| /* |
| * 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 java.util.Arrays; |
| |
| import org.apache.commons.math4.legacy.core.RealFieldElement; |
| import org.apache.commons.math4.legacy.linear.Array2DRowFieldMatrix; |
| import org.apache.commons.math4.legacy.ode.FieldEquationsMapper; |
| import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative; |
| import org.apache.commons.math4.legacy.ode.sampling.AbstractFieldStepInterpolator; |
| import org.apache.commons.math4.legacy.core.MathArrays; |
| |
| /** |
| * This class implements an interpolator for Adams integrators using Nordsieck representation. |
| * |
| * <p>This interpolator computes dense output around the current point. |
| * The interpolation equation is based on Taylor series formulas. |
| * |
| * @see AdamsBashforthFieldIntegrator |
| * @see AdamsMoultonFieldIntegrator |
| * @param <T> the type of the field elements |
| * @since 3.6 |
| */ |
| |
| class AdamsFieldStepInterpolator<T extends RealFieldElement<T>> extends AbstractFieldStepInterpolator<T> { |
| |
| /** Step size used in the first scaled derivative and Nordsieck vector. */ |
| private T scalingH; |
| |
| /** Reference state. |
| * <p>Sometimes, the reference state is the same as globalPreviousState, |
| * sometimes it is the same as globalCurrentState, so we use a separate |
| * field to avoid any confusion. |
| * </p> |
| */ |
| private final FieldODEStateAndDerivative<T> reference; |
| |
| /** First scaled derivative. */ |
| private final T[] scaled; |
| |
| /** Nordsieck vector. */ |
| private final Array2DRowFieldMatrix<T> nordsieck; |
| |
| /** Simple constructor. |
| * @param stepSize step size used in the scaled and Nordsieck arrays |
| * @param reference reference state from which Taylor expansion are estimated |
| * @param scaled first scaled derivative |
| * @param nordsieck Nordsieck vector |
| * @param isForward integration direction indicator |
| * @param globalPreviousState start of the global step |
| * @param globalCurrentState end of the global step |
| * @param equationsMapper mapper for ODE equations primary and secondary components |
| */ |
| AdamsFieldStepInterpolator(final T stepSize, final FieldODEStateAndDerivative<T> reference, |
| final T[] scaled, final Array2DRowFieldMatrix<T> nordsieck, |
| final boolean isForward, |
| final FieldODEStateAndDerivative<T> globalPreviousState, |
| final FieldODEStateAndDerivative<T> globalCurrentState, |
| final FieldEquationsMapper<T> equationsMapper) { |
| this(stepSize, reference, scaled, nordsieck, |
| isForward, globalPreviousState, globalCurrentState, |
| globalPreviousState, globalCurrentState, equationsMapper); |
| } |
| |
| /** Simple constructor. |
| * @param stepSize step size used in the scaled and Nordsieck arrays |
| * @param reference reference state from which Taylor expansion are estimated |
| * @param scaled first scaled derivative |
| * @param nordsieck Nordsieck vector |
| * @param isForward integration direction indicator |
| * @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 equationsMapper mapper for ODE equations primary and secondary components |
| */ |
| private AdamsFieldStepInterpolator(final T stepSize, final FieldODEStateAndDerivative<T> reference, |
| final T[] scaled, final Array2DRowFieldMatrix<T> nordsieck, |
| final boolean isForward, |
| final FieldODEStateAndDerivative<T> globalPreviousState, |
| final FieldODEStateAndDerivative<T> globalCurrentState, |
| final FieldODEStateAndDerivative<T> softPreviousState, |
| final FieldODEStateAndDerivative<T> softCurrentState, |
| final FieldEquationsMapper<T> equationsMapper) { |
| super(isForward, globalPreviousState, globalCurrentState, |
| softPreviousState, softCurrentState, equationsMapper); |
| this.scalingH = stepSize; |
| this.reference = reference; |
| this.scaled = scaled.clone(); |
| this.nordsieck = new Array2DRowFieldMatrix<>(nordsieck.getData(), false); |
| } |
| |
| /** Create a new instance. |
| * @param newForward integration direction indicator |
| * @param newGlobalPreviousState start of the global step |
| * @param newGlobalCurrentState end of the global step |
| * @param newSoftPreviousState start of the restricted step |
| * @param newSoftCurrentState end of the restricted step |
| * @param newMapper equations mapper for the all equations |
| * @return a new instance |
| */ |
| @Override |
| protected AdamsFieldStepInterpolator<T> create(boolean newForward, |
| FieldODEStateAndDerivative<T> newGlobalPreviousState, |
| FieldODEStateAndDerivative<T> newGlobalCurrentState, |
| FieldODEStateAndDerivative<T> newSoftPreviousState, |
| FieldODEStateAndDerivative<T> newSoftCurrentState, |
| FieldEquationsMapper<T> newMapper) { |
| return new AdamsFieldStepInterpolator<>(scalingH, reference, scaled, nordsieck, |
| newForward, |
| newGlobalPreviousState, newGlobalCurrentState, |
| newSoftPreviousState, newSoftCurrentState, |
| newMapper); |
| |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> equationsMapper, |
| final T time, final T theta, |
| final T thetaH, final T oneMinusThetaH) { |
| return taylor(reference, time, scalingH, scaled, nordsieck); |
| } |
| |
| /** Estimate state by applying Taylor formula. |
| * @param reference reference state |
| * @param time time at which state must be estimated |
| * @param stepSize step size used in the scaled and Nordsieck arrays |
| * @param scaled first scaled derivative |
| * @param nordsieck Nordsieck vector |
| * @return estimated state |
| * @param <S> the type of the field elements |
| */ |
| public static <S extends RealFieldElement<S>> FieldODEStateAndDerivative<S> taylor(final FieldODEStateAndDerivative<S> reference, |
| final S time, final S stepSize, |
| final S[] scaled, |
| final Array2DRowFieldMatrix<S> nordsieck) { |
| |
| final S x = time.subtract(reference.getTime()); |
| final S normalizedAbscissa = x.divide(stepSize); |
| |
| S[] stateVariation = MathArrays.buildArray(time.getField(), scaled.length); |
| Arrays.fill(stateVariation, time.getField().getZero()); |
| S[] estimatedDerivatives = MathArrays.buildArray(time.getField(), scaled.length); |
| Arrays.fill(estimatedDerivatives, time.getField().getZero()); |
| |
| // apply Taylor formula from high order to low order, |
| // for the sake of numerical accuracy |
| final S[][] nData = nordsieck.getDataRef(); |
| for (int i = nData.length - 1; i >= 0; --i) { |
| final int order = i + 2; |
| final S[] nDataI = nData[i]; |
| final S power = normalizedAbscissa.pow(order); |
| for (int j = 0; j < nDataI.length; ++j) { |
| final S d = nDataI[j].multiply(power); |
| stateVariation[j] = stateVariation[j].add(d); |
| estimatedDerivatives[j] = estimatedDerivatives[j].add(d.multiply(order)); |
| } |
| } |
| |
| S[] estimatedState = reference.getState(); |
| for (int j = 0; j < stateVariation.length; ++j) { |
| stateVariation[j] = stateVariation[j].add(scaled[j].multiply(normalizedAbscissa)); |
| estimatedState[j] = estimatedState[j].add(stateVariation[j]); |
| estimatedDerivatives[j] = |
| estimatedDerivatives[j].add(scaled[j].multiply(normalizedAbscissa)).divide(x); |
| } |
| |
| return new FieldODEStateAndDerivative<>(time, estimatedState, estimatedDerivatives); |
| |
| } |
| |
| } |