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Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/nonstiff/DormandPrince853FieldIntegrator.java')
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diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/DormandPrince853FieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/DormandPrince853FieldIntegrator.java new file mode 100644 index 0000000..3111756 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/DormandPrince853FieldIntegrator.java @@ -0,0 +1,454 @@ +/* + * 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; +import org.apache.commons.math3.util.MathArrays; +import org.apache.commons.math3.util.MathUtils; + + +/** + * This class implements the 8(5,3) Dormand-Prince integrator for Ordinary + * Differential Equations. + * + * <p>This integrator is an embedded Runge-Kutta integrator + * of order 8(5,3) used in local extrapolation mode (i.e. the solution + * is computed using the high order formula) with stepsize control + * (and automatic step initialization) and continuous output. This + * method uses 12 functions evaluations per step for integration and 4 + * evaluations for interpolation. However, since the first + * interpolation evaluation is the same as the first integration + * evaluation of the next step, we have included it in the integrator + * rather than in the interpolator and specified the method was an + * <i>fsal</i>. Hence, despite we have 13 stages here, the cost is + * really 12 evaluations per step even if no interpolation is done, + * and the overcost of interpolation is only 3 evaluations.</p> + * + * <p>This method is based on an 8(6) method by Dormand and Prince + * (i.e. order 8 for the integration and order 6 for error estimation) + * modified by Hairer and Wanner to use a 5th order error estimator + * with 3rd order correction. This modification was introduced because + * the original method failed in some cases (wrong steps can be + * accepted when step size is too large, for example in the + * Brusselator problem) and also had <i>severe difficulties when + * applied to problems with discontinuities</i>. This modification is + * explained in the second edition of the first volume (Nonstiff + * Problems) of the reference book by Hairer, Norsett and Wanner: + * <i>Solving Ordinary Differential Equations</i> (Springer-Verlag, + * ISBN 3-540-56670-8).</p> + * + * @param <T> the type of the field elements + * @since 3.6 + */ + +public class DormandPrince853FieldIntegrator<T extends RealFieldElement<T>> + extends EmbeddedRungeKuttaFieldIntegrator<T> { + + /** Integrator method name. */ + private static final String METHOD_NAME = "Dormand-Prince 8 (5, 3)"; + + /** First error weights array, element 1. */ + private final T e1_01; + + // elements 2 to 5 are zero, so they are neither stored nor used + + /** First error weights array, element 6. */ + private final T e1_06; + + /** First error weights array, element 7. */ + private final T e1_07; + + /** First error weights array, element 8. */ + private final T e1_08; + + /** First error weights array, element 9. */ + private final T e1_09; + + /** First error weights array, element 10. */ + private final T e1_10; + + /** First error weights array, element 11. */ + private final T e1_11; + + /** First error weights array, element 12. */ + private final T e1_12; + + + /** Second error weights array, element 1. */ + private final