/*
* 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<T>>
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<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 DormandPrince54FieldStepInterpolator<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) {
// 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);
}
}