home | career | drupal | java | mac | mysql | perl | scala | uml | unix  
* * <tr> * * <tr> * </table> * * @since 1.2 */ public class GraggBulirschStoerIntegrator extends AdaptiveStepsizeIntegrator { /** Integrator method name. */ private static final String METHOD_NAME = "Gragg-Bulirsch-Stoer"; /** maximal order. */ private int maxOrder; /** step size sequence. */ private int[] sequence; /** overall cost of applying step reduction up to iteration k+1, in number of calls. */ private int[] costPerStep; /** cost per unit step. */ private double[] costPerTimeUnit; /** optimal steps for each order. */ private double[] optimalStep; /** extrapolation coefficients. */ private double[][] coeff; /** stability check enabling parameter. */ private boolean performTest; /** maximal number of checks for each iteration. */ private int maxChecks; /** maximal number of iterations for which checks are performed. */ private int maxIter; /** stepsize reduction factor in case of stability check failure. */ private double stabilityReduction; /** first stepsize control factor. */ private double stepControl1; /** second stepsize control factor. */ private double stepControl2; /** third stepsize control factor. */ private double stepControl3; /** fourth stepsize control factor. */ private double stepControl4; /** first order control factor. */ private double orderControl1; /** second order control factor. */ private double orderControl2; /** use interpolation error in stepsize control. */ private boolean useInterpolationError; /** interpolation order control parameter. */ private int mudif; /** Simple constructor. * Build a Gragg-Bulirsch-Stoer integrator with the given step * bounds. All tuning parameters are set to their default * values. The default step handler does nothing. * @param minStep minimal step (sign is irrelevant, regardless of * integration direction, forward or backward), the last step can * be smaller than this * @param maxStep maximal step (sign is irrelevant, regardless of * integration direction, forward or backward), the last step can * be smaller than this * @param scalAbsoluteTolerance allowed absolute error * @param scalRelativeTolerance allowed relative error */ public GraggBulirschStoerIntegrator(final double minStep, final double maxStep, final double scalAbsoluteTolerance, final double scalRelativeTolerance) { super(METHOD_NAME, minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); setStabilityCheck(true, -1, -1, -1); setControlFactors(-1, -1, -1, -1); setOrderControl(-1, -1, -1); setInterpolationControl(true, -1); } /** Simple constructor. * Build a Gragg-Bulirsch-Stoer integrator with the given step * bounds. All tuning parameters are set to their default * values. The default step handler does nothing. * @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 GraggBulirschStoerIntegrator(final double minStep, final double maxStep, final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance) { super(METHOD_NAME, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); setStabilityCheck(true, -1, -1, -1); setControlFactors(-1, -1, -1, -1); setOrderControl(-1, -1, -1); setInterpolationControl(true, -1); } /** Set the stability check controls. * <p>The stability check is performed on the first few iterations of * the extrapolation scheme. If this test fails, the step is rejected * and the stepsize is reduced.</p> * <p>By default, the test is performed, at most during two * iterations at each step, and at most once for each of these * iterations. The default stepsize reduction factor is 0.5.</p> * @param performStabilityCheck if true, stability check will be performed, if false, the check will be skipped * @param maxNumIter maximal number of iterations for which checks are * performed (the number of iterations is reset to default if negative * or null) * @param maxNumChecks maximal number of checks for each iteration * (the number of checks is reset to default if negative or null) * @param stepsizeReductionFactor stepsize reduction factor in case of * failure (the factor is reset to default if lower than 0.0001 or * greater than 0.9999) */ public void setStabilityCheck(final boolean performStabilityCheck, final int maxNumIter, final int maxNumChecks, final double stepsizeReductionFactor) { this.performTest = performStabilityCheck; this.maxIter = (maxNumIter <= 0) ? 