Repository: commons-math Updated Branches: refs/heads/field-ode f4286ec26 -> e0c0398ca
Field-based version of Gill 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/e0c0398c Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/e0c0398c Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/e0c0398c Branch: refs/heads/field-ode Commit: e0c0398cad6e9598556c3a1f8a22ca45698ee086 Parents: f4286ec Author: Luc Maisonobe <l...@apache.org> Authored: Sun Nov 15 11:36:58 2015 +0100 Committer: Luc Maisonobe <l...@apache.org> Committed: Sun Nov 15 11:36:58 2015 +0100 ---------------------------------------------------------------------- .../math3/ode/nonstiff/GillFieldIntegrator.java | 79 ++++++++++ .../ode/nonstiff/GillFieldStepInterpolator.java | 157 +++++++++++++++++++ 2 files changed, 236 insertions(+) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-math/blob/e0c0398c/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.java new file mode 100644 index 0000000..21cd5d6 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldIntegrator.java @@ -0,0 +1,79 @@ +/* + * 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.FastMath; + + +/** + * This class implements the Gill fourth order Runge-Kutta + * integrator for Ordinary Differential Equations . + + * <p>This method is an explicit Runge-Kutta method, its Butcher-array + * is the following one : + * <pre> + * 0 | 0 0 0 0 + * 1/2 | 1/2 0 0 0 + * 1/2 | (q-1)/2 (2-q)/2 0 0 + * 1 | 0 -q/2 (2+q)/2 0 + * |------------------------------- + * | 1/6 (2-q)/6 (2+q)/6 1/6 + * </pre> + * where q = sqrt(2)</p> + * + * @see EulerFieldIntegrator + * @see ClassicalRungeKuttaFieldIntegrator + * @see MidpointFieldIntegrator + * @see ThreeEighthesFieldIntegrator + * @see LutherFieldIntegrator + * @param <T> the type of the field elements + * @since 3.6 + */ + +public class GillFieldIntegrator<T extends RealFieldElement<T>> + extends RungeKuttaFieldIntegrator<T> { + + /** Time steps Butcher array. */ + private static final double[] STATIC_C = { + 1.0 / 2.0, 1.0 / 2.0, 1.0 + }; + + /** Internal weights Butcher array. */ + private static final double[][] STATIC_A = { + { 1.0 / 2.0 }, + { (FastMath.sqrt(2.0) - 1.0) / 2.0, (2.0 - FastMath.sqrt(2.0)) / 2.0 }, + { 0.0, -FastMath.sqrt(2.0) / 2.0, (2.0 + FastMath.sqrt(2.0)) / 2.0 } + }; + + /** Propagation weights Butcher array. */ + private static final double[] STATIC_B = { + 1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0 + }; + + /** Simple constructor. + * Build a fourth-order Gill integrator with the given step. + * @param field field to which the time and state vector elements belong + * @param step integration step + */ + public GillFieldIntegrator(final Field<T> field, final T step) { + super(field, "Gill", STATIC_C, STATIC_A, STATIC_B, new GillFieldStepInterpolator<T>(), step); + } + +} http://git-wip-us.apache.org/repos/asf/commons-math/blob/e0c0398c/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java ---------------------------------------------------------------------- diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java new file mode 100644 index 0000000..3da3c09 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java @@ -0,0 +1,157 @@ +/* + * 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.FastMath; +import org.apache.commons.math3.util.MathArrays; + +/** + * This class implements a step interpolator for the Gill fourth + * order Runge-Kutta integrator. + * + * <p>This interpolator allows to compute dense output inside the last + * step computed. The interpolation equation is consistent with the + * integration scheme : + * <ul> + * <li>Using reference point at step start:<br> + * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>) + * + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub> + * + ( 6 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>) + * + ( - 3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub> + * ] + * </li> + * <li>Using reference point at step start:<br> + * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h) + * - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ<sup>2</sup>) y'<sub>1</sub> + * + (2 + 2 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>) + * + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub> + * ] + * </li> + * </ul> + * </p> + * where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub> + * are the four evaluations of the derivatives already computed during + * the step.