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From l..@apache.org
Subject [49/50] [abbrv] [math] Renamed abstract test classes to match build environment filters.
Date Wed, 06 Jan 2016 13:51:05 GMT
Renamed abstract test classes to match build environment filters.

Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/9d47e0f9
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/9d47e0f9
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/9d47e0f9

Branch: refs/heads/master
Commit: 9d47e0f911981bee44146aa40ade3571f64e2d3f
Parents: f0a39a8
Author: Luc Maisonobe <luc@apache.org>
Authored: Wed Jan 6 14:27:52 2016 +0100
Committer: Luc Maisonobe <luc@apache.org>
Committed: Wed Jan 6 14:27:52 2016 +0100

----------------------------------------------------------------------
 .../AbstractAdamsFieldIntegratorTest.java       | 260 --------
 ...ractRungeKuttaFieldStepInterpolatorTest.java | 305 ---------
 .../AdamsBashforthFieldIntegratorTest.java      |   2 +-
 .../AdamsFieldIntegratorAbstractTest.java       | 260 ++++++++
 .../AdamsMoultonFieldIntegratorTest.java        |   2 +-
 ...sicalRungKuttaFieldStepInterpolatorTest.java |   2 +-
 .../ClassicalRungeKuttaFieldIntegratorTest.java |   2 +-
 .../DormandPrince54FieldIntegratorTest.java     |   2 +-
 ...ormandPrince54FieldStepInterpolatorTest.java |   2 +-
 .../DormandPrince853FieldIntegratorTest.java    |   2 +-
 ...rmandPrince853FieldStepInterpolatorTest.java |   2 +-
 ...edRungeKuttaFieldIntegratorAbstractTest.java | 600 +++++++++++++++++
 .../ode/nonstiff/EulerFieldIntegratorTest.java  |   2 +-
 .../EulerFieldStepInterpolatorTest.java         |   2 +-
 .../ode/nonstiff/GillFieldIntegratorTest.java   |   2 +-
 .../nonstiff/GillFieldStepInterpolatorTest.java |   2 +-
 .../HighamHall54FieldIntegratorTest.java        |   2 +-
 .../HighamHall54FieldStepInterpolatorTest.java  |   2 +-
 .../ode/nonstiff/LutherFieldIntegratorTest.java |   2 +-
 .../LutherFieldStepInterpolatorTest.java        |   2 +-
 .../nonstiff/MidpointFieldIntegratorTest.java   |   2 +-
 .../MidpointFieldStepInterpolatorTest.java      |   2 +-
 .../RungeKuttaFieldIntegratorAbstractTest.java  | 662 +++++++++++++++++++
 ...eKuttaFieldStepInterpolatorAbstractTest.java | 305 +++++++++
 .../ThreeEighthesFieldIntegratorTest.java       |   2 +-
 .../ThreeEighthesFieldStepInterpolatorTest.java |   2 +-
 26 files changed, 1847 insertions(+), 585 deletions(-)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractAdamsFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractAdamsFieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractAdamsFieldIntegratorTest.java
deleted file mode 100644
index 606c9e8..0000000
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractAdamsFieldIntegratorTest.java
+++ /dev/null
@@ -1,260 +0,0 @@
-/*
- * 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.math4.ode.nonstiff;
-
-
-import org.apache.commons.math4.Field;
-import org.apache.commons.math4.RealFieldElement;
-import org.apache.commons.math4.exception.MathIllegalStateException;
-import org.apache.commons.math4.exception.MaxCountExceededException;
-import org.apache.commons.math4.exception.NumberIsTooSmallException;
-import org.apache.commons.math4.ode.AbstractFieldIntegrator;
-import org.apache.commons.math4.ode.FieldExpandableODE;
-import org.apache.commons.math4.ode.FieldODEState;
-import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
-import org.apache.commons.math4.ode.FirstOrderFieldIntegrator;
-import org.apache.commons.math4.ode.MultistepFieldIntegrator;
-import org.apache.commons.math4.ode.TestFieldProblem1;
-import org.apache.commons.math4.ode.TestFieldProblem5;
-import org.apache.commons.math4.ode.TestFieldProblem6;
-import org.apache.commons.math4.ode.TestFieldProblemAbstract;
-import org.apache.commons.math4.ode.TestFieldProblemHandler;
-import org.apache.commons.math4.ode.sampling.FieldStepHandler;
-import org.apache.commons.math4.ode.sampling.FieldStepInterpolator;
-import org.apache.commons.math4.util.FastMath;
-import org.junit.Assert;
-import org.junit.Test;
-
-public abstract class AbstractAdamsFieldIntegratorTest {
-
-    protected abstract <T extends RealFieldElement<T>> AdamsFieldIntegrator<T>
-    createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,
-                     final double scalAbsoluteTolerance, final double scalRelativeTolerance);
-
-    protected abstract <T extends RealFieldElement<T>> AdamsFieldIntegrator<T>
-    createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,
-                     final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance);
-
-    @Test(expected=NumberIsTooSmallException.class)
-    public abstract void testMinStep();
-
-    protected <T extends RealFieldElement<T>> void doDimensionCheck(final Field<T> field) {
-        TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
-
-        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.1).getReal();
-        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
-        double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
-        double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };
-
-        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 4, minStep, maxStep,
-                                                              vecAbsoluteTolerance,
-                                                              vecRelativeTolerance);
-        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
-        integ.addStepHandler(handler);
-        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
-
-    }
-
-    @Test
-    public abstract void testIncreasingTolerance();
-
-    protected <T extends RealFieldElement<T>> void doTestIncreasingTolerance(final Field<T> field,
-                                                                             double ratioMin, double ratioMax) {
-
-        int previousCalls = Integer.MAX_VALUE;
-        for (int i = -12; i < -2; ++i) {
-            TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
-            double minStep = 0;
-            double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
-            double scalAbsoluteTolerance = FastMath.pow(10.0, i);
-            double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
-
-            FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 4, minStep, maxStep,
-                                                                  scalAbsoluteTolerance,
-                                                                  scalRelativeTolerance);
-            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
-            integ.addStepHandler(handler);
-            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
-
-            Assert.assertTrue(handler.getMaximalValueError().getReal() > ratioMin * scalAbsoluteTolerance);
-            Assert.assertTrue(handler.getMaximalValueError().getReal() < ratioMax * scalAbsoluteTolerance);
-
-            int calls = pb.getCalls();
-            Assert.assertEquals(integ.getEvaluations(), calls);
-            Assert.assertTrue(calls <= previousCalls);
-            previousCalls = calls;
-
-        }
-
-    }
-
-    @Test(expected = MaxCountExceededException.class)
-    public abstract void exceedMaxEvaluations();
-
-    protected <T extends RealFieldElement<T>> void doExceedMaxEvaluations(final Field<T> field, final int max) {
-
-        TestFieldProblem1<T> pb  = new TestFieldProblem1<T>(field);
-        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
-
-        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 2, 0, range, 1.0e-12, 1.0e-12);
-        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
-        integ.addStepHandler(handler);
-        integ.setMaxEvaluations(max);
-        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
-
-    }
-
-    @Test
-    public abstract void backward();
-
-    protected <T extends RealFieldElement<T>> void doBackward(final Field<T> field,
-                                                              final double epsilonLast,
-                                                              final double epsilonMaxValue,
-                                                              final double epsilonMaxTime,
-                                                              final String name) {
-
-        TestFieldProblem5<T> pb = new TestFieldProblem5<T>(field);
-        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
-
-        AdamsFieldIntegrator<T> integ = createIntegrator(field, 4, 0, range, 1.0e-12, 1.0e-12);
-        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
-        integ.addStepHandler(handler);
-        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
-
-        Assert.assertEquals(0.0, handler.getLastError().getReal(), epsilonLast);
-        Assert.assertEquals(0.0, handler.getMaximalValueError().getReal(), epsilonMaxValue);
-        Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilonMaxTime);
-        Assert.assertEquals(name, integ.getName());
-    }
-
-    @Test
-    public abstract void polynomial();
-
-    protected <T extends RealFieldElement<T>> void doPolynomial(final Field<T> field,
-                                                                final int nLimit,
-                                                                final double epsilonBad,
-                                                                final double epsilonGood) {
-        TestFieldProblem6<T> pb = new TestFieldProblem6<T>(field);
-        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).abs().getReal();
-
-        for (int nSteps = 2; nSteps < 8; ++nSteps) {
-            AdamsFieldIntegrator<T> integ = createIntegrator(field, nSteps, 1.0e-6 * range, 0.1 * range, 1.0e-4, 1.0e-4);
-            integ.setStarterIntegrator(new PerfectStarter<T>(pb, nSteps));
-            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
-            integ.addStepHandler(handler);
-            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
-            if (nSteps < nLimit) {
-                Assert.assertTrue(handler.getMaximalValueError().getReal() > epsilonBad);
-            } else {
-                Assert.assertTrue(handler.getMaximalValueError().getReal() < epsilonGood);
-            }
-        }
-
-    }
-
-    @Test(expected=MathIllegalStateException.class)
-    public abstract void testStartFailure();
-
-    protected <T extends RealFieldElement<T>> void doTestStartFailure(final Field<T> field) {
-        TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
-        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.0001).getReal();
-        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
-        double scalAbsoluteTolerance = 1.0e-6;
-        double scalRelativeTolerance = 1.0e-7;
-
-        MultistepFieldIntegrator<T> integ = createIntegrator(field, 6, minStep, maxStep,
-                                                             scalAbsoluteTolerance,
-                                                             scalRelativeTolerance);
-        integ.setStarterIntegrator(new DormandPrince853FieldIntegrator<T>(field, maxStep * 0.5, maxStep, 0.1, 0.1));
-        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
-        integ.addStepHandler(handler);
-        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
-
-    }
-
-    private static class PerfectStarter<T extends RealFieldElement<T>> extends AbstractFieldIntegrator<T> {
-
-        private final PerfectInterpolator<T> interpolator;
-        private final int nbSteps;
-
-        public PerfectStarter(final TestFieldProblemAbstract<T> problem, final int nbSteps) {
-            super(problem.getField(), "perfect-starter");
-            this.interpolator = new PerfectInterpolator<T>(problem);
-            this.nbSteps      = nbSteps;
-        }
-
-        public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations,
-                                                       FieldODEState<T> initialState, T finalTime) {
-            T tStart = initialState.getTime().add(finalTime.subtract(initialState.getTime()).multiply(0.01));
-            getEvaluationsCounter().increment(nbSteps);
-            interpolator.setCurrentTime(initialState.getTime());
-            for (int i = 0; i < nbSteps; ++i) {
-                T tK = initialState.getTime().multiply(nbSteps - 1 - (i + 1)).add(tStart.multiply(i + 1)).divide(nbSteps - 1);
-                interpolator.setPreviousTime(interpolator.getCurrentTime());
-                interpolator.setCurrentTime(tK);
-                for (FieldStepHandler<T> handler : getStepHandlers()) {
-                    handler.handleStep(interpolator, i == nbSteps - 1);
-                }
-            }
-            return interpolator.getInterpolatedState(tStart);
-        }
-
-    }
-
-    private static class PerfectInterpolator<T extends RealFieldElement<T>> implements FieldStepInterpolator<T> {
-        private final TestFieldProblemAbstract<T> problem;
-        private T previousTime;
-        private T currentTime;
-
-        public PerfectInterpolator(final TestFieldProblemAbstract<T> problem) {
-            this.problem = problem;
-        }
-
-        public void setPreviousTime(T previousTime) {
-            this.previousTime = previousTime;
-        }
-
-        public void setCurrentTime(T currentTime) {
-            this.currentTime = currentTime;
-        }
-
-        public T getCurrentTime() {
-            return currentTime;
-        }
-
-        public boolean isForward() {
-            return problem.getFinalTime().subtract(problem.getInitialState().getTime()).getReal() >= 0;
-        }
-
-        public FieldODEStateAndDerivative<T> getPreviousState() {
-            return getInterpolatedState(previousTime);
-        }
-
-        public FieldODEStateAndDerivative<T> getCurrentState() {
-            return getInterpolatedState(currentTime);
-        }
-
-        public FieldODEStateAndDerivative<T> getInterpolatedState(T time) {
-            T[] y    = problem.computeTheoreticalState(time);
-            T[] yDot = problem.computeDerivatives(time, y);
-            return new FieldODEStateAndDerivative<T>(time, y, yDot);
-        }
-
-    }
-
-}