T e2_01; + + // elements 2 to 5 are zero, so they are neither stored nor used + + /** Second error weights array, element 6. */ + private final T e2_06; + + /** Second error weights array, element 7. */ + private final T e2_07; + + /** Second error weights array, element 8. */ + private final T e2_08; + + /** Second error weights array, element 9. */ + private final T e2_09; + + /** Second error weights array, element 10. */ + private final T e2_10; + + /** Second error weights array, element 11. */ + private final T e2_11; + + /** Second error weights array, element 12. */ + private final T e2_12; + + /** Simple constructor. + * Build an eighth order Dormand-Prince integrator with the given step bounds + * @param field field to which the time and state vector elements belong + * @param minStep minimal step (sign is irrelevant, regardless of + * integration direction, forward or backward), the last step can + * be smaller than this + * @param maxStep maximal step (sign is irrelevant, regardless of + * integration direction, forward or backward), the last step can + * be smaller than this + * @param scalAbsoluteTolerance allowed absolute error + * @param scalRelativeTolerance allowed relative error + */ + public DormandPrince853FieldIntegrator(final Field<T> field, + final double minStep, final double maxStep, + final double scalAbsoluteTolerance, + final double scalRelativeTolerance) { + super(field, METHOD_NAME, 12, + minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); + e1_01 = fraction( 116092271.0, 8848465920.0); + e1_06 = fraction( -1871647.0, 1527680.0); + e1_07 = fraction( -69799717.0, 140793660.0); + e1_08 = fraction( 1230164450203.0, 739113984000.0); + e1_09 = fraction(-1980813971228885.0, 5654156025964544.0); + e1_10 = fraction( 464500805.0, 1389975552.0); + e1_11 = fraction( 1606764981773.0, 19613062656000.0); + e1_12 = fraction( -137909.0, 6168960.0); + e2_01 = fraction( -364463.0, 1920240.0); + e2_06 = fraction( 3399327.0, 763840.0); + e2_07 = fraction( 66578432.0, 35198415.0); + e2_08 = fraction( -1674902723.0, 288716400.0); + e2_09 = fraction( -74684743568175.0, 176692375811392.0); + e2_10 = fraction( -734375.0, 4826304.0); + e2_11 = fraction( 171414593.0, 851261400.0); + e2_12 = fraction( 69869.0, 3084480.0); + } + + /** Simple constructor. + * Build an eighth order Dormand-Prince integrator with the given step bounds + * @param field field to which the time and state vector elements belong + * @param minStep minimal step (sign is irrelevant, regardless of + * integration direction, forward or backward), the last step can + * be smaller than this + * @param maxStep maximal step (sign is irrelevant, regardless of + * integration direction, forward or backward), the last step can + * be smaller than this + * @param vecAbsoluteTolerance allowed absolute error + * @param vecRelativeTolerance allowed relative error + */ + public DormandPrince853FieldIntegrator(final Field<T> field, + final double minStep, final double maxStep, + final double[] vecAbsoluteTolerance, + final double[] vecRelativeTolerance) { + super(field, METHOD_NAME, 12, + minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); + e1_01 = fraction( 116092271.0, 8848465920.0); + e1_06 = fraction( -1871647.0, 1527680.0); + e1_07 = fraction( -69799717.0, 140793660.0); + e1_08 = fraction( 1230164450203.0, 739113984000.0); + e1_09 = fraction(-1980813971228885.0, 5654156025964544.0); + e1_10 = fraction( 464500805.0, 1389975552.0); + e1_11 = fraction( 1606764981773.0, 19613062656000.0); + e1_12 = fraction( -137909.0, 6168960.0); + e2_01 = fraction( -364463.0, 1920240.0); + e2_06 = fraction( 3399327.0, 763840.0); + e2_07 = fraction( 66578432.0, 35198415.0); + e2_08 = fraction( -1674902723.0, 288716400.0); + e2_09 = fraction( -74684743568175.0, 176692375811392.0); + e2_10 = fraction( -734375.0, 4826304.0); + e2_11 = fraction( 171414593.0, 851261400.0); + e2_12 = fraction( 69869.0, 3084480.0); + } + + /** {@inheritDoc} */ + public T[] getC() { + + final T sqrt6 = getField().getOne().multiply(6).sqrt(); + + final T[] c = MathArrays.buildArray(getField(), 15); + c[ 0] = sqrt6.add(-6).divide(-67.5); + c[ 1] = sqrt6.add(-6).divide(-45.0); + c[ 2] = sqrt6.add(-6).divide(-30.0); + c[ 3] = sqrt6.add( 6).divide( 30.0); + c[ 4] = fraction(1, 3); + c[ 5] = fraction(1, 4); + c[ 6] = fraction(4, 13); + c[ 7] = fraction(127, 195); + c[ 8] = fraction(3, 5); + c[ 9] = fraction(6, 7); + c[10] = getField().getOne(); + c[11] = getField().getOne(); + c[12] = fraction(1.0, 10.0); + c[13] = fraction(1.0, 5.0); + c[14] = fraction(7.0, 9.0); + + return c; + + } + + /** {@inheritDoc} */ + public T[][] getA() { + + final T sqrt6 = getField().getOne().multiply(6).sqrt(); + + final T[][] a = MathArrays.buildArray(getField(), 15, -1); + for (int i = 0; i < a.length; ++i) { + a[i] = MathArrays.buildArray(getField(), i + 1); + } + + a[ 0][ 0] = sqrt6.add(-6).divide(-67.5); + + a[ 1][ 0] = sqrt6.add(-6).divide(-180); + a[ 1][ 1] = sqrt6.add(-6).divide( -60); + + a[ 2][ 0] = sqrt6.add(-6).divide(-120); + a[ 2][ 1] = getField().getZero(); + a[ 2][ 2] = sqrt6.add(-6).divide( -40); + + a[ 3][ 0] = sqrt6.multiply(107).add(462).divide( 3000); + a[ 3][ 1] = getField().getZero(); + a[ 3][ 2] = sqrt6.multiply(197).add(402).divide(-1000); + a[ 3][ 3] = sqrt6.multiply( 73).add(168).divide( 375); + + a[ 4][ 0] = fraction(1, 27); + a[ 4][ 1] = getField().getZero(); + a[ 4][ 2] = getField().getZero(); + a[ 4][ 3] = sqrt6.add( 16).divide( 108); + a[ 4][ 4] = sqrt6.add(-16).divide(-108); + + a[ 5][ 0] = fraction(19, 512); + a[ 5][ 1] = getField().getZero(); + a[ 5][ 2] = getField().getZero(); + a[ 5][ 3] = sqrt6.multiply( 23).add(118).divide(1024); + a[ 5][ 4] = sqrt6.multiply(-23).add(118).divide(1024); + a[ 5][ 5] = fraction(-9, 512); + + a[ 6][ 0] = fraction(13772, 371293); + a[ 6][ 1] = getField().getZero(); + a[ 6][ 2] = getField().getZero(); + a[ 6][ 3] = sqrt6.multiply( 4784).add(51544).divide(371293); + a[ 6][ 4] = sqrt6.multiply(-4784).add(51544).divide(371293); + a[ 6][ 5] = fraction(-5688, 371293); + a[ 6][ 6] = fraction( 3072, 371293); + + a[ 7][ 0] = fraction(58656157643.0, 93983540625.0); + a[ 7][ 1] = getField().getZero(); + a[ 7][ 2] = getField().getZero(); + a[ 7][ 3] = sqrt6.multiply(-318801444819.0).add(-1324889724104.0).divide(626556937500.0); + a[ 7][ 4] = sqrt6.multiply( 318801444819.0).add(-1324889724104.0).divide(626556937500.0); + a[ 7][ 5] = fraction(96044563816.0, 3480871875.0); + a[ 7][ 6] = fraction(5682451879168.0, 281950621875.0); + a[ 7][ 7] = fraction(-165125654.0, 3796875.0); + + a[ 8][ 0] = fraction(8909899.0, 18653125.0); + a[ 8][ 1] = getField().getZero(); + a[ 8][ 2] = getField().getZero(); + a[ 8][ 3] = sqrt6.multiply(-1137963.0).add(-4521408.0).divide(2937500.0); + a[ 8][ 4] = sqrt6.multiply( 1137963.0).add(-4521408.0).divide(2937500.0); + a[ 8][ 