| /* |
| * 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; |
| import org.apache.commons.math4.core.jdkmath.JdkMath; |
| |
| /** |
| * 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> |
| * 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 GillIntegrator |
| * @since 1.2 |
| */ |
| |
| class GillStepInterpolator |
| extends RungeKuttaStepInterpolator { |
| |
| /** First Gill coefficient. */ |
| private static final double ONE_MINUS_INV_SQRT_2 = 1 - JdkMath.sqrt(0.5); |
| |
| /** Second Gill coefficient. */ |
| private static final double ONE_PLUS_INV_SQRT_2 = 1 + JdkMath.sqrt(0.5); |
| |
| /** Serializable version identifier. */ |
| private static final long serialVersionUID = 20111120L; |
| |
| /** Simple constructor. |
| * This constructor builds an instance that is not usable yet, the |
| * {@link |
| * org.apache.commons.math4.legacy.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 |
| * RungeKuttaIntegrator} class uses the prototyping design pattern |
| * to create the step interpolators by cloning an uninitialized model |
| * and later initializing the copy. |
| */ |
| // CHECKSTYLE: stop RedundantModifier |
| // the public modifier here is needed for serialization |
| public GillStepInterpolator() { |
| } |
| // 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 |
| */ |
| GillStepInterpolator(final GillStepInterpolator interpolator) { |
| super(interpolator); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected StepInterpolator doCopy() { |
| return new GillStepInterpolator(this); |
| } |
| |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected void computeInterpolatedStateAndDerivatives(final double theta, |
| final double oneMinusThetaH) { |
| |
| final double twoTheta = 2 * theta; |
| final double fourTheta2 = twoTheta * twoTheta; |
| final double coeffDot1 = theta * (twoTheta - 3) + 1; |
| final double cDot23 = twoTheta * (1 - theta); |
| final double coeffDot2 = cDot23 * ONE_MINUS_INV_SQRT_2; |
| final double coeffDot3 = cDot23 * ONE_PLUS_INV_SQRT_2; |
| final double coeffDot4 = theta * (twoTheta - 1); |
| |
| if ((previousState != null) && (theta <= 0.5)) { |
| final double s = theta * h / 6.0; |
| final double c23 = s * (6 * theta - fourTheta2); |
| final double coeff1 = s * (6 - 9 * theta + fourTheta2); |
| final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2; |
| final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2; |
| final double coeff4 = s * (-3 * theta + fourTheta2); |
| for (int i = 0; i < interpolatedState.length; ++i) { |
| final double yDot1 = yDotK[0][i]; |
| final double yDot2 = yDotK[1][i]; |
| final double yDot3 = yDotK[2][i]; |
| final double yDot4 = yDotK[3][i]; |
| interpolatedState[i] = |
| previousState[i] + coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 + coeff4 * yDot4; |
| interpolatedDerivatives[i] = |
| coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4; |
| } |
| } else { |
| final double s = oneMinusThetaH / 6.0; |
| final double c23 = s * (2 + twoTheta - fourTheta2); |
| final double coeff1 = s * (1 - 5 * theta + fourTheta2); |
| final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2; |
| final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2; |
| final double coeff4 = s * (1 + theta + fourTheta2); |
| for (int i = 0; i < interpolatedState.length; ++i) { |
| final double yDot1 = yDotK[0][i]; |
| final double yDot2 = yDotK[1][i]; |
| final double yDot3 = yDotK[2][i]; |
| final double yDot4 = yDotK[3][i]; |
| interpolatedState[i] = |
| currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4; |
| interpolatedDerivatives[i] = |
| coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4; |
| } |
| } |
| |
| } |
| |
| } |
