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23 package org.hipparchus.ode.nonstiff;
24
25 import org.hipparchus.CalculusFieldElement;
26 import org.hipparchus.Field;
27 import org.hipparchus.exception.MathIllegalStateException;
28 import org.hipparchus.ode.FieldEquationsMapper;
29 import org.hipparchus.ode.FieldODEStateAndDerivative;
30 import org.hipparchus.util.MathArrays;
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40
41 class DormandPrince853FieldStateInterpolator<T extends CalculusFieldElement<T>>
42 extends RungeKuttaFieldStateInterpolator<T> {
43
44
45
46
47 private final T[][] d;
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59 DormandPrince853FieldStateInterpolator(final Field<T> field, final boolean forward,
60 final T[][] yDotK,
61 final FieldODEStateAndDerivative<T> globalPreviousState,
62 final FieldODEStateAndDerivative<T> globalCurrentState,
63 final FieldODEStateAndDerivative<T> softPreviousState,
64 final FieldODEStateAndDerivative<T> softCurrentState,
65 final FieldEquationsMapper<T> mapper) {
66 super(field, forward, yDotK,
67 globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
68 mapper);
69
70 d = MathArrays.buildArray(field, 7, 16);
71
72
73 d[0][ 0] = fraction(field, 104257, 1920240);
74 d[0][ 1] = field.getZero();
75 d[0][ 2] = field.getZero();
76 d[0][ 3] = field.getZero();
77 d[0][ 4] = field.getZero();
78 d[0][ 5] = fraction(field, 3399327.0, 763840.0);
79 d[0][ 6] = fraction(field, 66578432.0, 35198415.0);
80 d[0][ 7] = fraction(field, -1674902723.0, 288716400.0);
81 d[0][ 8] = fraction(field, 54980371265625.0, 176692375811392.0);
82 d[0][ 9] = fraction(field, -734375.0, 4826304.0);
83 d[0][10] = fraction(field, 171414593.0, 851261400.0);
84 d[0][11] = fraction(field, 137909.0, 3084480.0);
85 d[0][12] = field.getZero();
86 d[0][13] = field.getZero();
87 d[0][14] = field.getZero();
88 d[0][15] = field.getZero();
89
90 d[1][ 0] = d[0][ 0].negate().add(1);
91 d[1][ 1] = d[0][ 1].negate();
92 d[1][ 2] = d[0][ 2].negate();
93 d[1][ 3] = d[0][ 3].negate();
94 d[1][ 4] = d[0][ 4].negate();
95 d[1][ 5] = d[0][ 5].negate();
96 d[1][ 6] = d[0][ 6].negate();
97 d[1][ 7] = d[0][ 7].negate();
98 d[1][ 8] = d[0][ 8].negate();
99 d[1][ 9] = d[0][ 9].negate();
100 d[1][10] = d[0][10].negate();
101 d[1][11] = d[0][11].negate();
102 d[1][12] = d[0][12].negate();
103 d[1][13] = d[0][13].negate();
104 d[1][14] = d[0][14].negate();
105 d[1][15] = d[0][15].negate();
106
107 d[2][ 0] = d[0][ 0].multiply(2).subtract(1);
108 d[2][ 1] = d[0][ 1].multiply(2);
109 d[2][ 2] = d[0][ 2].multiply(2);
110 d[2][ 3] = d[0][ 3].multiply(2);
111 d[2][ 4] = d[0][ 4].multiply(2);
112 d[2][ 5] = d[0][ 5].multiply(2);
113 d[2][ 6] = d[0][ 6].multiply(2);
114 d[2][ 7] = d[0][ 7].multiply(2);
115 d[2][ 8] = d[0][ 8].multiply(2);
116 d[2][ 9] = d[0][ 9].multiply(2);
117 d[2][10] = d[0][10].multiply(2);
118 d[2][11] = d[0][11].multiply(2);
119 d[2][12] = d[0][12].multiply(2).subtract(1);
120 d[2][13] = d[0][13].multiply(2);
121 d[2][14] = d[0][14].multiply(2);
122 d[2][15] = d[0][15].multiply(2);
123
124 d[3][ 0] = fraction(field, -17751989329.0, 2106076560.0);
125 d[3][ 1] = field.getZero();
126 d[3][ 2] = field.getZero();
127 d[3][ 3] = field.getZero();
128 d[3][ 4] = field.getZero();
129 d[3][ 5] = fraction(field, 4272954039.0, 7539864640.0);
130 d[3][ 6] = fraction(field, -118476319744.0, 38604839385.0);
131 d[3][ 7] = fraction(field, 755123450731.0, 316657731600.0);
132 d[3][ 8] = fraction(field, 3692384461234828125.0, 1744130441634250432.0);
133 d[3][ 9] = fraction(field, -4612609375.0, 5293382976.0);
134 d[3][10] = fraction(field, 2091772278379.0, 933644586600.0);