2 : maxNumIter; this.maxChecks = (maxNumChecks <= 0) ? 1 : maxNumChecks; if ((stepsizeReductionFactor < 0.0001) || (stepsizeReductionFactor > 0.9999)) { this.stabilityReduction = 0.5; } else { this.stabilityReduction = stepsizeReductionFactor; } } /** Set the step size control factors. * <p>The new step size hNew is computed from the old one h by: * <pre> * hNew = h * stepControl2 / (err/stepControl1)^(1/(2k+1)) * </pre> * where err is the scaled error and k the iteration number of the * extrapolation scheme (counting from 0). The default values are * 0.65 for stepControl1 and 0.94 for stepControl2.</p> * <p>The step size is subject to the restriction: * <pre> * stepControl3^(1/(2k+1))/stepControl4 <= hNew/h <= 1/stepControl3^(1/(2k+1)) * </pre> * The default values are 0.02 for stepControl3 and 4.0 for * stepControl4.</p> * @param control1 first stepsize control factor (the factor is * reset to default if lower than 0.0001 or greater than 0.9999) * @param control2 second stepsize control factor (the factor * is reset to default if lower than 0.0001 or greater than 0.9999) * @param control3 third stepsize control factor (the factor is * reset to default if lower than 0.0001 or greater than 0.9999) * @param control4 fourth stepsize control factor (the factor * is reset to default if lower than 1.0001 or greater than 999.9) */ public void setControlFactors(final double control1, final double control2, final double control3, final double control4) { if ((control1 < 0.0001) || (control1 > 0.9999)) { this.stepControl1 = 0.65; } else { this.stepControl1 = control1; } if ((control2 < 0.0001) || (control2 > 0.9999)) { this.stepControl2 = 0.94; } else { this.stepControl2 = control2; } if ((control3 < 0.0001) || (control3 > 0.9999)) { this.stepControl3 = 0.02; } else { this.stepControl3 = control3; } if ((control4 < 1.0001) || (control4 > 999.9)) { this.stepControl4 = 4.0; } else { this.stepControl4 = control4; } } /** Set the order control parameters. * <p>The Gragg-Bulirsch-Stoer method changes both the step size and * the order during integration, in order to minimize computation * cost. Each extrapolation step increases the order by 2, so the * maximal order that will be used is always even, it is twice the * maximal number of columns in the extrapolation table.</p> * <pre> * order is decreased if w(k-1) <= w(k) * orderControl1 * order is increased if w(k) <= w(k-1) * orderControl2 * </pre> * <p>where w is the table of work per unit step for each order * (number of function calls divided by the step length), and k is * the current order.</p> * <p>The default maximal order after construction is 18 (i.e. the * maximal number of columns is 9). The default values are 0.8 for * orderControl1 and 0.9 for orderControl2.</p> * @param maximalOrder maximal order in the extrapolation table (the * maximal order is reset to default if order <= 6 or odd) * @param control1 first order control factor (the factor is * reset to default if lower than 0.0001 or greater than 0.9999) * @param control2 second order control factor (the factor * is reset to default if lower than 0.0001 or greater than 0.9999) */ public void setOrderControl(final int maximalOrder, final double control1, final double control2) { if ((maximalOrder <= 6) || (maximalOrder % 2 != 0)) { this.maxOrder = 18; } if ((control1 < 0.0001) || (control1 > 0.9999)) { this.orderControl1 = 0.8; } else { this.orderControl1 = control1; } if ((control2 < 0.0001) || (control2 > 0.9999)) { this.orderControl2 = 0.9; } else { this.orderControl2 = control2; } // reinitialize the arrays