You are viewing a plain text version of this content. The canonical link for it is here.
Posted to commits@commons.apache.org by lu...@apache.org on 2015/11/15 10:58:42 UTC
[math] Field-based version of midpoint method for solving ODE.
Repository: commons-math
Updated Branches:
refs/heads/field-ode c89d2453c -> d509c4a2a
Field-based version of midpoint 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/d509c4a2
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/d509c4a2
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/d509c4a2
Branch: refs/heads/field-ode
Commit: d509c4a2a09a4630d8462b6785ea2e5b2be3a2ea
Parents: c89d245
Author: Luc Maisonobe <lu...@apache.org>
Authored: Sun Nov 15 10:58:30 2015 +0100
Committer: Luc Maisonobe <lu...@apache.org>
Committed: Sun Nov 15 10:58:30 2015 +0100
----------------------------------------------------------------------
.../ode/nonstiff/MidpointFieldIntegrator.java | 73 ++++++++++++
.../nonstiff/MidpointFieldStepInterpolator.java | 119 +++++++++++++++++++
2 files changed, 192 insertions(+)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d509c4a2/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldIntegrator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldIntegrator.java
new file mode 100644
index 0000000..dd9f0bf
--- /dev/null
+++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldIntegrator.java
@@ -0,0 +1,73 @@
+/*
+ * 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;
+
+/**
+ * This class implements a second order Runge-Kutta integrator for
+ * Ordinary Differential Equations.
+ *
+ * <p>This method is an explicit Runge-Kutta method, its Butcher-array
+ * is the following one :
+ * <pre>
+ * 0 | 0 0
+ * 1/2 | 1/2 0
+ * |----------
+ * | 0 1
+ * </pre>
+ * </p>
+ *
+ * @see EulerFieldIntegrator
+ * @see ClassicalRungeKuttaFieldIntegrator
+ * @see GillFieldIntegrator
+ * @see ThreeEighthesFieldIntegrator
+ * @see LutherFieldIntegrator
+ *
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+
+public class MidpointFieldIntegrator<T extends RealFieldElement<T>> extends RungeKuttaFieldIntegrator<T> {
+
+ /** Time steps Butcher array. */
+ private static final double[] STATIC_C = {
+ 1.0 / 2.0
+ };
+
+ /** Internal weights Butcher array. */
+ private static final double[][] STATIC_A = {
+ { 1.0 / 2.0 }
+ };
+
+ /** Propagation weights Butcher array. */
+ private static final double[] STATIC_B = {
+ 0.0, 1.0
+ };
+
+ /** Simple constructor.
+ * Build a midpoint integrator with the given step.
+ * @param field field to which the time and state vector elements belong
+ * @param step integration step
+ */
+ public MidpointFieldIntegrator(final Field<T> field, final T step) {
+ super(field, "midpoint", STATIC_C, STATIC_A, STATIC_B, new MidpointFieldStepInterpolator<T>(), step);
+ }
+
+}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/d509c4a2/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldStepInterpolator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldStepInterpolator.java
new file mode 100644
index 0000000..1cbe756
--- /dev/null
+++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/MidpointFieldStepInterpolator.java
@@ -0,0 +1,119 @@
+/*
+ * 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 implements a step interpolator for second order
+ * Runge-Kutta integrator.
+ *
+ * <p>This interpolator computes dense output inside the last
+ * step computed. The interpolation equation is consistent with the
+ * integration scheme :
+ * <ul>
+ * <li>Using reference point at step start:<br>
+ * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>) + θ h [(1 - θ) y'<sub>1</sub> + θ y'<sub>2</sub>]
+ * </li>
+ * <li>Using reference point at step end:<br>
+ * y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h) + (1-θ) h [θ y'<sub>1</sub> - (1+θ) y'<sub>2</sub>]
+ * </li>
+ * </ul>
+ * </p>
+ *
+ * where θ belongs to [0 ; 1] and where y'<sub>1</sub> and y'<sub>2</sub> are the two
+ * evaluations of the derivatives already computed during the
+ * step.</p>
+ *
+ * @see MidpointFieldIntegrator
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+
+class MidpointFieldStepInterpolator<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
+ * RungeKuttaFieldIntegrator} class uses the prototyping design pattern
+ * to create the step interpolators by cloning an uninitialized model
+ * and later initializing the copy.
+ */
+ MidpointFieldStepInterpolator() {
+ }
+
+ /** 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
+ */
+ MidpointFieldStepInterpolator(final MidpointFieldStepInterpolator<T> interpolator) {
+ super(interpolator);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected MidpointFieldStepInterpolator<T> doCopy() {
+ return new MidpointFieldStepInterpolator<T>(this);
+ }
+
+
+ /** {@inheritDoc} */
+ @Override
+ protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
+ final T time, final T theta,
+ final T oneMinusThetaH) {
+
+ final T coeffDot2 = theta.multiply(2);
+ final T coeffDot1 = time.getField().getOne().subtract(coeffDot2);
+ 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 coeff1 = theta.multiply(oneMinusThetaH);
+ final T coeff2 = theta.multiply(theta).multiply(h);
+ for (int i = 0; i < previousState.length; ++i) {
+ final T yDot1 = yDotK[0][i];
+ final T yDot2 = yDotK[1][i];
+ interpolatedState[i] = previousState[i].add(coeff1.multiply(yDot1)).add(coeff2.multiply(yDot2));
+ interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2));
+ }
+ } else {
+ final T coeff1 = oneMinusThetaH.multiply(theta);
+ final T coeff2 = oneMinusThetaH.multiply(theta.add(1));
+ for (int i = 0; i < previousState.length; ++i) {
+ final T yDot1 = yDotK[0][i];
+ final T yDot2 = yDotK[1][i];
+ interpolatedState[i] = currentState[i].add(coeff1.multiply(yDot1)).subtract(coeff2.multiply(yDot2));
+ interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2));
+ }
+ }
+
+ return new FieldODEStateAndDerivative<T>(time, interpolatedState, yDotK[0]);
+
+ }
+
+}