/**
* Copyright (C) 2013 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.interpolation;
import static org.testng.Assert.assertEquals;
import static org.testng.Assert.assertTrue;
import org.testng.annotations.Test;
import com.opengamma.analytics.math.function.PiecewisePolynomialFunction1D;
/**
*
*/
public class SemiLocalCubicSplineInterpolatorTest {
private static final double EPS = 1e-13;
private static final double INF = 1. / 0.;
/**
* Recovering linear test
*/
@Test
public void linearTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6. };
final int nData = xValues.length;
final double[] yValues = new double[nData];
for (int i = 0; i < nData; ++i) {
yValues[i] = xValues[i] / 7. + 1 / 11.;
}
final double[][] coefsMatExp = new double[][] { {0., 0., 1. / 7., yValues[0] }, {0., 0., 1. / 7., yValues[1] }, {0., 0., 1. / 7., yValues[2] }, {0., 0., 1. / 7., yValues[3] },
{0., 0., 1. / 7., yValues[4] } };
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
assertEquals(result.getDimensions(), 1);
assertEquals(result.getNumberOfIntervals(), 5);
assertEquals(result.getOrder(), 4);
for (int i = 0; i < result.getNumberOfIntervals(); ++i) {
for (int j = 0; j < result.getOrder(); ++j) {
final double ref = Math.abs(coefsMatExp[i][j]) == 0. ? 1. : Math.abs(coefsMatExp[i][j]);
assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatExp[i][j], ref * EPS);
}
}
final int nKeys = 101;
for (int i = 0; i < nKeys; ++i) {
final double key = 1. + 5. / (nKeys - 1) * i;
final double ref = key / 7. + 1 / 11.;
assertEquals(function.evaluate(result, key).getData()[0], ref, ref * EPS);
// System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(result, key).getData()[0]);
}
}
/**
* Recovering quadratic function
*/
@Test
public void quadraticTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6. };
final int nData = xValues.length;
final double[] yValues = new double[nData];
for (int i = 0; i < nData; ++i) {
yValues[i] = xValues[i] * xValues[i] / 7. + xValues[i] / 13. + 1 / 11.;
}
final double[][] coefsMatExp = new double[][] { {0., 1. / 7., 2. / 7. * xValues[0] + 1. / 13., yValues[0] }, {0., 1. / 7., 2. / 7. * xValues[1] + 1. / 13., yValues[1] },
{0., 1. / 7., 2. / 7. * xValues[2] + 1. / 13., yValues[2] },
{0., 1. / 7., 2. / 7. * xValues[3] + 1. / 13., yValues[3] },
{0., 1. / 7., 2. / 7. * xValues[4] + 1. / 13., yValues[4] } };
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
assertEquals(result.getDimensions(), 1);
assertEquals(result.getNumberOfIntervals(), 5);
assertEquals(result.getOrder(), 4);
for (int i = 0; i < result.getNumberOfIntervals(); ++i) {
for (int j = 0; j < result.getOrder(); ++j) {
final double ref = Math.abs(coefsMatExp[i][j]) == 0. ? 1. : Math.abs(coefsMatExp[i][j]);
assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatExp[i][j], ref * EPS);
}
}
final int nKeys = 101;
for (int i = 0; i < nKeys; ++i) {
final double key = 1. + 5. / (nKeys - 1) * i;
final double ref = key * key / 7. + key / 13. + 1 / 11.;
assertEquals(function.evaluate(result, key).getData()[0], ref, ref * EPS);
// System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(result, key).getData()[0]);
}
}
/**
*
*/
@Test
public void quadraticMultiTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6. };
final int nData = xValues.length;
final double[][] yValues = new double[2][nData];
for (int i = 0; i < nData; ++i) {
yValues[0][i] = xValues[i] * xValues[i] / 7. + xValues[i] / 13. + 1 / 11.;
}
for (int i = 0; i < nData; ++i) {
yValues[1][i] = xValues[i] * xValues[i] / 3. + xValues[i] / 7. + 1 / 17.;
}
final double[][] coefsMatExp = new double[][] { {0., 1. / 7., 2. / 7. * xValues[0] + 1. / 13., yValues[0][0] }, {0., 1. / 3., 2. / 3. * xValues[0] + 1. / 7., yValues[1][0] },
{0., 1. / 7., 2. / 7. * xValues[1] + 1. / 13., yValues[0][1] }, {0., 1. / 3., 2. / 3. * xValues[1] + 1. / 7., yValues[1][1] },
{0., 1. / 7., 2. / 7. * xValues[2] + 1. / 13., yValues[0][2] }, {0., 1. / 3., 2. / 3. * xValues[2] + 1. / 7., yValues[1][2] },