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractRungeKuttaFieldStepInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractRungeKuttaFieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractRungeKuttaFieldStepInterpolatorTest.java
deleted file mode 100644
index 100db47..0000000
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/AbstractRungeKuttaFieldStepInterpolatorTest.java
+++ /dev/null
@@ -1,305 +0,0 @@
-/*
- * 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.math4.ode.nonstiff;
-
-
-import org.apache.commons.math4.Field;
-import org.apache.commons.math4.RealFieldElement;
-import org.apache.commons.math4.ode.AbstractIntegrator;
-import org.apache.commons.math4.ode.EquationsMapper;
-import org.apache.commons.math4.ode.ExpandableStatefulODE;
-import org.apache.commons.math4.ode.FieldEquationsMapper;
-import org.apache.commons.math4.ode.FieldExpandableODE;
-import org.apache.commons.math4.ode.FirstOrderFieldDifferentialEquations;
-import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
-import org.apache.commons.math4.ode.sampling.AbstractFieldStepInterpolator;
-import org.apache.commons.math4.util.FastMath;
-import org.apache.commons.math4.util.MathArrays;
-import org.junit.Assert;
-import org.junit.Test;
-
-public abstract class AbstractRungeKuttaFieldStepInterpolatorTest {
-
-    protected abstract <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T>
-        createInterpolator(Field<T> field, boolean forward, T[][] yDotK,
-                           FieldODEStateAndDerivative<T> globalPreviousState,
-                           FieldODEStateAndDerivative<T> globalCurrentState,
-                           FieldODEStateAndDerivative<T> softPreviousState,
-                           FieldODEStateAndDerivative<T> softCurrentState,
-                           FieldEquationsMapper<T> mapper);
-
-    protected abstract <T extends RealFieldElement<T>> FieldButcherArrayProvider<T>
-        createButcherArrayProvider(final Field<T> field);
-
-    @Test
-    public abstract void interpolationAtBounds();
-
-    protected <T extends RealFieldElement<T>> void doInterpolationAtBounds(final Field<T> field, double epsilon) {
-
-        RungeKuttaFieldStepInterpolator<T> interpolator = setUpInterpolator(field,
-                                                                            new SinCos<T>(field),
-                                                                            0.0, new double[] { 0.0, 1.0 }, 0.125);
-
-        Assert.assertEquals(0.0, interpolator.getPreviousState().getTime().getReal(), 1.0e-15);
-        for (int i = 0; i < 2; ++i) {
-            Assert.assertEquals(interpolator.getPreviousState().getState()[i].getReal(),
-                                interpolator.getInterpolatedState(interpolator.getPreviousState().getTime()).getState()[i].getReal(),
-                                epsilon);
-        }
-        Assert.assertEquals(0.125, interpolator.getCurrentState().getTime().getReal(), 1.0e-15);
-        for (int i = 0; i < 2; ++i) {
-            Assert.assertEquals(interpolator.getCurrentState().getState()[i].getReal(),
-                                interpolator.getInterpolatedState(interpolator.getCurrentState().getTime()).getState()[i].getReal(),
-                                epsilon);
-        }
-
-    }
-
-    @Test
-    public abstract void interpolationInside();
-
-    protected <T extends RealFieldElement<T>> void doInterpolationInside(final Field<T> field,
-                                                                         double epsilonSin, double epsilonCos) {
-
-        RungeKuttaFieldStepInterpolator<T> interpolator = setUpInterpolator(field,
-                                                                            new SinCos<T>(field),
-                                                                            0.0, new double[] { 0.0, 1.0 }, 0.0125);
-
-        int n = 100;
-        double maxErrorSin = 0;
-        double maxErrorCos = 0;
-        for (int i = 0; i <= n; ++i) {
-            T t =     interpolator.getPreviousState().getTime().multiply(n - i).
-                  add(interpolator.getCurrentState().getTime().multiply(i)).
-                  divide(n);
-            FieldODEStateAndDerivative<T> state = interpolator.getInterpolatedState(t);
-            maxErrorSin = FastMath.max(maxErrorSin, state.getState()[0].subtract(t.sin()).abs().getReal());
-            maxErrorCos = FastMath.max(maxErrorCos, state.getState()[1].subtract(t.cos()).abs().getReal());
-        }
-        Assert.assertEquals(0.0, maxErrorSin, epsilonSin);
-        Assert.assertEquals(0.0, maxErrorCos, epsilonCos);
-
-    }
-
-    @Test
-    public abstract void nonFieldInterpolatorConsistency();
-
-    protected <T extends RealFieldElement<T>> void doNonFieldInterpolatorConsistency(final Field<T> field,
-                                                                                     double epsilonSin, double epsilonCos,
-                                                                                     double epsilonSinDot, double epsilonCosDot) {
-
-        FirstOrderFieldDifferentialEquations<T> eqn = new SinCos<T>(field);
-        RungeKuttaFieldStepInterpolator<T> fieldInterpolator =
-                        setUpInterpolator(field, eqn, 0.0, new double[] { 0.0, 1.0 }, 0.125);
-        RungeKuttaStepInterpolator regularInterpolator = convertInterpolator(fieldInterpolator, eqn);
-
-        int n = 100;
-        double maxErrorSin    = 0;
-        double maxErrorCos    = 0;
-        double maxErrorSinDot = 0;
-        double maxErrorCosDot = 0;
-        for (int i = 0; i <= n; ++i) {
-
-            T t =     fieldInterpolator.getPreviousState().getTime().multiply(n - i).
-                  add(fieldInterpolator.getCurrentState().getTime().multiply(i)).
-                  divide(n);
-
-            FieldODEStateAndDerivative<T> state = fieldInterpolator.getInterpolatedState(t);
-            T[] fieldY    = state.getState();
-            T[] fieldYDot = state.getDerivative();
-
-            regularInterpolator.setInterpolatedTime(t.getReal());
-            double[] regularY     = regularInterpolator.getInterpolatedState();
-            double[] regularYDot  = regularInterpolator.getInterpolatedDerivatives();
-
-            maxErrorSin    = FastMath.max(maxErrorSin,    fieldY[0].subtract(regularY[0]).abs().getReal());
-            maxErrorCos    = FastMath.max(maxErrorCos,    fieldY[1].subtract(regularY[1]).abs().getReal());
-            maxErrorSinDot = FastMath.max(maxErrorSinDot, fieldYDot[0].subtract(regularYDot[0]).abs().getReal());
-            maxErrorCosDot = FastMath.max(maxErrorCosDot, fieldYDot[1].subtract(regularYDot[1]).abs().getReal());
-
-        }
-        Assert.assertEquals(0.0, maxErrorSin,    epsilonSin);
-        Assert.assertEquals(0.0, maxErrorCos,    epsilonCos);
-        Assert.assertEquals(0.0, maxErrorSinDot, epsilonSinDot);
-        Assert.assertEquals(0.0, maxErrorCosDot, epsilonCosDot);
-
-    }
-
-    private <T extends RealFieldElement<T>>
-    RungeKuttaFieldStepInterpolator<T> setUpInterpolator(final Field<T> field,
-                                                         final FirstOrderFieldDifferentialEquations<T> eqn,
-                                                         final double t0, final double[] y0,
-                                                         final double t1) {
-
-        // get the Butcher arrays from the field integrator
-        FieldButcherArrayProvider<T> provider = createButcherArrayProvider(field);
-        T[][] a = provider.getA();
-        T[]   b = provider.getB();
-        T[]   c = provider.getC();
-
-        // store initial state
-        T     t          = field.getZero().add(t0);
-        T[]   fieldY     = MathArrays.buildArray(field, eqn.getDimension());
-        T[][] fieldYDotK = MathArrays.buildArray(field, b.length, -1);
-        for (int i = 0; i < y0.length; ++i) {
-            fieldY[i] = field.getZero().add(y0[i]);
-        }
-        fieldYDotK[0] = eqn.computeDerivatives(t, fieldY);
-        FieldODEStateAndDerivative<T> s0 = new FieldODEStateAndDerivative<T>(t, fieldY, fieldYDotK[0]);
-
-        // perform one integration step, in order to get consistent derivatives
-        T h = field.getZero().add(t1 - t0);
-        for (int k = 0; k < a.length; ++k) {
-            for (int i = 0; i < y0.length; ++i) {
-                fieldY[i] = field.getZero().add(y0[i]);
-                for (int s = 0; s <= k; ++s) {
-                    fieldY[i] = fieldY[i].add(h.multiply(a[k][s].multiply(fieldYDotK[s][i])));
-                }
-            }
-            fieldYDotK[k + 1] = eqn.computeDerivatives(h.multiply(c[k]).add(t0), fieldY);
-        }
-
-        // store state at step end
-        t = field.getZero().add(t1);
-        for (int i = 0; i < y0.length; ++i) {
-            fieldY[i] = field.getZero().add(y0[i]);
-            for (int s = 0; s < b.length; ++s) {
-                fieldY[i] = fieldY[i].add(h.multiply(b[s].multiply(fieldYDotK[s][i])));
-            }
-        }
-        FieldODEStateAndDerivative<T> s1 = new FieldODEStateAndDerivative<T>(t, fieldY,
-                                                                             eqn.computeDerivatives(t, fieldY));
-
-        return createInterpolator(field, t1 > t0, fieldYDotK, s0, s1, s0, s1,
-                                  new FieldExpandableODE<T>(eqn).getMapper());
-
-    }
-
-    private <T extends RealFieldElement<T>>
-    RungeKuttaStepInterpolator convertInterpolator(final RungeKuttaFieldStepInterpolator<T> fieldInterpolator,
-                                                   final FirstOrderFieldDifferentialEquations<T> eqn) {
-
-        RungeKuttaStepInterpolator regularInterpolator = null;
-        try {
-
-            String interpolatorName = fieldInterpolator.getClass().getName();
-            String integratorName = interpolatorName.replaceAll("Field", "");
-            @SuppressWarnings("unchecked")
-            Class<RungeKuttaStepInterpolator> clz = (Class<RungeKuttaStepInterpolator>) Class.forName(integratorName);
-            regularInterpolator = clz.newInstance();
-
-            double[][] yDotArray = null;
-            java.lang.reflect.Field fYD = RungeKuttaFieldStepInterpolator.class.getDeclaredField("yDotK");
-            fYD.setAccessible(true);
-            @SuppressWarnings("unchecked")
-            T[][] fieldYDotk = (T[][]) fYD.get(fieldInterpolator);
-            yDotArray = new double[fieldYDotk.length][];
-            for (int i = 0; i < yDotArray.length; ++i) {
-                yDotArray[i] = new double[fieldYDotk[i].length];
-                for (int j = 0; j < yDotArray[i].length; ++j) {
-                    yDotArray[i][j] = fieldYDotk[i][j].getReal();
-                }
-            }
-            double[] y = new double[yDotArray[0].length];
-
-            EquationsMapper primaryMapper = null;
-            EquationsMapper[] secondaryMappers = null;
-            java.lang.reflect.Field fMapper = AbstractFieldStepInterpolator.class.getDeclaredField("mapper");
-            fMapper.setAccessible(true);
-            @SuppressWarnings("unchecked")
-            FieldEquationsMapper<T> mapper = (FieldEquationsMapper<T>) fMapper.get(fieldInterpolator);
-            java.lang.reflect.Field fStart = FieldEquationsMapper.class.getDeclaredField("start");
-            fStart.setAccessible(true);
-            int[] start = (int[]) fStart.get(mapper);
-            primaryMapper = new EquationsMapper(start[0], start[1]);
-            secondaryMappers = new EquationsMapper[mapper.getNumberOfEquations() - 1];
-            for (int i = 0; i < secondaryMappers.length; ++i) {
-                secondaryMappers[i] = new EquationsMapper(start[i + 1], start[i + 2]);
-            }
-
-            AbstractIntegrator dummyIntegrator = new AbstractIntegrator("dummy") {
-                @Override
-                public void integrate(ExpandableStatefulODE equations, double t) {
-                    Assert.fail("this method should not be called");
-                }
-                @Override
-                public void computeDerivatives(final double t, final double[] y, final double[] yDot) {
-                    T fieldT = fieldInterpolator.getCurrentState().getTime().getField().getZero().add(t);
-                    T[] fieldY = MathArrays.buildArray(fieldInterpolator.getCurrentState().getTime().getField(), y.length);
-                    for (int i = 0; i < y.length; ++i) {
-                        fieldY[i] = fieldInterpolator.getCurrentState().getTime().getField().getZero().add(y[i]);
-                    }
-                    T[] fieldYDot = eqn.computeDerivatives(fieldT, fieldY);
-                    for (int i = 0; i < yDot.length; ++i) {
-                        yDot[i] = fieldYDot[i].getReal();
-                    }
-                }
-            };
-            regularInterpolator.reinitialize(dummyIntegrator, y, yDotArray,
-                                             fieldInterpolator.isForward(),
-                                             primaryMapper, secondaryMappers);
-
-            T[] fieldPreviousY = fieldInterpolator.getPreviousState().getState();
-            for (int i = 0; i < y.length; ++i) {
-                y[i] = fieldPreviousY[i].getReal();
-            }
-            regularInterpolator.storeTime(fieldInterpolator.getPreviousState().getTime().getReal());
-
-            regularInterpolator.shift();
-
-            T[] fieldCurrentY = fieldInterpolator.getCurrentState().getState();
-            for (int i = 0; i < y.length; ++i) {
-                y[i] = fieldCurrentY[i].getReal();
-            }
-            regularInterpolator.storeTime(fieldInterpolator.getCurrentState().getTime().getReal());
-
-        } catch (ClassNotFoundException cnfe) {
-            Assert.fail(cnfe.getLocalizedMessage());
-        } catch (InstantiationException ie) {
-            Assert.fail(ie.getLocalizedMessage());
-        } catch (IllegalAccessException iae) {
-            Assert.fail(iae.getLocalizedMessage());
-        } catch (NoSuchFieldException nsfe) {
-            Assert.fail(nsfe.getLocalizedMessage());
-        } catch (IllegalArgumentException iae) {
-            Assert.fail(iae.getLocalizedMessage());
-        }
-
-        return regularInterpolator;
-
-    }
-
-    private static class SinCos<T extends RealFieldElement<T>> implements FirstOrderFieldDifferentialEquations<T> {
-        private final Field<T> field;
-        protected SinCos(final Field<T> field) {
-            this.field = field;
-        }
-        public int getDimension() {
-            return 2;
-        }
-        public void init(final T t0, final T[] y0, final T finalTime) {
-        }
-        public T[] computeDerivatives(final T t, final T[] y) {
-            T[] yDot = MathArrays.buildArray(field, 2);
-            yDot[0] = y[1];
-            yDot[1] = y[0].negate();
-            return yDot;
-        }
-    }
-
-}

