/*
* 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 org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.InsufficientDataException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
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.junit.Assert;
import org.junit.Test;
/**
* Test case for the piecewise bicubic interpolator.
*/
public final class PiecewiseBicubicSplineInterpolatorTest
{
/**
* 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" )
BivariateGridInterpolator interpolator = new PiecewiseBicubicSplineInterpolator();
try
{
interpolator.interpolate( null, yval, zval );
Assert.fail( "Failed to detect x null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
interpolator.interpolate( xval, null, zval );
Assert.fail( "Failed to detect y null pointer" );
}
catch ( NullArgumentException iae )
{
// Expected.
}
try
{
interpolator.interpolate( 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 };
interpolator.interpolate( 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 };
interpolator.interpolate( xval, yval1, zval );
Assert.fail( "Failed to detect insufficient y data" );
}
catch ( InsufficientDataException iae )
{
// Expected.
}
try
{
double zval1[][] = new double[4][4];
interpolator.interpolate( 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 };
interpolator.interpolate( 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 };
interpolator.interpolate( 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 };
interpolator.interpolate( 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 };
interpolator.interpolate( 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 testInterpolation1()
{
final int sz = 21;
double[] xval = new double[sz];
double[] yval = new double[sz];
// Coordinate values
final double delta = 1d / (sz - 1);
for ( int i = 0; i < sz; i++ )
{
xval[i] = -1 + 15 * i * delta;
yval[i] = -20 + 30 * i * delta;
}
// Function values
BivariateFunction f = new BivariateFunction()
{
public double value( double x, double y )
{
return 2 * x - 3 * y + 5;
}
};
double[][] zval = new double[xval.length][yval.length];
for ( int i = 0; i < xval.length; i++ )
{
for ( int j = 0; j < yval.length; j++ )
{
zval[i][j] = f.value(xval[i], yval[j]);
}
}
BivariateGridInterpolator interpolator = new PiecewiseBicubicSplineInterpolator();
BivariateFunction p = interpolator.interpolate(xval, yval, zval);
double x, y;
final RandomGenerator rng = new Well19937c(1234567L); // "tol" depends on the seed.
final UniformRealDistribution distX = new UniformRealDistribution( rng, xval[0], xval[xval.length - 1] );
final UniformRealDistribution distY = new UniformRealDistribution( rng, yval[0], yval[yval.length - 1] );
final int numSamples = 50;
final double tol = 2e-14;
for ( int i = 0; i < numSamples; i++ )
{
x = distX.sample();
for ( int j = 0; j < numSamples; j++ )
{
y = distY.sample();
// System.out.println(x + " " + y + " " + f.value(x, y) + " " + p.value(x, y));
Assert.assertEquals(f.value(x, y), p.value(x, y), tol);
}
// System.out.println();
}
}
/**
* Interpolating a paraboloid.
* <p>
* z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
*/
@Test
public void testInterpolation2()
{
final int sz = 21;
double[] xval = new double[sz];
double[] yval = new double[sz];
// Coordinate values
final double delta = 1d / (sz - 1);
for ( int i = 0; i < sz; i++ )
{
xval[i] = -1 + 15 * i * delta;
yval[i] = -20 + 30 * i * delta;
}
// Function values
BivariateFunction f = new BivariateFunction()
{
public double value( double x, double y )
{
return 2 * x * x - 3 * y * y + 4 * x * y - 5;
}
};
double[][] zval = new double[xval.length][yval.length];
for ( int i = 0; i < xval.length; i++ )
{
for ( int j = 0; j < yval.length; j++ )
{
zval[i][j] = f.value(xval[i], yval[j]);
}
}
BivariateGridInterpolator interpolator = new PiecewiseBicubicSplineInterpolator();
BivariateFunction p = interpolator.interpolate(xval, yval, zval);
double x, y;
final RandomGenerator rng = new Well19937c(1234567L); // "tol" depends on the seed.
final UniformRealDistribution distX = new UniformRealDistribution( rng, xval[0], xval[xval.length - 1] );
final UniformRealDistribution distY = new UniformRealDistribution( rng, yval[0], yval[yval.length - 1] );
final int numSamples = 50;
final double tol = 5e-13;
for ( int i = 0; i < numSamples; i++ )
{
x = distX.sample();
for ( int j = 0; j < numSamples; j++ )
{
y = distY.sample();
// System.out.println(x + " " + y + " " + f.value(x, y) + " " + p.value(x, y));
Assert.assertEquals(f.value(x, y), p.value(x, y), tol);
}
// System.out.println();
}
}
}