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 */
017 package org.apache.commons.math.transform;
018
019 import org.apache.commons.math.analysis.*;
020 import org.apache.commons.math.complex.*;
021 import org.apache.commons.math.MathException;
022 import junit.framework.TestCase;
023
024 /**
025 * Testcase for fast Fourier transformer.
026 * <p>
027 * FFT algorithm is exact, the small tolerance number is used only
028 * to account for round-off errors.
029 *
030 * @version $Revision: 762118 $ $Date: 2009-04-05 12:55:59 -0400 (Sun, 05 Apr 2009) $
031 */
032 public final class FastFourierTransformerTest extends TestCase {
033
034 /**
035 * Test of transformer for the ad hoc data taken from Mathematica.
036 */
037 public void testAdHocData() {
038 FastFourierTransformer transformer = new FastFourierTransformer();
039 Complex result[]; double tolerance = 1E-12;
040
041 double x[] = {1.3, 2.4, 1.7, 4.1, 2.9, 1.7, 5.1, 2.7};
042 Complex y[] = {
043 new Complex(21.9, 0.0),
044 new Complex(-2.09497474683058, 1.91507575950825),
045 new Complex(-2.6, 2.7),
046 new Complex(-1.10502525316942, -4.88492424049175),
047 new Complex(0.1, 0.0),
048 new Complex(-1.10502525316942, 4.88492424049175),
049 new Complex(-2.6, -2.7),
050 new Complex(-2.09497474683058, -1.91507575950825)};
051
052 result = transformer.transform(x);
053 for (int i = 0; i < result.length; i++) {
054 assertEquals(y[i].getReal(), result[i].getReal(), tolerance);
055 assertEquals(y[i].getImaginary(), result[i].getImaginary(), tolerance);
056 }
057
058 result = transformer.inversetransform(y);
059 for (int i = 0; i < result.length; i++) {
060 assertEquals(x[i], result[i].getReal(), tolerance);
061 assertEquals(0.0, result[i].getImaginary(), tolerance);
062 }
063
064 double x2[] = {10.4, 21.6, 40.8, 13.6, 23.2, 32.8, 13.6, 19.2};
065 FastFourierTransformer.scaleArray(x2, 1.0 / Math.sqrt(x2.length));
066 Complex y2[] = y;
067
068 result = transformer.transform2(y2);
069 for (int i = 0; i < result.length; i++) {
070 assertEquals(x2[i], result[i].getReal(), tolerance);
071 assertEquals(0.0, result[i].getImaginary(), tolerance);
072 }
073
074 result = transformer.inversetransform2(x2);
075 for (int i = 0; i < result.length; i++) {
076 assertEquals(y2[i].getReal(), result[i].getReal(), tolerance);
077 assertEquals(y2[i].getImaginary(), result[i].getImaginary(), tolerance);
078 }
079 }
080
081 public void test2DData() {
082 FastFourierTransformer transformer = new FastFourierTransformer();
083 double tolerance = 1E-12;
084 Complex[][] input = new Complex[][] {new Complex[] {new Complex(1, 0),
085 new Complex(2, 0)},
086 new Complex[] {new Complex(3, 1),
087 new Complex(4, 2)}};
088 Complex[][] goodOutput = new Complex[][] {new Complex[] {new Complex(5,
089 1.5), new Complex(-1, -.5)}, new Complex[] {new Complex(-2,
090 -1.5), new Complex(0, .5)}};
091 Complex[][] output = (Complex[][])transformer.mdfft(input, true);
092 Complex[][] output2 = (Complex[][])transformer.mdfft(output, false);
093
094 assertEquals(input.length, output.length);
095 assertEquals(input.length, output2.length);
096 assertEquals(input[0].length, output[0].length);
097 assertEquals(input[0].length, output2[0].length);
098 assertEquals(input[1].length, output[1].length);
099 assertEquals(input[1].length, output2[1].length);
100
101 for (int i = 0; i < input.length; i++) {
102 for (int j = 0; j < input[0].length; j++) {
103 assertEquals(input[i][j].getImaginary(), output2[i][j].getImaginary(),
104 tolerance);
105 assertEquals(input[i][j].getReal(), output2[i][j].getReal(), tolerance);
106 assertEquals(goodOutput[i][j].getImaginary(), output[i][j].getImaginary(),
107 tolerance);
108 assertEquals(goodOutput[i][j].getReal(), output[i][j].getReal(), tolerance);
109 }
110 }
111 }
112
113 /**
114 * Test of transformer for the sine function.
115 */
116 public void testSinFunction() throws MathException {
117 UnivariateRealFunction f = new SinFunction();
118 FastFourierTransformer transformer = new FastFourierTransformer();
119 Complex result[]; int N = 1 << 8;
120 double min, max, tolerance = 1E-12;
121
122 min = 0.0; max = 2.0 * Math.PI;
123 result = transformer.transform(f, min, max, N);
124 assertEquals(0.0, result[1].getReal(), tolerance);
125 assertEquals(-(N >> 1), result[1].getImaginary(), tolerance);
126 assertEquals(0.0, result[N-1].getReal(), tolerance);
127 assertEquals(N >> 1, result[N-1].getImaginary(), tolerance);
128 for (int i = 0; i < N-1; i += (i == 0 ? 2 : 1)) {
129 assertEquals(0.0, result[i].getReal(), tolerance);
130 assertEquals(0.0, result[i].getImaginary(), tolerance);
131 }
132
133 min = -Math.PI; max = Math.PI;
134 result = transformer.inversetransform(f, min, max, N);
135 assertEquals(0.0, result[1].getReal(), tolerance);
136 assertEquals(-0.5, result[1].getImaginary(), tolerance);
137 assertEquals(0.0, result[N-1].getReal(), tolerance);
138 assertEquals(0.5, result[N-1].getImaginary(), tolerance);
139 for (int i = 0; i < N-1; i += (i == 0 ? 2 : 1)) {
140 assertEquals(0.0, result[i].getReal(), tolerance);
141 assertEquals(0.0, result[i].getImaginary(), tolerance);
142 }
143 }
144
145 /**
146 * Test of parameters for the transformer.
147 */
148 public void testParameters() throws Exception {
149 UnivariateRealFunction f = new SinFunction();
150 FastFourierTransformer transformer = new FastFourierTransformer();
151
152 try {
153 // bad interval
154 transformer.transform(f, 1, -1, 64);
155 fail("Expecting IllegalArgumentException - bad interval");
156 } catch (IllegalArgumentException ex) {
157 // expected
158 }
159 try {
160 // bad samples number
161 transformer.transform(f, -1, 1, 0);
162 fail("Expecting IllegalArgumentException - bad samples number");
163 } catch (IllegalArgumentException ex) {
164 // expected
165 }
166 try {
167 // bad samples number
168 transformer.transform(f, -1, 1, 100);
169 fail("Expecting IllegalArgumentException - bad samples number");
170 } catch (IllegalArgumentException ex) {
171 // expected
172 }
173 }
174 }