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsBashforthFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsBashforthFieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsBashforthFieldIntegratorTest.java
index e9a046c..ed69ccd 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsBashforthFieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsBashforthFieldIntegratorTest.java
@@ -26,7 +26,7 @@ import org.apache.commons.math4.exception.NumberIsTooSmallException;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class AdamsBashforthFieldIntegratorTest extends AbstractAdamsFieldIntegratorTest {
+public class AdamsBashforthFieldIntegratorTest extends AdamsFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> AdamsFieldIntegrator<T>
     createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsFieldIntegratorAbstractTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsFieldIntegratorAbstractTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsFieldIntegratorAbstractTest.java
new file mode 100644
index 0000000..340dd48
--- /dev/null
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsFieldIntegratorAbstractTest.java
@@ -0,0 +1,260 @@
+/*
+ * 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.math4.ode.nonstiff;
+
+
+import org.apache.commons.math4.Field;
+import org.apache.commons.math4.RealFieldElement;
+import org.apache.commons.math4.exception.MathIllegalStateException;
+import org.apache.commons.math4.exception.MaxCountExceededException;
+import org.apache.commons.math4.exception.NumberIsTooSmallException;
+import org.apache.commons.math4.ode.AbstractFieldIntegrator;
+import org.apache.commons.math4.ode.FieldExpandableODE;
+import org.apache.commons.math4.ode.FieldODEState;
+import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
+import org.apache.commons.math4.ode.FirstOrderFieldIntegrator;
+import org.apache.commons.math4.ode.MultistepFieldIntegrator;
+import org.apache.commons.math4.ode.TestFieldProblem1;
+import org.apache.commons.math4.ode.TestFieldProblem5;
+import org.apache.commons.math4.ode.TestFieldProblem6;
+import org.apache.commons.math4.ode.TestFieldProblemAbstract;
+import org.apache.commons.math4.ode.TestFieldProblemHandler;
+import org.apache.commons.math4.ode.sampling.FieldStepHandler;
+import org.apache.commons.math4.ode.sampling.FieldStepInterpolator;
+import org.apache.commons.math4.util.FastMath;
+import org.junit.Assert;
+import org.junit.Test;
+
+public abstract class AdamsFieldIntegratorAbstractTest {
+
+    protected abstract <T extends RealFieldElement<T>> AdamsFieldIntegrator<T>
+    createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,
+                     final double scalAbsoluteTolerance, final double scalRelativeTolerance);
+
+    protected abstract <T extends RealFieldElement<T>> AdamsFieldIntegrator<T>
+    createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,
+                     final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance);
+
+    @Test(expected=NumberIsTooSmallException.class)
+    public abstract void testMinStep();
+
+    protected <T extends RealFieldElement<T>> void doDimensionCheck(final Field<T> field) {
+        TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+
+        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.1).getReal();
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+        double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
+        double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };
+
+        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 4, minStep, maxStep,
+                                                              vecAbsoluteTolerance,
+                                                              vecRelativeTolerance);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+    }
+
+    @Test
+    public abstract void testIncreasingTolerance();
+
+    protected <T extends RealFieldElement<T>> void doTestIncreasingTolerance(final Field<T> field,
+                                                                             double ratioMin, double ratioMax) {
+
+        int previousCalls = Integer.MAX_VALUE;
+        for (int i = -12; i < -2; ++i) {
+            TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+            double minStep = 0;
+            double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+            double scalAbsoluteTolerance = FastMath.pow(10.0, i);
+            double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
+
+            FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 4, minStep, maxStep,
+                                                                  scalAbsoluteTolerance,
+                                                                  scalRelativeTolerance);
+            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+            integ.addStepHandler(handler);
+            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+            Assert.assertTrue(handler.getMaximalValueError().getReal() > ratioMin * scalAbsoluteTolerance);
+            Assert.assertTrue(handler.getMaximalValueError().getReal() < ratioMax * scalAbsoluteTolerance);
+
+            int calls = pb.getCalls();
+            Assert.assertEquals(integ.getEvaluations(), calls);
+            Assert.assertTrue(calls <= previousCalls);
+            previousCalls = calls;
+
+        }
+
+    }
+
+    @Test(expected = MaxCountExceededException.class)
+    public abstract void exceedMaxEvaluations();
+
+    protected <T extends RealFieldElement<T>> void doExceedMaxEvaluations(final Field<T> field, final int max) {
+
+        TestFieldProblem1<T> pb  = new TestFieldProblem1<T>(field);
+        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+
+        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 2, 0, range, 1.0e-12, 1.0e-12);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+        integ.setMaxEvaluations(max);
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+    }
+
+    @Test
+    public abstract void backward();
+
+    protected <T extends RealFieldElement<T>> void doBackward(final Field<T> field,
+                                                              final double epsilonLast,
+                                                              final double epsilonMaxValue,
+                                                              final double epsilonMaxTime,
+                                                              final String name) {
+
+        TestFieldProblem5<T> pb = new TestFieldProblem5<T>(field);
+        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+
+        AdamsFieldIntegrator<T> integ = createIntegrator(field, 4, 0, range, 1.0e-12, 1.0e-12);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+        Assert.assertEquals(0.0, handler.getLastError().getReal(), epsilonLast);
+        Assert.assertEquals(0.0, handler.getMaximalValueError().getReal(), epsilonMaxValue);
+        Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilonMaxTime);
+        Assert.assertEquals(name, integ.getName());
+    }
+
+    @Test
+    public abstract void polynomial();
+
+    protected <T extends RealFieldElement<T>> void doPolynomial(final Field<T> field,
+                                                                final int nLimit,
+                                                                final double epsilonBad,
+                                                                final double epsilonGood) {
+        TestFieldProblem6<T> pb = new TestFieldProblem6<T>(field);
+        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).abs().getReal();
+
+        for (int nSteps = 2; nSteps < 8; ++nSteps) {
+            AdamsFieldIntegrator<T> integ = createIntegrator(field, nSteps, 1.0e-6 * range, 0.1 * range, 1.0e-4, 1.0e-4);
+            integ.setStarterIntegrator(new PerfectStarter<T>(pb, nSteps));
+            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+            integ.addStepHandler(handler);
+            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+            if (nSteps < nLimit) {
+                Assert.assertTrue(handler.getMaximalValueError().getReal() > epsilonBad);
+            } else {
+                Assert.assertTrue(handler.getMaximalValueError().getReal() < epsilonGood);
+            }
+        }
+
+    }
+
+    @Test(expected=MathIllegalStateException.class)
+    public abstract void testStartFailure();
+
+    protected <T extends RealFieldElement<T>> void doTestStartFailure(final Field<T> field) {
+        TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.0001).getReal();
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+        double scalAbsoluteTolerance = 1.0e-6;
+        double scalRelativeTolerance = 1.0e-7;
+
+        MultistepFieldIntegrator<T> integ = createIntegrator(field, 6, minStep, maxStep,
+                                                             scalAbsoluteTolerance,
+                                                             scalRelativeTolerance);
+        integ.setStarterIntegrator(new DormandPrince853FieldIntegrator<T>(field, maxStep * 0.5, maxStep, 0.1, 0.1));
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+    }
+
+    private static class PerfectStarter<T extends RealFieldElement<T>> extends AbstractFieldIntegrator<T> {
+
+        private final PerfectInterpolator<T> interpolator;
+        private final int nbSteps;
+
+        public PerfectStarter(final TestFieldProblemAbstract<T> problem, final int nbSteps) {
+            super(problem.getField(), "perfect-starter");
+            this.interpolator = new PerfectInterpolator<T>(problem);
+            this.nbSteps      = nbSteps;
+        }
+
+        public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations,
+                                                       FieldODEState<T> initialState, T finalTime) {
+            T tStart = initialState.getTime().add(finalTime.subtract(initialState.getTime()).multiply(0.01));
+            getEvaluationsCounter().increment(nbSteps);
+            interpolator.setCurrentTime(initialState.getTime());
+            for (int i = 0; i < nbSteps; ++i) {
+                T tK = initialState.getTime().multiply(nbSteps - 1 - (i + 1)).add(tStart.multiply(i + 1)).divide(nbSteps - 1);
+                interpolator.setPreviousTime(interpolator.getCurrentTime());
+                interpolator.setCurrentTime(tK);
+                for (FieldStepHandler<T> handler : getStepHandlers()) {
+                    handler.handleStep(interpolator, i == nbSteps - 1);
+                }
+            }
+            return interpolator.getInterpolatedState(tStart);
+        }
+
+    }
+
+    private static class PerfectInterpolator<T extends RealFieldElement<T>> implements FieldStepInterpolator<T> {
+        private final TestFieldProblemAbstract<T> problem;
+        private T previousTime;
+        private T currentTime;
+
+        public PerfectInterpolator(final TestFieldProblemAbstract<T> problem) {
+            this.problem = problem;
+        }
+
+        public void setPreviousTime(T previousTime) {
+            this.previousTime = previousTime;
+        }
+
+        public void setCurrentTime(T currentTime) {
+            this.currentTime = currentTime;
+        }
+
+        public T getCurrentTime() {
+            return currentTime;
+        }
+
+        public boolean isForward() {
+            return problem.getFinalTime().subtract(problem.getInitialState().getTime()).getReal() >= 0;
+        }
+
+        public FieldODEStateAndDerivative<T> getPreviousState() {
+            return getInterpolatedState(previousTime);
+        }
+
+        public FieldODEStateAndDerivative<T> getCurrentState() {
+            return getInterpolatedState(currentTime);
+        }
+
+        public FieldODEStateAndDerivative<T> getInterpolatedState(T time) {
+            T[] y    = problem.computeTheoreticalState(time);
+            T[] yDot = problem.computeDerivatives(time, y);
+            return new FieldODEStateAndDerivative<T>(time, y, yDot);
+        }
+
+    }
+
+}

