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Java example source code file (FastFourierTransformerTest.java)

This example Java source code file (FastFourierTransformerTest.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, dftnormalization, fastfouriertransformer, mathillegalargumentexception, n-1, notstrictlypositiveexception, numberistoolargeexception, random, sin, string, suppresswarnings, test, transformtype, univariatefunction, util

The FastFourierTransformerTest.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.util.Random;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.analysis.function.Sinc;
import org.apache.commons.math3.complex.Complex;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test case for fast Fourier transformer.
 * <p>
 * FFT algorithm is exact, the small tolerance number is used only
 * to account for round-off errors.
 *
 */
public final class FastFourierTransformerTest {
    /** The common seed of all random number generators used in this test. */
    private final static long SEED = 20110111L;

    /*
     * Precondition checks.
     */

    @Test
    public void testTransformComplexSizeNotAPowerOfTwo() {
        final int n = 127;
        final Complex[] x = createComplexData(n);
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                final FastFourierTransformer fft;
                fft = new FastFourierTransformer(norm[i]);
                try {
                    fft.transform(x, type[j]);
                    Assert.fail(norm[i] + ", " + type[j] +
                        ": MathIllegalArgumentException was expected");
                } catch (MathIllegalArgumentException e) {
                    // Expected behaviour
                }
            }
        }
    }

    @Test
    public void testTransformRealSizeNotAPowerOfTwo() {
        final int n = 127;
        final double[] x = createRealData(n);
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                final FastFourierTransformer fft;
                fft = new FastFourierTransformer(norm[i]);
                try {
                    fft.transform(x, type[j]);
                    Assert.fail(norm[i] + ", " + type[j] +
                        ": MathIllegalArgumentException was expected");
                } catch (MathIllegalArgumentException e) {
                    // Expected behaviour
                }
            }
        }
    }

    @Test
    public void testTransformFunctionSizeNotAPowerOfTwo() {
        final int n = 127;
        final UnivariateFunction f = new Sin();
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                final FastFourierTransformer fft;
                fft = new FastFourierTransformer(norm[i]);
                try {
                    fft.transform(f, 0.0, Math.PI, n, type[j]);
                    Assert.fail(norm[i] + ", " + type[j] +
                        ": MathIllegalArgumentException was expected");
                } catch (MathIllegalArgumentException e) {
                    // Expected behaviour
                }
            }
        }
    }

    @Test
    public void testTransformFunctionNotStrictlyPositiveNumberOfSamples() {
        final int n = -128;
        final UnivariateFunction f = new Sin();
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                final FastFourierTransformer fft;
                fft = new FastFourierTransformer(norm[i]);
                try {
                    fft.transform(f, 0.0, Math.PI, n, type[j]);
                    fft.transform(f, 0.0, Math.PI, n, type[j]);
                    Assert.fail(norm[i] + ", " + type[j] +
                        ": NotStrictlyPositiveException was expected");
                } catch (NotStrictlyPositiveException e) {
                    // Expected behaviour
                }
            }
        }
    }

    @Test
    public void testTransformFunctionInvalidBounds() {
        final int n = 128;
        final UnivariateFunction f = new Sin();
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                final FastFourierTransformer fft;
                fft = new FastFourierTransformer(norm[i]);
                try {
                    fft.transform(f, Math.PI, 0.0, n, type[j]);
                    Assert.fail(norm[i] + ", " + type[j] +
                        ": NumberIsTooLargeException was expected");
                } catch (NumberIsTooLargeException e) {
                    // Expected behaviour
                }
            }
        }
    }

    /*
     * Utility methods for checking (successful) transforms.
     */

    private static Complex[] createComplexData(final int n) {
        final Random random = new Random(SEED);
        final Complex[] data = new Complex[n];
        for (int i = 0; i < n; i++) {
            final double re = 2.0 * random.nextDouble() - 1.0;
            final double im = 2.0 * random.nextDouble() - 1.0;
            data[i] = new Complex(re, im);
        }
        return data;
    }

    private static double[] createRealData(final int n) {
        final Random random = new Random(SEED);
        final double[] data = new double[n];
        for (int i = 0; i < n; i++) {
            data[i] = 2.0 * random.nextDouble() - 1.0;
        }
        return data;
    }