</p> + * + * @see GillFieldIntegrator + * @param <T> the type of the field elements + * @since 3.6 + */ + +class GillFieldStepInterpolator<T extends RealFieldElement<T>> + extends RungeKuttaFieldStepInterpolator<T> { + + /** First Gill coefficient. */ + private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5); + + /** Second Gill coefficient. */ + private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5); + + /** Simple constructor. + * This constructor builds an instance that is not usable yet, the + * {@link + * org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator#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 + * RungeKuttaFieldIntegrator} class uses the prototyping design pattern + * to create the step interpolators by cloning an uninitialized model + * and later initializing the copy. + */ + GillFieldStepInterpolator() { + } + + /** 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 + */ + GillFieldStepInterpolator(final GillFieldStepInterpolator<T> interpolator) { + super(interpolator); + } + + /** {@inheritDoc} */ + @Override + protected GillFieldStepInterpolator<T> doCopy() { + return new GillFieldStepInterpolator<T>(this); + } + + + /** {@inheritDoc} */ + @Override + protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper, + final T time, final T theta, + final T oneMinusThetaH) { + + final T one = time.getField().getOne(); + final T twoTheta = theta.multiply(2); + final T fourTheta2 = twoTheta.multiply(twoTheta); + final T coeffDot1 = theta.multiply(twoTheta.subtract(3)).add(1); + final T cDot23 = twoTheta.multiply(one.subtract(theta)); + final T coeffDot2 = cDot23.multiply(ONE_MINUS_INV_SQRT_2); + final T coeffDot3 = cDot23.multiply(ONE_PLUS_INV_SQRT_2); + final T coeffDot4 = theta.multiply(twoTheta.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 s = theta.multiply(h).divide(6.0); + final T c23 = s.multiply(theta.multiply(6).subtract(fourTheta2)); + final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(6)).add(6)); + final T coeff2 = c23.multiply(ONE_MINUS_INV_SQRT_2); + final T coeff3 = c23.multiply(ONE_PLUS_INV_SQRT_2); + final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3))); + for (int i = 0; i < interpolatedState.length; ++i) { + final T yDot1 = yDotK[0][i]; + final T yDot2 = yDotK[1][i]; + final T yDot3 = yDotK[2][i]; + final T yDot4 = yDotK[3][i]; + interpolatedState[i] = previousState[i]. + add(coeff1.multiply(yDot1)).add(coeff2.multiply(yDot2)). + add(coeff3.multiply(yDot3)).add(coeff4.multiply(yDot4)); + interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2)). + add(coeffDot3.multiply(yDot3)).add(coeffDot4.multiply(yDot4)); + } + } else { + final T s = oneMinusThetaH.divide(6.0); + final T c23 = s .multiply(twoTheta.add(2).subtract(fourTheta2)); + final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(5)).add(1)); + final T coeff2 = c23.multiply(ONE_MINUS_INV_SQRT_2); + final T coeff3 = c23.multiply(ONE_PLUS_INV_SQRT_2); + final T coeff4 = s.multiply(fourTheta2.add(theta).add(1)); + for (int i = 0; i < interpolatedState.length; ++i) { + final T yDot1 = yDotK[0][i]; + final T yDot2 = yDotK[1][i]; + final T yDot3 = yDotK[2][i]; + final T yDot4 = yDotK[3][i]; + interpolatedState[i] = currentState[i]. + subtract(coeff1.multiply(yDot1)).subtract(coeff2.multiply(yDot2)). + subtract(coeff3.multiply(yDot3)).subtract(coeff4.multiply(yDot4)); + interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2)). + add(coeffDot3.multiply(yDot3)).add(coeffDot4.multiply(yDot4)); + } + } + + return new FieldODEStateAndDerivative<T>(time, interpolatedState, yDotK[0]); + + } + +}
