/*
* 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.analysis.MultivariateFunction;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case for the "microsphere projection" interpolator.
*
*/
public final class MicrosphereInterpolatorTest {
/**
* Test of interpolator for a plane.
* <p>
* y = 2 x<sub>1</sub> - 3 x<sub>2</sub> + 5
*/
@Test
public void testLinearFunction2D() {
MultivariateFunction f = new MultivariateFunction() {
public double value(double[] x) {
if (x.length != 2) {
throw new IllegalArgumentException();
}
return 2 * x[0] - 3 * x[1] + 5;
}
};
MultivariateInterpolator interpolator = new MicrosphereInterpolator();
// Interpolating points in [-1, 1][-1, 1] by steps of 1.
final int n = 9;
final int dim = 2;
double[][] x = new double[n][dim];
double[] y = new double[n];
int index = 0;
for (int i = -1; i <= 1; i++) {
for (int j = -1; j <= 1; j++) {
x[index][0] = i;
x[index][1] = j;
y[index] = f.value(x[index]);
++index;
}
}
MultivariateFunction p = interpolator.interpolate(x, y);
double[] c = new double[dim];
double expected, result;
c[0] = 0;
c[1] = 0;
expected = f.value(c);
result = p.value(c);
Assert.assertEquals("On sample point", expected, result, FastMath.ulp(1d));
c[0] = 0 + 1e-5;
c[1] = 1 - 1e-5;
expected = f.value(c);
result = p.value(c);
Assert.assertEquals("1e-5 away from sample point", expected, result, 1e-4);
}
/**
* Test of interpolator for a quadratic function.
* <p>
* y = 2 x<sub>1</sub><sup>2</sup> - 3 x<sub>2</sub><sup>2</sup>
* + 4 x<sub>1</sub> x<sub>2</sub> - 5
*/
@Test
public void testParaboloid2D() {
MultivariateFunction f = new MultivariateFunction() {
public double value(double[] x) {
if (x.length != 2) {
throw new IllegalArgumentException();
}
return 2 * x[0] * x[0] - 3 * x[1] * x[1] + 4 * x[0] * x[1] - 5;
}
};
MultivariateInterpolator interpolator = new MicrosphereInterpolator();
// Interpolating points in [-10, 10][-10, 10] by steps of 2.
final int n = 121;
final int dim = 2;
double[][] x = new double[n][dim];
double[] y = new double[n];
int index = 0;
for (int i = -10; i <= 10; i += 2) {
for (int j = -10; j <= 10; j += 2) {
x[index][0] = i;
x[index][1] = j;
y[index] = f.value(x[index]);
++index;
}
}
MultivariateFunction p = interpolator.interpolate(x, y);
double[] c = new double[dim];
double expected, result;
c[0] = 0;
c[1] = 0;
expected = f.value(c);
result = p.value(c);
Assert.assertEquals("On sample point", expected, result, FastMath.ulp(1d));
c[0] = 2 + 1e-5;
c[1] = 2 - 1e-5;
expected = f.value(c);
result = p.value(c);
Assert.assertEquals("1e-5 away from sample point", expected, result, 1e-3);
}
}