    /** Naive implementation of DFT, for reference. */
    private static Complex[] dft(final Complex[] x, final int sgn) {
        final int n = x.length;
        final double[] cos = new double[n];
        final double[] sin = new double[n];
        final Complex[] y = new Complex[n];
        for (int i = 0; i < n; i++) {
            final double arg = 2.0 * FastMath.PI * i / n;
            cos[i] = FastMath.cos(arg);
            sin[i] = FastMath.sin(arg);
        }
        for (int i = 0; i < n; i++) {
            double yr = 0.0;
            double yi = 0.0;
            for (int j = 0; j < n; j++) {
                final int index = (i * j) % n;
                final double c = cos[index];
                final double s = sin[index];
                final double xr = x[j].getReal();
                final double xi = x[j].getImaginary();
                yr += c * xr - sgn * s * xi;
                yi += sgn * s * xr + c * xi;
            }
            y[i] = new Complex(yr, yi);
        }
        return y;
    }

    private static void doTestTransformComplex(final int n, final double tol,
        final DftNormalization normalization,
        final TransformType type) {
        final FastFourierTransformer fft;
        fft = new FastFourierTransformer(normalization);
        final Complex[] x = createComplexData(n);
        final Complex[] expected;
        final double s;
        if (type==TransformType.FORWARD) {
            expected = dft(x, -1);
            if (normalization == DftNormalization.STANDARD){
                s = 1.0;
            } else {
                s = 1.0 / FastMath.sqrt(n);
            }
        } else {
            expected = dft(x, 1);
            if (normalization == DftNormalization.STANDARD) {
                s = 1.0 / n;
            } else {
                s = 1.0 / FastMath.sqrt(n);
            }
        }
        final Complex[] actual = fft.transform(x, type);
        for (int i = 0; i < n; i++) {
            final String msg;
            msg = String.format("%s, %s, %d, %d", normalization, type, n, i);
            final double re = s * expected[i].getReal();
            Assert.assertEquals(msg, re, actual[i].getReal(),
                tol * FastMath.abs(re));
            final double im = s * expected[i].getImaginary();
            Assert.assertEquals(msg, im, actual[i].getImaginary(), tol *
                FastMath.abs(re));
        }
    }

    private static void doTestTransformReal(final int n, final double tol,
        final DftNormalization normalization,
        final TransformType type) {
        final FastFourierTransformer fft;
        fft = new FastFourierTransformer(normalization);
        final double[] x = createRealData(n);
        final Complex[] xc = new Complex[n];
        for (int i = 0; i < n; i++) {
            xc[i] = new Complex(x[i], 0.0);
        }
        final Complex[] expected;
        final double s;
        if (type == TransformType.FORWARD) {
            expected = dft(xc, -1);
            if (normalization == DftNormalization.STANDARD) {
                s = 1.0;
            } else {
                s = 1.0 / FastMath.sqrt(n);
            }
        } else {
            expected = dft(xc, 1);
            if (normalization == DftNormalization.STANDARD) {
                s = 1.0 / n;
            } else {
                s = 1.0 / FastMath.sqrt(n);
            }
        }
        final Complex[] actual = fft.transform(x, type);
        for (int i = 0; i < n; i++) {
            final String msg;
            msg = String.format("%s, %s, %d, %d", normalization, type, n, i);
            final double re = s * expected[i].getReal();
            Assert.assertEquals(msg, re, actual[i].getReal(),
                tol * FastMath.abs(re));
            final double im = s * expected[i].getImaginary();
            Assert.assertEquals(msg, im, actual[i].getImaginary(), tol *
                FastMath.abs(re));
        }
    }