135 d[3][11] = fraction(field, 2136624137.0, 3382989120.0);
136 d[3][12] = fraction(field, -126493.0, 1421424.0);
137 d[3][13] = fraction(field, 98350000.0, 5419179.0);
138 d[3][14] = fraction(field, -18878125.0, 2053168.0);
139 d[3][15] = fraction(field, -1944542619.0, 438351368.0);
140
141 d[4][ 0] = fraction(field, 32941697297.0, 3159114840.0);
142 d[4][ 1] = field.getZero();
143 d[4][ 2] = field.getZero();
144 d[4][ 3] = field.getZero();
145 d[4][ 4] = field.getZero();
146 d[4][ 5] = fraction(field, 456696183123.0, 1884966160.0);
147 d[4][ 6] = fraction(field, 19132610714624.0, 115814518155.0);
148 d[4][ 7] = fraction(field, -177904688592943.0, 474986597400.0);
149 d[4][ 8] = fraction(field, -4821139941836765625.0, 218016305204281304.0);
150 d[4][ 9] = fraction(field, 30702015625.0, 3970037232.0);
151 d[4][10] = fraction(field, -85916079474274.0, 2800933759800.0);
152 d[4][11] = fraction(field, -5919468007.0, 634310460.0);
153 d[4][12] = fraction(field, 2479159.0, 157936.0);
154 d[4][13] = fraction(field, -18750000.0, 602131.0);
155 d[4][14] = fraction(field, -19203125.0, 2053168.0);
156 d[4][15] = fraction(field, 15700361463.0, 438351368.0);
157
158 d[5][ 0] = fraction(field, 12627015655.0, 631822968.0);
159 d[5][ 1] = field.getZero();
160 d[5][ 2] = field.getZero();
161 d[5][ 3] = field.getZero();
162 d[5][ 4] = field.getZero();
163 d[5][ 5] = fraction(field, -72955222965.0, 188496616.0);
164 d[5][ 6] = fraction(field, -13145744952320.0, 69488710893.0);
165 d[5][ 7] = fraction(field, 30084216194513.0, 56998391688.0);
166 d[5][ 8] = fraction(field, -296858761006640625.0, 25648977082856624.0);
167 d[5][ 9] = fraction(field, 569140625.0, 82709109.0);
168 d[5][10] = fraction(field, -18684190637.0, 18672891732.0);
169 d[5][11] = fraction(field, 69644045.0, 89549712.0);
170 d[5][12] = fraction(field, -11847025.0, 4264272.0);
171 d[5][13] = fraction(field, -978650000.0, 16257537.0);
172 d[5][14] = fraction(field, 519371875.0, 6159504.0);
173 d[5][15] = fraction(field, 5256837225.0, 438351368.0);
174
175 d[6][ 0] = fraction(field, -450944925.0, 17550638.0);
176 d[6][ 1] = field.getZero();
177 d[6][ 2] = field.getZero();
178 d[6][ 3] = field.getZero();
179 d[6][ 4] = field.getZero();
180 d[6][ 5] = fraction(field, -14532122925.0, 94248308.0);
181 d[6][ 6] = fraction(field, -595876966400.0, 2573655959.0);
182 d[6][ 7] = fraction(field, 188748653015.0, 527762886.0);
183 d[6][ 8] = fraction(field, 2545485458115234375.0, 27252038150535163.0);
184 d[6][ 9] = fraction(field, -1376953125.0, 36759604.0);
185 d[6][10] = fraction(field, 53995596795.0, 518691437.0);
186 d[6][11] = fraction(field, 210311225.0, 7047894.0);
187 d[6][12] = fraction(field, -1718875.0, 39484.0);
188 d[6][13] = fraction(field, 58000000.0, 602131.0);
189 d[6][14] = fraction(field, -1546875.0, 39484.0);
190 d[6][15] = fraction(field, -1262172375.0, 8429834.0);
191
192 }
193
194
195 @Override
196 protected DormandPrince853FieldStateInterpolator<T> create(final Field<T> newField, final boolean newForward, final T[][] newYDotK,
197 final FieldODEStateAndDerivative<T> newGlobalPreviousState,
198 final FieldODEStateAndDerivative<T> newGlobalCurrentState,
199 final FieldODEStateAndDerivative<T> newSoftPreviousState,
200 final FieldODEStateAndDerivative<T> newSoftCurrentState,
201 final FieldEquationsMapper<T> newMapper) {
202 return new DormandPrince853FieldStateInterpolator<T>(newField, newForward, newYDotK,
203 newGlobalPreviousState, newGlobalCurrentState,
204 newSoftPreviousState, newSoftCurrentState,
205 newMapper);
206 }
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213
214 private T fraction(final Field<T> field, final double p, final double q) {