initializeArrays(); } /** {@inheritDoc} */ @Override public void addStepHandler (final StepHandler handler) { super.addStepHandler(handler); // reinitialize the arrays initializeArrays(); } /** {@inheritDoc} */ @Override public void addEventHandler(final EventHandler function, final double maxCheckInterval, final double convergence, final int maxIterationCount, final UnivariateSolver solver) { super.addEventHandler(function, maxCheckInterval, convergence, maxIterationCount, solver); // reinitialize the arrays initializeArrays(); } /** Initialize the integrator internal arrays. */ private void initializeArrays() { final int size = maxOrder / 2; if ((sequence == null) || (sequence.length != size)) { // all arrays should be reallocated with the right size sequence = new int[size]; costPerStep = new int[size]; coeff = new double[size][]; costPerTimeUnit = new double[size]; optimalStep = new double[size]; } // step size sequence: 2, 6, 10, 14, ... for (int k = 0; k < size; ++k) { sequence[k] = 4 * k + 2; } // initialize the order selection cost array // (number of function calls for each column of the extrapolation table) costPerStep[0] = sequence[0] + 1; for (int k = 1; k < size; ++k) { costPerStep[k] = costPerStep[k-1] + sequence[k]; } // initialize the extrapolation tables for (int k = 0; k < size; ++k) { coeff[k] = (k > 0) ? new double[k] : null; for (int l = 0; l < k; ++l) { final double ratio = ((double) sequence[k]) / sequence[k-l-1]; coeff[k][l] = 1.0 / (ratio * ratio - 1.0); } } } /** Set the interpolation order control parameter. * The interpolation order for dense output is 2k - mudif + 1. The * default value for mudif is 4 and the interpolation error is used * in stepsize control by default. * @param useInterpolationErrorForControl if true, interpolation error is used * for stepsize control * @param mudifControlParameter interpolation order control parameter (the parameter * is reset to default if <= 0 or >= 7) */ public void setInterpolationControl(final boolean useInterpolationErrorForControl, final int mudifControlParameter) { this.useInterpolationError = useInterpolationErrorForControl; if ((mudifControlParameter <= 0) || (mudifControlParameter >= 7)) { this.mudif = 4; } else { this.mudif = mudifControlParameter; } } /** Update scaling array. * @param y1 first state vector to use for scaling * @param y2 second state vector to use for scaling * @param scale scaling array to update (can be shorter than state) */ private void rescale(final double[] y1, final double[] y2, final double[] scale) { if (vecAbsoluteTolerance == null) { for (int i = 0; i < scale.length; ++i) { final double yi = FastMath.max(FastMath.abs(y1[i]), FastMath.abs(y2[i])); scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * yi; } } else { for (int i = 0; i < scale.length; ++i) { final double yi = FastMath.max(FastMath.abs(y1[i]), FastMath.abs(y2[i])); scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i] * yi; } } } /** Perform integration over one step using substeps of a modified * midpoint method. * @param t0 initial time * @param y0 initial value of the state vector at t0 * @param step global step * @param k iteration number (from 0 to sequence.length - 1) * @param scale scaling array (can be shorter than state) * @param f placeholder where to put the state vector derivatives at each substep * (element 0 already contains initial derivative) * @param yMiddle placeholder where to put the state vector at the middle of the step * @param yEnd placeholder where to put the state vector at the end * @param yTmp placeholder for one state vector * @return true if computation was done properly, * false if stability check failed before end of computation * @exception MaxCountExceededException if the number of functions evaluations is exceeded * @exception DimensionMismatchException if arrays dimensions do not match equations settings */ private boolean tryStep(final double t0, final double[] y0, final double step, final int k, final