commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/function/SincTest.java

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 * 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
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 * 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
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package org.apache.commons.math4.legacy.analysis.function;

import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math4.legacy.core.dfp.Dfp;
import org.apache.commons.math4.legacy.core.dfp.DfpField;
import org.apache.commons.math4.legacy.core.dfp.DfpMath;
import org.apache.commons.math4.core.jdkmath.JdkMath;
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() {
           @Override
           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 *= JdkMath.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() {
               @Override
            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);
       }
   }
}