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Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java | 148 |
1 files changed, 148 insertions, 0 deletions
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..5639ed5 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/GillFieldStepInterpolator.java @@ -0,0 +1,148 @@ +/* + * 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.ode.FieldEquationsMapper; +import org.apache.commons.math3.ode.FieldODEStateAndDerivative; + +/** + * 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 final T one_minus_inv_sqrt_2; + + /** Second Gill coefficient. */ + private final T one_plus_inv_sqrt_2; + + /** Simple constructor. + * @param field field to which the time and state vector elements belong + * @param forward integration direction indicator + * @param yDotK slopes at the intermediate points + * @param globalPreviousState start of the global step + * @param globalCurrentState end of the global step + * @param softPreviousState start of the restricted step + * @param softCurrentState end of the restricted step + * @param mapper equations mapper for the all equations + */ + GillFieldStepInterpolator(final Field<T> field, final boolean forward, + final T[][] yDotK, + final FieldODEStateAndDerivative<T> globalPreviousState, + final FieldODEStateAndDerivative<T> globalCurrentState, + final FieldODEStateAndDerivative<T> softPreviousState, + final FieldODEStateAndDerivative<T> softCurrentState, + final FieldEquationsMapper<T> mapper) { + super(field, forward, yDotK, + globalPreviousState, globalCurrentState, softPreviousState, softCurrentState, + mapper); + final T sqrt = field.getZero().add(0.5).sqrt(); + one_minus_inv_sqrt_2 = field.getOne().subtract(sqrt); + one_plus_inv_sqrt_2 = field.getOne().add(sqrt); + } + + /** {@inheritDoc} */ + @Override + protected GillFieldStepInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK, + final FieldODEStateAndDerivative<T> newGlobalPreviousState, + final FieldODEStateAndDerivative<T> newGlobalCurrentState, + final FieldODEStateAndDerivative<T> newSoftPreviousState, + final FieldODEStateAndDerivative<T> newSoftCurrentState, + final FieldEquationsMapper<T> newMapper) { + return new GillFieldStepInterpolator<T>(newField, newForward, newYDotK, + newGlobalPreviousState, newGlobalCurrentState, + newSoftPreviousState, newSoftCurrentState, + newMapper); + } + + /** {@inheritDoc} */ + @SuppressWarnings("unchecked") + @Override + protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper, + final T time, final T theta, + final T thetaH, 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; + final T[] interpolatedDerivatives; + + if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) { + final T s = thetaH.divide(6.0); + final T c23 = s.multiply(theta.multiply(6).subtract(fourTheta2)); + final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(9)).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))); + interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4); + interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4); + } 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)); + interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4); + interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4); + } + + return new FieldODEStateAndDerivative<T>(time, interpolatedState, interpolatedDerivatives); + + } + +} |