/*
* 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 org.apache.commons.math4.analysis.UnivariateFunction;
import org.apache.commons.math4.analysis.function.Sin;
import org.apache.commons.math4.analysis.function.Sinc;
import org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.exception.MathIllegalStateException;
import org.apache.commons.math4.transform.DstNormalization;
import org.apache.commons.math4.transform.FastSineTransformer;
import org.apache.commons.math4.transform.RealTransformer;
import org.apache.commons.math4.transform.TransformType;
import org.apache.commons.math4.transform.TransformUtils;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
import org.junit.runner.RunWith;
import org.junit.runners.Parameterized;
import org.junit.runners.Parameterized.Parameters;
/**
* Test case for fast sine transformer.
* <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 DstNormalization normalization;
private final int[] invalidDataSize;
private final double[] relativeTolerance;
private final int[] validDataSize;
public FastSineTransformerTest(final DstNormalization 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 DstNormalization[] normalization = DstNormalization.values();
final Object[][] data = new DstNormalization[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] = 0.0;
return data;
}
@Override
RealTransformer createRealTransformer() {
return new FastSineTransformer(normalization);
}
@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
UnivariateFunction getValidFunction() {
return new Sinc();
}
@Override
double getValidLowerBound() {
return 0.0;
}
@Override
double getValidUpperBound() {
return FastMath.PI;
}
@Override
double[] transform(final double[] x, final TransformType type) {
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] = FastMath.sin(FastMath.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 (type == TransformType.FORWARD) {
if (normalization == DstNormalization.STANDARD_DST_I) {
s = 1.0;
} else if (normalization == DstNormalization.ORTHOGONAL_DST_I) {
s = FastMath.sqrt(2.0 / n);
} else {
throw new MathIllegalStateException();
}
} else if (type == TransformType.INVERSE) {
if (normalization == DstNormalization.STANDARD_DST_I) {
s = 2.0 / n;
} else if (normalization == DstNormalization.ORTHOGONAL_DST_I) {
s = FastMath.sqrt(2.0 / n);
} else {
throw new MathIllegalStateException();
}
} else {
/*
* Should never occur. This clause is a safeguard in case other
* types are used to TransformType (which should not be done).
*/
throw new MathIllegalStateException();
}
TransformUtils.scaleArray(y, s);
return y;
}
/*
* Additional tests.
*/
@Test
public void testTransformRealFirstElementNotZero() {
final TransformType[] type = TransformType.values();
final double[] data = new double[] {
1.0, 1.0, 1.0, 1.0
};
final RealTransformer transformer = createRealTransformer();
for (int j = 0; j < type.length; j++) {
try {
transformer.transform(data, type[j]);
Assert.fail(type[j].toString());
} catch (MathIllegalArgumentException e) {
// Expected: do nothing
}
}
}
/*
* Additional (legacy) tests.
*/
/**
* Test of transformer for the ad hoc data.
*/
@Test
public void testAdHocData() {
FastSineTransformer transformer;
transformer = new FastSineTransformer(DstNormalization.STANDARD_DST_I);
double result[], tolerance = 1E-12;
double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 };
double y[] = { 0.0, 20.1093579685034, -9.65685424949238,
5.98642305066196, -4.0, 2.67271455167720,
-1.65685424949238, 0.795649469518633 };
result = transformer.transform(x, TransformType.FORWARD);
for (int i = 0; i < result.length; i++) {
Assert.assertEquals(y[i], result[i], tolerance);
}
result = transformer.transform(y, TransformType.INVERSE);
for (int i = 0; i < result.length; i++) {
Assert.assertEquals(x[i], result[i], tolerance);
}
TransformUtils.scaleArray(x, FastMath.sqrt(x.length / 2.0));
transformer = new FastSineTransformer(DstNormalization.ORTHOGONAL_DST_I);
result = transformer.transform(y, TransformType.FORWARD);
for (int i = 0; i < result.length; i++) {
Assert.assertEquals(x[i], result[i], tolerance);
}
result = transformer.transform(x, TransformType.INVERSE);
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() {
UnivariateFunction f = new Sin();
FastSineTransformer transformer;
transformer = new FastSineTransformer(DstNormalization.STANDARD_DST_I);
double min, max, result[], tolerance = 1E-12; int N = 1 << 8;
min = 0.0; max = 2.0 * FastMath.PI;
result = transformer.transform(f, min, max, N, TransformType.FORWARD);
Assert.assertEquals(N >> 1, result[2], tolerance);
for (int i = 0; i < N; i += (i == 1 ? 2 : 1)) {
Assert.assertEquals(0.0, result[i], tolerance);
}
min = -FastMath.PI; max = FastMath.PI;
result = transformer.transform(f, min, max, N, TransformType.FORWARD);
Assert.assertEquals(-(N >> 1), result[2], tolerance);
for (int i = 0; i < N; i += (i == 1 ? 2 : 1)) {
Assert.assertEquals(0.0, result[i], tolerance);
}
}
/**
* Test of parameters for the transformer.
*/
@Test
public void testParameters() throws Exception {
UnivariateFunction f = new Sin();
FastSineTransformer transformer;
transformer = new FastSineTransformer(DstNormalization.STANDARD_DST_I);
try {
// bad interval
transformer.transform(f, 1, -1, 64, TransformType.FORWARD);
Assert.fail("Expecting MathIllegalArgumentException - bad interval");
} catch (MathIllegalArgumentException ex) {
// expected
}
try {
// bad samples number
transformer.transform(f, -1, 1, 0, TransformType.FORWARD);
Assert.fail("Expecting MathIllegalArgumentException - bad samples number");
} catch (MathIllegalArgumentException ex) {
// expected
}
try {
// bad samples number
transformer.transform(f, -1, 1, 100, TransformType.FORWARD);
Assert.fail("Expecting MathIllegalArgumentException - bad samples number");
} catch (MathIllegalArgumentException ex) {
// expected
}
}
}