/*
* 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.math.analysis.interpolation;
import org.apache.commons.math.MathException;
import org.apache.commons.math.exception.NonMonotonousSequenceException;
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NumberIsTooSmallException;
import org.apache.commons.math.TestUtils;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
import org.junit.Assert;
import org.junit.Test;
/**
* Test the LinearInterpolator.
*/
public class LinearInterpolatorTest {
/** error tolerance for spline interpolator value at knot points */
protected double knotTolerance = 1E-12;
/** error tolerance for interpolating polynomial coefficients */
protected double coefficientTolerance = 1E-6;
/** error tolerance for interpolated values */
protected double interpolationTolerance = 1E-12;
@Test
public void testInterpolateLinearDegenerateTwoSegment()
throws Exception {
double x[] = { 0.0, 0.5, 1.0 };
double y[] = { 0.0, 0.5, 1.0 };
UnivariateRealInterpolator i = new LinearInterpolator();
UnivariateRealFunction f = i.interpolate(x, y);
verifyInterpolation(f, x, y);
// Verify coefficients using analytical values
PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
double target[] = {y[0], 1d};
TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
target = new double[]{y[1], 1d};
TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
// Check interpolation
Assert.assertEquals(0.0,f.value(0.0), interpolationTolerance);
Assert.assertEquals(0.4,f.value(0.4), interpolationTolerance);
Assert.assertEquals(1.0,f.value(1.0), interpolationTolerance);
}
@Test
public void testInterpolateLinearDegenerateThreeSegment()
throws Exception {
double x[] = { 0.0, 0.5, 1.0, 1.5 };
double y[] = { 0.0, 0.5, 1.0, 1.5 };
UnivariateRealInterpolator i = new LinearInterpolator();
UnivariateRealFunction f = i.interpolate(x, y);
verifyInterpolation(f, x, y);
// Verify coefficients using analytical values
PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
double target[] = {y[0], 1d};
TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
target = new double[]{y[1], 1d};
TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
target = new double[]{y[2], 1d};
TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
// Check interpolation
Assert.assertEquals(0,f.value(0), interpolationTolerance);
Assert.assertEquals(1.4,f.value(1.4), interpolationTolerance);
Assert.assertEquals(1.5,f.value(1.5), interpolationTolerance);
}
@Test
public void testInterpolateLinear() throws Exception {
double x[] = { 0.0, 0.5, 1.0 };
double y[] = { 0.0, 0.5, 0.0 };
UnivariateRealInterpolator i = new LinearInterpolator();
UnivariateRealFunction f = i.interpolate(x, y);
verifyInterpolation(f, x, y);
// Verify coefficients using analytical values
PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
double target[] = {y[0], 1d};
TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
target = new double[]{y[1], -1d};
TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
}
@Test
public void testIllegalArguments() throws MathException {
// Data set arrays of different size.
UnivariateRealInterpolator i = new LinearInterpolator();
try {
double xval[] = { 0.0, 1.0 };
double yval[] = { 0.0, 1.0, 2.0 };
i.interpolate(xval, yval);
Assert.fail("Failed to detect data set array with different sizes.");
} catch (DimensionMismatchException iae) {
// Expected.
}
// X values not sorted.
try {
double xval[] = { 0.0, 1.0, 0.5 };
double yval[] = { 0.0, 1.0, 2.0 };
i.interpolate(xval, yval);
Assert.fail("Failed to detect unsorted arguments.");
} catch (NonMonotonousSequenceException iae) {
// Expected.
}
// Not enough data to interpolate.
try {
double xval[] = { 0.0 };
double yval[] = { 0.0 };
i.interpolate(xval, yval);
Assert.fail("Failed to detect unsorted arguments.");
} catch (NumberIsTooSmallException iae) {
// Expected.
}
}
/**
* verifies that f(x[i]) = y[i] for i = 0..n-1 where n is common length.
*/
protected void verifyInterpolation(UnivariateRealFunction f, double x[], double y[])
throws Exception{
for (int i = 0; i < x.length; i++) {
Assert.assertEquals(f.value(x[i]), y[i], knotTolerance);
}
}
}