/*
* 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 org.apache.commons.math4.analysis.BivariateFunction;
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.InsufficientDataException;
import org.apache.commons.math4.exception.NonMonotonicSequenceException;
import org.apache.commons.math4.exception.NullArgumentException;
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;
/**
* 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 testPlane() {
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() {
@Override
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 testParabaloid() {
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 = 1e-13;
final double maxTolerance = 6e-14;
// Function values
BivariateFunction f = new BivariateFunction() {
@Override
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);
}
/**
* @param minimumX Lower bound of interpolation range along the x-coordinate.
* @param maximumX Higher bound of interpolation range along the x-coordinate.
* @param minimumY Lower bound of interpolation range along the y-coordinate.
* @param maximumY Higher bound of interpolation range along the y-coordinate.
* @param numberOfElements Number of data points (along each dimension).
* @param numberOfSamples Number of test points.
* @param f Function to test.
* @param meanTolerance Allowed average error (mean error on all interpolated values).
* @param maxTolerance Allowed error on each interpolated value.
*/
private void testInterpolation(double minimumX,
double maximumX,
double minimumY,
double maximumY,
int numberOfElements,
int numberOfSamples,
BivariateFunction f,
double meanTolerance,
double maxTolerance) {
double expected;
double actual;
double currentX;
double currentY;
final double deltaX = (maximumX - minimumX) / ((double) numberOfElements);
final double deltaY = (maximumY - minimumY) / ((double) numberOfElements);
final double[] xValues = new double[numberOfElements];
final double[] yValues = new double[numberOfElements];
final 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]);
}
}
final 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);
Assert.assertTrue(Precision.equals(expected, actual));
}
}
final UniformRandomProvider rng = RandomSource.create(RandomSource.WELL_19937_C, 1234567L);
final RealDistribution.Sampler distX = new UniformRealDistribution(xValues[0], xValues[xValues.length - 1]).createSampler(rng);
final RealDistribution.Sampler distY = new UniformRealDistribution(yValues[0], yValues[yValues.length - 1]).createSampler(rng);
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);
Assert.assertEquals(expected, actual, maxTolerance);
}
final double meanError = sumError / numberOfSamples;
Assert.assertEquals(0, meanError, meanTolerance);
}
}