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsMoultonFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsMoultonFieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsMoultonFieldIntegratorTest.java
index c44124a..51eb7ef 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsMoultonFieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/AdamsMoultonFieldIntegratorTest.java
@@ -26,7 +26,7 @@ import org.apache.commons.math4.exception.NumberIsTooSmallException;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class AdamsMoultonFieldIntegratorTest extends AbstractAdamsFieldIntegratorTest {
+public class AdamsMoultonFieldIntegratorTest extends AdamsFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> AdamsFieldIntegrator<T>
     createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungKuttaFieldStepInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungKuttaFieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungKuttaFieldStepInterpolatorTest.java
index 527fe25..bbe30c2 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungKuttaFieldStepInterpolatorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungKuttaFieldStepInterpolatorTest.java
@@ -25,7 +25,7 @@ import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class ClassicalRungKuttaFieldStepInterpolatorTest extends AbstractRungeKuttaFieldStepInterpolatorTest {
+public class ClassicalRungKuttaFieldStepInterpolatorTest extends RungeKuttaFieldStepInterpolatorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T>
     createInterpolator(Field<T> field, boolean forward, T[][] yDotK,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
index eec1b56..3cd0e35 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/ClassicalRungeKuttaFieldIntegratorTest.java
@@ -22,7 +22,7 @@ import org.apache.commons.math4.Field;
 import org.apache.commons.math4.RealFieldElement;
 import org.apache.commons.math4.util.Decimal64Field;
 
