commons-math-transform/src/test/java/org/apache/commons/math4/transform/FastSineTransformerTest.java - commons-math - Git at Google

 /*
  * 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.math4.transform;

 import java.util.Arrays;
 import java.util.Collection;
 import java.util.function.DoubleUnaryOperator;

 import org.junit.Assert;
 import org.junit.Test;
 import org.junit.runner.RunWith;
 import org.junit.runners.Parameterized;
 import org.junit.runners.Parameterized.Parameters;

 import org.apache.commons.math3.analysis.UnivariateFunction;
 import org.apache.commons.math3.analysis.function.Sin;
 import org.apache.commons.math3.analysis.function.Sinc;

 /**
  * Test case for {@link FastSineTransform}.
  * <p>
  * FST algorithm is exact, the small tolerance number is used only
  * to account for round-off errors.
  */
 @RunWith(value = Parameterized.class)
 public final class FastSineTransformerTest extends RealTransformerAbstractTest {

     private final FastSineTransform.Norm normalization;

     private final int[] invalidDataSize;

     private final double[] relativeTolerance;

     private final int[] validDataSize;

     public FastSineTransformerTest(final FastSineTransform.Norm normalization) {
         this.normalization = normalization;
         this.validDataSize = new int[] {
             1, 2, 4, 8, 16, 32, 64, 128
         };
         this.invalidDataSize = new int[] {
             129
         };
         this.relativeTolerance = new double[] {
             1e-15, 1e-15, 1e-14, 1e-14, 1e-13, 1e-12, 1e-11, 1e-11
         };
     }

     /**
      * Returns an array containing {@code true, false} in order to check both
      * standard and orthogonal DSTs.
      *
      * @return an array of parameters for this parameterized test.
      */
     @Parameters
     public static Collection<Object[]> data() {
         final FastSineTransform.Norm[] normalization = FastSineTransform.Norm.values();
         final Object[][] data = new FastSineTransform.Norm[normalization.length][1];
         for (int i = 0; i < normalization.length; i++) {
             data[i][0] = normalization[i];
         }
         return Arrays.asList(data);
     }

     /**
      * {@inheritDoc}
      *
      * Overriding the default implementation allows to ensure that the first
      * element of the data set is zero.
      */
     @Override
     double[] createRealData(final int n) {
         final double[] data = super.createRealData(n);
         data[0] = 0;
         return data;
     }

     @Override
     RealTransform createRealTransformer(boolean inverse) {
         return new FastSineTransform(normalization, inverse);
     }

     @Override
     int getInvalidDataSize(final int i) {
         return invalidDataSize[i];
     }

     @Override
     int getNumberOfInvalidDataSizes() {
         return invalidDataSize.length;
     }

     @Override
     int getNumberOfValidDataSizes() {
         return validDataSize.length;
     }

     @Override
     double getRelativeTolerance(final int i) {
         return relativeTolerance[i];
     }

     @Override
     int getValidDataSize(final int i) {
         return validDataSize[i];
     }

     @Override
     DoubleUnaryOperator getValidFunction() {
         final UnivariateFunction sinc = new Sinc();
         return x -> sinc.value(x);
     }

     @Override
     double getValidLowerBound() {
         return 0.0;
     }

     @Override
     double getValidUpperBound() {
         return Math.PI;
     }

     @Override
     double[] transform(final double[] x, boolean inverse) {
         final int n = x.length;
         final double[] y = new double[n];
         final double[] sin = new double[2 * n];
         for (int i = 0; i < sin.length; i++) {
             sin[i] = Math.sin(Math.PI * i / n);
         }
         for (int j = 0; j < n; j++) {
             double yj = 0.0;
             for (int i = 0; i < n; i++) {
                 yj += x[i] * sin[(i * j) % sin.length];
             }
             y[j] = yj;
         }
         final double s;
         if (!inverse) {
             if (normalization == FastSineTransform.Norm.STD) {
                 s = 1;
             } else if (normalization == FastSineTransform.Norm.ORTHO) {
                 s = Math.sqrt(2d / n);
             } else {
                 throw new IllegalStateException();
             }
         } else {
             if (normalization == FastSineTransform.Norm.STD) {
                 s = 2d / n;
             } else if (normalization == FastSineTransform.Norm.ORTHO) {
                 s = Math.sqrt(2d / n);
             } else {
                 throw new IllegalStateException();
             }
         }

         TransformUtils.scaleInPlace(y, s);
         return y;
     }

     // Additional tests.

