/*
* 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.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import org.junit.Assert;
import org.junit.Test;
/**
* Test the SplineInterpolator.
*
*/
public class SplineInterpolatorTest {
/** error tolerance for spline interpolator value at knot points */
protected double knotTolerance = 1E-14;
/** error tolerance for interpolating polynomial coefficients */
protected double coefficientTolerance = 1E-14;
/** error tolerance for interpolated values -- high value is from sin test */
protected double interpolationTolerance = 1E-14;
@Test
public void testInterpolateLinearDegenerateTwoSegment()
{
double tolerance = 1e-15;
double x[] = { 0.0, 0.5, 1.0 };
double y[] = { 0.0, 0.5, 1.0 };
UnivariateInterpolator i = new SplineInterpolator();
UnivariateFunction f = i.interpolate(x, y);
verifyInterpolation(f, x, y);
verifyConsistency((PolynomialSplineFunction) f, x);
// 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), tolerance);
Assert.assertEquals(0.4,f.value(0.4), tolerance);
Assert.assertEquals(1.0,f.value(1.0), tolerance);
}
@Test
public void testInterpolateLinearDegenerateThreeSegment()
{
double tolerance = 1e-15;
double x[] = { 0.0, 0.5, 1.0, 1.5 };
double y[] = { 0.0, 0.5, 1.0, 1.5 };
UnivariateInterpolator i = new SplineInterpolator();
UnivariateFunction 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), tolerance);
Assert.assertEquals(1.4,f.value(1.4), tolerance);
Assert.assertEquals(1.5,f.value(1.5), tolerance);
}
@Test
public void testInterpolateLinear() {
double x[] = { 0.0, 0.5, 1.0 };
double y[] = { 0.0, 0.5, 0.0 };
UnivariateInterpolator i = new SplineInterpolator();
UnivariateFunction f = i.interpolate(x, y);
verifyInterpolation(f, x, y);
verifyConsistency((PolynomialSplineFunction) f, x);
// Verify coefficients using analytical values
PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
double target[] = {y[0], 1.5d, 0d, -2d};
TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
target = new double[]{y[1], 0d, -3d, 2d};
TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
}
@Test
public void testInterpolateSin() {
double sineCoefficientTolerance = 1e-6;
double sineInterpolationTolerance = 0.0043;
double x[] =
{
0.0,
FastMath.PI / 6d,
FastMath.PI / 2d,
5d * FastMath.PI / 6d,
FastMath.PI,
7d * FastMath.PI / 6d,
3d * FastMath.PI / 2d,
11d * FastMath.PI / 6d,
2.d * FastMath.PI };
double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
UnivariateInterpolator i = new SplineInterpolator();
UnivariateFunction f = i.interpolate(x, y);
verifyInterpolation(f, x, y);
verifyConsistency((PolynomialSplineFunction) f, x);
/* Check coefficients against values computed using R (version 1.8.1, Red Hat Linux 9)
*
* To replicate in R:
* x[1] <- 0
* x[2] <- pi / 6, etc, same for y[] (could use y <- scan() for y values)
* g <- splinefun(x, y, "natural")
* splinecoef <- eval(expression(z), envir = environment(g))
* print(splinecoef)
*/
PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
double target[] = {y[0], 1.002676d, 0d, -0.17415829d};
TestUtils.assertEquals(polynomials[0].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
TestUtils.assertEquals(polynomials[1].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
TestUtils.assertEquals(polynomials[2].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
TestUtils.assertEquals(polynomials[3].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
TestUtils.assertEquals(polynomials[4].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
TestUtils.assertEquals(polynomials[5].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
TestUtils.assertEquals(polynomials[6].getCoefficients(), target, sineCoefficientTolerance);
target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
TestUtils.assertEquals(polynomials[7].getCoefficients(), target, sineCoefficientTolerance);
//Check interpolation
Assert.assertEquals(FastMath.sqrt(2d) / 2d,f.value(FastMath.PI/4d),sineInterpolationTolerance);
Assert.assertEquals(FastMath.sqrt(2d) / 2d,f.value(3d*FastMath.PI/4d),sineInterpolationTolerance);
}
@Test
public void testIllegalArguments() {
// Data set arrays of different size.
UnivariateInterpolator i = new SplineInterpolator();
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 (NonMonotonicSequenceException iae) {
// Expected.
}
// Not enough data to interpolate.
try {
double xval[] = { 0.0, 1.0 };
double yval[] = { 0.0, 1.0 };
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(UnivariateFunction f, double x[], double y[])
{
for (int i = 0; i < x.length; i++) {
Assert.assertEquals(f.value(x[i]), y[i], knotTolerance);
}
}
/**
* Verifies that interpolating polynomials satisfy consistency requirement:
* adjacent polynomials must agree through two derivatives at knot points
*/
protected void verifyConsistency(PolynomialSplineFunction f, double x[])
{
PolynomialFunction polynomials[] = f.getPolynomials();
for (int i = 1; i < x.length - 2; i++) {
// evaluate polynomials and derivatives at x[i + 1]
Assert.assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
Assert.assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
polynomials[i + 1].derivative().value(0), 0.5);
Assert.assertEquals(polynomials[i].polynomialDerivative().derivative().value(x[i +1] - x[i]),
polynomials[i + 1].polynomialDerivative().derivative().value(0), 0.5);
}
}
}