-public class ClassicalRungeKuttaFieldIntegratorTest extends AbstractRungeKuttaFieldIntegratorTest {
+public class ClassicalRungeKuttaFieldIntegratorTest extends RungeKuttaFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldIntegrator<T>
     createIntegrator(Field<T> field, T step) {

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldIntegratorTest.java
index 75416ce..da90803 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldIntegratorTest.java
@@ -22,7 +22,7 @@ import org.apache.commons.math4.Field;
 import org.apache.commons.math4.RealFieldElement;
 import org.apache.commons.math4.util.Decimal64Field;
 
-public class DormandPrince54FieldIntegratorTest extends AbstractEmbeddedRungeKuttaFieldIntegratorTest {
+public class DormandPrince54FieldIntegratorTest extends EmbeddedRungeKuttaFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> EmbeddedRungeKuttaFieldIntegrator<T>
     createIntegrator(Field<T> field, final double minStep, final double maxStep,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldStepInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldStepInterpolatorTest.java
index ee17388..9b6d607 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldStepInterpolatorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince54FieldStepInterpolatorTest.java
@@ -25,7 +25,7 @@ import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class DormandPrince54FieldStepInterpolatorTest extends AbstractRungeKuttaFieldStepInterpolatorTest {
+public class DormandPrince54FieldStepInterpolatorTest extends RungeKuttaFieldStepInterpolatorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T>
     createInterpolator(Field<T> field, boolean forward, T[][] yDotK,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldIntegratorTest.java
index 065b24a..bc73968 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldIntegratorTest.java
@@ -22,7 +22,7 @@ import org.apache.commons.math4.Field;
 import org.apache.commons.math4.RealFieldElement;
 import org.apache.commons.math4.util.Decimal64Field;
 