     @Test
     public void testTransformRealFirstElementNotZero() {
         final double[] data = new double[] {
             1, 1, 1, 1
         };
         for (boolean type : new boolean[] {true, false}) {
             try {
                 final RealTransform transformer = createRealTransformer(type);
                 transformer.apply(data);
                 Assert.fail("type=" + type);
             } catch (IllegalArgumentException e) {
                 // Expected: do nothing
             }
         }
     }

     // Additional (legacy) tests.

     /**
      * Test of transformer for the ad hoc data.
      */
     @Test
     public void testAdHocData() {
         FastSineTransform transformer;
         double tolerance = 1e-12;

         final double[] x = {
             0, 1, 2, 3, 4, 5, 6, 7
         };
         final double[] y = {
             0.0, 20.1093579685034, -9.65685424949238,
             5.98642305066196, -4.0, 2.67271455167720,
             -1.65685424949238, 0.795649469518633
         };

         transformer = new FastSineTransform(FastSineTransform.Norm.STD);
         double[] result = transformer.apply(x);
         for (int i = 0; i < result.length; i++) {
             Assert.assertEquals(y[i], result[i], tolerance);
         }

         transformer = new FastSineTransform(FastSineTransform.Norm.STD, true);
         result = transformer.apply(y);
         for (int i = 0; i < result.length; i++) {
             Assert.assertEquals(x[i], result[i], tolerance);
         }

         TransformUtils.scaleInPlace(x, Math.sqrt(x.length / 2d));
         transformer = new FastSineTransform(FastSineTransform.Norm.ORTHO);

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

         transformer = new FastSineTransform(FastSineTransform.Norm.ORTHO, true);
         result = transformer.apply(x);
         for (int i = 0; i < result.length; i++) {
             Assert.assertEquals(y[i], result[i], tolerance);
         }
     }

     /**
      * Test of transformer for the sine function.
      */
     @Test
     public void testSinFunction() {
         final UnivariateFunction sinFunction = new Sin();
         final DoubleUnaryOperator f = x -> sinFunction.value(x);
         final FastSineTransform transformer = new FastSineTransform(FastSineTransform.Norm.STD);
         double tolerance = 1e-12;
         int size = 1 << 8;

         double min = 0.0;
         double max = 2 * Math.PI;
         double[] result = transformer.apply(f, min, max, size);
         Assert.assertEquals(size >> 1, result[2], tolerance);
         for (int i = 0; i < size; i += i == 1 ? 2 : 1) {
             Assert.assertEquals(0.0, result[i], tolerance);
         }

         min = -Math.PI;
         max = Math.PI;
         result = transformer.apply(f, min, max, size);
         Assert.assertEquals(-(size >> 1), result[2], tolerance);
         for (int i = 0; i < size; i += i == 1 ? 2 : 1) {
             Assert.assertEquals(0.0, result[i], tolerance);
         }
     }