    private static void doTestTransformFunction(final UnivariateFunction f,
        final double min, final double max, int n, final double tol,
        final DftNormalization normalization,
        final TransformType type) {
        final FastFourierTransformer fft;
        fft = new FastFourierTransformer(normalization);
        final Complex[] x = new Complex[n];
        for (int i = 0; i < n; i++) {
            final double t = min + i * (max - min) / n;
            x[i] = new Complex(f.value(t));
        }
        final Complex[] expected;
        final double s;
        if (type == TransformType.FORWARD) {
            expected = dft(x, -1);
            if (normalization == DftNormalization.STANDARD) {
                s = 1.0;
            } else {
                s = 1.0 / FastMath.sqrt(n);
            }
        } else {
            expected = dft(x, 1);
            if (normalization == DftNormalization.STANDARD) {
                s = 1.0 / n;
            } else {
                s = 1.0 / FastMath.sqrt(n);
            }
        }
        final Complex[] actual = fft.transform(f, min, max, n, type);
        for (int i = 0; i < n; i++) {
            final String msg = String.format("%d, %d", n, i);
            final double re = s * expected[i].getReal();
            Assert.assertEquals(msg, re, actual[i].getReal(),
                tol * FastMath.abs(re));
            final double im = s * expected[i].getImaginary();
            Assert.assertEquals(msg, im, actual[i].getImaginary(), tol *
                FastMath.abs(re));
        }
    }

    /*
     * Tests of standard transform (when data is valid).
     */

    @Test
    public void testTransformComplex() {
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                doTestTransformComplex(2, 1.0E-15, norm[i], type[j]);
                doTestTransformComplex(4, 1.0E-14, norm[i], type[j]);
                doTestTransformComplex(8, 1.0E-14, norm[i], type[j]);
                doTestTransformComplex(16, 1.0E-13, norm[i], type[j]);
                doTestTransformComplex(32, 1.0E-13, norm[i], type[j]);
                doTestTransformComplex(64, 1.0E-12, norm[i], type[j]);
                doTestTransformComplex(128, 1.0E-12, norm[i], type[j]);
            }
        }
    }

    @Test
    public void testStandardTransformReal() {
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                doTestTransformReal(2, 1.0E-15, norm[i], type[j]);
                doTestTransformReal(4, 1.0E-14, norm[i], type[j]);
                doTestTransformReal(8, 1.0E-14, norm[i], type[j]);
                doTestTransformReal(16, 1.0E-13, norm[i], type[j]);
                doTestTransformReal(32, 1.0E-13, norm[i], type[j]);
                doTestTransformReal(64, 1.0E-13, norm[i], type[j]);
                doTestTransformReal(128, 1.0E-11, norm[i], type[j]);
            }
        }
    }

    @Test
    public void testStandardTransformFunction() {
        final UnivariateFunction f = new Sinc();
        final double min = -FastMath.PI;
        final double max = FastMath.PI;
        final DftNormalization[] norm;
        norm = DftNormalization.values();
        final TransformType[] type;
        type = TransformType.values();
        for (int i = 0; i < norm.length; i++) {
            for (int j = 0; j < type.length; j++) {
                doTestTransformFunction(f, min, max, 2, 1.0E-15, norm[i], type[j]);
                doTestTransformFunction(f, min, max, 4, 1.0E-14, norm[i], type[j]);
                doTestTransformFunction(f, min, max, 8, 1.0E-14, norm[i], type[j]);
                doTestTransformFunction(f, min, max, 16, 1.0E-13, norm[i], type[j]);
                doTestTransformFunction(f, min, max, 32, 1.0E-13, norm[i], type[j]);
                doTestTransformFunction(f, min, max, 64, 1.0E-12, norm[i], type[j]);
                doTestTransformFunction(f, min, max, 128, 1.0E-11, norm[i], type[j]);
            }
        }
    }