-public class DormandPrince853FieldIntegratorTest extends AbstractEmbeddedRungeKuttaFieldIntegratorTest {
+public class DormandPrince853FieldIntegratorTest extends EmbeddedRungeKuttaFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> EmbeddedRungeKuttaFieldIntegrator<T>
     createIntegrator(Field<T> field, final double minStep, final double maxStep,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolatorTest.java
index a104867..5591b4d 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolatorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/DormandPrince853FieldStepInterpolatorTest.java
@@ -25,7 +25,7 @@ import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class DormandPrince853FieldStepInterpolatorTest extends AbstractRungeKuttaFieldStepInterpolatorTest {
+public class DormandPrince853FieldStepInterpolatorTest extends RungeKuttaFieldStepInterpolatorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T>
     createInterpolator(Field<T> field, boolean forward, T[][] yDotK,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/EmbeddedRungeKuttaFieldIntegratorAbstractTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/EmbeddedRungeKuttaFieldIntegratorAbstractTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/EmbeddedRungeKuttaFieldIntegratorAbstractTest.java
new file mode 100644
index 0000000..045e77d
--- /dev/null
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/EmbeddedRungeKuttaFieldIntegratorAbstractTest.java
@@ -0,0 +1,600 @@
+/*
+ * 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.math4.ode.nonstiff;
+
+
+import org.apache.commons.math4.Field;
+import org.apache.commons.math4.RealFieldElement;
+import org.apache.commons.math4.analysis.differentiation.DerivativeStructure;
+import org.apache.commons.math4.exception.DimensionMismatchException;
+import org.apache.commons.math4.exception.MaxCountExceededException;
+import org.apache.commons.math4.exception.NoBracketingException;
+import org.apache.commons.math4.exception.NumberIsTooSmallException;
+import org.apache.commons.math4.ode.FieldExpandableODE;
+import org.apache.commons.math4.ode.FirstOrderFieldDifferentialEquations;
+import org.apache.commons.math4.ode.FirstOrderFieldIntegrator;
+import org.apache.commons.math4.ode.FieldODEState;
+import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
+import org.apache.commons.math4.ode.TestFieldProblem1;
+import org.apache.commons.math4.ode.TestFieldProblem3;
+import org.apache.commons.math4.ode.TestFieldProblem4;
+import org.apache.commons.math4.ode.TestFieldProblem5;
+import org.apache.commons.math4.ode.TestFieldProblemHandler;
+import org.apache.commons.math4.ode.events.Action;
+import org.apache.commons.math4.ode.events.FieldEventHandler;
+import org.apache.commons.math4.ode.sampling.FieldStepHandler;
+import org.apache.commons.math4.ode.sampling.FieldStepInterpolator;
+import org.apache.commons.math4.util.FastMath;
+import org.apache.commons.math4.util.MathArrays;
+import org.junit.Assert;
+import org.junit.Test;
+
+public abstract class EmbeddedRungeKuttaFieldIntegratorAbstractTest {
+
+    protected abstract <T extends RealFieldElement<T>> EmbeddedRungeKuttaFieldIntegrator<T>
+    createIntegrator(Field<T> field, final double minStep, final double maxStep,
+                     final double scalAbsoluteTolerance, final double scalRelativeTolerance);
+
+    protected abstract <T extends RealFieldElement<T>> EmbeddedRungeKuttaFieldIntegrator<T>
+    createIntegrator(Field<T> field, final double minStep, final double maxStep,
+                     final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance);
+
+    @Test
+    public abstract void testNonFieldIntegratorConsistency();
+
+    protected <T extends RealFieldElement<T>> void doTestNonFieldIntegratorConsistency(final Field<T> field) {
+        try {
+
+            // get the Butcher arrays from the field integrator
+            EmbeddedRungeKuttaFieldIntegrator<T> fieldIntegrator = createIntegrator(field, 0.001, 1.0, 1.0, 1.0);
+            T[][] fieldA = fieldIntegrator.getA();
+            T[]   fieldB = fieldIntegrator.getB();
+            T[]   fieldC = fieldIntegrator.getC();
+            if (fieldIntegrator instanceof DormandPrince853FieldIntegrator) {
+                // special case for Dormand-Prince 8(5,3), the array in the regular
+                // integrator is smaller because as of 3.X, the interpolation steps
+                // are not performed by the integrator itself
+                T[][] reducedFieldA = MathArrays.buildArray(field, 12, -1);
+                T[]   reducedFieldB = MathArrays.buildArray(field, 13);
+                T[]   reducedFieldC = MathArrays.buildArray(field, 12);
+                System.arraycopy(fieldA, 0, reducedFieldA, 0, reducedFieldA.length);
+                System.arraycopy(fieldB, 0, reducedFieldB, 0, reducedFieldB.length);
+                System.arraycopy(fieldC, 0, reducedFieldC, 0, reducedFieldC.length);
+                fieldA = reducedFieldA;
+                fieldB = reducedFieldB;
+                fieldC = reducedFieldC;
+            }
+
+            String fieldName   = fieldIntegrator.getClass().getName();
+            String regularName = fieldName.replaceAll("Field", "");
+
+            // get the Butcher arrays from the regular integrator
+            @SuppressWarnings("unchecked")
+            Class<RungeKuttaIntegrator> c = (Class<RungeKuttaIntegrator>) Class.forName(regularName);
+            java.lang.reflect.Field jlrFieldA = c.getDeclaredField("STATIC_A");
+            jlrFieldA.setAccessible(true);
+            double[][] regularA = (double[][]) jlrFieldA.get(null);
+            java.lang.reflect.Field jlrFieldB = c.getDeclaredField("STATIC_B");
+            jlrFieldB.setAccessible(true);
+            double[]   regularB = (double[])   jlrFieldB.get(null);
+            java.lang.reflect.Field jlrFieldC = c.getDeclaredField("STATIC_C");
+            jlrFieldC.setAccessible(true);
+            double[]   regularC = (double[])   jlrFieldC.get(null);
+
+            Assert.assertEquals(regularA.length, fieldA.length);
+            for (int i = 0; i < regularA.length; ++i) {
+                checkArray(regularA[i], fieldA[i]);
+            }
+            checkArray(regularB, fieldB);
+            checkArray(regularC, fieldC);
+
+        } catch (ClassNotFoundException cnfe) {
+            Assert.fail(cnfe.getLocalizedMessage());
+        } catch (IllegalAccessException iae) {
+            Assert.fail(iae.getLocalizedMessage());
+        } catch (IllegalArgumentException iae) {
+            Assert.fail(iae.getLocalizedMessage());
+        } catch (SecurityException se) {
+            Assert.fail(se.getLocalizedMessage());
+        } catch (NoSuchFieldException nsfe) {
+            Assert.fail(nsfe.getLocalizedMessage());
+        }
+    }
+
+    private <T extends RealFieldElement<T>> void checkArray(double[] regularArray, T[] fieldArray) {
+        Assert.assertEquals(regularArray.length, fieldArray.length);
+        for (int i = 0; i < regularArray.length; ++i) {
+            if (regularArray[i] == 0) {
+                Assert.assertTrue(0.0 == fieldArray[i].getReal());
+            } else {
+                Assert.assertEquals(regularArray[i], fieldArray[i].getReal(), FastMath.ulp(regularArray[i]));
+            }
+        }
+    }
+
+    @Test
+    public abstract void testForwardBackwardExceptions();
+
+    protected <T extends RealFieldElement<T>> void doTestForwardBackwardExceptions(final Field<T> field) {
+        FirstOrderFieldDifferentialEquations<T> equations = new FirstOrderFieldDifferentialEquations<T>() {
+
+            public int getDimension() {
+                return 1;
+            }
+
+            public void init(T t0, T[] y0, T t) {
+            }
+
+            public T[] computeDerivatives(T t, T[] y) {
+                if (t.getReal() < -0.5) {
+                    throw new LocalException();
+                } else {
+                    throw new RuntimeException("oops");
+                }
+            }
+        };
+
+        EmbeddedRungeKuttaFieldIntegrator<T> integrator = createIntegrator(field, 0.0, 1.0, 1.0e-10, 1.0e-10);
+
+        try  {
+            integrator.integrate(new FieldExpandableODE<T>(equations),
+                                 new FieldODEState<T>(field.getOne().negate(),
+                                                      MathArrays.buildArray(field, 1)),
+                                 field.getZero());
+            Assert.fail("an exception should have been thrown");
+          } catch(LocalException de) {
+            // expected behavior
+          }
+
+          try  {
+              integrator.integrate(new FieldExpandableODE<T>(equations),
+                                   new FieldODEState<T>(field.getZero(),
+                                                        MathArrays.buildArray(field, 1)),
+                                   field.getOne());
+               Assert.fail("an exception should have been thrown");
+          } catch(RuntimeException de) {
+            // expected behavior
+          }
+    }
+
+    protected static class LocalException extends RuntimeException {
+        private static final long serialVersionUID = 20151208L;
+    }
+
+    @Test(expected=NumberIsTooSmallException.class)
+    public abstract void testMinStep();
+
+    protected <T extends RealFieldElement<T>> void doTestMinStep(final Field<T> field)
+        throws NumberIsTooSmallException {
+
+        TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.1).getReal();
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+        double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
+        double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };
+
+        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                              vecAbsoluteTolerance, vecRelativeTolerance);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+        Assert.fail("an exception should have been thrown");
+
+    }
+
+    @Test
+    public abstract void testIncreasingTolerance();
+
+    protected <T extends RealFieldElement<T>> void doTestIncreasingTolerance(final Field<T> field,
+                                                                             double factor,
+                                                                             double epsilon) {
+
+        int previousCalls = Integer.MAX_VALUE;
+        for (int i = -12; i < -2; ++i) {
+            TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+            double minStep = 0;
+            double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+            double scalAbsoluteTolerance = FastMath.pow(10.0, i);
+            double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
+
+            FirstOrderFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                                  scalAbsoluteTolerance, scalRelativeTolerance);
+            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+            integ.addStepHandler(handler);
+            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+            Assert.assertTrue(handler.getMaximalValueError().getReal() < (factor * scalAbsoluteTolerance));
+            Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilon);
+
+            int calls = pb.getCalls();
+            Assert.assertEquals(integ.getEvaluations(), calls);
+            Assert.assertTrue(calls <= previousCalls);
+            previousCalls = calls;
+
+        }
+
+    }
+
+    @Test
+    public abstract void testEvents();
+
+    protected <T extends RealFieldElement<T>> void doTestEvents(final Field<T> field,
+                                                                final double epsilonMaxValue,
+                                                                final String name) {
+
+      TestFieldProblem4<T> pb = new TestFieldProblem4<T>(field);
+      double minStep = 0;
+      double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+      double scalAbsoluteTolerance = 1.0e-8;
+      double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
+
+      FirstOrderFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                            scalAbsoluteTolerance, scalRelativeTolerance);
+      TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+      integ.addStepHandler(handler);
+      FieldEventHandler<T>[] functions = pb.getEventsHandlers();
+      double convergence = 1.0e-8 * maxStep;
+      for (int l = 0; l < functions.length; ++l) {
+          integ.addEventHandler(functions[l], Double.POSITIVE_INFINITY, convergence, 1000);
+      }
+      Assert.assertEquals(functions.length, integ.getEventHandlers().size());
+      integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+      Assert.assertEquals(0, handler.getMaximalValueError().getReal(), epsilonMaxValue);
+      Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), convergence);
+      Assert.assertEquals(12.0, handler.getLastTime().getReal(), convergence);
+      Assert.assertEquals(name, integ.getName());
+      integ.clearEventHandlers();
+      Assert.assertEquals(0, integ.getEventHandlers().size());
+
+    }
+
+    @Test(expected=LocalException.class)
+    public abstract void testEventsErrors();
+
+    protected <T extends RealFieldElement<T>> void doTestEventsErrors(final Field<T> field)
+        throws LocalException {
+        final TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+        double minStep = 0;
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+        double scalAbsoluteTolerance = 1.0e-8;
+        double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
+
+        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                              scalAbsoluteTolerance, scalRelativeTolerance);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+
+        integ.addEventHandler(new FieldEventHandler<T>() {
+          public void init(FieldODEStateAndDerivative<T> state0, T t) {
+          }
+          public Action eventOccurred(FieldODEStateAndDerivative<T> state, boolean increasing) {
+            return Action.CONTINUE;
+          }
+          public T g(FieldODEStateAndDerivative<T> state) {
+            T middle = pb.getInitialState().getTime().add(pb.getFinalTime()).multiply(0.5);