     /**
      * Test of parameters for the transformer.
      */
     @Test
     public void testParameters() throws Exception {
         final UnivariateFunction sinFunction = new Sin();
         final DoubleUnaryOperator f = x -> sinFunction.value(x);
         final FastSineTransform transformer = new FastSineTransform(FastSineTransform.Norm.STD);

         try {
             // bad interval
             transformer.apply(f, 1, -1, 64);
             Assert.fail("Expecting IllegalArgumentException - bad interval");
         } catch (IllegalArgumentException ex) {
             // expected
         }
         try {
             // bad samples number
             transformer.apply(f, -1, 1, 0);
             Assert.fail("Expecting IllegalArgumentException - bad samples number");
         } catch (IllegalArgumentException ex) {
             // expected
         }
         try {
             // bad samples number
             transformer.apply(f, -1, 1, 100);
             Assert.fail("Expecting IllegalArgumentException - bad samples number");
         } catch (IllegalArgumentException ex) {
             // expected
         }
     }
 }
	/*
	* 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.math4.transform;

	import java.util.Arrays;
	import java.util.Collection;
	import java.util.function.DoubleUnaryOperator;

	import org.junit.Assert;
	import org.junit.Test;
	import org.junit.runner.RunWith;
	import org.junit.runners.Parameterized;
	import org.junit.runners.Parameterized.Parameters;

	import org.apache.commons.math3.analysis.UnivariateFunction;
	import org.apache.commons.math3.analysis.function.Sin;
	import org.apache.commons.math3.analysis.function.Sinc;

	/**
	* Test case for {@link FastSineTransform}.
	* <p>
	* FST algorithm is exact, the small tolerance number is used only
	* to account for round-off errors.
	*/
	@RunWith(value = Parameterized.class)
	public final class FastSineTransformerTest extends RealTransformerAbstractTest {

	private final FastSineTransform.Norm normalization;

	private final int[] invalidDataSize;

	private final double[] relativeTolerance;

	private final int[] validDataSize;

	public FastSineTransformerTest(final FastSineTransform.Norm normalization) {
	this.normalization = normalization;
	this.validDataSize = new int[] {
	1, 2, 4, 8, 16, 32, 64, 128
	};
	this.invalidDataSize = new int[] {
	129
	};
	this.relativeTolerance = new double[] {
	1e-15, 1e-15, 1e-14, 1e-14, 1e-13, 1e-12, 1e-11, 1e-11
	};
	}

	/**
	* Returns an array containing {@code true, false} in order to check both
	* standard and orthogonal DSTs.
	*
	* @return an array of parameters for this parameterized test.
	*/
	@Parameters
	public static Collection<Object[]> data() {
	final FastSineTransform.Norm[] normalization = FastSineTransform.Norm.values();
	final Object[][] data = new FastSineTransform.Norm[normalization.length][1];
	for (int i = 0; i < normalization.length; i++) {
	data[i][0] = normalization[i];
	}
	return Arrays.asList(data);
	}

	/**
	* {@inheritDoc}
	*
	* Overriding the default implementation allows to ensure that the first
	* element of the data set is zero.
	*/
	@Override
	double[] createRealData(final int n) {
	final double[] data = super.createRealData(n);
	data[0] = 0;
	return data;
	}

	@Override
	RealTransform createRealTransformer(boolean inverse) {
	return new FastSineTransform(normalization, inverse);
	}

	@Override
	int getInvalidDataSize(final int i) {
	return invalidDataSize[i];
	}

	@Override
	int getNumberOfInvalidDataSizes() {
	return invalidDataSize.length;
	}

	@Override
	int getNumberOfValidDataSizes() {
	return validDataSize.length;
	}

	@Override
	double getRelativeTolerance(final int i) {
	return relativeTolerance[i];
	}

	@Override
	int getValidDataSize(final int i) {
	return validDataSize[i];
	}

	@Override
	DoubleUnaryOperator getValidFunction() {
	final UnivariateFunction sinc = new Sinc();
	return x -> sinc.value(x);
	}

