Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | package org.apache.commons.math.transform; |
| 18 | |
| 19 | import org.apache.commons.math.FunctionEvaluationException; |
| 20 | import org.apache.commons.math.MathRuntimeException; |
| 21 | import org.apache.commons.math.analysis.UnivariateRealFunction; |
| 22 | import org.apache.commons.math.complex.Complex; |
| 23 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 24 | import org.apache.commons.math.util.FastMath; |
| 25 | |
| 26 | /** |
| 27 | * Implements the <a href="http://documents.wolfram.com/v5/Add-onsLinks/ |
| 28 | * StandardPackages/LinearAlgebra/FourierTrig.html">Fast Sine Transform</a> |
| 29 | * for transformation of one-dimensional data sets. For reference, see |
| 30 | * <b>Fast Fourier Transforms</b>, ISBN 0849371635, chapter 3. |
| 31 | * <p> |
| 32 | * FST is its own inverse, up to a multiplier depending on conventions. |
| 33 | * The equations are listed in the comments of the corresponding methods.</p> |
| 34 | * <p> |
| 35 | * Similar to FFT, we also require the length of data set to be power of 2. |
| 36 | * In addition, the first element must be 0 and it's enforced in function |
| 37 | * transformation after sampling.</p> |
| 38 | * <p>As of version 2.0 this no longer implements Serializable</p> |
| 39 | * |
| 40 | * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ |
| 41 | * @since 1.2 |
| 42 | */ |
| 43 | public class FastSineTransformer implements RealTransformer { |
| 44 | |
| 45 | /** |
| 46 | * Construct a default transformer. |
| 47 | */ |
| 48 | public FastSineTransformer() { |
| 49 | super(); |
| 50 | } |
| 51 | |
| 52 | /** |
| 53 | * Transform the given real data set. |
| 54 | * <p> |
| 55 | * The formula is F<sub>n</sub> = ∑<sub>k=0</sub><sup>N-1</sup> f<sub>k</sub> sin(π nk/N) |
| 56 | * </p> |
| 57 | * |
| 58 | * @param f the real data array to be transformed |
| 59 | * @return the real transformed array |
| 60 | * @throws IllegalArgumentException if any parameters are invalid |
| 61 | */ |
| 62 | public double[] transform(double f[]) |
| 63 | throws IllegalArgumentException { |
| 64 | return fst(f); |
| 65 | } |
| 66 | |
| 67 | /** |
| 68 | * Transform the given real function, sampled on the given interval. |
| 69 | * <p> |
| 70 | * The formula is F<sub>n</sub> = ∑<sub>k=0</sub><sup>N-1</sup> f<sub>k</sub> sin(π nk/N) |
| 71 | * </p> |
| 72 | * |
| 73 | * @param f the function to be sampled and transformed |
| 74 | * @param min the lower bound for the interval |
| 75 | * @param max the upper bound for the interval |
| 76 | * @param n the number of sample points |
| 77 | * @return the real transformed array |
| 78 | * @throws FunctionEvaluationException if function cannot be evaluated |
| 79 | * at some point |
| 80 | * @throws IllegalArgumentException if any parameters are invalid |
| 81 | */ |
| 82 | public double[] transform(UnivariateRealFunction f, |
| 83 | double min, double max, int n) |
| 84 | throws FunctionEvaluationException, IllegalArgumentException { |
| 85 | |
| 86 | double data[] = FastFourierTransformer.sample(f, min, max, n); |
| 87 | data[0] = 0.0; |
| 88 | return fst(data); |
| 89 | } |
| 90 | |
| 91 | /** |
| 92 | * Transform the given real data set. |
| 93 | * <p> |
| 94 | * The formula is F<sub>n</sub> = √(2/N) ∑<sub>k=0</sub><sup>N-1</sup> f<sub>k</sub> sin(π nk/N) |
| 95 | * </p> |
| 96 | * |
