/*
* 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.analysis.interpolation;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertTrue;
import org.apache.commons.math4.analysis.UnivariateFunction;
import org.apache.commons.math4.distribution.RealDistribution;
import org.apache.commons.math4.distribution.UniformRealDistribution;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.NonMonotonicSequenceException;
import org.apache.commons.math4.exception.NullArgumentException;
import org.apache.commons.math4.exception.NumberIsTooSmallException;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.numbers.core.Precision;
import org.junit.Assert;
import org.junit.Test;
public class AkimaSplineInterpolatorTest
{
@Test
public void testIllegalArguments()
{
// Data set arrays of different size.
UnivariateInterpolator i = new AkimaSplineInterpolator();
try
{
double yval[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
i.interpolate( null, yval );
Assert.fail( "Failed to detect x null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
double xval[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
i.interpolate( xval, null );
Assert.fail( "Failed to detect y null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
double xval[] = { 0.0, 1.0, 2.0, 3.0 };
double yval[] = { 0.0, 1.0, 2.0, 3.0 };
i.interpolate( xval, yval );
Assert.fail( "Failed to detect insufficient data" );
}
catch ( NumberIsTooSmallException iae )
{
// Expected.
}
try
{
double xval[] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
double yval[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
i.interpolate( xval, yval );
Assert.fail( "Failed to detect data set array with different sizes." );
}
catch ( DimensionMismatchException iae )
{
// Expected.
}
// X values not sorted.
try
{
double xval[] = { 0.0, 1.0, 0.5, 7.0, 3.5, 2.2, 8.0 };
double yval[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
i.interpolate( xval, yval );
Assert.fail( "Failed to detect unsorted arguments." );
}
catch ( NonMonotonicSequenceException iae )
{
// Expected.
}
}
/*
* Interpolate a straight line. <p> y = 2 x - 5 <p> Tolerances determined by performing same calculation using
* Math.NET over ten runs of 100 random number draws for the same function over the same span with the same number
* of elements
*/
@Test
public void testInterpolateLine()
{
final int numberOfElements = 10;
final double minimumX = -10;
final double maximumX = 10;
final int numberOfSamples = 100;
final double interpolationTolerance = 1e-15;
final double maxTolerance = 1e-15;
UnivariateFunction f = new UnivariateFunction()
{
@Override
public double value( double x )
{
return 2 * x - 5;
}
};
testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance,
maxTolerance );
}
/*
* Interpolate a straight line. <p> y = 3 x<sup>2</sup> - 5 x + 7 <p> Tolerances determined by performing same
* calculation using Math.NET over ten runs of 100 random number draws for the same function over the same span with
* the same number of elements
*/
@Test
public void testInterpolateParabola()
{
final int numberOfElements = 10;
final double minimumX = -10;
final double maximumX = 10;
final int numberOfSamples = 100;
final double interpolationTolerance = 7e-15;
final double maxTolerance = 6e-14;
UnivariateFunction f = new UnivariateFunction()
{
@Override
public double value( double x )
{
return ( 3 * x * x ) - ( 5 * x ) + 7;
}
};
testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance,
maxTolerance );
}
/*
* Interpolate a straight line. <p> y = 3 x<sup>3</sup> - 0.5 x<sup>2</sup> + x - 1 <p> Tolerances determined by
* performing same calculation using Math.NET over ten runs of 100 random number draws for the same function over
* the same span with the same number of elements
*/
@Test
public void testInterpolateCubic()
{
final int numberOfElements = 10;
final double minimumX = -3;
final double maximumX = 3;
final int numberOfSamples = 100;
final double interpolationTolerance = 0.37;
final double maxTolerance = 3.8;
UnivariateFunction f = new UnivariateFunction()
{
@Override
public double value( double x )
{
return ( 3 * x * x * x ) - ( 0.5 * x * x ) + ( 1 * x ) - 1;
}
};
testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance,
maxTolerance );
}
private void testInterpolation( double minimumX, double maximumX, int numberOfElements, int numberOfSamples,
UnivariateFunction f, double tolerance, double maxTolerance )
{
double expected;
double actual;
double currentX;
final double delta = ( maximumX - minimumX ) / ( (double) numberOfElements );
double xValues[] = new double[numberOfElements];
double yValues[] = new double[numberOfElements];
for ( int i = 0; i < numberOfElements; i++ )
{
xValues[i] = minimumX + delta * (double) i;
yValues[i] = f.value( xValues[i] );
}
UnivariateFunction interpolation = new AkimaSplineInterpolator().interpolate( xValues, yValues );
for ( int i = 0; i < numberOfElements; i++ )
{
currentX = xValues[i];
expected = f.value( currentX );
actual = interpolation.value( currentX );
assertTrue( Precision.equals( expected, actual ) );
}
final UniformRandomProvider rng = RandomSource.create(RandomSource.WELL_19937_C, 1234567L); // "tol" depends on the seed.
final RealDistribution.Sampler distX =
new UniformRealDistribution(xValues[0], xValues[xValues.length - 1]).createSampler(rng);
double sumError = 0;
for ( int i = 0; i < numberOfSamples; i++ )
{
currentX = distX.sample();
expected = f.value( currentX );
actual = interpolation.value( currentX );
sumError += FastMath.abs( actual - expected );
assertEquals( expected, actual, maxTolerance );
}
assertEquals( 0.0, ( sumError / (double) numberOfSamples ), tolerance );
}
}