	@Override
	double getValidLowerBound() {
	return 0.0;
	}

	@Override
	double getValidUpperBound() {
	return Math.PI;
	}

	@Override
	double[] transform(final double[] x, boolean inverse) {
	final int n = x.length;
	final double[] y = new double[n];
	final double[] sin = new double[2 * n];
	for (int i = 0; i < sin.length; i++) {
	sin[i] = Math.sin(Math.PI * i / n);
	}
	for (int j = 0; j < n; j++) {
	double yj = 0.0;
	for (int i = 0; i < n; i++) {
	yj += x[i] * sin[(i * j) % sin.length];
	}
	y[j] = yj;
	}
	final double s;
	if (!inverse) {
	if (normalization == FastSineTransform.Norm.STD) {
	s = 1;
	} else if (normalization == FastSineTransform.Norm.ORTHO) {
	s = Math.sqrt(2d / n);
	} else {
	throw new IllegalStateException();
	}
	} else {
	if (normalization == FastSineTransform.Norm.STD) {
	s = 2d / n;
	} else if (normalization == FastSineTransform.Norm.ORTHO) {
	s = Math.sqrt(2d / n);
	} else {
	throw new IllegalStateException();
	}
	}

	TransformUtils.scaleInPlace(y, s);
	return y;
	}

	// Additional tests.

	@Test
	public void testTransformRealFirstElementNotZero() {
	final double[] data = new double[] {
	1, 1, 1, 1
	};
	for (boolean type : new boolean[] {true, false}) {
	try {
	final RealTransform transformer = createRealTransformer(type);
	transformer.apply(data);
	Assert.fail("type=" + type);
	} catch (IllegalArgumentException e) {
	// Expected: do nothing
	}
	}
	}

	// Additional (legacy) tests.

	/**
	* Test of transformer for the ad hoc data.
	*/
	@Test
	public void testAdHocData() {
	FastSineTransform transformer;
	double tolerance = 1e-12;

	final double[] x = {
	0, 1, 2, 3, 4, 5, 6, 7
	};
	final double[] y = {
	0.0, 20.1093579685034, -9.65685424949238,
	5.98642305066196, -4.0, 2.67271455167720,
	-1.65685424949238, 0.795649469518633
	};

	transformer = new FastSineTransform(FastSineTransform.Norm.STD);
	double[] result = transformer.apply(x);
	for (int i = 0; i < result.length; i++) {
	Assert.assertEquals(y[i], result[i], tolerance);
	}

	transformer = new FastSineTransform(FastSineTransform.Norm.STD, true);
	result = transformer.apply(y);
	for (int i = 0; i < result.length; i++) {
	Assert.assertEquals(x[i], result[i], tolerance);
	}

	TransformUtils.scaleInPlace(x, Math.sqrt(x.length / 2d));
	transformer = new FastSineTransform(FastSineTransform.Norm.ORTHO);

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

	transformer = new FastSineTransform(FastSineTransform.Norm.ORTHO, true);
	result = transformer.apply(x);
	for (int i = 0; i < result.length; i++) {
	Assert.assertEquals(y[i], result[i], tolerance);
	}
	}

	/**
	* Test of transformer for the sine function.
	*/
	@Test
	public void testSinFunction() {
	final UnivariateFunction sinFunction = new Sin();
	final DoubleUnaryOperator f = x -> sinFunction.value(x);
	final FastSineTransform transformer = new FastSineTransform(FastSineTransform.Norm.STD);
	double tolerance = 1e-12;
	int size = 1 << 8;

	double min = 0.0;
	double max = 2 * Math.PI;
	double[] result = transformer.apply(f, min, max, size);
	Assert.assertEquals(size >> 1, result[2], tolerance);
	for (int i = 0; i < size; i += i == 1 ? 2 : 1) {
	Assert.assertEquals(0.0, result[i], tolerance);
	}

	min = -Math.PI;
	max = Math.PI;
	result = transformer.apply(f, min, max, size);
	Assert.assertEquals(-(size >> 1), result[2], tolerance);
	for (int i = 0; i < size; i += i == 1 ? 2 : 1) {
	Assert.assertEquals(0.0, result[i], tolerance);
	}
	}

	/**
	* Test of parameters for the transformer.
	*/
	@Test
	public void testParameters() throws Exception {
	final UnivariateFunction sinFunction = new Sin();
	final DoubleUnaryOperator f = x -> sinFunction.value(x);
	final FastSineTransform transformer = new FastSineTransform(FastSineTransform.Norm.STD);

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