/*
 * 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.analysis.*;
import org.apache.commons.math.complex.*;
import org.apache.commons.math.MathException;
import junit.framework.TestCase;

/**
 * Testcase for fast Fourier transformer.
 * <p>
 * FFT algorithm is exact, the small tolerance number is used only to account
 * for round-off errors.
 * 
 * @version $Revision$ $Date$
 */
public final class FastFourierTransformerTest extends TestCase {

	/**
	 * Test of transformer for the ad hoc data taken from Mathematica.
	 */
	public void testAdHocData() {
		FastFourierTransformer transformer = new FastFourierTransformer();
		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);
		for (int i = 0; i < result.length; i++) {
			assertEquals(y[i].getReal(), result[i].getReal(), tolerance);
			assertEquals(y[i].getImaginary(), result[i].getImaginary(), tolerance);
		}

		result = transformer.inversetransform(y);
		for (int i = 0; i < result.length; i++) {
			assertEquals(x[i], result[i].getReal(), tolerance);
			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 };
		FastFourierTransformer.scaleArray(x2, 1.0 / Math.sqrt(x2.length));
		Complex y2[] = y;

		result = transformer.transform2(y2);
		for (int i = 0; i < result.length; i++) {
			assertEquals(x2[i], result[i].getReal(), tolerance);
			assertEquals(0.0, result[i].getImaginary(), tolerance);
		}

		result = transformer.inversetransform2(x2);
		for (int i = 0; i < result.length; i++) {
			assertEquals(y2[i].getReal(), result[i].getReal(), tolerance);
			assertEquals(y2[i].getImaginary(), result[i].getImaginary(), tolerance);
		}
	}

	public void test2DData() {
		FastFourierTransformer transformer = new FastFourierTransformer();
		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, true);
		Complex[][] output2 = (Complex[][]) transformer.mdfft(output, false);

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

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

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

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

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

	/**
	 * Test of parameters for the transformer.
	 */
	public void testParameters() throws Exception {
		UnivariateRealFunction f = new SinFunction();
		FastFourierTransformer transformer = new FastFourierTransformer();

		try {
			// bad interval
			transformer.transform(f, 1, -1, 64);
			fail("Expecting IllegalArgumentException - bad interval");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			// bad samples number
			transformer.transform(f, -1, 1, 0);
			fail("Expecting IllegalArgumentException - bad samples number");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			// bad samples number
			transformer.transform(f, -1, 1, 100);
			fail("Expecting IllegalArgumentException - bad samples number");
		} catch (IllegalArgumentException ex) {
			// expected
		}
	}
}
