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Diffstat (limited to 'src/main/java/org/apache/commons/math/analysis/solvers/SecantSolver.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math/analysis/solvers/SecantSolver.java | 230 |
1 files changed, 230 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/analysis/solvers/SecantSolver.java b/src/main/java/org/apache/commons/math/analysis/solvers/SecantSolver.java new file mode 100644 index 0000000..325b662 --- /dev/null +++ b/src/main/java/org/apache/commons/math/analysis/solvers/SecantSolver.java @@ -0,0 +1,230 @@ +/* + * 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.MathRuntimeException; +import org.apache.commons.math.MaxIterationsExceededException; +import org.apache.commons.math.analysis.UnivariateRealFunction; +import org.apache.commons.math.exception.util.LocalizedFormats; +import org.apache.commons.math.util.FastMath; + + +/** + * Implements a modified version of the + * <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a> + * for approximating a zero of a real univariate function. + * <p> + * The algorithm is modified to maintain bracketing of a root by successive + * approximations. Because of forced bracketing, convergence may be slower than + * the unrestricted secant algorithm. However, this implementation should in + * general outperform the + * <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html"> + * regula falsi method.</a></p> + * <p> + * The function is assumed to be continuous but not necessarily smooth.</p> + * + * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ + */ +public class SecantSolver 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 SecantSolver(UnivariateRealFunction f) { + super(f, 100, 1E-6); + } + + /** + * Construct a solver. + * @deprecated in 2.2 (to be removed in 3.0). + */ + @Deprecated + public SecantSolver() { + 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 zero in the given interval. + * + * @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 (ignored) + * @param maxEval Maximum number of evaluations. + * @return the value where the function is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if min is not less than max or the + * signs of the values of the function at the endpoints are not opposites + */ + @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 zero in the given interval. + * + * @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 (ignored) + * @return the value where the function is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if min is not less than max or the + * signs of the values of the function at the endpoints are not opposites + * @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 { + return solve(f, min, max); + } + + /** + * Find a zero in the given interval. + * @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 value where the function is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if min is not less than max or the + * signs of the values of the function at the endpoints are not opposites + */ + @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 zero in the given interval. + * @param f the function to solve + * @param min the lower bound for the interval. + * @param max the upper bound for the interval. + * @return the value where the function is zero + * @throws MaxIterationsExceededException if the maximum iteration count is exceeded + * @throws FunctionEvaluationException if an error occurs evaluating the function + * @throws IllegalArgumentException if min is not less than max or the + * signs of the values of the function at the endpoints are not opposites + * @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 { + + clearResult(); + verifyInterval(min, max); + + // Index 0 is the old approximation for the root. + // Index 1 is the last calculated approximation for the root. + // Index 2 is a bracket for the root with respect to x0. + // OldDelta is the length of the bracketing interval of the last + // iteration. + double x0 = min; + double x1 = max; + double y0 = f.value(x0); + double y1 = f.value(x1); + + // Verify bracketing + if (y0 * y1 >= 0) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.SAME_SIGN_AT_ENDPOINTS, min, max, y0, y1); + } + + double x2 = x0; + double y2 = y0; + double oldDelta = x2 - x1; + int i = 0; + while (i < maximalIterationCount) { + if (FastMath.abs(y2) < FastMath.abs(y1)) { + x0 = x1; + x1 = x2; + x2 = x0; + y0 = y1; + y1 = y2; + y2 = y0; + } + if (FastMath.abs(y1) <= functionValueAccuracy) { + setResult(x1, i); + return result; + } + if (FastMath.abs(oldDelta) < + FastMath.max(relativeAccuracy * FastMath.abs(x1), absoluteAccuracy)) { + setResult(x1, i); + return result; + } + double delta; + if (FastMath.abs(y1) > FastMath.abs(y0)) { + // Function value increased in last iteration. Force bisection. + delta = 0.5 * oldDelta; + } else { + delta = (x0 - x1) / (1 - y0 / y1); + if (delta / oldDelta > 1) { + // New approximation falls outside bracket. + // Fall back to bisection. + delta = 0.5 * oldDelta; + } + } + x0 = x1; + y0 = y1; + x1 = x1 + delta; + y1 = f.value(x1); + if ((y1 > 0) == (y2 > 0)) { + // New bracket is (x0,x1). + x2 = x0; + y2 = y0; + } + oldDelta = x2 - x1; + i++; + } + throw new MaxIterationsExceededException(maximalIterationCount); + } + +} |