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* 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.
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package org.apache.commons.math3.analysis.function;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.dfp.Dfp;
import org.apache.commons.math3.dfp.DfpField;
import org.apache.commons.math3.dfp.DfpMath;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class SincTest {
@Test
public void testShortcut() {
final Sinc s = new Sinc();
final UnivariateFunction f = new UnivariateFunction() {
public double value(double x) {
Dfp dfpX = new DfpField(25).newDfp(x);
return DfpMath.sin(dfpX).divide(dfpX).toDouble();
}
};
for (double x = 1e-30; x < 1e10; x *= 2) {
final double fX = f.value(x);
final double sX = s.value(x);
Assert.assertEquals("x=" + x, fX, sX, 2.0e-16);
}
}
@Test
public void testCrossings() {
final Sinc s = new Sinc(true);
final int numCrossings = 1000;
final double tol = 2e-16;
for (int i = 1; i <= numCrossings; i++) {
Assert.assertEquals("i=" + i, 0, s.value(i), tol);
}
}
@Test
public void testZero() {
final Sinc s = new Sinc();
Assert.assertEquals(1d, s.value(0), 0);
}
@Test
public void testEuler() {
final Sinc s = new Sinc();
final double x = 123456.789;
double prod = 1;
double xOverPow2 = x / 2;
while (xOverPow2 > 0) {
prod *= FastMath.cos(xOverPow2);
xOverPow2 /= 2;
}
Assert.assertEquals(prod, s.value(x), 1e-13);
}
@Test
public void testDerivativeZero() {
final DerivativeStructure s0 = new Sinc(true).value(new DerivativeStructure(1, 1, 0, 0.0));
Assert.assertEquals(0, s0.getPartialDerivative(1), 0);
}
@Test
public void testDerivatives1Dot2Unnormalized() {
DerivativeStructure s = new Sinc(false).value(new DerivativeStructure(1, 5, 0, 1.2));
Assert.assertEquals( 0.77669923830602195806, s.getPartialDerivative(0), 1.0e-16);
Assert.assertEquals(-0.34528456985779031701, s.getPartialDerivative(1), 1.0e-16);
Assert.assertEquals(-0.2012249552097047631, s.getPartialDerivative(2), 1.0e-16);
Assert.assertEquals( 0.2010975926270339262, s.getPartialDerivative(3), 4.0e-16);
Assert.assertEquals( 0.106373929549242204, s.getPartialDerivative(4), 1.0e-15);
Assert.assertEquals(-0.1412599110579478695, s.getPartialDerivative(5), 3.0e-15);
}
@Test
public void testDerivatives1Dot2Normalized() {
DerivativeStructure s = new Sinc(true).value(new DerivativeStructure(1, 5, 0, 1.2));
Assert.assertEquals(-0.15591488063143983888, s.getPartialDerivative(0), 6.0e-17);
Assert.assertEquals(-0.54425176145292298767, s.getPartialDerivative(1), 2.0e-16);
Assert.assertEquals(2.4459044611635856107, s.getPartialDerivative(2), 9.0e-16);
Assert.assertEquals(0.5391369206235909586, s.getPartialDerivative(3), 7.0e-16);
Assert.assertEquals(-16.984649869728849865, s.getPartialDerivative(4), 8.0e-15);
Assert.assertEquals(5.0980327462666316586, s.getPartialDerivative(5), 9.0e-15);
}
@Test
public void testDerivativeShortcut() {
final Sinc sinc = new Sinc();
final UnivariateFunction f = new UnivariateFunction() {
public double value(double x) {
Dfp dfpX = new DfpField(25).newDfp(x);
return DfpMath.cos(dfpX).subtract(DfpMath.sin(dfpX).divide(dfpX)).divide(dfpX).toDouble();
}
};
for (double x = 1e-30; x < 1e10; x *= 2) {
final double fX = f.value(x);
final DerivativeStructure sX = sinc.value(new DerivativeStructure(1, 1, 0, x));
Assert.assertEquals("x=" + x, fX, sX.getPartialDerivative(1), 3.0e-13);
}
}
}