Repository: commons-numbers Updated Branches: refs/heads/feature-NUMBERS-12 [created] 44fa5ca2b
Establish baseline of files copied from commons-math. (Will not build.) Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/c4cae1c2 Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/c4cae1c2 Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/c4cae1c2 Branch: refs/heads/feature-NUMBERS-12 Commit: c4cae1c29e8afe249896cc096f6977da0950e1c8 Parents: e2668df Author: Ray DeCampo <r...@decampo.org> Authored: Sat Apr 15 12:03:24 2017 -0400 Committer: Ray DeCampo <r...@decampo.org> Committed: Sat Apr 15 12:03:24 2017 -0400 ---------------------------------------------------------------------- .../numbers/fraction/ContinuedFraction.java | 181 +++++++++++++++++++ .../numbers/fraction/ContinuedFractionTest.java | 46 +++++ 2 files changed, 227 insertions(+) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4cae1c2/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java ---------------------------------------------------------------------- diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java new file mode 100644 index 0000000..56b7267 --- /dev/null +++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/ContinuedFraction.java @@ -0,0 +1,181 @@ +/* + * 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.math4.util; + +import org.apache.commons.math4.exception.ConvergenceException; +import org.apache.commons.math4.exception.MaxCountExceededException; +import org.apache.commons.math4.exception.util.LocalizedFormats; + +/** + * Provides a generic means to evaluate continued fractions. Subclasses simply + * provided the a and b coefficients to evaluate the continued fraction. + * + * <p> + * References: + * <ul> + * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html";> + * Continued Fraction</a></li> + * </ul> + * </p> + * + */ +public abstract class ContinuedFraction { + /** Maximum allowed numerical error. */ + private static final double DEFAULT_EPSILON = 10e-9; + + /** + * Default constructor. + */ + protected ContinuedFraction() { + super(); + } + + /** + * Access the n-th a coefficient of the continued fraction. Since a can be + * a function of the evaluation point, x, that is passed in as well. + * @param n the coefficient index to retrieve. + * @param x the evaluation point. + * @return the n-th a coefficient. + */ + protected abstract double getA(int n, double x); + + /** + * Access the n-th b coefficient of the continued fraction. Since b can be + * a function of the evaluation point, x, that is passed in as well. + * @param n the coefficient index to retrieve. + * @param x the evaluation point. + * @return the n-th b coefficient. + */ + protected abstract double getB(int n, double x); + + /** + * Evaluates the continued fraction at the value x. + * @param x the evaluation point. + * @return the value of the continued fraction evaluated at x. + * @throws ConvergenceException if the algorithm fails to converge. + */ + public double evaluate(double x) throws ConvergenceException { + return evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE); + } + + /** + * Evaluates the continued fraction at the value x. + * @param x the evaluation point. + * @param epsilon maximum error allowed. + * @return the value of the continued fraction evaluated at x. + * @throws ConvergenceException if the algorithm fails to converge. + */ + public double evaluate(double x, double epsilon) throws ConvergenceException { + return evaluate(x, epsilon, Integer.MAX_VALUE); + } + + /** + * Evaluates the continued fraction at the value x. + * @param x the evaluation point. + * @param maxIterations maximum number of convergents + * @return the value of the continued fraction evaluated at x. + * @throws ConvergenceException if the algorithm fails to converge. + * @throws MaxCountExceededException if maximal number of iterations is reached + */ + public double evaluate(double x, int maxIterations) + throws ConvergenceException, MaxCountExceededException { + return evaluate(x, DEFAULT_EPSILON, maxIterations); + } + + /** + * Evaluates the continued fraction at the value x. + * <p> + * The implementation of this method is based on the modified Lentz algorithm as described + * on page 18 ff. in: + * <ul> + * <li> + * I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order." + * <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf";> + * http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a> + * </li> + * </ul> + * <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in + * <a href="http://mathworld.wolfram.com/ContinuedFraction.html";>Continued Fraction @ MathWorld</a>. + * </p> + * + * @param x the evaluation point. + * @param epsilon maximum error allowed. + * @param maxIterations maximum number of convergents + * @return the value of the continued fraction evaluated at x. + * @throws ConvergenceException if the algorithm fails to converge. + * @throws MaxCountExceededException if maximal number of iterations is reached + */ + public double evaluate(double x, double epsilon, int maxIterations) + throws ConvergenceException, MaxCountExceededException { + final double small = 1e-50; + double hPrev = getA(0, x); + + // use the value of small as epsilon criteria for zero checks + if (Precision.equals(hPrev, 0.0, small)) { + hPrev = small; + } + + int n = 1; + double dPrev = 0.0; + double cPrev = hPrev; + double hN = hPrev; + + while (n < maxIterations) { + final double a = getA(n, x); + final double b = getB(n, x); + + double dN = a + b * dPrev; + if (Precision.equals(dN, 0.0, small)) { + dN = small; + } + double cN = a + b / cPrev; + if (Precision.equals(cN, 0.0, small)) { + cN = small; + } + + dN = 1 / dN; + final double deltaN = cN * dN; + hN = hPrev * deltaN; + + if (Double.isInfinite(hN)) { + throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE, + x); + } + if (Double.isNaN(hN)) { + throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE, + x); + } + + if (FastMath.abs(deltaN - 1.0) < epsilon) { + break; + } + + dPrev = dN; + cPrev = cN; + hPrev = hN; + n++; + } + + if (n >= maxIterations) { + throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION, + maxIterations, x); + } + + return hN; + } + +} http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4cae1c2/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/ContinuedFractionTest.java ---------------------------------------------------------------------- diff --git a/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/ContinuedFractionTest.java b/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/ContinuedFractionTest.java new file mode 100644 index 0000000..686fb51 --- /dev/null +++ b/commons-numbers-fraction/src/test/java/org/apache/commons/numbers/fraction/ContinuedFractionTest.java @@ -0,0 +1,46 @@ +/* + * 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.math4.util; + +import org.apache.commons.math4.util.ContinuedFraction; +import org.junit.Assert; +import org.junit.Test; + + +/** + */ +public class ContinuedFractionTest { + + @Test + public void testGoldenRatio() throws Exception { + ContinuedFraction cf = new ContinuedFraction() { + + @Override + public double getA(int n, double x) { + return 1.0; + } + + @Override + public double getB(int n, double x) { + return 1.0; + } + }; + + double gr = cf.evaluate(0.0, 10e-9); + Assert.assertEquals(1.61803399, gr, 10e-9); + } +}
