/*
* 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.exception.MaxCountExceededException;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
/**
* This class represents an interpolator over the last step during an
* ODE integration for the 8(5,3) Dormand-Prince integrator.
*
* @see DormandPrince853FieldIntegrator
*
* @param <T> the type of the field elements
* @since 3.6
*/
class DormandPrince853FieldStepInterpolator<T extends RealFieldElement<T>>
extends RungeKuttaFieldStepInterpolator<T> {
/** Interpolation weights.
* (beware that only the non-null values are in the table)
*/
private final T[][] d;
/** 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
*/
DormandPrince853FieldStepInterpolator(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);
// interpolation weights
d = MathArrays.buildArray(field, 7, 16);
// this row is the same as the b array
d[0][ 0] = fraction(field, 104257, 1920240);
d[0][ 1] = field.getZero();
d[0][ 2] = field.getZero();
d[0][ 3] = field.getZero();
d[0][ 4] = field.getZero();
d[0][ 5] = fraction(field, 3399327.0, 763840.0);
d[0][ 6] = fraction(field, 66578432.0, 35198415.0);
d[0][ 7] = fraction(field, -1674902723.0, 288716400.0);
d[0][ 8] = fraction(field, 54980371265625.0, 176692375811392.0);
d[0][ 9] = fraction(field, -734375.0, 4826304.0);
d[0][10] = fraction(field, 171414593.0, 851261400.0);
d[0][11] = fraction(field, 137909.0, 3084480.0);
d[0][12] = field.getZero();
d[0][13] = field.getZero();
d[0][14] = field.getZero();
d[0][15] = field.getZero();
d[1][ 0] = d[0][ 0].negate().add(1);
d[1][ 1] = d[0][ 1].negate();
d[1][ 2] = d[0][ 2].negate();
d[1][ 3] = d[0][ 3].negate();
d[1][ 4] = d[0][ 4].negate();
d[1][ 5] = d[0][ 5].negate();
d[1][ 6] = d[0][ 6].negate();
d[1][ 7] = d[0][ 7].negate();
d[1][ 8] = d[0][ 8].negate();
d[1][ 9] = d[0][ 9].negate();
d[1][10] = d[0][10].negate();
d[1][11] = d[0][11].negate();
d[1][12] = d[0][12].negate(); // really 0
d[1][13] = d[0][13].negate(); // really 0
d[1][14] = d[0][14].negate(); // really 0
d[1][15] = d[0][15].negate(); // really 0
d[2][ 0] = d[0][ 0].multiply(2).subtract(1);
d[2][ 1] = d[0][ 1].multiply(2);
d[2][ 2] = d[0][ 2].multiply(2);
d[2][ 3] = d[0][ 3].multiply(2);
d[2][ 4] = d[0][ 4].multiply(2);
d[2][ 5] = d[0][ 5].multiply(2);
d[2][ 6] = d[0][ 6].multiply(2);
d[2][ 7] = d[0][ 7].multiply(2);
d[2][ 8] = d[0][ 8].multiply(2);
d[2][ 9] = d[0][ 9].multiply(2);
d[2][10] = d[0][10].multiply(2);
d[2][11] = d[0][11].multiply(2);
d[2][12] = d[0][12].multiply(2).subtract(1); // really -1
d[2][13] = d[0][13].multiply(2); // really 0
d[2][14] = d[0][14].multiply(2); // really 0
d[2][15] = d[0][15].multiply(2); // really 0
d[3][ 0] = fraction(field, -17751989329.0, 2106076560.0);
d[3][ 1] = field.getZero();
d[3][ 2] = field.getZero();
d[3][ 3] = field.getZero();
d[3][ 4] = field.getZero();
d[3][ 5] = fraction(field, 4272954039.0, 7539864640.0);
d[3][ 6] = fraction(field, -118476319744.0, 38604839385.0);
d[3][ 7] = fraction(field, 755123450731.0, 316657731600.0);
d[3][ 8] = fraction(field, 3692384461234828125.0, 1744130441634250432.0);