    /*
     * Additional tests for 1D data.
     */

    /**
     * Test of transformer for the ad hoc data taken from Mathematica.
     */
    @Test
    public void testAdHocData() {
        FastFourierTransformer transformer;
        transformer = new FastFourierTransformer(DftNormalization.STANDARD);
        Complex result[]; double tolerance = 1E-12;

        double x[] = {1.3, 2.4, 1.7, 4.1, 2.9, 1.7, 5.1, 2.7};
        Complex y[] = {
            new Complex(21.9, 0.0),
            new Complex(-2.09497474683058, 1.91507575950825),
            new Complex(-2.6, 2.7),
            new Complex(-1.10502525316942, -4.88492424049175),
            new Complex(0.1, 0.0),
            new Complex(-1.10502525316942, 4.88492424049175),
            new Complex(-2.6, -2.7),
            new Complex(-2.09497474683058, -1.91507575950825)};

        result = transformer.transform(x, TransformType.FORWARD);
        for (int i = 0; i < result.length; i++) {
            Assert.assertEquals(y[i].getReal(), result[i].getReal(), tolerance);
            Assert.assertEquals(y[i].getImaginary(), result[i].getImaginary(), tolerance);
        }

        result = transformer.transform(y, TransformType.INVERSE);
        for (int i = 0; i < result.length; i++) {
            Assert.assertEquals(x[i], result[i].getReal(), tolerance);
            Assert.assertEquals(0.0, result[i].getImaginary(), tolerance);
        }

        double x2[] = {10.4, 21.6, 40.8, 13.6, 23.2, 32.8, 13.6, 19.2};
        TransformUtils.scaleArray(x2, 1.0 / FastMath.sqrt(x2.length));
        Complex y2[] = y;

        transformer = new FastFourierTransformer(DftNormalization.UNITARY);
        result = transformer.transform(y2, TransformType.FORWARD);
        for (int i = 0; i < result.length; i++) {
            Assert.assertEquals(x2[i], result[i].getReal(), tolerance);
            Assert.assertEquals(0.0, result[i].getImaginary(), tolerance);
        }

        result = transformer.transform(x2, TransformType.INVERSE);
        for (int i = 0; i < result.length; i++) {
            Assert.assertEquals(y2[i].getReal(), result[i].getReal(), tolerance);
            Assert.assertEquals(y2[i].getImaginary(), result[i].getImaginary(), tolerance);
        }
    }

    /**
     * Test of transformer for the sine function.
     */
    @Test
    public void testSinFunction() {
        UnivariateFunction f = new Sin();
        FastFourierTransformer transformer;
        transformer = new FastFourierTransformer(DftNormalization.STANDARD);
        Complex result[]; int N = 1 << 8;
        double min, max, tolerance = 1E-12;

        min = 0.0; max = 2.0 * FastMath.PI;
        result = transformer.transform(f, min, max, N, TransformType.FORWARD);
        Assert.assertEquals(0.0, result[1].getReal(), tolerance);
        Assert.assertEquals(-(N >> 1), result[1].getImaginary(), tolerance);
        Assert.assertEquals(0.0, result[N-1].getReal(), tolerance);
        Assert.assertEquals(N >> 1, result[N-1].getImaginary(), tolerance);
        for (int i = 0; i < N-1; i += (i == 0 ? 2 : 1)) {
            Assert.assertEquals(0.0, result[i].getReal(), tolerance);
            Assert.assertEquals(0.0, result[i].getImaginary(), tolerance);
        }

        min = -FastMath.PI; max = FastMath.PI;
        result = transformer.transform(f, min, max, N, TransformType.INVERSE);
        Assert.assertEquals(0.0, result[1].getReal(), tolerance);
        Assert.assertEquals(-0.5, result[1].getImaginary(), tolerance);
        Assert.assertEquals(0.0, result[N-1].getReal(), tolerance);
        Assert.assertEquals(0.5, result[N-1].getImaginary(), tolerance);
        for (int i = 0; i < N-1; i += (i == 0 ? 2 : 1)) {
            Assert.assertEquals(0.0, result[i].getReal(), tolerance);
            Assert.assertEquals(0.0, result[i].getImaginary(), tolerance);
        }
    }

