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Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/nonstiff/GillStepInterpolator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/ode/nonstiff/GillStepInterpolator.java | 151 |
1 files changed, 151 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/GillStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillStepInterpolator.java new file mode 100644 index 0000000..72dec69 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillStepInterpolator.java @@ -0,0 +1,151 @@ +/* + * 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.ode.sampling.StepInterpolator; +import org.apache.commons.math3.util.FastMath; + +/** + * 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 GillIntegrator + * @since 1.2 + */ + +class GillStepInterpolator + extends RungeKuttaStepInterpolator { + + /** 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); + + /** 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.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 + * 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; + } + } + + } + +} |