| /* |
| * 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.math.ode.nonstiff; |
| |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.ode.AbstractIntegrator; |
| import org.apache.commons.math.ode.DerivativeException; |
| import org.apache.commons.math.ode.ExtendedFirstOrderDifferentialEquations; |
| import org.apache.commons.math.ode.FirstOrderDifferentialEquations; |
| import org.apache.commons.math.ode.IntegratorException; |
| import org.apache.commons.math.util.FastMath; |
| |
| /** |
| * This abstract class holds the common part of all adaptive |
| * stepsize integrators for Ordinary Differential Equations. |
| * |
| * <p>These algorithms perform integration with stepsize control, which |
| * means the user does not specify the integration step but rather a |
| * tolerance on error. The error threshold is computed as |
| * <pre> |
| * threshold_i = absTol_i + relTol_i * max (abs (ym), abs (ym+1)) |
| * </pre> |
| * where absTol_i is the absolute tolerance for component i of the |
| * state vector and relTol_i is the relative tolerance for the same |
| * component. The user can also use only two scalar values absTol and |
| * relTol which will be used for all components. |
| * </p> |
| * |
| * <p>If the Ordinary Differential Equations is an {@link ExtendedFirstOrderDifferentialEquations |
| * extended ODE} rather than a {@link FirstOrderDifferentialEquations basic ODE}, |
| * then <em>only</em> the {@link ExtendedFirstOrderDifferentialEquations#getMainSetDimension() |
| * main set} part of the state vector is used for stepsize control, not the complete |
| * state vector. |
| * </p> |
| * |
| * <p>If the estimated error for ym+1 is such that |
| * <pre> |
| * sqrt((sum (errEst_i / threshold_i)^2 ) / n) < 1 |
| * </pre> |
| * |
| * (where n is the main set dimension) then the step is accepted, |
| * otherwise the step is rejected and a new attempt is made with a new |
| * stepsize.</p> |
| * |
| * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ |
| * @since 1.2 |
| * |
| */ |
| |
| public abstract class AdaptiveStepsizeIntegrator |
| extends AbstractIntegrator { |
| |
| /** Allowed absolute scalar error. */ |
| protected final double scalAbsoluteTolerance; |
| |
| /** Allowed relative scalar error. */ |
| protected final double scalRelativeTolerance; |
| |
| /** Allowed absolute vectorial error. */ |
| protected final double[] vecAbsoluteTolerance; |
| |
| /** Allowed relative vectorial error. */ |
| protected final double[] vecRelativeTolerance; |
| |
| /** Main set dimension. */ |
| protected int mainSetDimension; |
| |
| /** User supplied initial step. */ |
| private double initialStep; |
| |
| /** Minimal step. */ |
| private final double minStep; |
| |
| /** Maximal step. */ |
| private final double maxStep; |
| |
| /** Build an integrator with the given stepsize bounds. |
| * The default step handler does nothing. |
| * @param name name of the method |
| * @param minStep minimal step (must be positive even for backward |
| * integration), the last step can be smaller than this |
| * @param maxStep maximal step (must be positive even for backward |
| * integration) |
| * @param scalAbsoluteTolerance allowed absolute error |
| * @param scalRelativeTolerance allowed relative error |
| */ |
| public AdaptiveStepsizeIntegrator(final String name, |
| final double minStep, final double maxStep, |
| final double scalAbsoluteTolerance, |
| final double scalRelativeTolerance) { |
| |
| super(name); |
| |
| this.minStep = FastMath.abs(minStep); |
| this.maxStep = FastMath.abs(maxStep); |
| this.initialStep = -1.0; |
| |
| this.scalAbsoluteTolerance = scalAbsoluteTolerance; |
| this.scalRelativeTolerance = scalRelativeTolerance; |
| this.vecAbsoluteTolerance = null; |
| this.vecRelativeTolerance = null; |
| |
| resetInternalState(); |
| |
| } |
| |
| /** Build an integrator with the given stepsize bounds. |
