/*
* 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.MathIllegalArgumentException;
import org.apache.commons.math4.exception.OutOfRangeException;
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 bicubic function.
*/
public final class BicubicInterpolatingFunctionTest {
/**
* Test preconditions.
*/
@Test
public void testPreconditions() {
double[] xval = new double[] {3, 4, 5, 6.5};
double[] yval = new double[] {-4, -3, -1, 2.5};
double[][] zval = new double[xval.length][yval.length];
@SuppressWarnings("unused")
BivariateFunction bcf = new BicubicInterpolatingFunction(xval, yval, zval,
zval, zval, zval);
double[] wxval = new double[] {3, 2, 5, 6.5};
try {
bcf = new BicubicInterpolatingFunction(wxval, yval, zval, zval, zval, zval);
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException e) {
// Expected
}
double[] wyval = new double[] {-4, -1, -1, 2.5};
try {
bcf = new BicubicInterpolatingFunction(xval, wyval, zval, zval, zval, zval);
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException e) {
// Expected
}
double[][] wzval = new double[xval.length][yval.length - 1];
try {
bcf = new BicubicInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
try {
bcf = new BicubicInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
try {
bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
try {
bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
wzval = new double[xval.length - 1][yval.length];
try {
bcf = new BicubicInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
try {
bcf = new BicubicInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
try {
bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
try {
bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
}
@Test
public void testIsValidPoint() {
final double xMin = -12;
final double xMax = 34;
final double yMin = 5;
final double yMax = 67;
final double[] xval = new double[] { xMin, xMax };
final double[] yval = new double[] { yMin, yMax };
final double[][] f = new double[][] { { 1, 2 },
{ 3, 4 } };
final double[][] dFdX = f;
final double[][] dFdY = f;
final double[][] dFdXdY = f;
final BicubicInterpolatingFunction bcf
= new BicubicInterpolatingFunction(xval, yval, f,
dFdX, dFdY, dFdXdY);
double x, y;
x = xMin;
y = yMin;
Assert.assertTrue(bcf.isValidPoint(x, y));
// Ensure that no exception is thrown.
bcf.value(x, y);
x = xMax;
y = yMax;
Assert.assertTrue(bcf.isValidPoint(x, y));
// Ensure that no exception is thrown.
bcf.value(x, y);
final double xRange = xMax - xMin;
final double yRange = yMax - yMin;
x = xMin + xRange / 3.4;
y = yMin + yRange / 1.2;
Assert.assertTrue(bcf.isValidPoint(x, y));
// Ensure that no exception is thrown.
bcf.value(x, y);
final double small = 1e-8;
x = xMin - small;
y = yMax;
Assert.assertFalse(bcf.isValidPoint(x, y));
// Ensure that an exception would have been thrown.
try {
bcf.value(x, y);
Assert.fail("OutOfRangeException expected");
} catch (OutOfRangeException expected) {}
x = xMin;
y = yMax + small;
Assert.assertFalse(bcf.isValidPoint(x, y));
// Ensure that an exception would have been thrown.
try {
bcf.value(x, y);
Assert.fail("OutOfRangeException expected");
} catch (OutOfRangeException 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 = 1000;
final double interpolationTolerance = 1e-15;
final double maxTolerance = 1e-14;
// Function values
BivariateFunction f = new BivariateFunction() {
@Override
public double value(double x, double y) {
return 2 * x - 3 * y + 5;
}
};
BivariateFunction dfdx = new BivariateFunction() {
@Override
public double value(double x, double y) {
return 2;
}
};
BivariateFunction dfdy = new BivariateFunction() {
@Override
public double value(double x, double y) {
return -3;
}
};
BivariateFunction d2fdxdy = new BivariateFunction() {
@Override
public double value(double x, double y) {
return 0;
}
};
testInterpolation(minimumX,
maximumX,
minimumY,
maximumY,
numberOfElements,
numberOfSamples,
f,
dfdx,
dfdy,
d2fdxdy,
interpolationTolerance,
maxTolerance,
false);
}
/**
* Interpolating a paraboloid.
* <p>
* z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
*/
@Test
public void testParaboloid() {
final int numberOfElements = 10;
final double minimumX = -10;
final double maximumX = 10;
final double minimumY = -10;
final double maximumY = 10;
final int numberOfSamples = 1000;
final double interpolationTolerance = 2e-14;
final double maxTolerance = 1e-12;
// 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;
}
};
BivariateFunction dfdx = new BivariateFunction() {
@Override
public double value(double x, double y) {
return 4 * (x + y);
}
};
BivariateFunction dfdy = new BivariateFunction() {
@Override
public double value(double x, double y) {
return 4 * x - 6 * y;
}
};
BivariateFunction d2fdxdy = new BivariateFunction() {
@Override
public double value(double x, double y) {
return 4;
}
};
testInterpolation(minimumX,
maximumX,
minimumY,
maximumY,
numberOfElements,
numberOfSamples,
f,
dfdx,
dfdy,
d2fdxdy,
interpolationTolerance,
maxTolerance,
false);
}
/**
* @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 dfdx Partial derivative w.r.t. x of the function to test.
* @param dfdy Partial derivative w.r.t. y of the function to test.
* @param d2fdxdy Second partial cross-derivative of the 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,
BivariateFunction dfdx,
BivariateFunction dfdy,
BivariateFunction d2fdxdy,
double meanTolerance,
double maxTolerance,
boolean print) {
double expected;
double actual;
double currentX;
double currentY;
final double deltaX = (maximumX - minimumX) / numberOfElements;
final double deltaY = (maximumY - minimumY) / numberOfElements;
final double[] xValues = new double[numberOfElements];
final double[] yValues = new double[numberOfElements];
final double[][] zValues = new double[numberOfElements][numberOfElements];
final double[][] dzdx = new double[numberOfElements][numberOfElements];
final double[][] dzdy = new double[numberOfElements][numberOfElements];
final double[][] d2zdxdy = new double[numberOfElements][numberOfElements];
for (int i = 0; i < numberOfElements; i++) {
xValues[i] = minimumX + deltaX * i;
final double x = xValues[i];
for (int j = 0; j < numberOfElements; j++) {
yValues[j] = minimumY + deltaY * j;
final double y = yValues[j];
zValues[i][j] = f.value(x, y);
dzdx[i][j] = dfdx.value(x, y);
dzdy[i][j] = dfdy.value(x, y);
d2zdxdy[i][j] = d2fdxdy.value(x, y);
}
}
final BivariateFunction interpolation
= new BicubicInterpolatingFunction(xValues,
yValues,
zValues,
dzdx,
dzdy,
d2zdxdy);
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("On data point: " + expected + " != " + actual,
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);
if (print) {
System.out.println(currentX + " " + currentY + " -> ");
}
actual = interpolation.value(currentX, currentY);
sumError += FastMath.abs(actual - expected);
if (print) {
System.out.println(actual + " (diff=" + (expected - actual) + ")");
}
Assert.assertEquals(expected, actual, maxTolerance);
}
final double meanError = sumError / numberOfSamples;
Assert.assertEquals(0, meanError, meanTolerance);
}
}