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Java example source code file (DormandPrince54FieldStepInterpolator.java)

This example Java source code file (DormandPrince54FieldStepInterpolator.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

dormandprince54fieldstepinterpolator, fieldequationsmapper, fieldodestateandderivative, override, realfieldelement, rungekuttafieldstepinterpolator, suppresswarnings

The DormandPrince54FieldStepInterpolator.java Java example source code

/*
 * 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 represents an interpolator over the last step during an
 * ODE integration for the 5(4) Dormand-Prince integrator.
 *
 * @see DormandPrince54Integrator
 *
 * @param <T> the type of the field elements
 * @since 3.6
 */

class DormandPrince54FieldStepInterpolator<T extends RealFieldElement
      extends RungeKuttaFieldStepInterpolator<T> {

    /** Last row of the Butcher-array internal weights, element 0. */
    private final T a70;

    // element 1 is zero, so it is neither stored nor used

    /** Last row of the Butcher-array internal weights, element 2. */
    private final T a72;

    /** Last row of the Butcher-array internal weights, element 3. */
    private final T a73;

    /** Last row of the Butcher-array internal weights, element 4. */
    private final T a74;

    /** Last row of the Butcher-array internal weights, element 5. */
    private final T a75;

    /** Shampine (1986) Dense output, element 0. */
    private final T d0;

    // element 1 is zero, so it is neither stored nor used

    /** Shampine (1986) Dense output, element 2. */
    private final T d2;

    /** Shampine (1986) Dense output, element 3. */
    private final T d3;

    /** Shampine (1986) Dense output, element 4. */
    private final T d4;

    /** Shampine (1986) Dense output, element 5. */
    private final T d5;

    /** Shampine (1986) Dense output, element 6. */
    private final T d6;

    /** 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
     */
    DormandPrince54FieldStepInterpolator(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 one = field.getOne();
        a70 = one.multiply(   35.0).divide( 384.0);
        a72 = one.multiply(  500.0).divide(1113.0);
        a73 = one.multiply(  125.0).divide( 192.0);
        a74 = one.multiply(-2187.0).divide(6784.0);
        a75 = one.multiply(   11.0).divide(  84.0);
        d0  = one.multiply(-12715105075.0).divide( 11282082432.0);
        d2  = one.multiply( 87487479700.0).divide( 32700410799.0);
        d3  = one.multiply(-10690763975.0).divide(  1880347072.0);
        d4  = one.multiply(701980252875.0).divide(199316789632.0);
        d5  = one.multiply( -1453857185.0).divide(   822651844.0);
        d6  = one.multiply(    69997945.0).divide(    29380423.0);
    }

    /** {@inheritDoc} */
    @Override
    protected DormandPrince54FieldStepInterpolator<T> create(final Field 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 DormandPrince54FieldStepInterpolator<T>(newField, newForward, newYDotK,
                                                           newGlobalPreviousState, newGlobalCurrentState,
                                                           newSoftPreviousState, newSoftCurrentState,
                                                           newMapper);
    }
    /** {@inheritDoc} */
    @SuppressWarnings("unchecked")
    @Override
    protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper mapper,
                                                                                   final T time, final T theta,
                                                                                   final T thetaH, final T oneMinusThetaH) {