5] = fraction(96663078.0, 4553125.0); + a[ 8][ 6] = fraction(2107245056.0, 137915625.0); + a[ 8][ 7] = fraction(-4913652016.0, 147609375.0); + a[ 8][ 8] = fraction(-78894270.0, 3880452869.0); + + a[ 9][ 0] = fraction(-20401265806.0, 21769653311.0); + a[ 9][ 1] = getField().getZero(); + a[ 9][ 2] = getField().getZero(); + a[ 9][ 3] = sqrt6.multiply( 94326.0).add(354216.0).divide(112847.0); + a[ 9][ 4] = sqrt6.multiply(-94326.0).add(354216.0).divide(112847.0); + a[ 9][ 5] = fraction(-43306765128.0, 5313852383.0); + a[ 9][ 6] = fraction(-20866708358144.0, 1126708119789.0); + a[ 9][ 7] = fraction(14886003438020.0, 654632330667.0); + a[ 9][ 8] = fraction(35290686222309375.0, 14152473387134411.0); + a[ 9][ 9] = fraction(-1477884375.0, 485066827.0); + + a[10][ 0] = fraction(39815761.0, 17514443.0); + a[10][ 1] = getField().getZero(); + a[10][ 2] = getField().getZero(); + a[10][ 3] = sqrt6.multiply(-960905.0).add(-3457480.0).divide(551636.0); + a[10][ 4] = sqrt6.multiply( 960905.0).add(-3457480.0).divide(551636.0); + a[10][ 5] = fraction(-844554132.0, 47026969.0); + a[10][ 6] = fraction(8444996352.0, 302158619.0); + a[10][ 7] = fraction(-2509602342.0, 877790785.0); + a[10][ 8] = fraction(-28388795297996250.0, 3199510091356783.0); + a[10][ 9] = fraction(226716250.0, 18341897.0); + a[10][10] = fraction(1371316744.0, 2131383595.0); + + // the following stage is both for interpolation and the first stage in next step + // (the coefficients are identical to the B array) + a[11][ 0] = fraction(104257.0, 1920240.0); + a[11][ 1] = getField().getZero(); + a[11][ 2] = getField().getZero(); + a[11][ 3] = getField().getZero(); + a[11][ 4] = getField().getZero(); + a[11][ 5] = fraction(3399327.0, 763840.0); + a[11][ 6] = fraction(66578432.0, 35198415.0); + a[11][ 7] = fraction(-1674902723.0, 288716400.0); + a[11][ 8] = fraction(54980371265625.0, 176692375811392.0); + a[11][ 9] = fraction(-734375.0, 4826304.0); + a[11][10] = fraction(171414593.0, 851261400.0); + a[11][11] = fraction(137909.0, 3084480.0); + + // the following stages are for interpolation only + a[12][ 0] = fraction( 13481885573.0, 240030000000.0); + a[12][ 1] = getField().getZero(); + a[12][ 2] = getField().getZero(); + a[12][ 3] = getField().getZero(); + a[12][ 4] = getField().getZero(); + a[12][ 5] = getField().getZero(); + a[12][ 6] = fraction( 139418837528.0, 549975234375.0); + a[12][ 7] = fraction( -11108320068443.0, 45111937500000.0); + a[12][ 8] = fraction(-1769651421925959.0, 14249385146080000.0); + a[12][ 9] = fraction( 57799439.0, 377055000.0); + a[12][10] = fraction( 793322643029.0, 96734250000000.0); + a[12][11] = fraction( 1458939311.0, 192780000000.0); + a[12][12] = fraction( -4149.0, 500000.0); + + a[13][ 0] = fraction( 1595561272731.0, 50120273500000.0); + a[13][ 1] = getField().getZero(); + a[13][ 2] = getField().getZero(); + a[13][ 3] = getField().getZero(); + a[13][ 4] = getField().getZero(); + a[13][ 5] = fraction( 975183916491.0, 34457688031250.0); + a[13][ 6] = fraction( 38492013932672.0, 718912673015625.0); + a[13][ 7] = fraction(-1114881286517557.0, 20298710767500000.0); + a[13][ 8] = getField().getZero(); + a[13][ 9] = getField().getZero(); + a[13][10] = fraction( -2538710946863.0, 23431227861250000.0); + a[13][11] = fraction( 8824659001.0, 23066716781250.0); + a[13][12] = fraction( -11518334563.0, 33831184612500.0); + a[13][13] = fraction( 1912306948.0, 13532473845.0); + + a[14][ 0] = fraction( -13613986967.0, 