| /* |
| * 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.math4.legacy.ode.nonstiff; |
| |
| import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator; |
| |
| /** |
| * This class implements a step interpolator for the classical 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>) (y'<sub>2</sub> + y'<sub>3</sub>) |
| * + ( -3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub> |
| * ] |
| * </li> |
| * <li>Using reference point at step end:<br> |
| * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h) |
| * + (1 - θ) (h/6) [ (-4 θ^2 + 5 θ - 1) y'<sub>1</sub> |
| * +(4 θ^2 - 2 θ - 2) (y'<sub>2</sub> + y'<sub>3</sub>) |
| * -(4 θ^2 + θ + 1) y'<sub>4</sub> |
| * ] |
| * </li> |
| * </ul> |
| * |
| * 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. |
| * |
| * @see ClassicalRungeKuttaIntegrator |
| * @since 1.2 |
| */ |
| |
| class ClassicalRungeKuttaStepInterpolator |
| extends RungeKuttaStepInterpolator { |
| |
| /** Serializable version identifier. */ |
| private static final long serialVersionUID = 20111120L; |
| |
| /** Simple constructor. |
| * This constructor builds an instance that is not usable yet, the |
| * {@link RungeKuttaStepInterpolator#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 RungeKuttaIntegrator} |
| * class uses the prototyping design pattern to create the step |
| * interpolators by cloning an uninitialized model and latter initializing |
| * the copy. |
| */ |
| // CHECKSTYLE: stop RedundantModifier |
| // the public modifier here is needed for serialization |
| public ClassicalRungeKuttaStepInterpolator() { |
| } |
| // CHECKSTYLE: resume RedundantModifier |
| |
| /** 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 |
| */ |
| ClassicalRungeKuttaStepInterpolator(final ClassicalRungeKuttaStepInterpolator interpolator) { |
| super(interpolator); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected StepInterpolator doCopy() { |
| return new ClassicalRungeKuttaStepInterpolator(this); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected void computeInterpolatedStateAndDerivatives(final double theta, |
| final double oneMinusThetaH) { |
| |
| final double oneMinusTheta = 1 - theta; |
| final double oneMinus2Theta = 1 - 2 * theta; |
| final double coeffDot1 = oneMinusTheta * oneMinus2Theta; |
| final double coeffDot23 = 2 * theta * oneMinusTheta; |
| final double coeffDot4 = -theta * oneMinus2Theta; |
| if ((previousState != null) && (theta <= 0.5)) { |
| final double fourTheta2 = 4 * theta * theta; |
| final double s = theta * h / 6.0; |
| final double coeff1 = s * ( 6 - 9 * theta + fourTheta2); |
| final double coeff23 = s * ( 6 * theta - fourTheta2); |
| final double coeff4 = s * (-3 * theta + fourTheta2); |
| for (int i = 0; i < interpolatedState.length; ++i) { |
| final double yDot1 = yDotK[0][i]; |
| final double yDot23 = yDotK[1][i] + yDotK[2][i]; |
| final double yDot4 = yDotK[3][i]; |
| interpolatedState[i] = |
| previousState[i] + coeff1 * yDot1 + coeff23 * yDot23 + coeff4 * yDot4; |
| interpolatedDerivatives[i] = |
| coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4; |
| } |
| } else { |
| final double fourTheta = 4 * theta; |
| final double s = oneMinusThetaH / 6.0; |
| final double coeff1 = s * ((-fourTheta + 5) * theta - 1); |
| final double coeff23 = s * (( fourTheta - 2) * theta - 2); |
| final double coeff4 = s * ((-fourTheta - 1) * theta - 1); |
| for (int i = 0; i < interpolatedState.length; ++i) { |
| final double yDot1 = yDotK[0][i]; |
| final double yDot23 = yDotK[1][i] + yDotK[2][i]; |
| final double yDot4 = yDotK[3][i]; |
| interpolatedState[i] = |
| currentState[i] + coeff1 * yDot1 + coeff23 * yDot23 + coeff4 * yDot4; |
| interpolatedDerivatives[i] = |
| coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4; |
| } |
| } |
| |
| } |
| |
| } |