{0., 1. / 7., 2. / 7. * xValues[3] + 1. / 13., yValues[0][3] }, {0., 1. / 3., 2. / 3. * xValues[3] + 1. / 7., yValues[1][3] },
{0., 1. / 7., 2. / 7. * xValues[4] + 1. / 13., yValues[0][4] }, {0., 1. / 3., 2. / 3. * xValues[4] + 1. / 7., yValues[1][4] } };
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
assertEquals(result.getDimensions(), 2);
assertEquals(result.getNumberOfIntervals(), 5);
assertEquals(result.getOrder(), 4);
for (int i = 0; i < result.getNumberOfIntervals() * 2; ++i) {
for (int j = 0; j < result.getOrder(); ++j) {
final double ref = Math.abs(coefsMatExp[i][j]) == 0. ? 1. : Math.abs(coefsMatExp[i][j]);
assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatExp[i][j], ref * EPS);
}
}
final int nKeys = 101;
for (int i = 0; i < nKeys; ++i) {
final double key = 1. + 5. / (nKeys - 1) * i;
final double ref = key * key / 7. + key / 13. + 1 / 11.;
assertEquals(function.evaluate(result, key).getData()[0], ref, ref * EPS);
// System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(result, key).getData()[0]);
}
}
/**
* Sample data given in the original paper, consisting of constant part and monotonically increasing part
*/
@Test
public void sampleDataTest() {
final double[] xValues = new double[] {0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10. };
final double[] yValues = new double[] {10., 10., 10., 10., 10., 10., 10.5, 15., 50., 60., 85. };
final double[][] coefsMatPartExp = new double[][] { {0., 0., 0., 10. }, {0., 0., 0., 10. }, {0., 0., 0., 10. }, {0., 0., 0., 10. }, {0., 0., 0., 10. } };
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interp = new SemiLocalCubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
assertEquals(result.getDimensions(), 1);
assertEquals(result.getNumberOfIntervals(), 10);
assertEquals(result.getOrder(), 4);
for (int i = 0; i < 5; ++i) {
for (int j = 0; j < 4; ++j) {
final double ref = Math.abs(coefsMatPartExp[i][j]) == 0. ? 1. : Math.abs(coefsMatPartExp[i][j]);
assertEquals(result.getCoefMatrix().getData()[i][j], coefsMatPartExp[i][j], ref * EPS);
}
}
final int nKeys = 101;
double key0 = 5.;
for (int i = 1; i < nKeys; ++i) {
final double key = 5. + 5. / (nKeys - 1) * i;
assertTrue(function.evaluate(result, key).getData()[0] - function.evaluate(result, key0).getData()[0] >= 0.);
key0 = 5. + 5. / (nKeys - 1) * i;
}
key0 = 0.;
for (int i = 1; i < nKeys; ++i) {
final double key = 0. + 5. / (nKeys - 1) * i;
assertTrue(function.evaluate(result, key).getData()[0] - function.evaluate(result, key0).getData()[0] == 0.);
key0 = 0. + 5. / (nKeys - 1) * i;
}
}
/*
* Error tests
*/
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void dataShortTest() {
final double[] xValues = new double[] {1., 2. };
final double[] yValues = new double[] {0., 0.1 };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void dataShortMultiTest() {
final double[] xValues = new double[] {1., 2., };
final double[][] yValues = new double[][] { {0., 0.1, }, {0., 0.1, } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void dataDiffTest() {
final double[] xValues = new double[] {1., 2., 3., 4. };
final double[] yValues = new double[] {0., 0.1, 3. };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void dataDiffMultiTest() {
final double[] xValues = new double[] {1., 2., 3., 4. };
final double[][] yValues = new double[][] { {0., 0.1, 3. }, {0., 0.1, 3. } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void coincideDataTest() {
final double[] xValues = new double[] {1., 1., 3. };
final double[] yValues = new double[] {0., 0.1, 0.05 };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void coincideDataMultiTest() {
final double[] xValues = new double[] {1., 2., 2. };
final double[][] yValues = new double[][] { {0., 0.1, 0.05 }, {0., 0.1, 1.05 } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullXdataTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[] yValues = new double[] {0., 0.1, 0.05, 0.2 };
xValues = null;
