Repository: commons-math Updated Branches: refs/heads/field-ode 779e52410 -> b990f6f2a
Field-based version of Higham-Hall 5(4) method for solving ODE. Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/b990f6f2 Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/b990f6f2 Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/b990f6f2 Branch: refs/heads/field-ode Commit: b990f6f2adc41b00490ef19f8abcf29214074970 Parents: 779e524 Author: Luc Maisonobe <l...@apache.org> Authored: Tue Nov 17 18:25:02 2015 +0100 Committer: Luc Maisonobe <l...@apache.org> Committed: Tue Nov 17 18:25:02 2015 +0100 ---------------------------------------------------------------------- .../nonstiff/HighamHall54FieldIntegrator.java | 143 +++++++++++++++++++ .../HighamHall54FieldStepInterpolator.java | 139 ++++++++++++++++++ 2 files changed, 282 insertions(+) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-math/blob/b990f6f2/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java new file mode 100644 index 0000000..e3a1829 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java @@ -0,0 +1,143 @@ +/* + * 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.Field; +import org.apache.commons.math3.RealFieldElement; +import org.apache.commons.math3.util.MathUtils; + + +/** + * This class implements the 5(4) Higham and Hall integrator for + * Ordinary Differential Equations. + * + * <p>This integrator is an embedded Runge-Kutta integrator + * of order 5(4) used in local extrapolation mode (i.e. the solution + * is computed using the high order formula) with stepsize control + * (and automatic step initialization) and continuous output. This + * method uses 7 functions evaluations per step.</p> + * + * @param <T> the type of the field elements + * @since 3.6 + */ + +public class HighamHall54FieldIntegrator<T extends RealFieldElement<T>> + extends EmbeddedRungeKuttaFieldIntegrator<T> { + + /** Integrator method name. */ + private static final String METHOD_NAME = "Higham-Hall 5(4)"; + + /** Time steps Butcher array. */ + private static final double[] STATIC_C = { + 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0 + }; + + /** Internal weights Butcher array. */ + private static final double[][] STATIC_A = { + {2.0/9.0}, + {1.0/12.0, 1.0/4.0}, + {1.0/8.0, 0.0, 3.0/8.0}, + {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0}, + {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0}, + {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0} + }; + + /** Propagation weights Butcher array. */ + private static final double[] STATIC_B = { + 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0 + }; + + /** Error weights Butcher array. */ + private static final double[] STATIC_E = { + -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0 + }; + + /** Simple constructor. + * Build a fifth order Higham and Hall integrator with the given step bounds + * @param field field to which the time and state vector elements belong + * @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 HighamHall54FieldIntegrator(final Field<T> field, + final double minStep, final double maxStep, + final double scalAbsoluteTolerance, + final double scalRelativeTolerance) { + super(field, METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, + new HighamHall54FieldStepInterpolator<T>(), + minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); + } + + /** Simple constructor. + * Build a fifth order Higham and Hall integrator with the given step bounds + * @param field field to which the time and state vector elements belong + * @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 vecAbsoluteTolerance allowed absolute error + * @param vecRelativeTolerance allowed relative error + */ + public HighamHall54FieldIntegrator(final Field<T> field, + final double minStep, final double maxStep, + final double[] vecAbsoluteTolerance, + final double[] vecRelativeTolerance) { + super(field, METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, + new HighamHall54FieldStepInterpolator<T>(), + minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); + } + + /** {@inheritDoc} */ + @Override + public int getOrder() { + return 5; + } + + /** {@inheritDoc} */ + @Override + protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) { + + T error = getField().getZero(); + + for (int j = 0; j < mainSetDimension; ++j) { + T errSum = yDotK[0][j].multiply(STATIC_E[0]); + for (int l = 1; l < STATIC_E.length; ++l) { + errSum = errSum.add(yDotK[l][j].multiply(STATIC_E[l])); + } + + final T yScale = MathUtils.max(y0[j].abs(), y1[j].abs()); + final T tol = (vecAbsoluteTolerance == null) ? + yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) : + yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]); + final T ratio = h.multiply(errSum).divide(tol); + error = error.add(ratio.multiply(ratio)); + + } + + return error.divide(mainSetDimension).sqrt(); + + } + +} http://git-wip-us.apache.org/repos/asf/commons-math/blob/b990f6f2/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java new file mode 100644 index 0000000..7c46eb0 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java @@ -0,0 +1,139 @@ +/* + * 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.RealFieldElement; +import