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Posted to commits@commons.apache.org by lu...@apache.org on 2015/11/17 18:25:19 UTC
[math] Field-based version of Higham-Hall 5(4) method for solving ODE.
Repository: commons-math
Updated Branches:
refs/heads/field-ode 779e52410 -> b990f6f2a
Field-based version of Higham-Hall 5(4) method for solving ODE.
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/b990f6f2
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/b990f6f2
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/b990f6f2
Branch: refs/heads/field-ode
Commit: b990f6f2adc41b00490ef19f8abcf29214074970
Parents: 779e524
Author: Luc Maisonobe <lu...@apache.org>
Authored: Tue Nov 17 18:25:02 2015 +0100
Committer: Luc Maisonobe <lu...@apache.org>
Committed: Tue Nov 17 18:25:02 2015 +0100
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.../nonstiff/HighamHall54FieldIntegrator.java | 143 +++++++++++++++++++
.../HighamHall54FieldStepInterpolator.java | 139 ++++++++++++++++++
2 files changed, 282 insertions(+)
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http://git-wip-us.apache.org/repos/asf/commons-math/blob/b990f6f2/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java
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diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java
new file mode 100644
index 0000000..e3a1829
--- /dev/null
+++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java
@@ -0,0 +1,143 @@
+/*
+ * 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.util.MathUtils;
+
+
+/**
+ * This class implements the 5(4) Higham and Hall integrator for
+ * Ordinary Differential Equations.
+ *
+ * <p>This integrator is an embedded Runge-Kutta integrator
+ * of order 5(4) 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 7 functions evaluations per step.</p>
+ *
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+
+public class HighamHall54FieldIntegrator<T extends RealFieldElement<T>>
+ extends EmbeddedRungeKuttaFieldIntegrator<T> {
+
+ /** Integrator method name. */
+ private static final String METHOD_NAME = "Higham-Hall 5(4)";
+
+ /** Time steps Butcher array. */
+ private static final double[] STATIC_C = {
+ 2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
+ };
+
+ /** Internal weights Butcher array. */
+ private static final double[][] STATIC_A = {
+ {2.0/9.0},
+ {1.0/12.0, 1.0/4.0},
+ {1.0/8.0, 0.0, 3.0/8.0},
+ {91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
+ {-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
+ {1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
+ };
+
+ /** Propagation weights Butcher array. */
+ private static final double[] STATIC_B = {
+ 1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
+ };
+
+ /** Error weights Butcher array. */
+ private static final double[] STATIC_E = {
+ -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
+ };
+
+ /** Simple constructor.
+ * Build a fifth order Higham and Hall 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 HighamHall54FieldIntegrator(final Field<T> field,
+ final double minStep, final double maxStep,
+ final double scalAbsoluteTolerance,
+ final double scalRelativeTolerance) {
+ super(field, METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B,
+ new HighamHall54FieldStepInterpolator<T>(),
+ minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
+ }
+
+ /** Simple constructor.
+ * Build a fifth order Higham and Hall 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 HighamHall54FieldIntegrator(final Field<T> field,
+ final double minStep, final double maxStep,
+ final double[] vecAbsoluteTolerance,
+ final double[] vecRelativeTolerance) {
+ super(field, METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B,
+ new HighamHall54FieldStepInterpolator<T>(),
+ minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public int getOrder() {
+ return 5;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {
+
+ T error = getField().getZero();
+
+ for (int j = 0; j < mainSetDimension; ++j) {
+ T errSum = yDotK[0][j].multiply(STATIC_E[0]);
+ for (int l = 1; l < STATIC_E.length; ++l) {
+ errSum = errSum.add(yDotK[l][j].multiply(STATIC_E[l]));
+ }
+
+ 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 ratio = h.multiply(errSum).divide(tol);
+ error = error.add(ratio.multiply(ratio));
+
+ }
+
+ return error.divide(mainSetDimension).sqrt();
+
+ }
+
+}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/b990f6f2/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java
new file mode 100644
index 0000000..7c46eb0
--- /dev/null
+++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldStepInterpolator.java
@@ -0,0 +1,139 @@
+/*
+ * 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.RealFieldElement;
+import org.apache.commons.math3.ode.FieldEquationsMapper;
+import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
+import org.apache.commons.math3.util.MathArrays;
+
+/**
+ * This class represents an interpolator over the last step during an
+ * ODE integration for the 5(4) Higham and Hall integrator.
+ *
+ * @see HighamHall54FieldIntegrator
+ *
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+
+class HighamHall54FieldStepInterpolator<T extends RealFieldElement<T>>
+ extends RungeKuttaFieldStepInterpolator<T> {
+
+ /** Simple constructor.
+ * This constructor builds an instance that is not usable yet, the
+ * {@link
+ * org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#reinitialize}
+ * method should be called before using the instance in order to
+ * initialize the internal arrays. This constructor is used only
+ * in order to delay the initialization in some cases. The {@link
+ * EmbeddedRungeKuttaIntegrator} uses the prototyping design pattern
+ * to create the step interpolators by cloning an uninitialized model
+ * and later initializing the copy.
+ */
+ HighamHall54FieldStepInterpolator() {
+ super();
+ }
+
+ /** Copy constructor.