double[] scale, final double[][] f, final double[] yMiddle, final double[] yEnd, final double[] yTmp) throws MaxCountExceededException, DimensionMismatchException { final int n = sequence[k]; final double subStep = step / n; final double subStep2 = 2 * subStep; // first substep double t = t0 + subStep; for (int i = 0; i < y0.length; ++i) { yTmp[i] = y0[i]; yEnd[i] = y0[i] + subStep * f[0][i]; } computeDerivatives(t, yEnd, f[1]); // other substeps for (int j = 1; j < n; ++j) { if (2 * j == n) { // save the point at the middle of the step System.arraycopy(yEnd, 0, yMiddle, 0, y0.length); } t += subStep; for (int i = 0; i < y0.length; ++i) { final double middle = yEnd[i]; yEnd[i] = yTmp[i] + subStep2 * f[j][i]; yTmp[i] = middle; } computeDerivatives(t, yEnd, f[j+1]); // stability check if (performTest && (j <= maxChecks) && (k < maxIter)) { double initialNorm = 0.0; for (int l = 0; l < scale.length; ++l) { final double ratio = f[0][l] / scale[l]; initialNorm += ratio * ratio; } double deltaNorm = 0.0; for (int l = 0; l < scale.length; ++l) { final double ratio = (f[j+1][l] - f[0][l]) / scale[l]; deltaNorm += ratio * ratio; } if (deltaNorm > 4 * FastMath.max(1.0e-15, initialNorm)) { return false; } } } // correction of the last substep (at t0 + step) for (int i = 0; i < y0.length; ++i) { yEnd[i] = 0.5 * (yTmp[i] + yEnd[i] + subStep * f[n][i]); } return true; } /** Extrapolate a vector. * @param offset offset to use in the coefficients table * @param k index of the last updated point * @param diag working diagonal of the Aitken-Neville's * triangle, without the last element * @param last last element */ private void extrapolate(final int offset, final int k, final double[][] diag, final double[] last) { // update the diagonal for (int j = 1; j < k; ++j) { for (int i = 0; i < last.length; ++i) { // Aitken-Neville's recursive formula diag[k-j-1][i] = diag[k-j][i] + coeff[k+offset][j-1] * (diag[k-j][i] - diag[k-j-1][i]); } } // update the last element for (int i = 0; i < last.length; ++i) { // Aitken-Neville's recursive formula last[i] = diag[0][i] + coeff[k+offset][k-1] * (diag[0][i] - last[i]); } } /** {@inheritDoc} */ @Override public void integrate(final ExpandableStatefulODE equations, final double t) throws NumberIsTooSmallException, DimensionMismatchException, MaxCountExceededException, NoBracketingException { sanityChecks(equations, t); setEquations(equations); final boolean forward = t > equations.getTime(); // create some internal working arrays final double[] y0 = equations.getCompleteState(); final double[] y = y0.clone(); final double[] yDot0 = new double[y.length]; final double[] y1 = new double[y.length]; final double[] yTmp = new double[y.length]; final double[] yTmpDot = new double[y.length]; final double[][] diagonal = new double[sequence.length-1][]; final double[][] y1Diag = new double[sequence.length-1][]; for (int k = 0; k < sequence.length-1; ++k) { diagonal[k] = new double[y.length]; y1Diag[k] = new double[y.length]; } final double[][][] fk = new double[sequence.length][][]; for (int k = 0; k < sequence.length; ++k) { fk[k] = new double[sequence[k] + 1][]; // all substeps start at the same point, so share the first array fk[k][0] = yDot0; for (int l = 0; l < sequence[k]; ++l) { fk[k][l+1] = new double[y0.length]; } } if (y != y0) { System.arraycopy(y0, 0, y, 0, y0.length); } final double[] yDot1 = new double[y0.length]; final double[][] yMidDots = new double[1 + 2 * sequence.length][y0.length]; // initial scaling final double[] scale = new double[mainSetDimension]; rescale(y, y, scale); // initial order selection final double tol = (vecRelativeTolerance == null) ? scalRelativeTolerance : vecRelativeTolerance[0]; final double log10R = FastMath.log10(FastMath.max(1.0e-10, tol)); int targetIter = FastMath.max(1, FastMath.min(sequence.length - 2, (int) FastMath.floor(0.5 - 0.6 * log10R))); // set up an interpolator sharing the integrator arrays final AbstractStepInterpolator interpolator = new GraggBulirschStoerStepInterpolator(y, yDot0, y1, yDot1, yMidDots, forward, equations.getPrimaryMapper(), equations.getSecondaryMappers()); interpolator.storeTime(equations.getTime()); stepStart = equations.getTime(); double hNew = 0; double maxError = Double.MAX_VALUE; boolean previousRejected = false; boolean firstTime = true; boolean newStep = true; boolean firstStepAlreadyComputed = false; initIntegration(equations.getTime(), y0, t); costPerTimeUnit[0] = 0; isLastStep = false; do { double error; boolean reject = false; if (newStep) { interpolator.shift(); // first evaluation, at the beginning of the step if (! firstStepAlreadyComputed) { computeDerivatives(stepStart, y, yDot0); } if (firstTime) { hNew = initializeStep(forward, 2 * targetIter + 1, scale, stepStart, y, yDot0, yTmp, yTmpDot); } newStep = false; } stepSize = hNew; // step adjustment near bounds if ((forward && (stepStart + stepSize > t)) || ((! forward) && (stepStart + stepSize < t))) { stepSize = t - stepStart; } final double nextT = stepStart + stepSize; isLastStep = forward ? (nextT >= t) : (nextT <= t); // iterate over several substep sizes int k = -1; for (boolean loop = true; loop; ) { ++k; // modified midpoint integration with the current substep if ( ! tryStep(stepStart, y, stepSize, k, scale, fk[k], (k == 0) ? yMidDots[0] : diagonal[k-1], (k == 0) ? y1 : y1Diag[k-1], yTmp)) { // the stability check failed, we reduce the global step hNew = FastMath.abs(filterStep(stepSize * stabilityReduction, forward, false)); reject = true; loop = false; } else { // the substep was computed successfully if (k > 0) { // extrapolate the state at the end of the step // using last iteration data extrapolate(0, k, y1Diag, y1); rescale(y, y1, scale); // estimate the error at the end of the step. error = 0; for (int j = 0; j < mainSetDimension; ++j) { final double e = FastMath.abs(y1[j] - y1Diag[0][j]) / scale[j]; error += e * e; } error = FastMath.sqrt(error / mainSetDimension); if ((error > 1.0e15) || ((k > 1) && (error > maxError))) { // error is too big, we reduce the global step hNew = FastMath.abs(filterStep(stepSize * stabilityReduction, forward, false)); reject = true; loop = false; } else { maxError = FastMath.max(4 * error, 1.0); // compute optimal stepsize for this order final double exp = 1.0 / (2 * k + 1); double fac = stepControl2 / FastMath.pow(error / stepControl1, exp); final double pow = FastMath.pow(stepControl3, exp); fac = FastMath.max(pow / stepControl4, FastMath.min(1 / pow, fac)); optimalStep[k] = FastMath.abs(filterStep(stepSize * fac, forward, true)); costPerTimeUnit[k] = costPerStep[k] / optimalStep[k]; // check convergence switch (k - targetIter) { case -1 : if ((targetIter > 1) && ! previousRejected) { // check if we can stop iterations now if (error <= 1.0) { // convergence have been reached just before targetIter loop = false; } else { // estimate if there is a chance convergence will // be reached on next iteration, using the // asymptotic evolution of error final double ratio = ((double) sequence [targetIter] * sequence[targetIter + 1]) / (sequence[0] * sequence[0]); if (error > ratio * ratio) { // we don't expect to converge on next iteration // we reject the step immediately and reduce order reject = true; loop = false; targetIter = k; if ((targetIter > 1) && (costPerTimeUnit[targetIter-1] < orderControl1 * costPerTimeUnit[targetIter])) { --targetIter; } hNew = optimalStep[targetIter]; } } } break; case 0: if (error <= 1.0) { // convergence has been reached exactly at targetIter loop = false; } else { // estimate if there is a chance convergence will // be reached on next iteration, using the // asymptotic evolution of error final double ratio = ((double) sequence[k+1]) / sequence[0]; if (error > ratio * ratio) { // we don't expect to converge on next iteration // we reject the step immediately reject = true; loop = false; if ((targetIter > 1) && (costPerTimeUnit[targetIter-1] < orderControl1 * costPerTimeUnit[targetIter])) { --targetIter; } hNew = optimalStep[targetIter]; } } break; case 1 : if (error > 1.0) { reject = true; if ((targetIter > 1) && (costPerTimeUnit[targetIter-1] < orderControl1 * costPerTimeUnit[targetIter])) { --targetIter; } hNew = optimalStep[targetIter]; } loop = false; break; default : if ((firstTime || isLastStep) && (error <= 1.0)) { loop = false; } break; } } } } } if (! reject) { // derivatives at end of step computeDerivatives(stepStart + stepSize, y1, yDot1); } // dense output handling double hInt = getMaxStep(); if (! reject) { // extrapolate state at middle point of the step for (int j = 1; j <= k; ++j) { extrapolate(0, j, diagonal, yMidDots[0]); } final int mu = 2 * k - mudif + 3; for (int l = 0; l < mu; ++l) { // derivative at middle point of the step final int l2 = l / 2; double factor = FastMath.pow(0.5 * sequence[l2], l); int middleIndex = fk[l2].length / 2; for (int i = 0; i < y0.length; ++i) { yMidDots[l+1][i] = factor * fk[l2][middleIndex + l][i]; } for (int j = 1; j <= k - l2; ++j) { factor = FastMath.pow(0.5 * sequence[j + l2], l); middleIndex = fk[l2+j].length / 2; for (int i = 0; i < y0.length; ++i) { diagonal[j-1][i] = factor * fk[l2+j][middleIndex+l][i]; } extrapolate(l2, j, diagonal, yMidDots[l+1]); } for (int i = 0; i < y0.length; ++i) { yMidDots[l+1][i] *= stepSize; } // compute centered differences to evaluate next derivatives for (int j = (l + 1) / 2; j <= k; ++j) { for (int m = fk[j].length - 1; m >= 2 * (l + 1); --m) { for (int i = 0; i < y0.length; ++i) { fk[j][m][i] -= fk[j][m-2][i]; } } } } if (mu >= 0) { // estimate the dense output coefficients final GraggBulirschStoerStepInterpolator gbsInterpolator = (GraggBulirschStoerStepInterpolator) interpolator; gbsInterpolator.computeCoefficients(mu, stepSize); if (useInterpolationError) { // use the interpolation error to limit stepsize final double interpError = gbsInterpolator.estimateError(scale); hInt = FastMath.abs(stepSize / FastMath.max(FastMath.pow(interpError, 1.0 / (mu+4)), 0.01)); if (interpError > 10.0) { hNew = hInt; reject = true; } } } } if (! reject) { // Discrete events handling interpolator.storeTime(stepStart + stepSize); stepStart = acceptStep(interpolator, y1, yDot1, t); // prepare next step interpolator.storeTime(stepStart); System.arraycopy(y1, 0, y, 0, y0.length); System.arraycopy(yDot1, 0, yDot0, 0, y0.length); firstStepAlreadyComputed = true; int optimalIter; if (k == 1) { optimalIter = 2; if (previousRejected) { optimalIter = 1; } } else if (k <= targetIter) { optimalIter = k; if (costPerTimeUnit[k-1] < orderControl1 * costPerTimeUnit[k]) { optimalIter = k-1; } else if (costPerTimeUnit[k] < orderControl2 * costPerTimeUnit[k-1]) { optimalIter = FastMath.min(k+1, sequence.length - 2); } } else { optimalIter = k - 1; if ((k > 2) && (costPerTimeUnit[k-2] < orderControl1 * costPerTimeUnit[k-1])) { optimalIter = k - 2; } if (costPerTimeUnit[k] < orderControl2 * costPerTimeUnit[optimalIter]) { optimalIter = FastMath.min(k, sequence.length - 2); } } if (previousRejected) { // after a rejected step neither order nor stepsize // should increase targetIter = FastMath.min(optimalIter, k); hNew = FastMath.min(FastMath.abs(stepSize), optimalStep[targetIter]); } else { // stepsize control if (optimalIter <= k) { hNew = optimalStep[optimalIter]; } else { if ((k < targetIter) && (costPerTimeUnit[k] < orderControl2 * costPerTimeUnit[k-1])) { hNew = filterStep(optimalStep[k] * costPerStep[optimalIter+1] / costPerStep[k], forward, false); } else { hNew = filterStep(optimalStep[k] * costPerStep[optimalIter] / costPerStep[k], forward, false); } } targetIter = optimalIter; } newStep = true; } hNew = FastMath.min(hNew, hInt); if (! forward) { hNew = -hNew; } firstTime = false; if (reject) { isLastStep = false; previousRejected = true; } else { previousRejected = false; } } while (!isLastStep); // dispatch results equations.setTime(stepStart); equations.setCompleteState(y); resetInternalState(); } }