org.apache.commons.math3.ode.FieldEquationsMapper; +import org.apache.commons.math3.ode.FieldODEStateAndDerivative; +import org.apache.commons.math3.util.MathArrays; + +/** + * This class represents an interpolator over the last step during an + * ODE integration for the 5(4) Higham and Hall integrator. + * + * @see HighamHall54FieldIntegrator + * + * @param <T> the type of the field elements + * @since 3.6 + */ + +class HighamHall54FieldStepInterpolator<T extends RealFieldElement<T>> + extends RungeKuttaFieldStepInterpolator<T> { + + /** Simple constructor. + * This constructor builds an instance that is not usable yet, the + * {@link + * org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#reinitialize} + * method should be called before using the instance in order to + * initialize the internal arrays. This constructor is used only + * in order to delay the initialization in some cases. The {@link + * EmbeddedRungeKuttaIntegrator} uses the prototyping design pattern + * to create the step interpolators by cloning an uninitialized model + * and later initializing the copy. + */ + HighamHall54FieldStepInterpolator() { + super(); + } + + /** Copy constructor. + * @param interpolator interpolator to copy from. The copy is a deep + * copy: its arrays are separated from the original arrays of the + * instance + */ + HighamHall54FieldStepInterpolator(final HighamHall54FieldStepInterpolator<T> interpolator) { + super(interpolator); + } + + /** {@inheritDoc} */ + @Override + protected HighamHall54FieldStepInterpolator<T> doCopy() { + return new HighamHall54FieldStepInterpolator<T>(this); + } + + + /** {@inheritDoc} */ + @Override + protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper, + final T time, final T theta, + final T oneMinusThetaH) { + + final T bDot0 = theta.multiply(theta.multiply(theta.multiply( -10.0 ).add( 16.0 )).add(-15.0 / 2.0)).add(1); + final T bDot2 = theta.multiply(theta.multiply(theta.multiply( 135.0 / 2.0).add(-729.0 / 8.0)).add(459.0 / 16.0)); + final T bDot3 = theta.multiply(theta.multiply(theta.multiply(-120.0 ).add( 152.0 )).add(-44.0 )); + final T bDot4 = theta.multiply(theta.multiply(theta.multiply( 125.0 / 2.0).add(-625.0 / 8.0)).add(375.0 / 16.0)); + final T bDot5 = theta.multiply( 5.0 / 8.0).multiply(theta.multiply(2).subtract(1)); + final T[] interpolatedState = MathArrays.buildArray(theta.getField(), previousState.length); + final T[] interpolatedDerivatives = MathArrays.buildArray(theta.getField(), previousState.length); + + if ((previousState != null) && (theta.getReal() <= 0.5)) { + final T hTheta = h.multiply(theta); + final T b0 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply( -5.0 / 2.0).add( 16.0 / 3.0)).add(-15.0 / 4.0)).add(1)); + final T b2 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply(135.0 / 8.0).add(-243.0 / 8.0)).add(459.0 / 32.0))); + final T b3 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply(-30.0 ).add( 152.0 / 3.0)).add(-22.0 ))); + final T b4 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply(125.0 / 8.0).add(-625.0 / 24.0)).add(375.0 / 32.0))); + final T b5 = hTheta.multiply(theta.multiply(theta.multiply( 5.0 / 12.0)).add( -5.0 / 16.0)); + for (int i = 0; i < interpolatedState.length; ++i) { + final T yDot0 = yDotK[0][i]; + final T yDot2 = yDotK[2][i]; + final T yDot3 = yDotK[3][i]; + final T yDot4 = yDotK[4][i]; + final T yDot5 = yDotK[5][i]; + interpolatedState[i] = previousState[i]. + add(b0.multiply(yDot0)). + add(b2.multiply(yDot2)). + add(b3.multiply(yDot3)). + add(b4.multiply(yDot4)). + add(b5.multiply(yDot5)); + interpolatedDerivatives[i] = bDot0.multiply(yDot0). + add(bDot2.multiply(yDot2)). + add(bDot3.multiply(yDot3)). + add(bDot4.multiply(yDot4)). + add(bDot5.multiply(yDot5)); + } + } else { + final T theta2 = theta.multiply(theta); + final T b0 = h.multiply( theta.multiply(theta.multiply(theta.multiply(theta.multiply(-5.0 / 2.0).add( 16.0 / 3.0)).add( -15.0 / 4.0)).add( 1.0 )).add( -1.0 / 12.0)); + final T b2 = h.multiply(theta2.multiply(theta.multiply(theta.multiply( 135.0 / 8.0 ).add(-243.0 / 8.0)).add(459.0 / 32.0)).add( -27.0 / 32.0)); + final T b3 = h.multiply(theta2.multiply(theta.multiply(theta.multiply( -30.0 ).add( 152.0 / 3.0)).add(-22.0 )).add( 4.0 / 3.0)); + final T b4 = h.multiply(theta2.multiply(theta.multiply(theta.multiply( 125.0 / 8.0 ).add(-625.0 / 24.0)).add(375.0 / 32.0)).add(-125.0 / 96.0)); + final T b5 = h.multiply(theta2.multiply(theta.multiply( 5.0 / 12.0 ).add(-5.0 / 16.0)).add( -5.0 / 48.0)); + for (int i = 0; i < interpolatedState.length; ++i) { + final T yDot0 = yDotK[0][i]; + final T yDot2 = yDotK[2][i]; + final T yDot3 = yDotK[3][i]; + final T yDot4 = yDotK[4][i]; + final T yDot5 = yDotK[5][i]; + interpolatedState[i] = currentState[i]. + add(b0.multiply(yDot0)). + add(b2.multiply(yDot2)). + add(b3.multiply(yDot3)). + add(b4.multiply(yDot4)). + add(b5.multiply(yDot5)); + interpolatedDerivatives[i] = bDot0.multiply(yDot0). + add(bDot2.multiply(yDot2)). + add(bDot3.multiply(yDot3)). + add(bDot4.multiply(yDot4)). + add(bDot5.multiply(yDot5)); + } + } + + return new FieldODEStateAndDerivative<T>(time, interpolatedState, yDotK[0]); + + } + +}