215 return field.getZero().add(p).divide(q);
216 }
217
218
219 @SuppressWarnings("unchecked")
220 @Override
221 protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
222 final T time, final T theta,
223 final T thetaH, final T oneMinusThetaH)
224 throws MathIllegalStateException {
225
226 final T one = time.getField().getOne();
227 final T eta = one.subtract(theta);
228 final T twoTheta = theta.multiply(2);
229 final T theta2 = theta.multiply(theta);
230 final T dot1 = one.subtract(twoTheta);
231 final T dot2 = theta.multiply(theta.multiply(-3).add(2));
232 final T dot3 = twoTheta.multiply(theta.multiply(twoTheta.subtract(3)).add(1));
233 final T dot4 = theta2.multiply(theta.multiply(theta.multiply(5).subtract(8)).add(3));
234 final T dot5 = theta2.multiply(theta.multiply(theta.multiply(theta.multiply(-6).add(15)).subtract(12)).add(3));
235 final T dot6 = theta2.multiply(theta.multiply(theta.multiply(theta.multiply(theta.multiply(-7).add(18)).subtract(15)).add(4)));
236 final T[] interpolatedState;
237 final T[] interpolatedDerivatives;
238
239
240 if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
241 final T f0 = thetaH;
242 final T f1 = f0.multiply(eta);
243 final T f2 = f1.multiply(theta);
244 final T f3 = f2.multiply(eta);
245 final T f4 = f3.multiply(theta);
246 final T f5 = f4.multiply(eta);
247 final T f6 = f5.multiply(theta);
248 final T[] p = MathArrays.buildArray(time.getField(), 16);
249 final T[] q = MathArrays.buildArray(time.getField(), 16);
250 for (int i = 0; i < p.length; ++i) {
251 p[i] = f0.multiply(d[0][i]).
252 add(f1.multiply(d[1][i])).
253 add(f2.multiply(d[2][i])).
254 add(f3.multiply(d[3][i])).
255 add(f4.multiply(d[4][i])).
256 add(f5.multiply(d[5][i])).
257 add(f6.multiply(d[6][i]));
258 q[i] = d[0][i].
259 add(dot1.multiply(d[1][i])).
260 add(dot2.multiply(d[2][i])).
261 add(dot3.multiply(d[3][i])).
262 add(dot4.multiply(d[4][i])).
263 add(dot5.multiply(d[5][i])).
264 add(dot6.multiply(d[6][i]));
265 }
266 interpolatedState = previousStateLinearCombination(p[0], p[1], p[ 2], p[ 3], p[ 4], p[ 5], p[ 6], p[ 7],
267 p[8], p[9], p[10], p[11], p[12], p[13], p[14], p[15]);
268 interpolatedDerivatives = derivativeLinearCombination(q[0], q[1], q[ 2], q[ 3], q[ 4], q[ 5], q[ 6], q[ 7],
269 q[8], q[9], q[10], q[11], q[12], q[13], q[14], q[15]);
270 } else {
271 final T f0 = oneMinusThetaH.negate();
272 final T f1 = f0.multiply(theta).negate();
273 final T f2 = f1.multiply(theta);
274 final T f3 = f2.multiply(eta);
275 final T f4 = f3.multiply(theta);
276 final T f5 = f4.multiply(eta);
277 final T f6 = f5.multiply(theta);
278 final T[] p = MathArrays.buildArray(time.getField(), 16);
279 final T[] q = MathArrays.buildArray(time.getField(), 16);
280 for (int i = 0; i < p.length; ++i) {
281 p[i] = f0.multiply(d[0][i]).
282 add(f1.multiply(d[1][i])).
283 add(f2.multiply(d[2][i])).
284 add(f3.multiply(d[3][i])).
285 add(f4.multiply(d[4][i])).
286 add(f5.multiply(d[5][i])).
287 add(f6.multiply(d[6][i]));
288 q[i] = d[0][i].
289 add(dot1.multiply(d[1][i])).
290 add(dot2.multiply(d[2][i])).
291 add(dot3.multiply(d[3][i])).
292 add(dot4.multiply(d[4][i])).
293 add(dot5.multiply(d[5][i])).
294 add(dot6.multiply(d[6][i]));
295 }
296 interpolatedState = currentStateLinearCombination(p[0], p[1], p[ 2], p[ 3], p[ 4], p[ 5], p[ 6], p[ 7],
297 p[8], p[9], p[10], p[11], p[12], p[13], p[14], p[15]);
298 interpolatedDerivatives = derivativeLinearCombination(q[0], q[1], q[ 2], q[ 3], q[ 4], q[ 5], q[ 6], q[ 7],
299 q[8], q[9], q[10], q[11], q[12], q[13], q[14], q[15]);
300 }
301
302 return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
303
304 }
305
306 }