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Diffstat (limited to 'src/main/java/org/apache/commons/math/analysis/solvers/RiddersSolver.java')
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1 files changed, 247 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/analysis/solvers/RiddersSolver.java b/src/main/java/org/apache/commons/math/analysis/solvers/RiddersSolver.java new file mode 100644 index 0000000..4f316c7 --- /dev/null +++ b/src/main/java/org/apache/commons/math/analysis/solvers/RiddersSolver.java @@ -0,0 +1,247 @@ +/* + * 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.math.analysis.solvers; + +import org.apache.commons.math.ConvergenceException; +import org.apache.commons.math.FunctionEvaluationException; +import org.apache.commons.math.MaxIterationsExceededException; +import org.apache.commons.math.analysis.UnivariateRealFunction; +import org.apache.commons.math.util.FastMath; +import org.apache.commons.math.util.MathUtils; + +/** + * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html"> + * Ridders' Method</a> for root finding of real univariate functions. For + * reference, see C. Ridders, <i>A new algorithm for computing a single root + * of a real continuous function </i>, IEEE Transactions on Circuits and + * Systems, 26 (1979), 979 - 980. + * <p> + * The function should be continuous but not necessarily smooth.</p> + * + * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ + * @since 1.2 + */ +public class RiddersSolver extends UnivariateRealSolverImpl { + + /** + * Construct a solver for the given function. + * + * @param f function to solve + * @deprecated as of 2.0 the function to solve is passed as an argument + * to the {@link #solve(UnivariateRealFunction, double, double)} or + * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)} + * method. + */ + @Deprecated + public RiddersSolver(UnivariateRealFunction f) { + super(f, 100, 1E-6); + } + + /** + * Construct a solver. + * @deprecated in 2.2 + */ + @Deprecated + public RiddersSolver() { + super(100, 1E-6); + } + + /** {@inheritDoc} */ + @Deprecated + public double solve(final double min, final double max) + throws ConvergenceException, FunctionEvaluationException { + return solve(f, min, max); + } + + /** {@inheritDoc} */ + @Deprecated + public double solve(final double min, final double max, final double initial) + throws ConvergenceException, FunctionEvaluationException { + return solve(f, min, max, initial); + } + + /** + * Find a root in the given interval with initial value. + * <p> + * Requires bracketing condition.</p> + * + * @param f the function to solve + * @param min the lower bound for the interval + * @param max the upper bound for the interval + * @param initial the start value to use + * @param maxEval Maximum number of evaluations. + * @return the point at which the function value is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if any parameters are invalid + */ + @Override + public double solve(int maxEval, final UnivariateRealFunction f, + final double min, final double max, final double initial) + throws MaxIterationsExceededException, FunctionEvaluationException { + setMaximalIterationCount(maxEval); + return solve(f, min, max, initial); + } + + /** + * Find a root in the given interval with initial value. + * <p> + * Requires bracketing condition.</p> + * + * @param f the function to solve + * @param min the lower bound for the interval + * @param max the upper bound for the interval + * @param initial the start value to use + * @return the point at which the function value is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if any parameters are invalid + * @deprecated in 2.2 (to be removed in 3.0). + */ + @Deprecated + public double solve(final UnivariateRealFunction f, + final double min, final double max, final double initial) + throws MaxIterationsExceededException, FunctionEvaluationException { + + // check for zeros before verifying bracketing + if (f.value(min) == 0.0) { return min; } + if (f.value(max) == 0.0) { return max; } + if (f.value(initial) == 0.0) { return initial; } + + verifyBracketing(min, max, f); + verifySequence(min, initial, max); + if (isBracketing(min, initial, f)) { + return solve(f, min, initial); + } else { + return solve(f, initial, max); + } + } + + /** + * Find a root in the given interval. + * <p> + * Requires bracketing condition.</p> + * + * @param f the function to solve + * @param min the lower bound for the interval + * @param max the upper bound for the interval + * @param maxEval Maximum number of evaluations. + * @return the point at which the function value is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if any parameters are invalid + */ + @Override + public double solve(int maxEval, final UnivariateRealFunction f, + final double min, final double max) + throws MaxIterationsExceededException, FunctionEvaluationException { + setMaximalIterationCount(maxEval); + return solve(f, min, max); + } + + /** + * Find a root in the given interval. + * <p> + * Requires bracketing condition.</p> + * + * @param f the function to solve + * @param min the lower bound for the interval + * @param max the upper bound for the interval + * @return the point at which the function value is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if any parameters are invalid + * @deprecated in 2.2 (to be removed in 3.0). + */ + @Deprecated + public double solve(final UnivariateRealFunction f, + final double min, final double max) + throws MaxIterationsExceededException, FunctionEvaluationException { + + // [x1, x2] is the bracketing interval in each iteration + // x3 is the midpoint of [x1, x2] + // x is the new root approximation and an endpoint of the new interval + double x1 = min; + double y1 = f.value(x1); + double x2 = max; + double y2 = f.value(x2); + + // check for zeros before verifying bracketing + if (y1 == 0.0) { + return min; + } + if (y2 == 0.0) { + return max; + } + verifyBracketing(min, max, f); + + int i = 1; + double oldx = Double.POSITIVE_INFINITY; + while (i <= maximalIterationCount) { + // calculate the new root approximation + final double x3 = 0.5 * (x1 + x2); + final double y3 = f.value(x3); + if (FastMath.abs(y3) <= functionValueAccuracy) { + setResult(x3, i); + return result; + } + final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing + final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) * + (x3 - x1) / FastMath.sqrt(delta); + final double x = x3 - correction; // correction != 0 + final double y = f.value(x); + + // check for convergence + final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy); + if (FastMath.abs(x - oldx) <= tolerance) { + setResult(x, i); + return result; + } + if (FastMath.abs(y) <= functionValueAccuracy) { + setResult(x, i); + return result; + } + + // prepare the new interval for next iteration + // Ridders' method guarantees x1 < x < x2 + if (correction > 0.0) { // x1 < x < x3 + if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) { + x2 = x; + y2 = y; + } else { + x1 = x; + x2 = x3; + y1 = y; + y2 = y3; + } + } else { // x3 < x < x2 + if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) { + x1 = x; + y1 = y; + } else { + x1 = x3; + x2 = x; + y1 = y3; + y2 = y; + } + } + oldx = x; + i++; + } + throw new MaxIterationsExceededException(maximalIterationCount); + } +} |