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullYdataTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[] yValues = new double[] {0., 0.1, 0.05, 0.2 };
yValues = null;
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullXdataMultiTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[][] yValues = new double[][] { {0., 0.1, 0.05, 0.2 }, {0., 0.1, 0.05, 0.2 } };
xValues = null;
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullYdataMultiTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[][] yValues = new double[][] { {0., 0.1, 0.05, 0.2 }, {0., 0.1, 0.05, 0.2 } };
yValues = null;
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void infXdataTest() {
double[] xValues = new double[] {1., 2., 3., INF };
double[] yValues = new double[] {0., 0.1, 0.05, 0.2 };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void infYdataTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[] yValues = new double[] {0.1, 0.05, 0.2, INF };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nanXdataTest() {
double[] xValues = new double[] {1., 2., 3., Double.NaN };
double[] yValues = new double[] {0., 0.1, 0.05, 0.2 };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nanYdataTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[] yValues = new double[] {0.1, 0.05, 0.2, Double.NaN };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void infXdataMultiTest() {
double[] xValues = new double[] {1., 2., 3., INF };
double[][] yValues = new double[][] { {0., 0.1, 0.05, 0.2 }, {0., 0.1, 0.05, 0.2 } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void infYdataMultiTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[][] yValues = new double[][] { {0.1, 0.05, 0.2, 1. }, {0.1, 0.05, 0.2, INF } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nanXdataMultiTest() {
double[] xValues = new double[] {1., 2., 3., Double.NaN };
double[][] yValues = new double[][] { {0., 0.1, 0.05, 0.2 }, {0., 0.1, 0.05, 0.2 } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nanYdataMultiTest() {
double[] xValues = new double[] {1., 2., 3., 4. };
double[][] yValues = new double[][] { {0.1, 0.05, 0.2, 1.1 }, {0.1, 0.05, 0.2, Double.NaN } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/*
* Tests below are for debugging
*/
/**
*
*/
@Test
(enabled = false)
public void print3Test() {
final double[] xValues = new double[] {0.1, 1., 4., 9., 20., 30. };
final double[][] yValues = new double[][] {{8.1, 7., 4.4, 7., 4., 3. } };
PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
System.out.println(resultPos.getCoefMatrix());
final int nKeys = 101;
for (int i = 0; i < nKeys; ++i) {
final double key = +30. / (nKeys - 1) * i;
System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
}
}
/**
*
*/
@Test
(enabled = false)
public void print4Test() {
// final double[] xValues = new double[] {1., 2., 3., 4., 5., 6. };
// final double[] yValues = new double[] {3. * 1, 3. * 8., 3. * 27., 3. * 64., 3. * 125., 3. * 216. };
final double[] xValues = new double[] {1., 2. };
final double[] yValues = new double[] {3. * 1, 3. * 8. };
PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
System.out.println(resultPos.getCoefMatrix());
final int nKeys = 101;
for (int i = 0; i < nKeys; ++i) {
final double key = 1. + 5. / (nKeys - 1) * i;
System.out.println(key + "\t" + function.evaluate(result, key).getData()[0] + "\t" + function.evaluate(resultPos, key).getData()[0]);
}
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void notReconnectedTest() {
double[] xValues = new double[] {1., 2.0000000001, 2., 4. };
double[] yValues = new double[] {2., 400., 3., 500000000. };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
/**
*
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void notReconnectedMultiTest() {
double[] xValues = new double[] {1., 2., 4., 2.0000000001 };
double[][] yValues = new double[][] {{2., 3., 500000000., 400. } };
PiecewisePolynomialInterpolator interpPos = new SemiLocalCubicSplineInterpolator();
interpPos.interpolate(xValues, yValues);
}
}