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Commons Math example source code file (FastHadamardTransformer.java)

This example Commons Math source code file (FastHadamardTransformer.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

fasthadamardtransformer, fasthadamardtransformer, functionevaluationexception, functionevaluationexception, illegalargumentexception, illegalargumentexception, realtransformer, realtransformer

The Commons Math FastHadamardTransformer.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;

/**
 * Implements the <a href="http://www.archive.chipcenter.com/dsp/DSP000517F1.html">Fast Hadamard Transform (FHT).
 * Transformation of an input vector x to the output vector y.
 * <p>In addition to transformation of real vectors, the Hadamard transform can
 * transform integer vectors into integer vectors. However, this integer transform
 * cannot be inverted directly. Due to a scaling factor it may lead to rational results.
 * As an example, the inverse transform of integer vector (0, 1, 0, 1) is rational
 * vector (1/2, -1/2, 0, 0).</p>
 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
 * @since 2.0
 */
public class FastHadamardTransformer implements RealTransformer {

    /** {@inheritDoc} */
    public double[] transform(double f[])
        throws IllegalArgumentException {
        return fht(f);
    }

    /** {@inheritDoc} */
    public double[] transform(UnivariateRealFunction f,
                              double min, double max, int n)
        throws FunctionEvaluationException, IllegalArgumentException {
        return fht(FastFourierTransformer.sample(f, min, max, n));
    }

    /** {@inheritDoc} */
    public double[] inversetransform(double f[])
    throws IllegalArgumentException {
        return FastFourierTransformer.scaleArray(fht(f), 1.0 / f.length);
   }

    /** {@inheritDoc} */
    public double[] inversetransform(UnivariateRealFunction f,
                                     double min, double max, int n)
        throws FunctionEvaluationException, IllegalArgumentException {
        final double[] unscaled =
            fht(FastFourierTransformer.sample(f, min, max, n));
        return FastFourierTransformer.scaleArray(unscaled, 1.0 / n);
    }

    /**
     * Transform the given real data set.
     * <p>The integer transform cannot be inverted directly, due to a scaling
     * factor it may lead to double results.</p>
     * @param f the integer data array to be transformed (signal)
     * @return the integer transformed array (spectrum)
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public int[] transform(int f[])
        throws IllegalArgumentException {
        return fht(f);
    }