        // interpolate
        final T one      = time.getField().getOne();
        final T eta      = one.subtract(theta);
        final T twoTheta = theta.multiply(2);
        final T dot2     = one.subtract(twoTheta);
        final T dot3     = theta.multiply(theta.multiply(-3).add(2));
        final T dot4     = twoTheta.multiply(theta.multiply(twoTheta.subtract(3)).add(1));
        final T[] interpolatedState;
        final T[] interpolatedDerivatives;
        if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
            final T f1        = thetaH;
            final T f2        = f1.multiply(eta);
            final T f3        = f2.multiply(theta);
            final T f4        = f3.multiply(eta);
            final T coeff0    = f1.multiply(a70).
                                subtract(f2.multiply(a70.subtract(1))).
                                add(f3.multiply(a70.multiply(2).subtract(1))).
                                add(f4.multiply(d0));
            final T coeff1    = time.getField().getZero();
            final T coeff2    = f1.multiply(a72).
                                subtract(f2.multiply(a72)).
                                add(f3.multiply(a72.multiply(2))).
                                add(f4.multiply(d2));
            final T coeff3    = f1.multiply(a73).
                                subtract(f2.multiply(a73)).
                                add(f3.multiply(a73.multiply(2))).
                                add(f4.multiply(d3));
            final T coeff4    = f1.multiply(a74).
                                subtract(f2.multiply(a74)).
                                add(f3.multiply(a74.multiply(2))).
                                add(f4.multiply(d4));
            final T coeff5    = f1.multiply(a75).
                                subtract(f2.multiply(a75)).
                                add(f3.multiply(a75.multiply(2))).
                                add(f4.multiply(d5));
            final T coeff6    = f4.multiply(d6).subtract(f3);
            final T coeffDot0 = a70.
                                subtract(dot2.multiply(a70.subtract(1))).
                                add(dot3.multiply(a70.multiply(2).subtract(1))).
                                add(dot4.multiply(d0));
            final T coeffDot1 = time.getField().getZero();
            final T coeffDot2 = a72.
                                subtract(dot2.multiply(a72)).
                                add(dot3.multiply(a72.multiply(2))).
                                add(dot4.multiply(d2));
            final T coeffDot3 = a73.
                                subtract(dot2.multiply(a73)).
                                add(dot3.multiply(a73.multiply(2))).
                                add(dot4.multiply(d3));
            final T coeffDot4 = a74.
                                subtract(dot2.multiply(a74)).
                                add(dot3.multiply(a74.multiply(2))).
                                add(dot4.multiply(d4));
            final T coeffDot5 = a75.
                                subtract(dot2.multiply(a75)).
                                add(dot3.multiply(a75.multiply(2))).
                                add(dot4.multiply(d5));
            final T coeffDot6 = dot4.multiply(d6).subtract(dot3);
            interpolatedState       = previousStateLinearCombination(coeff0, coeff1, coeff2, coeff3,
                                                                     coeff4, coeff5, coeff6);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot0, coeffDot1, coeffDot2, coeffDot3,
                                                                  coeffDot4, coeffDot5, coeffDot6);
        } else {
            final T f1        = oneMinusThetaH.negate();
            final T f2        = oneMinusThetaH.multiply(theta);
            final T f3        = f2.multiply(theta);
            final T f4        = f3.multiply(eta);
            final T coeff0    = f1.multiply(a70).
                                subtract(f2.multiply(a70.subtract(1))).
                                add(f3.multiply(a70.multiply(2).subtract(1))).
                                add(f4.multiply(d0));
            final T coeff1    = time.getField().getZero();
            final T coeff2    = f1.multiply(a72).
                                subtract(f2.multiply(a72)).
                                add(f3.multiply(a72.multiply(2))).
                                add(f4.multiply(d2));
            final T coeff3    = f1.multiply(a73).
                                subtract(f2.multiply(a73)).
                                add(f3.multiply(a73.multiply(2))).
                                add(f4.multiply(d3));
            final T coeff4    = f1.multiply(a74).
                                subtract(f2.multiply(a74)).
                                add(f3.multiply(a74.multiply(2))).
                                add(f4.multiply(d4));
            final T coeff5    = f1.multiply(a75).
                                subtract(f2.multiply(a75)).
                                add(f3.multiply(a75.multiply(2))).
                                add(f4.multiply(d5));
            final T coeff6    = f4.multiply(d6).subtract(f3);
            final T coeffDot0 = a70.
                                subtract(dot2.multiply(a70.subtract(1))).
                                add(dot3.multiply(a70.multiply(2).subtract(1))).
                                add(dot4.multiply(d0));
            final T coeffDot1 = time.getField().getZero();
            final T coeffDot2 = a72.
                                subtract(dot2.multiply(a72)).
                                add(dot3.multiply(a72.multiply(2))).
                                add(dot4.multiply(d2));
            final T coeffDot3 = a73.
                                subtract(dot2.multiply(a73)).
                                add(dot3.multiply(a73.multiply(2))).
                                add(dot4.multiply(d3));
            final T coeffDot4 = a74.
                                subtract(dot2.multiply(a74)).
                                add(dot3.multiply(a74.multiply(2))).
                                add(dot4.multiply(d4));
            final T coeffDot5 = a75.
                                subtract(dot2.multiply(a75)).
                                add(dot3.multiply(a75.multiply(2))).
                                add(dot4.multiply(d5));
            final T coeffDot6 = dot4.multiply(d6).subtract(dot3);
            interpolatedState       = currentStateLinearCombination(coeff0, coeff1, coeff2, coeff3,
                                                                    coeff4, coeff5, coeff6);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot0, coeffDot1, coeffDot2, coeffDot3,
                                                                  coeffDot4, coeffDot5, coeffDot6);
        }
        return new FieldODEStateAndDerivative<T>(time, interpolatedState, interpolatedDerivatives);

    }

}

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