/*
* 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.math3.analysis.interpolation;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertTrue;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.InsufficientDataException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.analysis.BivariateFunction;
import org.apache.commons.math3.distribution.UniformRealDistribution;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case for the piecewise bicubic function.
*/
public final class PiecewiseBicubicSplineInterpolatingFunctionTest
{
/**
* Test preconditions.
*/
@Test
public void testPreconditions()
{
double[] xval = new double[] { 3, 4, 5, 6.5, 7.5 };
double[] yval = new double[] { -4, -3, -1, 2.5, 3.5 };
double[][] zval = new double[xval.length][yval.length];
@SuppressWarnings("unused")
PiecewiseBicubicSplineInterpolatingFunction bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, yval, zval );
try
{
bcf = new PiecewiseBicubicSplineInterpolatingFunction( null, yval, zval );
Assert.fail( "Failed to detect x null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, null, zval );
Assert.fail( "Failed to detect y null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, yval, null );
Assert.fail( "Failed to detect z null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
double xval1[] = { 0.0, 1.0, 2.0, 3.0 };
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval1, yval, zval );
Assert.fail( "Failed to detect insufficient x data" );
}
catch ( InsufficientDataException iae )
{
// Expected.
}
try
{
double yval1[] = { 0.0, 1.0, 2.0, 3.0 };
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, yval1, zval );
Assert.fail( "Failed to detect insufficient y data" );
}
catch ( InsufficientDataException iae )
{
// Expected.
}
try
{
double zval1[][] = new double[4][4];
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, yval, zval1 );
Assert.fail( "Failed to detect insufficient z data" );
}
catch ( InsufficientDataException iae )
{
// Expected.
}
try
{
double xval1[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval1, yval, zval );
Assert.fail( "Failed to detect data set array with different sizes." );
}
catch ( DimensionMismatchException iae )
{
// Expected.
}
try
{
double yval1[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, yval1, zval );
Assert.fail( "Failed to detect data set array with different sizes." );
}
catch ( DimensionMismatchException iae )
{
// Expected.
}
// X values not sorted.
try
{
double xval1[] = { 0.0, 1.0, 0.5, 7.0, 3.5 };
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval1, yval, zval );
Assert.fail( "Failed to detect unsorted x arguments." );
}
catch ( NonMonotonicSequenceException iae )
{
// Expected.
}
// Y values not sorted.
try
{
double yval1[] = { 0.0, 1.0, 1.5, 0.0, 3.0 };
bcf = new PiecewiseBicubicSplineInterpolatingFunction( xval, yval1, zval );
Assert.fail( "Failed to detect unsorted y arguments." );
}
catch ( NonMonotonicSequenceException iae )
{
// Expected.
}
}
/**
* Interpolating a plane.
* <p>
* z = 2 x - 3 y + 5
*/
@Test
public void testInterpolatePlane()
{
final int numberOfElements = 10;
final double minimumX = -10;
final double maximumX = 10;
final double minimumY = -10;
final double maximumY = 10;
final int numberOfSamples = 100;
final double interpolationTolerance = 7e-15;
final double maxTolerance = 6e-14;
// Function values
BivariateFunction f = new BivariateFunction()
{
public double value( double x, double y )
{
return 2 * x - 3 * y + 5;
}
};
testInterpolation( minimumX, maximumX, minimumY, maximumY, numberOfElements, numberOfSamples, f,
interpolationTolerance, maxTolerance );
}
/**
* Interpolating a paraboloid.
* <p>
* z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
*/
@Test
public void testInterpolationParabaloid()
{
final int numberOfElements = 10;
final double minimumX = -10;
final double maximumX = 10;
final double minimumY = -10;
final double maximumY = 10;
final int numberOfSamples = 100;
final double interpolationTolerance = 2e-14;
final double maxTolerance = 6e-14;
// Function values
BivariateFunction f = new BivariateFunction()
{
public double value( double x, double y )
{
return 2 * x * x - 3 * y * y + 4 * x * y - 5;
}
};
testInterpolation( minimumX, maximumX, minimumY, maximumY, numberOfElements, numberOfSamples, f,
interpolationTolerance, maxTolerance );
}
private void testInterpolation( double minimumX, double maximumX, double minimumY, double maximumY,
int numberOfElements, int numberOfSamples, BivariateFunction f, double tolerance,
double maxTolerance )
{
double expected;
double actual;
double currentX;
double currentY;
final double deltaX = ( maximumX - minimumX ) / ( (double) numberOfElements );
final double deltaY = ( maximumY - minimumY ) / ( (double) numberOfElements );
double xValues[] = new double[numberOfElements];
double yValues[] = new double[numberOfElements];
double zValues[][] = new double[numberOfElements][numberOfElements];
for ( int i = 0; i < numberOfElements; i++ )
{
xValues[i] = minimumX + deltaX * (double) i;
for ( int j = 0; j < numberOfElements; j++ )
{
yValues[j] = minimumY + deltaY * (double) j;
zValues[i][j] = f.value( xValues[i], yValues[j] );
}
}
BivariateFunction interpolation = new PiecewiseBicubicSplineInterpolatingFunction( xValues, yValues, zValues );
for ( int i = 0; i < numberOfElements; i++ )
{
currentX = xValues[i];
for ( int j = 0; j < numberOfElements; j++ )
{
currentY = yValues[j];
expected = f.value( currentX, currentY );
actual = interpolation.value( currentX, currentY );
assertTrue( Precision.equals( expected, actual ) );
}
}
final RandomGenerator rng = new Well19937c( 1234567L ); // "tol" depends on the seed.
final UniformRealDistribution distX =
new UniformRealDistribution( rng, xValues[0], xValues[xValues.length - 1] );
final UniformRealDistribution distY =
new UniformRealDistribution( rng, yValues[0], yValues[yValues.length - 1] );
double sumError = 0;
for ( int i = 0; i < numberOfSamples; i++ )
{
currentX = distX.sample();
currentY = distY.sample();
expected = f.value( currentX, currentY );
actual = interpolation.value( currentX, currentY );
sumError += FastMath.abs( actual - expected );
assertEquals( expected, actual, maxTolerance );
}
assertEquals( 0.0, ( sumError / (double) numberOfSamples ), tolerance );
}
}