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Commons Math example source code file (FastCosineTransformer.java)

This example Commons Math source code file (FastCosineTransformer.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

complex, fastcosinetransformer, fastcosinetransformer, fastfouriertransformer, fastfouriertransformer, functionevaluationexception, functionevaluationexception, illegalargumentexception, illegalargumentexception, realtransformer

The Commons Math FastCosineTransformer.java source code

/*
 * 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.transform;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.complex.Complex;

/**
 * Implements the <a href="http://documents.wolfram.com/v5/Add-onsLinks/
 * StandardPackages/LinearAlgebra/FourierTrig.html">Fast Cosine Transform</a>
 * for transformation of one-dimensional data sets. For reference, see
 * <b>Fast Fourier Transforms, ISBN 0849371635, chapter 3.
 * <p>
 * FCT is its own inverse, up to a multiplier depending on conventions.
 * The equations are listed in the comments of the corresponding methods.</p>
 * <p>
 * Different from FFT and FST, FCT requires the length of data set to be
 * power of 2 plus one. Users should especially pay attention to the
 * function transformation on how this affects the sampling.</p>
 * <p>As of version 2.0 this no longer implements Serializable

* * @version $Revision:670469 $ $Date:2008-06-23 10:01:38 +0200 (lun., 23 juin 2008) $ * @since 1.2 */ public class FastCosineTransformer implements RealTransformer { /** * Construct a default transformer. */ public FastCosineTransformer() { super(); } /** * Transform the given real data set. * <p> * The formula is F<sub>n = (1/2) [f0 + (-1)n fN] + * ∑<sub>k=1N-1 fk cos(π nk/N) * </p> * * @param f the real data array to be transformed * @return the real transformed array * @throws IllegalArgumentException if any parameters are invalid */ public double[] transform(double f[]) throws IllegalArgumentException { return fct(f); } /** * Transform the given real function, sampled on the given interval. * <p> * The formula is F<sub>n = (1/2) [f0 + (-1)n fN] + * ∑<sub>k=1N-1 fk cos(π nk/N) * </p> * * @param f the function to be sampled and transformed * @param min the lower bound for the interval * @param max the upper bound for the interval * @param n the number of sample points * @return the real transformed array * @throws FunctionEvaluationException if function cannot be evaluated * at some point * @throws IllegalArgumentException if any parameters are invalid */ public double[] transform(UnivariateRealFunction f, double min, double max, int n) throws FunctionEvaluationException, IllegalArgumentException { double data[] = FastFourierTransformer.sample(f, min, max, n); return fct(data); } /** * Transform the given real data set. * <p> * The formula is F<sub>n = √(1/2N) [f0 + (-1)n fN] + * √(2/N) ∑<sub>k=1N-1 fk cos(π nk/N) * </p> * * @param f the real data array to be transformed * @return the real transformed array * @throws IllegalArgumentException if any parameters are invalid */ public double[] transform2(double f[]) throws IllegalArgumentException { double scaling_coefficient = Math.sqrt(2.0 / (f.length-1)); return FastFourierTransformer.scaleArray(fct(f), scaling_coefficient); } /** * Transform the given real function, sampled on the given interval. * <p> * The formula is F<sub>n = √(1/2N) [f0 + (-1)n fN] + * √(2/N) ∑<sub>k=1N-1 fk cos(π nk/N) * * </p> * * @param f the function to be sampled and transformed * @param min the lower bound for the interval * @param max the upper bound for the interval * @param n the number of sample points * @return the real transformed array * @throws FunctionEvaluationException if function cannot be evaluated * at some point * @throws IllegalArgumentException if any parameters are invalid */ public double[] transform2(UnivariateRealFunction f, double min, double max, int n) throws FunctionEvaluationException, IllegalArgumentException { double data[] = FastFourierTransformer.sample(f, min, max, n); double scaling_coefficient = Math.sqrt(2.0 / (n-1)); return FastFourierTransformer.scaleArray(fct(data), scaling_coefficient); } /** * Inversely transform the given