zIndex = startIndex; for (int l = 0; l < stateDim; ++l) { s += dFdYi[l] * z[zIndex]; zIndex += stateDim; } zDot[startIndex + i * stateDim] = s; } } if (paramDim != 0) { // compute Jacobian matrices with respect to parameters double[] dFdP = new double[stateDim]; int startIndex = stateDim * stateDim; for (ParameterConfiguration param: selectedParameters) { boolean found = false; for (int k = 0 ; (!found) && (k < jacobianProviders.size()); ++k) { final ParameterJacobianProvider provider = jacobianProviders.get(k); if (provider.isSupported(param.getParameterName())) { provider.computeParameterJacobian(t, y, yDot, param.getParameterName(), dFdP); for (int i = 0; i < stateDim; ++i) { final double[] dFdYi = dFdY[i]; int zIndex = startIndex; double s = dFdP[i]; for (int l = 0; l < stateDim; ++l) { s += dFdYi[l] * z[zIndex]; zIndex++; } zDot[startIndex + i] = s; } found = true; } } if (! found) { Arrays.fill(zDot, startIndex, startIndex + stateDim, 0.0); } startIndex += stateDim; } } } } /** Wrapper class to compute jacobian matrices by finite differences for ODE * which do not compute them by themselves. */ private static class MainStateJacobianWrapper implements MainStateJacobianProvider { /** Raw ODE without jacobians computation skill to be wrapped into a MainStateJacobianProvider. */ private final FirstOrderDifferentialEquations ode; /** Steps for finite difference computation of the jacobian df/dy w.r.t. state. */ private final double[] hY; /** Wrap a {@link FirstOrderDifferentialEquations} into a {@link MainStateJacobianProvider}. * @param ode original ODE problem, without jacobians computation skill * @param hY step sizes to compute the jacobian df/dy * @exception DimensionMismatchException if there is a dimension mismatch between * the steps array {@code hY} and the equation dimension */ MainStateJacobianWrapper(final FirstOrderDifferentialEquations ode, final double[] hY) throws DimensionMismatchException { this.ode = ode; this.hY = hY.clone(); if (hY.length != ode.getDimension()) { throw new DimensionMismatchException(ode.getDimension(), hY.length); } } /** {@inheritDoc} */ public int getDimension() { return ode.getDimension(); } /** {@inheritDoc} */ public void computeDerivatives(double t, double[] y, double[] yDot) throws MaxCountExceededException, DimensionMismatchException { ode.computeDerivatives(t, y, yDot); } /** {@inheritDoc} */ public void computeMainStateJacobian(double t, double[] y, double[] yDot, double[][] dFdY) throws MaxCountExceededException, DimensionMismatchException { final int n = ode.getDimension(); final double[] tmpDot = new double[n]; for (int j = 0; j < n; ++j) { final double savedYj = y[j]; y[j] += hY[j]; ode.computeDerivatives(t, y, tmpDot); for (int i = 0; i < n; ++i) { dFdY[i][j] = (tmpDot[i] - yDot[i]) / hY[j]; } y[j] = savedYj; } } } /** * Special exception for equations mismatch. * @since 3.1 */ public static class MismatchedEquations extends MathIllegalArgumentException { /** Serializable UID. */ private static final long serialVersionUID = 20120902L; /** Simple constructor. */ public MismatchedEquations() { super(LocalizedFormats.UNMATCHED_ODE_IN_EXPANDED_SET); } } }

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