+ * @param interpolator interpolator to copy from. The copy is a deep
+ * copy: its arrays are separated from the original arrays of the
+ * instance
+ */
+ HighamHall54FieldStepInterpolator(final HighamHall54FieldStepInterpolator<T> interpolator) {
+ super(interpolator);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected HighamHall54FieldStepInterpolator<T> doCopy() {
+ return new HighamHall54FieldStepInterpolator<T>(this);
+ }
+
+
+ /** {@inheritDoc} */
+ @Override
+ protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
+ final T time, final T theta,
+ final T oneMinusThetaH) {
+
+ final T bDot0 = theta.multiply(theta.multiply(theta.multiply( -10.0 ).add( 16.0 )).add(-15.0 / 2.0)).add(1);
+ final T bDot2 = theta.multiply(theta.multiply(theta.multiply( 135.0 / 2.0).add(-729.0 / 8.0)).add(459.0 / 16.0));
+ final T bDot3 = theta.multiply(theta.multiply(theta.multiply(-120.0 ).add( 152.0 )).add(-44.0 ));
+ final T bDot4 = theta.multiply(theta.multiply(theta.multiply( 125.0 / 2.0).add(-625.0 / 8.0)).add(375.0 / 16.0));
+ final T bDot5 = theta.multiply( 5.0 / 8.0).multiply(theta.multiply(2).subtract(1));
+ final T[] interpolatedState = MathArrays.buildArray(theta.getField(), previousState.length);
+ final T[] interpolatedDerivatives = MathArrays.buildArray(theta.getField(), previousState.length);
+
+ if ((previousState != null) && (theta.getReal() <= 0.5)) {
+ final T hTheta = h.multiply(theta);
+ final T b0 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply( -5.0 / 2.0).add( 16.0 / 3.0)).add(-15.0 / 4.0)).add(1));
+ final T b2 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply(135.0 / 8.0).add(-243.0 / 8.0)).add(459.0 / 32.0)));
+ final T b3 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply(-30.0 ).add( 152.0 / 3.0)).add(-22.0 )));
+ final T b4 = hTheta.multiply(theta.multiply(theta.multiply(theta.multiply(125.0 / 8.0).add(-625.0 / 24.0)).add(375.0 / 32.0)));
+ final T b5 = hTheta.multiply(theta.multiply(theta.multiply( 5.0 / 12.0)).add( -5.0 / 16.0));
+ for (int i = 0; i < interpolatedState.length; ++i) {
+ final T yDot0 = yDotK[0][i];
+ final T yDot2 = yDotK[2][i];
+ final T yDot3 = yDotK[3][i];
+ final T yDot4 = yDotK[4][i];
+ final T yDot5 = yDotK[5][i];
+ interpolatedState[i] = previousState[i].
+ add(b0.multiply(yDot0)).
+ add(b2.multiply(yDot2)).
+ add(b3.multiply(yDot3)).
+ add(b4.multiply(yDot4)).
+ add(b5.multiply(yDot5));
+ interpolatedDerivatives[i] = bDot0.multiply(yDot0).
+ add(bDot2.multiply(yDot2)).
+ add(bDot3.multiply(yDot3)).
+ add(bDot4.multiply(yDot4)).
+ add(bDot5.multiply(yDot5));
+ }
+ } else {
+ final T theta2 = theta.multiply(theta);
+ final T b0 = h.multiply( theta.multiply(theta.multiply(theta.multiply(theta.multiply(-5.0 / 2.0).add( 16.0 / 3.0)).add( -15.0 / 4.0)).add( 1.0 )).add( -1.0 / 12.0));
+ final T b2 = h.multiply(theta2.multiply(theta.multiply(theta.multiply( 135.0 / 8.0 ).add(-243.0 / 8.0)).add(459.0 / 32.0)).add( -27.0 / 32.0));
+ final T b3 = h.multiply(theta2.multiply(theta.multiply(theta.multiply( -30.0 ).add( 152.0 / 3.0)).add(-22.0 )).add( 4.0 / 3.0));
+ final T b4 = h.multiply(theta2.multiply(theta.multiply(theta.multiply( 125.0 / 8.0 ).add(-625.0 / 24.0)).add(375.0 / 32.0)).add(-125.0 / 96.0));
+ final T b5 = h.multiply(theta2.multiply(theta.multiply( 5.0 / 12.0 ).add(-5.0 / 16.0)).add( -5.0 / 48.0));
+ for (int i = 0; i < interpolatedState.length; ++i) {
+ final T yDot0 = yDotK[0][i];
+ final T yDot2 = yDotK[2][i];
+ final T yDot3 = yDotK[3][i];
+ final T yDot4 = yDotK[4][i];
+ final T yDot5 = yDotK[5][i];
+ interpolatedState[i] = currentState[i].
+ add(b0.multiply(yDot0)).
+ add(b2.multiply(yDot2)).
+ add(b3.multiply(yDot3)).
+ add(b4.multiply(yDot4)).
+ add(b5.multiply(yDot5));
+ interpolatedDerivatives[i] = bDot0.multiply(yDot0).
+ add(bDot2.multiply(yDot2)).
+ add(bDot3.multiply(yDot3)).
+ add(bDot4.multiply(yDot4)).
+ add(bDot5.multiply(yDot5));
+ }
+ }
+
+ return new FieldODEStateAndDerivative<T>(time, interpolatedState, yDotK[0]);
+
+ }
+
+}