| * The default step handler does nothing. |
| * @param name name of the method |
| * @param minStep minimal step (must be positive even for backward |
| * integration), the last step can be smaller than this |
| * @param maxStep maximal step (must be positive even for backward |
| * integration) |
| * @param vecAbsoluteTolerance allowed absolute error |
| * @param vecRelativeTolerance allowed relative error |
| */ |
| public AdaptiveStepsizeIntegrator(final String name, |
| final double minStep, final double maxStep, |
| final double[] vecAbsoluteTolerance, |
| final double[] vecRelativeTolerance) { |
| |
| super(name); |
| |
| this.minStep = minStep; |
| this.maxStep = maxStep; |
| this.initialStep = -1.0; |
| |
| this.scalAbsoluteTolerance = 0; |
| this.scalRelativeTolerance = 0; |
| this.vecAbsoluteTolerance = vecAbsoluteTolerance.clone(); |
| this.vecRelativeTolerance = vecRelativeTolerance.clone(); |
| |
| resetInternalState(); |
| |
| } |
| |
| /** Set the initial step size. |
| * <p>This method allows the user to specify an initial positive |
| * step size instead of letting the integrator guess it by |
| * itself. If this method is not called before integration is |
| * started, the initial step size will be estimated by the |
| * integrator.</p> |
| * @param initialStepSize initial step size to use (must be positive even |
| * for backward integration ; providing a negative value or a value |
| * outside of the min/max step interval will lead the integrator to |
| * ignore the value and compute the initial step size by itself) |
| */ |
| public void setInitialStepSize(final double initialStepSize) { |
| if ((initialStepSize < minStep) || (initialStepSize > maxStep)) { |
| initialStep = -1.0; |
| } else { |
| initialStep = initialStepSize; |
| } |
| } |
| |
| /** Perform some sanity checks on the integration parameters. |
| * @param equations differential equations set |
| * @param t0 start time |
| * @param y0 state vector at t0 |
| * @param t target time for the integration |
| * @param y placeholder where to put the state vector |
| * @exception IntegratorException if some inconsistency is detected |
| */ |
| @Override |
| protected void sanityChecks(final FirstOrderDifferentialEquations equations, |
| final double t0, final double[] y0, |
| final double t, final double[] y) |
| throws IntegratorException { |
| |
| super.sanityChecks(equations, t0, y0, t, y); |
| |
| if (equations instanceof ExtendedFirstOrderDifferentialEquations) { |
| mainSetDimension = ((ExtendedFirstOrderDifferentialEquations) equations).getMainSetDimension(); |
| } else { |
| mainSetDimension = equations.getDimension(); |
| } |
| |
| if ((vecAbsoluteTolerance != null) && (vecAbsoluteTolerance.length != mainSetDimension)) { |
| throw new IntegratorException( |
| LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, mainSetDimension, vecAbsoluteTolerance.length); |
| } |
| |
| if ((vecRelativeTolerance != null) && (vecRelativeTolerance.length != mainSetDimension)) { |
| throw new IntegratorException( |
| LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, mainSetDimension, vecRelativeTolerance.length); |
| } |
| |
| } |
| |
| /** Initialize the integration step. |
| * @param equations differential equations set |
| * @param forward forward integration indicator |
| * @param order order of the method |
| * @param scale scaling vector for the state vector (can be shorter than state vector) |
| * @param t0 start time |
| * @param y0 state vector at t0 |
| * @param yDot0 first time derivative of y0 |
| * @param y1 work array for a state vector |
| * @param yDot1 work array for the first time derivative of y1 |
| * @return first integration step |
| * @exception DerivativeException this exception is propagated to |
| * the caller if the underlying user function triggers one |
| */ |
