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Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java | 205 |
1 files changed, 205 insertions, 0 deletions
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..d7d6f63 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/HighamHall54FieldIntegrator.java @@ -0,0 +1,205 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package org.apache.commons.math3.ode.nonstiff; + +import org.apache.commons.math3.Field; +import org.apache.commons.math3.RealFieldElement; +import org.apache.commons.math3.ode.FieldEquationsMapper; +import org.apache.commons.math3.ode.FieldODEStateAndDerivative; +import org.apache.commons.math3.util.MathArrays; +import org.apache.commons.math3.util.MathUtils; + + +/** + * This class implements the 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)"; + + /** Error weights Butcher array. */ + private final T[] e ; + + /** 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, -1, + minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance); + e = MathArrays.buildArray(field, 7); + e[0] = fraction(-1, 20); + e[1] = field.getZero(); + e[2] = fraction(81, 160); + e[3] = fraction(-6, 5); + e[4] = fraction(25, 32); + e[5] = fraction( 1, 16); + e[6] = fraction(-1, 10); + } + + /** 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, -1, + minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); + e = MathArrays.buildArray(field, 7); + e[0] = fraction(-1, 20); + e[1] = field.getZero(); + e[2] = fraction(81, 160); + e[3] = fraction(-6, 5); + e[4] = fraction(25, 32); + e[5] = fraction( 1, 16); + e[6] = fraction(-1, 10); + } + + /** {@inheritDoc} */ + public T[] getC() { + final T[] c = MathArrays.buildArray(getField(), 6); + c[0] = fraction(2, 9); + c[1] = fraction(1, 3); + c[2] = fraction(1, 2); + c[3] = fraction(3, 5); + c[4] = getField().getOne(); + c[5] = getField().getOne(); + return c; + } + + /** {@inheritDoc} */ + public T[][] getA() { + final T[][] a = MathArrays.buildArray(getField(), 6, -1); + for (int i = 0; i < a.length; ++i) { + a[i] = MathArrays.buildArray(getField(), i + 1); + } + a[0][0] = fraction( 2, 9); + a[1][0] = fraction( 1, 12); + a[1][1] = fraction( 1, 4); + a[2][0] = fraction( 1, 8); + a[2][1] = getField().getZero(); + a[2][2] = fraction( 3, 8); + a[3][0] = fraction( 91, 500); + a[3][1] = fraction( -27, 100); + a[3][2] = fraction( 78, 125); + a[3][3] = fraction( 8, 125); + a[4][0] = fraction( -11, 20); + a[4][1] = fraction( 27, 20); + a[4][2] = fraction( 12, 5); + a[4][3] = fraction( -36, 5); + a[4][4] = fraction( 5, 1); + a[5][0] = fraction( 1, 12); + a[5][1] = getField().getZero(); + a[5][2] = fraction( 27, 32); + a[5][3] = fraction( -4, 3); + a[5][4] = fraction( 125, 96); + a[5][5] = fraction( 5, 48); + return a; + } + + /** {@inheritDoc} */ + public T[] getB() { + final T[] b = MathArrays.buildArray(getField(), 7); + b[0] = fraction( 1, 12); + b[1] = getField().getZero(); + b[2] = fraction( 27, 32); + b[3] = fraction( -4, 3); + b[4] = fraction(125, 96); + b[5] = fraction( 5, 48); + b[6] = getField().getZero(); + return b; + } + + /** {@inheritDoc} */ + @Override + protected HighamHall54FieldStepInterpolator<T> + createInterpolator(final boolean forward, T[][] yDotK, + final FieldODEStateAndDerivative<T> globalPreviousState, + final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) { + return new HighamHall54FieldStepInterpolator<T>(getField(), forward, yDotK, + globalPreviousState, globalCurrentState, + globalPreviousState, globalCurrentState, + mapper); + } + + /** {@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(e[0]); + for (int l = 1; l < e.length; ++l) { + errSum = errSum.add(yDotK[l][j].multiply(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(); + + } + +} |