fastcosinetransformer.java

Apache的common math数学软件包

/*
 * 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 java.io.Serializable;
import org.apache.commons.math.analysis.*;
import org.apache.commons.math.complex.*;
import org.apache.commons.math.MathException;

/**
 * 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>
 *
 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
 * @since 1.2
 */
public class FastCosineTransformer implements Serializable {

    /** serializable version identifier */
    static final long serialVersionUID = -7673941545134707766L;

    /**
     * Construct a default transformer.
     */
    public FastCosineTransformer() {
        super();
    }

    /**
     * Transform the given real data set.
     * <p>
     * The formula is $ F_n = (1/2) [f_0 + (-1)^n f_N] +
     *                        \Sigma_{k=0}^{N-1} f_k \cos(\pi nk/N) $
     * </p>
     * 
     * @param f the real data array to be transformed
     * @return the real transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] transform(double f[]) throws MathException,
        IllegalArgumentException {

        return fct(f);
    }

    /**
     * Transform the given real function, sampled on the given interval.
     * <p>
     * The formula is $ F_n = (1/2) [f_0 + (-1)^n f_N] +
     *                        \Sigma_{k=0}^{N-1} f_k \cos(\pi 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 MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] transform(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, IllegalArgumentException {

        double data[] = FastFourierTransformer.sample(f, min, max, n);
        return fct(data);
    }

    /**
     * Transform the given real data set.
     * <p>
     * The formula is $ F_n = \sqrt{1/2N} [f_0 + (-1)^n f_N] +
     *                        \sqrt{2/N} \Sigma_{k=0}^{N-1} f_k \cos(\pi nk/N) $
     * </p>
     * 
     * @param f the real data array to be transformed
     * @return the real transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] transform2(double f[]) throws MathException,
        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_n = \sqrt{1/2N} [f_0 + (-1)^n f_N] +
     *                        \sqrt{2/N} \Sigma_{k=0}^{N-1} f_k \cos(\pi 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 MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] transform2(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, 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_k = (1/N) [F_0 + (-1)^k F_N] +
     *                        (2/N) \Sigma_{n=0}^{N-1} F_n \cos(\pi nk/N) $
     * </p>
     * 
     * @param f the real data array to be inversely transformed
     * @return the real inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] inversetransform(double f[]) throws MathException,
        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_k = (1/N) [F_0 + (-1)^k F_N] +
     *                        (2/N) \Sigma_{n=0}^{N-1} F_n \cos(\pi 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 MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] inversetransform(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, 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_k = \sqrt{1/2N} [F_0 + (-1)^k F_N] +
     *                        \sqrt{2/N} \Sigma_{n=0}^{N-1} F_n \cos(\pi nk/N) $
     * </p>
     * 
     * @param f the real data array to be inversely transformed
     * @return the real inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] inversetransform2(double f[]) throws MathException,
        IllegalArgumentException {

        return transform2(f);
    }

    /**
     * Inversely transform the given real function, sampled on the given interval.
     * <p>
     * The formula is $ f_k = \sqrt{1/2N} [F_0 + (-1)^k F_N] +
     *                        \sqrt{2/N} \Sigma_{n=0}^{N-1} F_n \cos(\pi 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 MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public double[] inversetransform2(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, 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 MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    protected double[] fct(double f[]) throws MathException,
        IllegalArgumentException {

        double A, B, C, F1, x[], F[] = new double[f.length];

        int N = f.length - 1;
        if (!FastFourierTransformer.isPowerOf2(N)) {
            throw new IllegalArgumentException
                ("Number of samples not power of 2 plus one: " + f.length);
        }
        if (N == 1) {       // trivial case
            F[0] = 0.5 * (f[0] + f[1]);
            F[1] = 0.5 * (f[0] - f[1]);
            return F;
        }

        // construct a new array and perform FFT on it
        x = new double[N];
        x[0] = 0.5 * (f[0] + f[N]);
        x[N >> 1] = f[N >> 1];
        F1 = 0.5 * (f[0] - f[N]);   // temporary variable for F[1]
        for (int i = 1; i < (N >> 1); i++) {
            A = 0.5 * (f[i] + f[N-i]);
            B = Math.sin(i * Math.PI / N) * (f[i] - f[N-i]);
            C = Math.cos(i * Math.PI / N) * (f[i] - f[N-i]);
            x[i] = A - B;
            x[N-i] = A + B;
            F1 += C;
        }
        FastFourierTransformer transformer = new FastFourierTransformer();
        Complex y[] = transformer.transform(x);

        // reconstruct the FCT result for the original array
        F[0] = y[0].getReal();
        F[1] = F1;
        for (int i = 1; i < (N >> 1); i++) {
            F[2*i] = y[i].getReal();
            F[2*i+1] = F[2*i-1] - y[i].getImaginary();
        }
        F[N] = y[N >> 1].getReal();

        return F;
    }
}