+            T offset = state.getTime().subtract(middle);
+            if (offset.getReal() > 0) {
+              throw new LocalException();
+            }
+            return offset;
+          }
+          public FieldODEState<T> resetState(FieldODEStateAndDerivative<T> state) {
+              return state;
+          }
+        }, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 1000);
+
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+    }
+
+    @Test
+    public abstract void testEventsNoConvergence();
+
+    protected <T extends RealFieldElement<T>> void doTestEventsNoConvergence(final Field<T> field){
+
+        final TestFieldProblem1<T> pb = new TestFieldProblem1<T>(field);
+        double minStep = 0;
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+        double scalAbsoluteTolerance = 1.0e-8;
+        double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
+
+        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                              scalAbsoluteTolerance, scalRelativeTolerance);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+
+        integ.addEventHandler(new FieldEventHandler<T>() {
+            public void init(FieldODEStateAndDerivative<T> state0, T t) {
+            }
+            public Action eventOccurred(FieldODEStateAndDerivative<T> state, boolean increasing) {
+                return Action.CONTINUE;
+            }
+            public T g(FieldODEStateAndDerivative<T> state) {
+                T middle = pb.getInitialState().getTime().add(pb.getFinalTime()).multiply(0.5);
+                T offset = state.getTime().subtract(middle);
+                return (offset.getReal() > 0) ? offset.add(0.5) : offset.subtract(0.5);
+            }
+            public FieldODEState<T> resetState(FieldODEStateAndDerivative<T> state) {
+                return state;
+            }
+        }, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 3);
+
+        try {
+            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+            Assert.fail("an exception should have been thrown");
+        } catch (MaxCountExceededException mcee) {
+            // Expected.
+        }
+
+    }
+
+    @Test
+    public abstract void testSanityChecks();
+
+    protected <T extends RealFieldElement<T>> void doTestSanityChecks(Field<T> field) {
+        TestFieldProblem3<T> pb = new TestFieldProblem3<T>(field);
+        try  {
+            EmbeddedRungeKuttaFieldIntegrator<T> integrator = createIntegrator(field, 0,
+                                                                               pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal(),
+                                                                               new double[4], new double[4]);
+            integrator.integrate(new FieldExpandableODE<T>(pb),
+                                 new FieldODEState<T>(pb.getInitialState().getTime(),
+                                                      MathArrays.buildArray(field, 6)),
+                                 pb.getFinalTime());
+            Assert.fail("an exception should have been thrown");
+        } catch(DimensionMismatchException ie) {
+        }
+        try  {
+            EmbeddedRungeKuttaFieldIntegrator<T> integrator =
+                            createIntegrator(field, 0,
+                                             pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal(),
+                                             new double[2], new double[4]);
+            integrator.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+            Assert.fail("an exception should have been thrown");
+        } catch(DimensionMismatchException ie) {
+        }
+        try  {
+            EmbeddedRungeKuttaFieldIntegrator<T> integrator =
+                            createIntegrator(field, 0,
+                                             pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal(),
+                                             new double[4], new double[4]);
+            integrator.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getInitialState().getTime());
+            Assert.fail("an exception should have been thrown");
+        } catch(NumberIsTooSmallException ie) {
+        }
+    }
+
+    @Test
+    public abstract void testBackward();
+
+    protected <T extends RealFieldElement<T>> void doTestBackward(Field<T> field,
+                                                                  final double epsilonLast,
+                                                                  final double epsilonMaxValue,
+                                                                  final double epsilonMaxTime,
+                                                                  final String name)
+        throws DimensionMismatchException, NumberIsTooSmallException,
+               MaxCountExceededException, NoBracketingException {
+
+        TestFieldProblem5<T> pb = new TestFieldProblem5<T>(field);
+        double minStep = 0;
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).abs().getReal();
+        double scalAbsoluteTolerance = 1.0e-8;
+        double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
+
+        EmbeddedRungeKuttaFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                                      scalAbsoluteTolerance,
+                                                                      scalRelativeTolerance);
+        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler<T>(pb, integ);
+        integ.addStepHandler(handler);
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+
+        Assert.assertEquals(0, handler.getLastError().getReal(),         epsilonLast);
+        Assert.assertEquals(0, handler.getMaximalValueError().getReal(), epsilonMaxValue);
+        Assert.assertEquals(0, handler.getMaximalTimeError().getReal(),  epsilonMaxTime);
+        Assert.assertEquals(name, integ.getName());
+
+    }
+
+    @Test
+    public abstract void testKepler();
+
+    protected <T extends RealFieldElement<T>> void doTestKepler(Field<T> field, double epsilon) {
+
+        final TestFieldProblem3<T> pb  = new TestFieldProblem3<T>(field, field.getZero().add(0.9));
+        double minStep = 0;
+        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
+        double[] vecAbsoluteTolerance = { 1.0e-8, 1.0e-8, 1.0e-10, 1.0e-10 };
+        double[] vecRelativeTolerance = { 1.0e-10, 1.0e-10, 1.0e-8, 1.0e-8 };
+
+        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, minStep, maxStep,
+                                                              vecAbsoluteTolerance, vecRelativeTolerance);
+        integ.addStepHandler(new KeplerHandler<T>(pb, epsilon));
+        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
+    }
+
+    private static class KeplerHandler<T extends RealFieldElement<T>> implements FieldStepHandler<T> {
+        private T maxError;
+        private final TestFieldProblem3<T> pb;
+        private final double epsilon;
+        public KeplerHandler(TestFieldProblem3<T> pb, double epsilon) {
+            this.pb      = pb;
+            this.epsilon = epsilon;
+            maxError = pb.getField().getZero();
+        }
+        public void init(FieldODEStateAndDerivative<T> state0, T t) {
+            maxError = pb.getField().getZero();
+        }
+        public void handleStep(FieldStepInterpolator<T> interpolator, boolean isLast)
+                        throws MaxCountExceededException {
+
+            FieldODEStateAndDerivative<T> current = interpolator.getCurrentState();
+            T[] theoreticalY  = pb.computeTheoreticalState(current.getTime());
+            T dx = current.getState()[0].subtract(theoreticalY[0]);
+            T dy = current.getState()[1].subtract(theoreticalY[1]);
+            T error = dx.multiply(dx).add(dy.multiply(dy));
+            if (error.subtract(maxError).getReal() > 0) {
+                maxError = error;
+            }
+            if (isLast) {
+                Assert.assertEquals(0.0, maxError.getReal(), epsilon);
+            }
+        }
+    }
+
+    @Test
+    public abstract void testPartialDerivatives();
+
+    protected void doTestPartialDerivatives(final double epsilonY,
+                                            final double[] epsilonPartials) {
+
+        // parameters indices
+        final int parameters = 5;
+        final int order      = 1;
+        final int parOmega   = 0;
+        final int parTO      = 1;
+        final int parY00     = 2;
+        final int parY01     = 3;
+        final int parT       = 4;
+
+        DerivativeStructure omega = new DerivativeStructure(parameters, order, parOmega, 1.3);
+        DerivativeStructure t0    = new DerivativeStructure(parameters, order, parTO, 1.3);
+        DerivativeStructure[] y0  = new DerivativeStructure[] {
+            new DerivativeStructure(parameters, order, parY00, 3.0),
+            new DerivativeStructure(parameters, order, parY01, 4.0)
+        };
+        DerivativeStructure t     = new DerivativeStructure(parameters, order, parT, 6.0);
+        SinCos sinCos = new SinCos(omega);
+
+        EmbeddedRungeKuttaFieldIntegrator<DerivativeStructure> integrator =
+                        createIntegrator(omega.getField(),
+                                         t.subtract(t0).multiply(0.001).getReal(), t.subtract(t0).getReal(),
+                                         1.0e-12, 1.0e-12);
+        FieldODEStateAndDerivative<DerivativeStructure> result =
+                        integrator.integrate(new FieldExpandableODE<DerivativeStructure>(sinCos),
+                                             new FieldODEState<DerivativeStructure>(t0, y0),
+                                             t);
+
+        // check values
+        for (int i = 0; i < sinCos.getDimension(); ++i) {
+            Assert.assertEquals(sinCos.theoreticalY(t.getReal())[i], result.getState()[i].getValue(), epsilonY);
+        }
+
+        // check derivatives
+        final double[][] derivatives = sinCos.getDerivatives(t.getReal());
+        for (int i = 0; i < sinCos.getDimension(); ++i) {
+            for (int parameter = 0; parameter < parameters; ++parameter) {
+                Assert.assertEquals(derivatives[i][parameter], dYdP(result.getState()[i], parameter), epsilonPartials[parameter]);
+            }
+        }
+
+    }
+
+    private double dYdP(final DerivativeStructure y, final int parameter) {
+        int[] orders = new int[y.getFreeParameters()];
+        orders[parameter] = 1;
+        return y.getPartialDerivative(orders);
+    }
+
+    private static class SinCos implements FirstOrderFieldDifferentialEquations<DerivativeStructure> {
+
+        private final DerivativeStructure omega;
+        private       DerivativeStructure r;
+        private       DerivativeStructure alpha;
+
+        private double dRdY00;
+        private double dRdY01;
+        private double dAlphadOmega;
+        private double dAlphadT0;
+        private double dAlphadY00;
+        private double dAlphadY01;
+
+        protected SinCos(final DerivativeStructure omega) {
+            this.omega = omega;
+        }
+
+        public int getDimension() {
+            return 2;
+        }
+
+        public void init(final DerivativeStructure t0, final DerivativeStructure[] y0,
+                         final DerivativeStructure finalTime) {
+
+            // theoretical solution is y(t) = { r * sin(omega * t + alpha), r * cos(omega * t + alpha) }
+            // so we retrieve alpha by identification from the initial state
+            final DerivativeStructure r2 = y0[0].multiply(y0[0]).add(y0[1].multiply(y0[1]));
+
+            this.r            = r2.sqrt();
+            this.dRdY00       = y0[0].divide(r).getReal();
+            this.dRdY01       = y0[1].divide(r).getReal();
+
+            this.alpha        = y0[0].atan2(y0[1]).subtract(t0.multiply(omega));
+            this.dAlphadOmega = -t0.getReal();
+            this.dAlphadT0    = -omega.getReal();
+            this.dAlphadY00   = y0[1].divide(r2).getReal();
+            this.dAlphadY01   = y0[0].negate().divide(r2).getReal();
+
+        }
+
+        public DerivativeStructure[] computeDerivatives(final DerivativeStructure t, final DerivativeStructure[] y) {
+            return new DerivativeStructure[] {
+                omega.multiply(y[1]),
+                omega.multiply(y[0]).negate()
+            };
+        }
+
+        public double[] theoreticalY(final double t) {
+            final double theta = omega.getReal() * t + alpha.getReal();
+            return new double[] {
+                r.getReal() * FastMath.sin(theta), r.getReal() * FastMath.cos(theta)
+            };
+        }
+
+        public double[][] getDerivatives(final double t) {
+
+            // intermediate angle and state
+            final double theta        = omega.getReal() * t + alpha.getReal();
+            final double sin          = FastMath.sin(theta);
+            final double cos          = FastMath.cos(theta);
+            final double y0           = r.getReal() * sin;
+            final double y1           = r.getReal() * cos;
+
+            // partial derivatives of the state first component
+            final double dY0dOmega    =                y1 * (t + dAlphadOmega);
+            final double dY0dT0       =                y1 * dAlphadT0;
+            final double dY0dY00      = dRdY00 * sin + y1 * dAlphadY00;
+            final double dY0dY01      = dRdY01 * sin + y1 * dAlphadY01;
+            final double dY0dT        =                y1 * omega.getReal();
+
+            // partial derivatives of the state second component
+            final double dY1dOmega    =              - y0 * (t + dAlphadOmega);
+            final double dY1dT0       =              - y0 * dAlphadT0;
+            final double dY1dY00      = dRdY00 * cos - y0 * dAlphadY00;
+            final double dY1dY01      = dRdY01 * cos - y0 * dAlphadY01;
+            final double dY1dT        =              - y0 * omega.getReal();
+
+            return new double[][] {
+                { dY0dOmega, dY0dT0, dY0dY00, dY0dY01, dY0dT },
+                { dY1dOmega, dY1dT0, dY1dY00, dY1dY01, dY1dT }
+            };
+
+        }
+
+    }
+
+}