d[3][ 9] = fraction(field, -4612609375.0, 5293382976.0);
d[3][10] = fraction(field, 2091772278379.0, 933644586600.0);
d[3][11] = fraction(field, 2136624137.0, 3382989120.0);
d[3][12] = fraction(field, -126493.0, 1421424.0);
d[3][13] = fraction(field, 98350000.0, 5419179.0);
d[3][14] = fraction(field, -18878125.0, 2053168.0);
d[3][15] = fraction(field, -1944542619.0, 438351368.0);
d[4][ 0] = fraction(field, 32941697297.0, 3159114840.0);
d[4][ 1] = field.getZero();
d[4][ 2] = field.getZero();
d[4][ 3] = field.getZero();
d[4][ 4] = field.getZero();
d[4][ 5] = fraction(field, 456696183123.0, 1884966160.0);
d[4][ 6] = fraction(field, 19132610714624.0, 115814518155.0);
d[4][ 7] = fraction(field, -177904688592943.0, 474986597400.0);
d[4][ 8] = fraction(field, -4821139941836765625.0, 218016305204281304.0);
d[4][ 9] = fraction(field, 30702015625.0, 3970037232.0);
d[4][10] = fraction(field, -85916079474274.0, 2800933759800.0);
d[4][11] = fraction(field, -5919468007.0, 634310460.0);
d[4][12] = fraction(field, 2479159.0, 157936.0);
d[4][13] = fraction(field, -18750000.0, 602131.0);
d[4][14] = fraction(field, -19203125.0, 2053168.0);
d[4][15] = fraction(field, 15700361463.0, 438351368.0);
d[5][ 0] = fraction(field, 12627015655.0, 631822968.0);
d[5][ 1] = field.getZero();
d[5][ 2] = field.getZero();
d[5][ 3] = field.getZero();
d[5][ 4] = field.getZero();
d[5][ 5] = fraction(field, -72955222965.0, 188496616.0);
d[5][ 6] = fraction(field, -13145744952320.0, 69488710893.0);
d[5][ 7] = fraction(field, 30084216194513.0, 56998391688.0);
d[5][ 8] = fraction(field, -296858761006640625.0, 25648977082856624.0);
d[5][ 9] = fraction(field, 569140625.0, 82709109.0);
d[5][10] = fraction(field, -18684190637.0, 18672891732.0);
d[5][11] = fraction(field, 69644045.0, 89549712.0);
d[5][12] = fraction(field, -11847025.0, 4264272.0);
d[5][13] = fraction(field, -978650000.0, 16257537.0);
d[5][14] = fraction(field, 519371875.0, 6159504.0);
d[5][15] = fraction(field, 5256837225.0, 438351368.0);
d[6][ 0] = fraction(field, -450944925.0, 17550638.0);
d[6][ 1] = field.getZero();
d[6][ 2] = field.getZero();
d[6][ 3] = field.getZero();
d[6][ 4] = field.getZero();
d[6][ 5] = fraction(field, -14532122925.0, 94248308.0);
d[6][ 6] = fraction(field, -595876966400.0, 2573655959.0);
d[6][ 7] = fraction(field, 188748653015.0, 527762886.0);
d[6][ 8] = fraction(field, 2545485458115234375.0, 27252038150535163.0);
d[6][ 9] = fraction(field, -1376953125.0, 36759604.0);
d[6][10] = fraction(field, 53995596795.0, 518691437.0);
d[6][11] = fraction(field, 210311225.0, 7047894.0);
d[6][12] = fraction(field, -1718875.0, 39484.0);
d[6][13] = fraction(field, 58000000.0, 602131.0);
d[6][14] = fraction(field, -1546875.0, 39484.0);
d[6][15] = fraction(field, -1262172375.0, 8429834.0);
}
/** {@inheritDoc} */
@Override
protected DormandPrince853FieldStepInterpolator<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 DormandPrince853FieldStepInterpolator<T>(newField, newForward, newYDotK,
newGlobalPreviousState, newGlobalCurrentState,
newSoftPreviousState, newSoftCurrentState,
newMapper);
}
/** Create a fraction.
