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Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.java | 273 |
1 files changed, 273 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.java new file mode 100644 index 0000000..a97e9f5 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/nonstiff/RungeKuttaFieldIntegrator.java @@ -0,0 +1,273 @@ +/* + * 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.exception.DimensionMismatchException; +import org.apache.commons.math3.exception.MaxCountExceededException; +import org.apache.commons.math3.exception.NoBracketingException; +import org.apache.commons.math3.exception.NumberIsTooSmallException; +import org.apache.commons.math3.ode.AbstractFieldIntegrator; +import org.apache.commons.math3.ode.FieldEquationsMapper; +import org.apache.commons.math3.ode.FieldExpandableODE; +import org.apache.commons.math3.ode.FirstOrderFieldDifferentialEquations; +import org.apache.commons.math3.ode.FieldODEState; +import org.apache.commons.math3.ode.FieldODEStateAndDerivative; +import org.apache.commons.math3.util.MathArrays; + +/** + * This class implements the common part of all fixed step Runge-Kutta + * integrators for Ordinary Differential Equations. + * + * <p>These methods are explicit Runge-Kutta methods, their Butcher + * arrays are as follows : + * <pre> + * 0 | + * c2 | a21 + * c3 | a31 a32 + * ... | ... + * cs | as1 as2 ... ass-1 + * |-------------------------- + * | b1 b2 ... bs-1 bs + * </pre> + * </p> + * + * @see EulerFieldIntegrator + * @see ClassicalRungeKuttaFieldIntegrator + * @see GillFieldIntegrator + * @see MidpointFieldIntegrator + * @param <T> the type of the field elements + * @since 3.6 + */ + +public abstract class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>> + extends AbstractFieldIntegrator<T> + implements FieldButcherArrayProvider<T> { + + /** Time steps from Butcher array (without the first zero). */ + private final T[] c; + + /** Internal weights from Butcher array (without the first empty row). */ + private final T[][] a; + + /** External weights for the high order method from Butcher array. */ + private final T[] b; + + /** Integration step. */ + private final T step; + + /** Simple constructor. + * Build a Runge-Kutta integrator with the given + * step. The default step handler does nothing. + * @param field field to which the time and state vector elements belong + * @param name name of the method + * @param step integration step + */ + protected RungeKuttaFieldIntegrator(final Field<T> field, final String name, final T step) { + super(field, name); + this.c = getC(); + this.a = getA(); + this.b = getB(); + this.step = step.abs(); + } + + /** Create a fraction. + * @param p numerator + * @param q denominator + * @return p/q computed in the instance field + */ + protected T fraction(final int p, final int q) { + return getField().getZero().add(p).divide(q); + } + + /** Create an interpolator. + * @param forward integration direction indicator + * @param yDotK slopes at the intermediate points + * @param globalPreviousState start of the global step + * @param globalCurrentState end of the global step + * @param mapper equations mapper for the all equations + * @return external weights for the high order method from Butcher array + */ + protected abstract RungeKuttaFieldStepInterpolator<T> createInterpolator(boolean forward, T[][] yDotK, + final FieldODEStateAndDerivative<T> globalPreviousState, + final FieldODEStateAndDerivative<T> globalCurrentState, + FieldEquationsMapper<T> mapper); + + /** {@inheritDoc} */ + public FieldODEStateAndDerivative<T> integrate(final FieldExpandableODE<T> equations, + final FieldODEState<T> initialState, final T finalTime) + throws NumberIsTooSmallException, DimensionMismatchException, + MaxCountExceededException, NoBracketingException { + + sanityChecks(initialState, finalTime); + final T t0 = initialState.getTime(); + final T[] y0 = equations.getMapper().mapState(initialState); + setStepStart(initIntegration(equations, t0, y0, finalTime)); + final boolean forward = finalTime.subtract(initialState.getTime()).getReal() > 0; + + // create some internal working arrays + final int stages = c.length + 1; + T[] y = y0; + final T[][] yDotK = MathArrays.buildArray(getField(), stages, -1); + final T[] yTmp = MathArrays.buildArray(getField(), y0.length); + + // set up integration control objects + if (forward) { + if (getStepStart().getTime().add(step).subtract(finalTime).getReal() >= 