real data set. * <p> * The formula is f<sub>k = (1/N) [F0 + (-1)k FN] + * (2/N) ∑<sub>n=1N-1 Fn cos(π nk/N) * </p> * * @param f the real data array to be inversely transformed * @return the real inversely transformed array * @throws IllegalArgumentException if any parameters are invalid */ public double[] inversetransform(double f[]) throws IllegalArgumentException { double scaling_coefficient = 2.0 / (f.length - 1); return FastFourierTransformer.scaleArray(fct(f), scaling_coefficient); } /** * Inversely transform the given real function, sampled on the given interval. * <p> * The formula is f<sub>k = (1/N) [F0 + (-1)k FN] + * (2/N) ∑<sub>n=1N-1 Fn cos(π nk/N) * </p> * * @param f the function to be sampled and inversely transformed * @param min the lower bound for the interval * @param max the upper bound for the interval * @param n the number of sample points * @return the real inversely transformed array * @throws FunctionEvaluationException if function cannot be evaluated * at some point * @throws IllegalArgumentException if any parameters are invalid */ public double[] inversetransform(UnivariateRealFunction f, double min, double max, int n) throws FunctionEvaluationException, IllegalArgumentException { double data[] = FastFourierTransformer.sample(f, min, max, n); double scaling_coefficient = 2.0 / (n - 1); return FastFourierTransformer.scaleArray(fct(data), scaling_coefficient); } /** * Inversely transform the given real data set. * <p> * The formula is f<sub>k = √(1/2N) [F0 + (-1)k FN] + * √(2/N) ∑<sub>n=1N-1 Fn cos(π nk/N) * </p> * * @param f the real data array to be inversely transformed * @return the real inversely transformed array * @throws IllegalArgumentException if any parameters are invalid */ public double[] inversetransform2(double f[]) throws IllegalArgumentException { return transform2(f); } /** * Inversely transform the given real function, sampled on the given interval. * <p> * The formula is f<sub>k = √(1/2N) [F0 + (-1)k FN] + * √(2/N) ∑<sub>n=1N-1 Fn cos(π nk/N) * </p> * * @param f the function to be sampled and inversely transformed * @param min the lower bound for the interval * @param max the upper bound for the interval * @param n the number of sample points * @return the real inversely transformed array * @throws FunctionEvaluationException if function cannot be evaluated * at some point * @throws IllegalArgumentException if any parameters are invalid */ public double[] inversetransform2(UnivariateRealFunction f, double min, double max, int n) throws FunctionEvaluationException, IllegalArgumentException { return transform2(f, min, max, n); } /** * Perform the FCT algorithm (including inverse). * * @param f the real data array to be transformed * @return the real transformed array * @throws IllegalArgumentException if any parameters are invalid */ protected double[] fct(double f[]) throws IllegalArgumentException { final double transformed[] = new double[f.length]; final int n = f.length - 1; if (!FastFourierTransformer.isPowerOf2(n)) { throw MathRuntimeException.createIllegalArgumentException( "{0} is not a power of 2 plus one", f.length); } if (n == 1) { // trivial case transformed[0] = 0.5 * (f[0] + f[1]); transformed[1] = 0.5 * (f[0] - f[1]); return transformed; } // construct a new array and perform FFT on it final double[] x = new double[n]; x[0] = 0.5 * (f[0] + f[n]); x[n >> 1] = f[n >> 1]; double t1 = 0.5 * (f[0] - f[n]); // temporary variable for transformed[1] for (int i = 1; i < (n >> 1); i++) { final double a = 0.5 * (f[i] + f[n-i]); final double b = Math.sin(i * Math.PI / n) * (f[i] - f[n-i]); final double c = Math.cos(i * Math.PI / n) * (f[i] - f[n-i]); x[i] = a - b; x[n-i] = a + b; t1 += c; } FastFourierTransformer transformer = new FastFourierTransformer(); Complex y[] = transformer.transform(x); // reconstruct the FCT result for the original array transformed[0] = y[0].getReal(); transformed[1] = t1; for (int i = 1; i < (n >> 1); i++) { transformed[2 * i] = y[i].getReal(); transformed[2 * i + 1] = transformed[2 * i - 1] - y[i].getImaginary(); } transformed[n] = y[n >> 1].getReal(); return transformed; } }

Other Commons Math examples (source code examples)

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