| 97 | * @param f the real data array to be transformed |
| 98 | * @return the real transformed array |
| 99 | * @throws IllegalArgumentException if any parameters are invalid |
| 100 | */ |
| 101 | public double[] transform2(double f[]) throws IllegalArgumentException { |
| 102 | |
| 103 | double scaling_coefficient = FastMath.sqrt(2.0 / f.length); |
| 104 | return FastFourierTransformer.scaleArray(fst(f), scaling_coefficient); |
| 105 | } |
| 106 | |
| 107 | /** |
| 108 | * Transform the given real function, sampled on the given interval. |
| 109 | * <p> |
| 110 | * The formula is F<sub>n</sub> = √(2/N) ∑<sub>k=0</sub><sup>N-1</sup> f<sub>k</sub> sin(π nk/N) |
| 111 | * </p> |
| 112 | * |
| 113 | * @param f the function to be sampled and transformed |
| 114 | * @param min the lower bound for the interval |
| 115 | * @param max the upper bound for the interval |
| 116 | * @param n the number of sample points |
| 117 | * @return the real transformed array |
| 118 | * @throws FunctionEvaluationException if function cannot be evaluated |
| 119 | * at some point |
| 120 | * @throws IllegalArgumentException if any parameters are invalid |
| 121 | */ |
| 122 | public double[] transform2( |
| 123 | UnivariateRealFunction f, double min, double max, int n) |
| 124 | throws FunctionEvaluationException, IllegalArgumentException { |
| 125 | |
| 126 | double data[] = FastFourierTransformer.sample(f, min, max, n); |
| 127 | data[0] = 0.0; |
| 128 | double scaling_coefficient = FastMath.sqrt(2.0 / n); |
| 129 | return FastFourierTransformer.scaleArray(fst(data), scaling_coefficient); |
| 130 | } |
| 131 | |
| 132 | /** |
| 133 | * Inversely transform the given real data set. |
| 134 | * <p> |
| 135 | * The formula is f<sub>k</sub> = (2/N) ∑<sub>n=0</sub><sup>N-1</sup> F<sub>n</sub> sin(π nk/N) |
| 136 | * </p> |
| 137 | * |
| 138 | * @param f the real data array to be inversely transformed |
| 139 | * @return the real inversely transformed array |
| 140 | * @throws IllegalArgumentException if any parameters are invalid |
| 141 | */ |
| 142 | public double[] inversetransform(double f[]) throws IllegalArgumentException { |
| 143 | |
| 144 | double scaling_coefficient = 2.0 / f.length; |
| 145 | return FastFourierTransformer.scaleArray(fst(f), scaling_coefficient); |
| 146 | } |
| 147 | |
| 148 | /** |
| 149 | * Inversely transform the given real function, sampled on the given interval. |
| 150 | * <p> |
| 151 | * The formula is f<sub>k</sub> = (2/N) ∑<sub>n=0</sub><sup>N-1</sup> F<sub>n</sub> sin(π nk/N) |
| 152 | * </p> |
| 153 | * |
| 154 | * @param f the function to be sampled and inversely transformed |
| 155 | * @param min the lower bound for the interval |
| 156 | * @param max the upper bound for the interval |
| 157 | * @param n the number of sample points |
| 158 | * @return the real inversely transformed array |
| 159 | * @throws FunctionEvaluationException if function cannot be evaluated at some point |
| 160 | * @throws IllegalArgumentException if any parameters are invalid |
| 161 | */ |
| 162 | public double[] inversetransform(UnivariateRealFunction f, double min, double max, int n) |
| 163 | throws FunctionEvaluationException, IllegalArgumentException { |
| 164 | |
| 165 | double data[] = FastFourierTransformer.sample(f, min, max, n); |
| 166 | data[0] = 0.0; |
| 167 | double scaling_coefficient = 2.0 / n; |
