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Diffstat (limited to 'src/main/java/org/apache/commons/math/transform/FastCosineTransformer.java')
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diff --git a/src/main/java/org/apache/commons/math/transform/FastCosineTransformer.java b/src/main/java/org/apache/commons/math/transform/FastCosineTransformer.java new file mode 100644 index 0000000..bda0fe2 --- /dev/null +++ b/src/main/java/org/apache/commons/math/transform/FastCosineTransformer.java @@ -0,0 +1,262 @@ +/* + * 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; +import org.apache.commons.math.exception.util.LocalizedFormats; +import org.apache.commons.math.util.FastMath; + +/** + * 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</b>, 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</p> + * + * @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</sub> = (1/2) [f<sub>0</sub> + (-1)<sup>n</sup> f<sub>N</sub>] + + * ∑<sub>k=1</sub><sup>N-1</sup> f<sub>k</sub> 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</sub> = (1/2) [f<sub>0</sub> + (-1)<sup>n</sup> f<sub>N</sub>] + + * ∑<sub>k=1</sub><sup>N-1</sup> f<sub>k</sub> 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</sub> = √(1/2N) [f<sub>0</sub> + (-1)<sup>n</sup> f<sub>N</sub>] + + * √(2/N) ∑<sub>k=1</sub><sup>N-1</sup> f<sub>k</sub> 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 = FastMath.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</sub> = √(1/2N) [f<sub>0</sub> + (-1)<sup>n</sup> f<sub>N</sub>] + + * √(2/N) ∑<sub>k=1</sub><sup>N-1</sup> f<sub>k</sub> 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 = FastMath.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</sub> = (1/N) [F<sub>0</sub> + (-1)<sup>k</sup> F<sub>N</sub>] + + * (2/N) ∑<sub>n=1</sub><sup>N-1</sup> F<sub>n</sub> 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</sub> = (1/N) [F<sub>0</sub> + (-1)<sup>k</sup> F<sub>N</sub>] + + * (2/N) ∑<sub>n=1</sub><sup>N-1</sup> F<sub>n</sub> 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</sub> = √(1/2N) [F<sub>0</sub> + (-1)<sup>k</sup> F<sub>N</sub>] + + * √(2/N) ∑<sub>n=1</sub><sup>N-1</sup> F<sub>n</sub> 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</sub> = √(1/2N) [F<sub>0</sub> + (-1)<sup>k</sup> F<sub>N</sub>] + + * √(2/N) ∑<sub>n=1</sub><sup>N-1</sup> F<sub>n</sub> 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( + LocalizedFormats.NOT_POWER_OF_TWO_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 = FastMath.sin(i * FastMath.PI / n) * (f[i] - f[n-i]); + final double c = FastMath.cos(i * FastMath.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; + } +} |