* @param field field to which the elements belong
* @param p numerator
* @param q denominator
* @return p/q computed in the instance field
*/
private T fraction(final Field<T> field, final double p, final double q) {
return field.getZero().add(p).divide(q);
}
/** {@inheritDoc} */
@SuppressWarnings("unchecked")
@Override
protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
final T time, final T theta,
final T thetaH, final T oneMinusThetaH)
throws MaxCountExceededException {
final T one = time.getField().getOne();
final T eta = one.subtract(theta);
final T twoTheta = theta.multiply(2);
final T theta2 = theta.multiply(theta);
final T dot1 = one.subtract(twoTheta);
final T dot2 = theta.multiply(theta.multiply(-3).add(2));
final T dot3 = twoTheta.multiply(theta.multiply(twoTheta.subtract(3)).add(1));
final T dot4 = theta2.multiply(theta.multiply(theta.multiply(5).subtract(8)).add(3));
final T dot5 = theta2.multiply(theta.multiply(theta.multiply(theta.multiply(-6).add(15)).subtract(12)).add(3));
final T dot6 = theta2.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(-7).add(18)).subtract(15)).add(4)));
final T[] interpolatedState;
final T[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
final T f0 = thetaH;
final T f1 = f0.multiply(eta);
final T f2 = f1.multiply(theta);
final T f3 = f2.multiply(eta);
final T f4 = f3.multiply(theta);
final T f5 = f4.multiply(eta);
final T f6 = f5.multiply(theta);
final T[] p = MathArrays.buildArray(time.getField(), 16);
final T[] q = MathArrays.buildArray(time.getField(), 16);
for (int i = 0; i < p.length; ++i) {
p[i] = f0.multiply(d[0][i]).
add(f1.multiply(d[1][i])).
add(f2.multiply(d[2][i])).
add(f3.multiply(d[3][i])).
add(f4.multiply(d[4][i])).
add(f5.multiply(d[5][i])).
add(f6.multiply(d[6][i]));
q[i] = d[0][i].
add(dot1.multiply(d[1][i])).
add(dot2.multiply(d[2][i])).
add(dot3.multiply(d[3][i])).
add(dot4.multiply(d[4][i])).
add(dot5.multiply(d[5][i])).
add(dot6.multiply(d[6][i]));
}
interpolatedState = previousStateLinearCombination(p[0], p[1], p[ 2], p[ 3], p[ 4], p[ 5], p[ 6], p[ 7],
p[8], p[9], p[10], p[11], p[12], p[13], p[14], p[15]);
interpolatedDerivatives = derivativeLinearCombination(q[0], q[1], q[ 2], q[ 3], q[ 4], q[ 5], q[ 6], q[ 7],
q[8], q[9], q[10], q[11], q[12], q[13], q[14], q[15]);
} else {
final T f0 = oneMinusThetaH.negate();
final T f1 = f0.multiply(theta).negate();
final T f2 = f1.multiply(theta);
final T f3 = f2.multiply(eta);
final T f4 = f3.multiply(theta);
final T f5 = f4.multiply(eta);
final T f6 = f5.multiply(theta);
final T[] p = MathArrays.buildArray(time.getField(), 16);
final T[] q = MathArrays.buildArray(time.getField(), 16);
for (int i = 0; i < p.length; ++i) {
p[i] = f0.multiply(d[0][i]).
add(f1.multiply(d[1][i])).
add(f2.multiply(d[2][i])).
add(f3.multiply(d[3][i])).
add(f4.multiply(d[4][i])).
add(f5.multiply(d[5][i])).
add(f6.multiply(d[6][i]));
q[i] = d[0][i].
add(dot1.multiply(d[1][i])).
add(dot2.multiply(d[2][i])).
add(dot3.multiply(d[3][i])).
add(dot4.multiply(d[4][i])).
add(dot5.multiply(d[5][i])).
add(dot6.multiply(d[6][i]));
}
interpolatedState = currentStateLinearCombination(p[0], p[1], p[ 2], p[ 3], p[ 4], p[ 5], p[ 6], p[ 7],
p[8], p[9], p[10], p[11], p[12], p[13], p[14], p[15]);
interpolatedDerivatives = derivativeLinearCombination(q[0], q[1], q[ 2], q[ 3], q[ 4], q[ 5], q[ 6], q[ 7],
q[8], q[9], q[10], q[11], q[12], q[13], q[14], q[15]);
}
return new FieldODEStateAndDerivative<T>(time, interpolatedState, interpolatedDerivatives);
}
}