001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math3.transform;
018
019import java.io.Serializable;
020
021import org.apache.commons.math3.analysis.FunctionUtils;
022import org.apache.commons.math3.analysis.UnivariateFunction;
023import org.apache.commons.math3.complex.Complex;
024import org.apache.commons.math3.exception.MathIllegalArgumentException;
025import org.apache.commons.math3.exception.util.LocalizedFormats;
026import org.apache.commons.math3.util.ArithmeticUtils;
027import org.apache.commons.math3.util.FastMath;
028
029/**
030 * Implements the Fast Sine Transform for transformation of one-dimensional real
031 * data sets. For reference, see James S. Walker, <em>Fast Fourier
032 * Transforms</em>, chapter 3 (ISBN 0849371635).
033 * <p>
034 * There are several variants of the discrete sine transform. The present
035 * implementation corresponds to DST-I, with various normalization conventions,
036 * which are specified by the parameter {@link DstNormalization}.
037 * <strong>It should be noted that regardless to the convention, the first
038 * element of the dataset to be transformed must be zero.</strong>
039 * <p>
040 * DST-I is equivalent to DFT of an <em>odd extension</em> of the data series.
041 * More precisely, if x<sub>0</sub>, &hellip;, x<sub>N-1</sub> is the data set
042 * to be sine transformed, the extended data set x<sub>0</sub><sup>&#35;</sup>,
043 * &hellip;, x<sub>2N-1</sub><sup>&#35;</sup> is defined as follows
044 * <ul>
045 * <li>x<sub>0</sub><sup>&#35;</sup> = x<sub>0</sub> = 0,</li>
046 * <li>x<sub>k</sub><sup>&#35;</sup> = x<sub>k</sub> if 1 &le; k &lt; N,</li>
047 * <li>x<sub>N</sub><sup>&#35;</sup> = 0,</li>
048 * <li>x<sub>k</sub><sup>&#35;</sup> = -x<sub>2N-k</sub> if N + 1 &le; k &lt;
049 * 2N.</li>
050 * </ul>
051 * <p>
052 * Then, the standard DST-I y<sub>0</sub>, &hellip;, y<sub>N-1</sub> of the real
053 * data set x<sub>0</sub>, &hellip;, x<sub>N-1</sub> is equal to <em>half</em>
054 * of i (the pure imaginary number) times the N first elements of the DFT of the
055 * extended data set x<sub>0</sub><sup>&#35;</sup>, &hellip;,
056 * x<sub>2N-1</sub><sup>&#35;</sup> <br />
057 * y<sub>n</sub> = (i / 2) &sum;<sub>k=0</sub><sup>2N-1</sup>
058 * x<sub>k</sub><sup>&#35;</sup> exp[-2&pi;i nk / (2N)]
059 * &nbsp;&nbsp;&nbsp;&nbsp;k = 0, &hellip;, N-1.
060 * <p>
061 * The present implementation of the discrete sine transform as a fast sine
062 * transform requires the length of the data to be a power of two. Besides,
063 * it implicitly assumes that the sampled function is odd. In particular, the
064 * first element of the data set must be 0, which is enforced in
065 * {@link #transform(UnivariateFunction, double, double, int, TransformType)},
066 * after sampling.
067 *
068 * @version $Id: FastSineTransformer.java 1385310 2012-09-16 16:32:10Z tn $
069 * @since 1.2
070 */
071public class FastSineTransformer implements RealTransformer, Serializable {
072
073    /** Serializable version identifier. */
074    static final long serialVersionUID = 20120211L;
075
076    /** The type of DST to be performed. */
077    private final DstNormalization normalization;
078
079    /**
080     * Creates a new instance of this class, with various normalization conventions.
081     *
082     * @param normalization the type of normalization to be applied to the transformed data
083     */
084    public FastSineTransformer(final DstNormalization normalization) {
085        this.normalization = normalization;
086    }
087
088    /**
089     * {@inheritDoc}
090     *
091     * The first element of the specified data set is required to be {@code 0}.
092     *
093     * @throws MathIllegalArgumentException if the length of the data array is
094     *   not a power of two, or the first element of the data array is not zero
095     */
096    public double[] transform(final double[] f, final TransformType type) {
097        if (normalization == DstNormalization.ORTHOGONAL_DST_I) {
098            final double s = FastMath.sqrt(2.0 / f.length);
099            return TransformUtils.scaleArray(fst(f), s);
100        }
101        if (type == TransformType.FORWARD) {
102            return fst(f);
103        }
104        final double s = 2.0 / f.length;
105        return TransformUtils.scaleArray(fst(f), s);
106    }
107
108    /**
109     * {@inheritDoc}
110     *
111     * This implementation enforces {@code f(x) = 0.0} at {@code x = 0.0}.
112     *
113     * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException
114     *   if the lower bound is greater than, or equal to the upper bound
115     * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException
116     *   if the number of sample points is negative
117     * @throws MathIllegalArgumentException if the number of sample points is not a power of two
118     */
119    public double[] transform(final UnivariateFunction f,
120        final double min, final double max, final int n,
121        final TransformType type) {
122
123        final double[] data = FunctionUtils.sample(f, min, max, n);
124        data[0] = 0.0;
125        return transform(data, type);
126    }
127
128    /**
129     * Perform the FST algorithm (including inverse). The first element of the
130     * data set is required to be {@code 0}.
131     *
132     * @param f the real data array to be transformed
133     * @return the real transformed array
134     * @throws MathIllegalArgumentException if the length of the data array is
135     *   not a power of two, or the first element of the data array is not zero
136     */
137    protected double[] fst(double[] f) throws MathIllegalArgumentException {
138
139        final double[] transformed = new double[f.length];
140
141        if (!ArithmeticUtils.isPowerOfTwo(f.length)) {
142            throw new MathIllegalArgumentException(
143                    LocalizedFormats.NOT_POWER_OF_TWO_CONSIDER_PADDING,
144                    Integer.valueOf(f.length));
145        }
146        if (f[0] != 0.0) {
147            throw new MathIllegalArgumentException(
148                    LocalizedFormats.FIRST_ELEMENT_NOT_ZERO,
149                    Double.valueOf(f[0]));
150        }
151        final int n = f.length;
152        if (n == 1) {       // trivial case
153            transformed[0] = 0.0;
154            return transformed;
155        }
156
157        // construct a new array and perform FFT on it
158        final double[] x = new double[n];
159        x[0] = 0.0;
160        x[n >> 1] = 2.0 * f[n >> 1];
161        for (int i = 1; i < (n >> 1); i++) {
162            final double a = FastMath.sin(i * FastMath.PI / n) * (f[i] + f[n - i]);
163            final double b = 0.5 * (f[i] - f[n - i]);
164            x[i]     = a + b;
165            x[n - i] = a - b;
166        }
167        FastFourierTransformer transformer;
168        transformer = new FastFourierTransformer(DftNormalization.STANDARD);
169        Complex[] y = transformer.transform(x, TransformType.FORWARD);
170
171        // reconstruct the FST result for the original array
172        transformed[0] = 0.0;
173        transformed[1] = 0.5 * y[0].getReal();
174        for (int i = 1; i < (n >> 1); i++) {
175            transformed[2 * i]     = -y[i].getImaginary();
176            transformed[2 * i + 1] = y[i].getReal() + transformed[2 * i - 1];
177        }
178
179        return transformed;
180    }
181}