0) { + setStepSize(finalTime.subtract(getStepStart().getTime())); + } else { + setStepSize(step); + } + } else { + if (getStepStart().getTime().subtract(step).subtract(finalTime).getReal() <= 0) { + setStepSize(finalTime.subtract(getStepStart().getTime())); + } else { + setStepSize(step.negate()); + } + } + + // main integration loop + setIsLastStep(false); + do { + + // first stage + y = equations.getMapper().mapState(getStepStart()); + yDotK[0] = equations.getMapper().mapDerivative(getStepStart()); + + // next stages + for (int k = 1; k < stages; ++k) { + + for (int j = 0; j < y0.length; ++j) { + T sum = yDotK[0][j].multiply(a[k-1][0]); + for (int l = 1; l < k; ++l) { + sum = sum.add(yDotK[l][j].multiply(a[k-1][l])); + } + yTmp[j] = y[j].add(getStepSize().multiply(sum)); + } + + yDotK[k] = computeDerivatives(getStepStart().getTime().add(getStepSize().multiply(c[k-1])), yTmp); + + } + + // estimate the state at the end of the step + for (int j = 0; j < y0.length; ++j) { + T sum = yDotK[0][j].multiply(b[0]); + for (int l = 1; l < stages; ++l) { + sum = sum.add(yDotK[l][j].multiply(b[l])); + } + yTmp[j] = y[j].add(getStepSize().multiply(sum)); + } + final T stepEnd = getStepStart().getTime().add(getStepSize()); + final T[] yDotTmp = computeDerivatives(stepEnd, yTmp); + final FieldODEStateAndDerivative<T> stateTmp = new FieldODEStateAndDerivative<T>(stepEnd, yTmp, yDotTmp); + + // discrete events handling + System.arraycopy(yTmp, 0, y, 0, y0.length); + setStepStart(acceptStep(createInterpolator(forward, yDotK, getStepStart(), stateTmp, equations.getMapper()), + finalTime)); + + if (!isLastStep()) { + + // stepsize control for next step + final T nextT = getStepStart().getTime().add(getStepSize()); + final boolean nextIsLast = forward ? + (nextT.subtract(finalTime).getReal() >= 0) : + (nextT.subtract(finalTime).getReal() <= 0); + if (nextIsLast) { + setStepSize(finalTime.subtract(getStepStart().getTime())); + } + } + + } while (!isLastStep()); + + final FieldODEStateAndDerivative<T> finalState = getStepStart(); + setStepStart(null); + setStepSize(null); + return finalState; + + } + + /** Fast computation of a single step of ODE integration. + * <p>This method is intended for the limited use case of + * very fast computation of only one step without using any of the + * rich features of general integrators that may take some time + * to set up (i.e. no step handlers, no events handlers, no additional + * states, no interpolators, no error control, no evaluations count, + * no sanity checks ...). It handles the strict minimum of computation, + * so it can be embedded in outer loops.</p> + * <p> + * This method is <em>not</em> used at all by the {@link #integrate(FieldExpandableODE, + * FieldODEState, RealFieldElement)} method. It also completely ignores the step set at + * construction time, and uses only a single step to go from {@code t0} to {@code t}. + * </p> + * <p> + * As this method does not use any of the state-dependent features of the integrator, + * it should be reasonably thread-safe <em>if and only if</em> the provided differential + * equations are themselves thread-safe. + * </p> + * @param equations differential equations to integrate + * @param t0 initial time + * @param y0 initial value of the state vector at t0 + * @param t target time for the integration + * (can be set to a value smaller than {@code t0} for backward integration) + * @return state vector at {@code t} + */ + public T[] singleStep(final FirstOrderFieldDifferentialEquations<T> equations, + final T t0, final T[] y0, final T t) { + + // create some internal working arrays + final T[] y = y0.clone(); + final int stages = c.length + 1; + final T[][] yDotK = MathArrays.buildArray(getField(), stages, -1); + final T[] yTmp = y0.clone(); + + // first stage + final T h = t.subtract(t0); + yDotK[0] = equations.computeDerivatives(t0, y); + + // next stages + for (int k = 1; k < stages; ++k) { + + for (int j = 0; j < y0.length; ++j) { + T sum = yDotK[0][j].multiply(a[k-1][0]); + for (int l = 1; l < k; ++l) { + sum = sum.add(yDotK[l][j].multiply(a[k-1][l])); + } + yTmp[j] = y[j].add(h.multiply(sum)); + } + + yDotK[k] = equations.computeDerivatives(t0.add(h.multiply(c[k-1])), yTmp); + + } + + // estimate the state at the end of the step + for (int j = 0; j < y0.length; ++j) { + T sum = yDotK[0][j].multiply(b[0]); + for (int l = 1; l < stages; ++l) { + sum = sum.add(yDotK[l][j].multiply(b[l])); + } + y[j] = y[j].add(h.multiply(sum)); + } + + return y; + + } + +} |