    /**
     * The FHT (Fast Hadamard Transformation) which uses only subtraction and addition.
     * <br>
     * Requires <b>Nlog2N = n2n additions.
     * <br>
     * <br>
     * <b>Short Table of manual calculation for N=8:
     * <ol>
     * <li>x is the input vector we want to transform
     * <li>y is the output vector which is our desired result
     * <li>a and b are just helper rows
     * </ol>
     * <pre>
     * <code>
     * +----+----------+---------+----------+
     * | <b>x  |    a     |    b    |    y     |
     * +----+----------+---------+----------+
     * | x<sub>0 | a0=x0+x1 | b0=a0+a1 | y0=b0+b1 |
     * +----+----------+---------+----------+
     * | x<sub>1 | a1=x2+x3 | b0=a2+a3 | y0=b2+b3 |
     * +----+----------+---------+----------+
     * | x<sub>2 | a2=x4+x5 | b0=a4+a5 | y0=b4+b5 |
     * +----+----------+---------+----------+
     * | x<sub>3 | a3=x6+x7 | b0=a6+a7 | y0=b6+b7 |
     * +----+----------+---------+----------+
     * | x<sub>4 | a0=x0-x1 | b0=a0-a1 | y0=b0-b1 |
     * +----+----------+---------+----------+
     * | x<sub>5 | a1=x2-x3 | b0=a2-a3 | y0=b2-b3 |
     * +----+----------+---------+----------+
     * | x<sub>6 | a2=x4-x5 | b0=a4-a5 | y0=b4-b5 |
     * +----+----------+---------+----------+
     * | x<sub>7 | a3=x6-x7 | b0=a6-a7 | y0=b6-b7 |
     * +----+----------+---------+----------+
     * </code>
     * </pre>
     *
     * <b>How it works
     * <ol>
     * <li>Construct a matrix with N rows and n+1 columns
hadm[n+1][N] * <br>(If I use [x][y] it always means [row-offset][column-offset] of a Matrix with n rows and m columns. Its entries go from M[0][0] to M[n][m]) * <li>Place the input vector x[N] in the first column of the matrix hadm * <li>The entries of the submatrix Dtop are calculated as follows. * <br>Dtop goes from entry [0][1] to [N/2-1][n+1]. * <br>The columns of Dtop are the pairwise mutually exclusive sums of the previous column * </li> * <li>The entries of the submatrix Dbottom are calculated as follows. * <br>Dbottom goes from entry [N/2][1] to [N][n+1]. * <br>The columns of Dbottom are the pairwise differences of the previous column * </li> * <li>How Dtop and Dbottom you can understand best with the example for N=8 above. * <li>The output vector y is now in the last column of hadm * <li>Algorithm from: http://www.archive.chipcenter.com/dsp/DSP000517F1.html * </ol> * <br> * <b>Visually * <pre> * +--------+---+---+---+-----+---+ * | 0 | 1 | 2 | 3 | ... |n+1| * +------+--------+---+---+---+-----+---+ * |0 | x<sub>0 | /\ | * |1 | x<sub>1 | || | * |2 | x<sub>2 | <= Dtop => | * |... | ... | || | * |N/2-1 | x<sub>N/2-1 | \/ | * +------+--------+---+---+---+-----+---+ * |N/2 | x<sub>N/2 | /\ | * |N/2+1 | x<sub>N/2+1 | || | * |N/2+2 | x<sub>N/2+2 | <= Dbottom => | which is in the last column of the matrix * |... | ... | || | * |N | x<sub>N/2 | \/ | * +------+--------+---+---+---+-----+---+ * </pre> * * @param x input vector * @return y output vector * @exception IllegalArgumentException if input array is not a power of 2 */ protected double[] fht(double x[]) throws IllegalArgumentException { // n is the row count of the input vector x final int n = x.length; final int halfN = n / 2; // n has to be of the form n = 2^p !! if (!FastFourierTransformer.isPowerOf2(n)) { throw MathRuntimeException.createIllegalArgumentException( "{0} is not a power of 2", n); } // Instead of creating a matrix with p+1 columns and n rows // we will use two single dimension arrays which we will use in an alternating way. double[] yPrevious = new double[n]; double[] yCurrent = x.clone(); // iterate from left to right (column) for (int j = 1; j < n; j <<= 1) { // switch columns final double[] yTmp = yCurrent; yCurrent = yPrevious; yPrevious = yTmp; // iterate from top to bottom (row) for (int i = 0; i < halfN; ++i) { // D<sub>top // The top part works with addition final int twoI = 2 * i; yCurrent[i] = yPrevious[twoI] + yPrevious[twoI + 1]; } for (int i = halfN; i < n; ++i) { // D<sub>bottom // The bottom part works with subtraction final int twoI = 2 * i; yCurrent[i] = yPrevious[twoI - n] - yPrevious[twoI - n + 1]; } } // return the last computed output vector y return yCurrent; } /** * The FHT (Fast Hadamard Transformation) which uses only subtraction and addition. * @param x input vector * @return y output vector * @exception IllegalArgumentException if input array is not a power of 2 */ protected int[] fht(int x[]) throws IllegalArgumentException { // n is the row count of the input vector x final int n = x.length; final int halfN = n / 2; // n has to be of the form n = 2^p !! if (!FastFourierTransformer.isPowerOf2(n)) { throw MathRuntimeException.createIllegalArgumentException( "{0} is not a power of 2", n); } // Instead of creating a matrix with p+1 columns and n rows // we will use two single dimension arrays which we will use in an alternating way. int[] yPrevious = new int[n]; int[] yCurrent = x.clone(); // iterate from left to right (column) for (int j = 1; j < n; j <<= 1) { // switch columns final int[] yTmp = yCurrent; yCurrent = yPrevious; yPrevious = yTmp; // iterate from top to bottom (row) for (int i = 0; i < halfN; ++i) { // D<sub>top // The top part works with addition final int twoI = 2 * i; yCurrent[i] = yPrevious[twoI] + yPrevious[twoI + 1]; } for (int i = halfN; i < n; ++i) { // D<sub>bottom // The bottom part works with subtraction final int twoI = 2 * i; yCurrent[i] = yPrevious[twoI - n] - yPrevious[twoI - n + 1]; } } // return the last computed output vector y return yCurrent; } }

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