Other Java examples (source code examples)

Here is a short list of links related to this Java GraggBulirschStoerIntegrator.java source code file:

Java example source code file (GraggBulirschStoerIntegrator.java)

This example Java source code file (GraggBulirschStoerIntegrator.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

abstractstepinterpolator, adaptivestepsizeintegrator, dimensionmismatchexception, eventhandler, gragg-bulirsch-stoer, graggbulirschstoerintegrator, graggbulirschstoerstepinterpolator, maxcountexceededexception, method_name, numberistoosmallexception, override, stephandler, string, univariatesolver

The GraggBulirschStoerIntegrator.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.nonstiff;

import org.apache.commons.math3.analysis.solvers.UnivariateSolver;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.ExpandableStatefulODE;
import org.apache.commons.math3.ode.events.EventHandler;
import org.apache.commons.math3.ode.sampling.AbstractStepInterpolator;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.util.FastMath;

/**
 * This class implements a Gragg-Bulirsch-Stoer integrator for
 * Ordinary Differential Equations.
 *
 * <p>The Gragg-Bulirsch-Stoer algorithm is one of the most efficient
 * ones currently available for smooth problems. It uses Richardson
 * extrapolation to estimate what would be the solution if the step
 * size could be decreased down to zero.</p>
 *
 * <p>
 * This method changes both the step size and the order during
 * integration, in order to minimize computation cost. It is
 * particularly well suited when a very high precision is needed. The
 * limit where this method becomes more efficient than high-order
 * embedded Runge-Kutta methods like {@link DormandPrince853Integrator
 * Dormand-Prince 8(5,3)} depends on the problem. Results given in the
 * Hairer, Norsett and Wanner book show for example that this limit
 * occurs for accuracy around 1e-6 when integrating Saltzam-Lorenz
 * equations (the authors note this problem is <i>extremely sensitive
 * to the errors in the first integration steps</i>), and around 1e-11
 * for a two dimensional celestial mechanics problems with seven
 * bodies (pleiades problem, involving quasi-collisions for which
 * <i>automatic step size control is essential).
 * </p>
 *
 * <p>
 * This implementation is basically a reimplementation in Java of the
 * <a
 * href="http://www.unige.ch/math/folks/hairer/prog/nonstiff/odex.f">odex</a>
 * fortran code by E. Hairer and G. Wanner. The redistribution policy
 * for this code is available <a
 * href="http://www.unige.ch/~hairer/prog/licence.txt">here</a>, for
 * convenience, it is reproduced below.</p>
 * </p>
 *
 * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
 * <tr>
Copyright (c) 2004, Ernst Hairer
Redistribution and use in source and binary forms, with or * without modification, are permitted provided that the following * conditions are met: * <ul> * <li>Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer.</li> * <li>Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution.</li> * </ul>
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</strong>


my book on functional programming

 

new blog posts

 

Copyright 1998-2021 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.