| 168 | return FastFourierTransformer.scaleArray(fst(data), scaling_coefficient); |
| 169 | } |
| 170 | |
| 171 | /** |
| 172 | * Inversely transform the given real data set. |
| 173 | * <p> |
| 174 | * The formula is f<sub>k</sub> = √(2/N) ∑<sub>n=0</sub><sup>N-1</sup> F<sub>n</sub> sin(π nk/N) |
| 175 | * </p> |
| 176 | * |
| 177 | * @param f the real data array to be inversely transformed |
| 178 | * @return the real inversely transformed array |
| 179 | * @throws IllegalArgumentException if any parameters are invalid |
| 180 | */ |
| 181 | public double[] inversetransform2(double f[]) throws IllegalArgumentException { |
| 182 | |
| 183 | return transform2(f); |
| 184 | } |
| 185 | |
| 186 | /** |
| 187 | * Inversely transform the given real function, sampled on the given interval. |
| 188 | * <p> |
| 189 | * The formula is f<sub>k</sub> = √(2/N) ∑<sub>n=0</sub><sup>N-1</sup> F<sub>n</sub> sin(π nk/N) |
| 190 | * </p> |
| 191 | * |
| 192 | * @param f the function to be sampled and inversely transformed |
| 193 | * @param min the lower bound for the interval |
| 194 | * @param max the upper bound for the interval |
| 195 | * @param n the number of sample points |
| 196 | * @return the real inversely transformed array |
| 197 | * @throws FunctionEvaluationException if function cannot be evaluated at some point |
| 198 | * @throws IllegalArgumentException if any parameters are invalid |
| 199 | */ |
| 200 | public double[] inversetransform2(UnivariateRealFunction f, double min, double max, int n) |
| 201 | throws FunctionEvaluationException, IllegalArgumentException { |
| 202 | |
| 203 | return transform2(f, min, max, n); |
| 204 | } |
| 205 | |
| 206 | /** |
| 207 | * Perform the FST algorithm (including inverse). |
| 208 | * |
| 209 | * @param f the real data array to be transformed |
| 210 | * @return the real transformed array |
| 211 | * @throws IllegalArgumentException if any parameters are invalid |
| 212 | */ |
| 213 | protected double[] fst(double f[]) throws IllegalArgumentException { |
| 214 | |
| 215 | final double transformed[] = new double[f.length]; |
| 216 | |
| 217 | FastFourierTransformer.verifyDataSet(f); |
| 218 | if (f[0] != 0.0) { |
| 219 | throw MathRuntimeException.createIllegalArgumentException( |
| 220 | LocalizedFormats.FIRST_ELEMENT_NOT_ZERO, |
| 221 | f[0]); |
| 222 | } |
| 223 | final int n = f.length; |
| 224 | if (n == 1) { // trivial case |
| 225 | transformed[0] = 0.0; |
| 226 | return transformed; |
| 227 | } |
| 228 | |
| 229 | // construct a new array and perform FFT on it |
| 230 | final double[] x = new double[n]; |
| 231 | x[0] = 0.0; |
| 232 | x[n >> 1] = 2.0 * f[n >> 1]; |
| 233 | for (int i = 1; i < (n >> 1); i++) { |
| 234 | final double a = FastMath.sin(i * FastMath.PI / n) * (f[i] + f[n-i]); |
| 235 | final double b = 0.5 * (f[i] - f[n-i]); |
| 236 | x[i] = a + b; |
| 237 | x[n - i] = a - b; |
| 238 | } |
| 239 | FastFourierTransformer transformer = new FastFourierTransformer(); |
| 240 | Complex y[] = transformer.transform(x); |
| 241 | |
| 242 | // reconstruct the FST result for the original array |
| 243 | transformed[0] = 0.0; |
| 244 | transformed[1] = 0.5 * y[0].getReal(); |
| 245 | for (int i = 1; i < (n >> 1); i++) { |
| 246 | transformed[2 * i] = -y[i].getImaginary(); |
| 247 | transformed[2 * i + 1] = y[i].getReal() + transformed[2 * i - 1]; |
| 248 | } |
| 249 | |
| 250 | return transformed; |
| 251 | } |
| 252 | } |