| public double initializeStep(final FirstOrderDifferentialEquations equations, |
| final boolean forward, final int order, final double[] scale, |
| final double t0, final double[] y0, final double[] yDot0, |
| final double[] y1, final double[] yDot1) |
| throws DerivativeException { |
| |
| if (initialStep > 0) { |
| // use the user provided value |
| return forward ? initialStep : -initialStep; |
| } |
| |
| // very rough first guess : h = 0.01 * ||y/scale|| / ||y'/scale|| |
| // this guess will be used to perform an Euler step |
| double ratio; |
| double yOnScale2 = 0; |
| double yDotOnScale2 = 0; |
| for (int j = 0; j < scale.length; ++j) { |
| ratio = y0[j] / scale[j]; |
| yOnScale2 += ratio * ratio; |
| ratio = yDot0[j] / scale[j]; |
| yDotOnScale2 += ratio * ratio; |
| } |
| |
| double h = ((yOnScale2 < 1.0e-10) || (yDotOnScale2 < 1.0e-10)) ? |
| 1.0e-6 : (0.01 * FastMath.sqrt(yOnScale2 / yDotOnScale2)); |
| if (! forward) { |
| h = -h; |
| } |
| |
| // perform an Euler step using the preceding rough guess |
| for (int j = 0; j < y0.length; ++j) { |
| y1[j] = y0[j] + h * yDot0[j]; |
| } |
| computeDerivatives(t0 + h, y1, yDot1); |
| |
| // estimate the second derivative of the solution |
| double yDDotOnScale = 0; |
| for (int j = 0; j < scale.length; ++j) { |
| ratio = (yDot1[j] - yDot0[j]) / scale[j]; |
| yDDotOnScale += ratio * ratio; |
| } |
| yDDotOnScale = FastMath.sqrt(yDDotOnScale) / h; |
| |
| // step size is computed such that |
| // h^order * max (||y'/tol||, ||y''/tol||) = 0.01 |
| final double maxInv2 = FastMath.max(FastMath.sqrt(yDotOnScale2), yDDotOnScale); |
| final double h1 = (maxInv2 < 1.0e-15) ? |
| FastMath.max(1.0e-6, 0.001 * FastMath.abs(h)) : |
| FastMath.pow(0.01 / maxInv2, 1.0 / order); |
| h = FastMath.min(100.0 * FastMath.abs(h), h1); |
| h = FastMath.max(h, 1.0e-12 * FastMath.abs(t0)); // avoids cancellation when computing t1 - t0 |
| if (h < getMinStep()) { |
| h = getMinStep(); |
| } |
| if (h > getMaxStep()) { |
| h = getMaxStep(); |
| } |
| if (! forward) { |
| h = -h; |
| } |
| |
| return h; |
| |
| } |
| |
| /** Filter the integration step. |
| * @param h signed step |
| * @param forward forward integration indicator |
| * @param acceptSmall if true, steps smaller than the minimal value |
| * are silently increased up to this value, if false such small |
| * steps generate an exception |
| * @return a bounded integration step (h if no bound is reach, or a bounded value) |
| * @exception IntegratorException if the step is too small and acceptSmall is false |
| */ |
| protected double filterStep(final double h, final boolean forward, final boolean acceptSmall) |
| throws IntegratorException { |
| |
| double filteredH = h; |
| if (FastMath.abs(h) < minStep) { |
| if (acceptSmall) { |
| filteredH = forward ? minStep : -minStep; |
| } else { |
| throw new IntegratorException( |
| LocalizedFormats.MINIMAL_STEPSIZE_REACHED_DURING_INTEGRATION, |
| minStep, FastMath.abs(h)); |
| } |
| } |
| |
| if (filteredH > maxStep) { |
| filteredH = maxStep; |
| } else if (filteredH < -maxStep) { |
| filteredH = -maxStep; |
| } |
| |
| return filteredH; |
| |
| } |
| |
| /** {@inheritDoc} */ |
| public abstract double integrate (FirstOrderDifferentialEquations equations, |
| double t0, double[] y0, |
| double t, double[] y) |
| throws DerivativeException, IntegratorException; |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double getCurrentStepStart() { |
| return stepStart; |
| } |
| |
| /** Reset internal state to dummy values. */ |
| protected void resetInternalState() { |
| stepStart = Double.NaN; |
| stepSize = FastMath.sqrt(minStep * maxStep); |
| } |
| |
| /** Get the minimal step. |
| * @return minimal step |
| */ |
| public double getMinStep() { |
| return minStep; |
| } |
| |
| /** Get the maximal step. |
| * @return maximal step |
| */ |
| public double getMaxStep() { |
| return maxStep; |
| } |
| |
| } |