    /*
     * Additional tests for 2D data.
     */

    @SuppressWarnings("deprecation")
    @Test
    public void test2DData() {
        FastFourierTransformer transformer;
        transformer = new FastFourierTransformer(DftNormalization.STANDARD);

        double tolerance = 1E-12;
        Complex[][] input = new Complex[][] {new Complex[] {new Complex(1, 0),
                                                            new Complex(2, 0)},
                                             new Complex[] {new Complex(3, 1),
                                                            new Complex(4, 2)}};
        Complex[][] goodOutput = new Complex[][] {new Complex[] {new Complex(5,
                1.5), new Complex(-1, -.5)}, new Complex[] {new Complex(-2,
                -1.5), new Complex(0, .5)}};
        for (int i = 0; i < goodOutput.length; i++) {
            TransformUtils.scaleArray(
                goodOutput[i],
                FastMath.sqrt(goodOutput[i].length) *
                    FastMath.sqrt(goodOutput.length));
        }
        Complex[][] output = (Complex[][])transformer.mdfft(input, TransformType.FORWARD);
        Complex[][] output2 = (Complex[][])transformer.mdfft(output, TransformType.INVERSE);

        Assert.assertEquals(input.length, output.length);
        Assert.assertEquals(input.length, output2.length);
        Assert.assertEquals(input[0].length, output[0].length);
        Assert.assertEquals(input[0].length, output2[0].length);
        Assert.assertEquals(input[1].length, output[1].length);
        Assert.assertEquals(input[1].length, output2[1].length);

        for (int i = 0; i < input.length; i++) {
            for (int j = 0; j < input[0].length; j++) {
                Assert.assertEquals(input[i][j].getImaginary(), output2[i][j].getImaginary(),
                             tolerance);
                Assert.assertEquals(input[i][j].getReal(), output2[i][j].getReal(), tolerance);
                Assert.assertEquals(goodOutput[i][j].getImaginary(), output[i][j].getImaginary(),
                             tolerance);
                Assert.assertEquals(goodOutput[i][j].getReal(), output[i][j].getReal(), tolerance);
            }
        }
    }

    @SuppressWarnings("deprecation")
    @Test
    public void test2DDataUnitary() {
        FastFourierTransformer transformer;
        transformer = new FastFourierTransformer(DftNormalization.UNITARY);
        double tolerance = 1E-12;
        Complex[][] input = new Complex[][] {new Complex[] {new Complex(1, 0),
                                                            new Complex(2, 0)},
                                             new Complex[] {new Complex(3, 1),
                                                            new Complex(4, 2)}};
        Complex[][] goodOutput = new Complex[][] {new Complex[] {new Complex(5,
                1.5), new Complex(-1, -.5)}, new Complex[] {new Complex(-2,
                -1.5), new Complex(0, .5)}};
        Complex[][] output = (Complex[][])transformer.mdfft(input, TransformType.FORWARD);
        Complex[][] output2 = (Complex[][])transformer.mdfft(output, TransformType.INVERSE);

        Assert.assertEquals(input.length, output.length);
        Assert.assertEquals(input.length, output2.length);
        Assert.assertEquals(input[0].length, output[0].length);
        Assert.assertEquals(input[0].length, output2[0].length);
        Assert.assertEquals(input[1].length, output[1].length);
        Assert.assertEquals(input[1].length, output2[1].length);

        for (int i = 0; i < input.length; i++) {
            for (int j = 0; j < input[0].length; j++) {
                Assert.assertEquals(input[i][j].getImaginary(), output2[i][j].getImaginary(),
                             tolerance);
                Assert.assertEquals(input[i][j].getReal(), output2[i][j].getReal(), tolerance);
                Assert.assertEquals(goodOutput[i][j].getImaginary(), output[i][j].getImaginary(),
                             tolerance);
                Assert.assertEquals(goodOutput[i][j].getReal(), output[i][j].getReal(), tolerance);
            }
        }
    }

}

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