31741908048.0); + a[14][ 1] = getField().getZero(); + a[14][ 2] = getField().getZero(); + a[14][ 3] = getField().getZero(); + a[14][ 4] = getField().getZero(); + a[14][ 5] = fraction( -4755612631.0, 1012344804.0); + a[14][ 6] = fraction( 42939257944576.0, 5588559685701.0); + a[14][ 7] = fraction( 77881972900277.0, 19140370552944.0); + a[14][ 8] = fraction( 22719829234375.0, 63689648654052.0); + a[14][ 9] = getField().getZero(); + a[14][10] = getField().getZero(); + a[14][11] = getField().getZero(); + a[14][12] = fraction( -1199007803.0, 857031517296.0); + a[14][13] = fraction( 157882067000.0, 53564469831.0); + a[14][14] = fraction( -290468882375.0, 31741908048.0); + + return a; + + } + + /** {@inheritDoc} */ + public T[] getB() { + final T[] b = MathArrays.buildArray(getField(), 16); + b[ 0] = fraction(104257, 1920240); + b[ 1] = getField().getZero(); + b[ 2] = getField().getZero(); + b[ 3] = getField().getZero(); + b[ 4] = getField().getZero(); + b[ 5] = fraction( 3399327.0, 763840.0); + b[ 6] = fraction( 66578432.0, 35198415.0); + b[ 7] = fraction( -1674902723.0, 288716400.0); + b[ 8] = fraction( 54980371265625.0, 176692375811392.0); + b[ 9] = fraction( -734375.0, 4826304.0); + b[10] = fraction( 171414593.0, 851261400.0); + b[11] = fraction( 137909.0, 3084480.0); + b[12] = getField().getZero(); + b[13] = getField().getZero(); + b[14] = getField().getZero(); + b[15] = getField().getZero(); + return b; + } + + /** {@inheritDoc} */ + @Override + protected DormandPrince853FieldStepInterpolator<T> + createInterpolator(final boolean forward, T[][] yDotK, + final FieldODEStateAndDerivative<T> globalPreviousState, + final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) { + return new DormandPrince853FieldStepInterpolator<T>(getField(), forward, yDotK, + globalPreviousState, globalCurrentState, + globalPreviousState, globalCurrentState, + mapper); + } + + /** {@inheritDoc} */ + @Override + public int getOrder() { + return 8; + } + + /** {@inheritDoc} */ + @Override + protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) { + T error1 = h.getField().getZero(); + T error2 = h.getField().getZero(); + + for (int j = 0; j < mainSetDimension; ++j) { + final T errSum1 = yDotK[ 0][j].multiply(e1_01). + add(yDotK[ 5][j].multiply(e1_06)). + add(yDotK[ 6][j].multiply(e1_07)). + add(yDotK[ 7][j].multiply(e1_08)). + add(yDotK[ 8][j].multiply(e1_09)). + add(yDotK[ 9][j].multiply(e1_10)). + add(yDotK[10][j].multiply(e1_11)). + add(yDotK[11][j].multiply(e1_12)); + final T errSum2 = yDotK[ 0][j].multiply(e2_01). + add(yDotK[ 5][j].multiply(e2_06)). + add(yDotK[ 6][j].multiply(e2_07)). + add(yDotK[ 7][j].multiply(e2_08)). + add(yDotK[ 8][j].multiply(e2_09)). + add(yDotK[ 9][j].multiply(e2_10)). + add(yDotK[10][j].multiply(e2_11)). + add(yDotK[11][j].multiply(e2_12)); + + final T yScale = MathUtils.max(y0[j].abs(), y1[j].abs()); + final T tol = vecAbsoluteTolerance == null ? + yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) : + yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]); + final T ratio1 = errSum1.divide(tol); + error1 = error1.add(ratio1.multiply(ratio1)); + final T ratio2 = errSum2.divide(tol); + error2 = error2.add(ratio2.multiply(ratio2)); + } + + T den = error1.add(error2.multiply(0.01)); + if (den.getReal() <= 0.0) { + den = h.getField().getOne(); + } + + return h.abs().multiply(error1).divide(den.multiply(mainSetDimension).sqrt()); + + } + +} |