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldIntegratorTest.java
index 1a44551..9a48986 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldIntegratorTest.java
@@ -22,7 +22,7 @@ import org.apache.commons.math4.Field;
 import org.apache.commons.math4.RealFieldElement;
 import org.apache.commons.math4.util.Decimal64Field;
 
-public class EulerFieldIntegratorTest extends AbstractRungeKuttaFieldIntegratorTest {
+public class EulerFieldIntegratorTest extends RungeKuttaFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldIntegrator<T>
     createIntegrator(Field<T> field, T step) {

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldStepInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldStepInterpolatorTest.java
index 0458f5c..c5d1c3b 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldStepInterpolatorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/EulerFieldStepInterpolatorTest.java
@@ -25,7 +25,7 @@ import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class EulerFieldStepInterpolatorTest extends AbstractRungeKuttaFieldStepInterpolatorTest {
+public class EulerFieldStepInterpolatorTest extends RungeKuttaFieldStepInterpolatorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T>
     createInterpolator(Field<T> field, boolean forward, T[][] yDotK,

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldIntegratorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldIntegratorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldIntegratorTest.java
index a04c6eb..877321b 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldIntegratorTest.java
@@ -22,7 +22,7 @@ import org.apache.commons.math4.Field;
 import org.apache.commons.math4.RealFieldElement;
 import org.apache.commons.math4.util.Decimal64Field;
 
-public class GillFieldIntegratorTest extends AbstractRungeKuttaFieldIntegratorTest {
+public class GillFieldIntegratorTest extends RungeKuttaFieldIntegratorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldIntegrator<T>
     createIntegrator(Field<T> field, T step) {

http://git-wip-us.apache.org/repos/asf/commons-math/blob/9d47e0f9/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldStepInterpolatorTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldStepInterpolatorTest.java b/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldStepInterpolatorTest.java
index 54f0098..87a9b10 100644
--- a/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldStepInterpolatorTest.java
+++ b/src/test/java/org/apache/commons/math4/ode/nonstiff/GillFieldStepInterpolatorTest.java
@@ -25,7 +25,7 @@ import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
 import org.apache.commons.math4.util.Decimal64Field;
 import org.junit.Test;
 
-public class GillFieldStepInterpolatorTest extends AbstractRungeKuttaFieldStepInterpolatorTest {
+public class GillFieldStepInterpolatorTest extends RungeKuttaFieldStepInterpolatorAbstractTest {
 
     protected <T extends RealFieldElement<T>> RungeKuttaFieldStepInterpolator<T>
     createInterpolator(Field<T> field, boolean forward, T[][] yDotK,


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