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Java example source code file (FastCosineTransformer.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

complex, dctnormalization, fastcosinetransformer, fastfouriertransformer, mathillegalargumentexception, realtransformer, serializable, transformtype, univariatefunction

The FastCosineTransformer.java Java example 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.math3.transform;

import java.io.Serializable;

import org.apache.commons.math3.analysis.FunctionUtils;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.complex.Complex;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.FastMath;

/**
 * Implements the Fast Cosine Transform for transformation of one-dimensional
 * real data sets. For reference, see James S. Walker, <em>Fast Fourier
 * Transforms</em>, chapter 3 (ISBN 0849371635).
 * <p>
 * There are several variants of the discrete cosine transform. The present
 * implementation corresponds to DCT-I, with various normalization conventions,
 * which are specified by the parameter {@link DctNormalization}.
 * <p>
 * DCT-I is equivalent to DFT of an <em>even extension of the data series.
 * More precisely, if x<sub>0, …, xN-1 is the data set
 * to be cosine transformed, the extended data set
 * x<sub>0#, …, x2N-3#
 * is defined as follows
 * <ul>
 * <li>xk# = xk if 0 ≤ k < N,
 * <li>xk# = x2N-2-k
 * if N ≤ k < 2N - 2.</li>
 * </ul>
 * <p>
 * Then, the standard DCT-I y<sub>0, …, yN-1 of the real
 * data set x<sub>0, …, xN-1 is equal to half
 * of the N first elements of the DFT of the extended data set
 * x<sub>0#, …, x2N-3#
 * <br/>
 * y<sub>n = (1 / 2) ∑k=02N-3
 * x<sub>k# exp[-2πi nk / (2N - 2)]
 *     k = 0, …, N-1.
 * <p>
 * The present implementation of the discrete cosine transform as a fast cosine
 * transform requires the length of the data set to be a power of two plus one
 * (N = 2<sup>n + 1). Besides, it implicitly assumes
 * that the sampled function is even.
 *
 * @since 1.2
 */
public class FastCosineTransformer implements RealTransformer, Serializable {

    /** Serializable version identifier. */
    static final long serialVersionUID = 20120212L;

    /** The type of DCT to be performed. */
    private final DctNormalization normalization;

    /**
     * Creates a new instance of this class, with various normalization
     * conventions.
     *
     * @param normalization the type of normalization to be applied to the
     * transformed data
     */
    public FastCosineTransformer(final DctNormalization normalization) {
        this.normalization = normalization;
    }

    /**
     * {@inheritDoc}
     *
     * @throws MathIllegalArgumentException if the length of the data array is
     * not a power of two plus one
     */
    public double[] transform(final double[] f, final TransformType type)
      throws MathIllegalArgumentException {
        if (type == TransformType.FORWARD) {
            if (normalization == DctNormalization.ORTHOGONAL_DCT_I) {
                final double s = FastMath.sqrt(2.0 / (f.length - 1));
                return TransformUtils.scaleArray(fct(f), s);
            }
            return fct(f);
        }
        final double s2 = 2.0 / (f.length - 1);
        final double s1;
        if (normalization == DctNormalization.ORTHOGONAL_DCT_I) {
            s1 = FastMath.sqrt(s2);
        } else {
            s1 = s2;
        }
        return TransformUtils.scaleArray(fct(f), s1);
    }

    /**
     * {@inheritDoc}
     *
     * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException
     * if the lower bound is greater than, or equal to the upper bound
     * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException
     * if the number of sample points is negative
     * @throws MathIllegalArgumentException if the number of sample points is
     * not a power of two plus one
     */
    public double[] transform(final UnivariateFunction f,
        final double min, final double max, final int n,
        final TransformType type) throws MathIllegalArgumentException {

        final double[] data = FunctionUtils.sample(f, min, max, n);
        return transform(data, type);
    }

    /**
     * Perform the FCT algorithm (including inverse).
     *
     * @param f the real data array to be transformed
     * @return the real transformed array
     * @throws MathIllegalArgumentException if the length of the data array is
     * not a power of two plus one
     */
    protected double[] fct(double[] f)
        throws MathIllegalArgumentException {

        final double[] transformed = new double[f.length];

        final int n = f.length - 1;
        if (!ArithmeticUtils.isPowerOfTwo(n)) {
            throw new MathIllegalArgumentException(
                LocalizedFormats.NOT_POWER_OF_TWO_PLUS_ONE,
                Integer.valueOf(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];
        // temporary variable for transformed[1]
        double t1 = 0.5 * (f[0] - f[n]);
        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;
        transformer = new FastFourierTransformer(DftNormalization.STANDARD);
        Complex[] y = transformer.transform(x, TransformType.FORWARD);

        // 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;
    }
}

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