/**
* Copyright (C) 2014 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.interpolation;
import java.util.Arrays;
import org.testng.annotations.Test;
import com.opengamma.analytics.math.function.PiecewisePolynomialWithSensitivityFunction1D;
import com.opengamma.analytics.math.interpolation.data.Interpolator1DDataBundle;
import com.opengamma.util.test.TestGroup;
/**
*
*/
@Test(groups = TestGroup.UNIT)
public class ReciprocalExtrapolator1DTest {
private static final PiecewisePolynomialInterpolator[] INTERP_SENSE;
static {
PiecewisePolynomialInterpolator cubic = new CubicSplineInterpolator();
PiecewisePolynomialInterpolator natural = new NaturalSplineInterpolator();
PiecewiseCubicHermiteSplineInterpolatorWithSensitivity pchip =
new PiecewiseCubicHermiteSplineInterpolatorWithSensitivity();
PiecewisePolynomialInterpolator hymanNat = new MonotonicityPreservingCubicSplineInterpolator(natural);
INTERP_SENSE = new PiecewisePolynomialInterpolator[] {cubic, natural, pchip, hymanNat };
}
private static final PiecewisePolynomialWithSensitivityFunction1D FUNC =
new PiecewisePolynomialWithSensitivityFunction1D();
private static final double EPS = 1.0e-12;
private static final double DELTA = 1.0e-6;
/**
* No clamped points added.
* checking agreement with the extrapolation done by the underlying interpolation
*/
@Test
public void notClampedTest() {
double[][] xValuesSet = new double[][] { {-5.0, -1.4, 3.2, 3.5, 7.6 }, {1., 2., 4.5, 12.1, 14.2 },
{-5.2, -3.4, -3.2, -0.9, -0.2 } };
double[][] yValuesSet = new double[][] { {-2.2, 1.1, 1.9, 2.3, -0.1 }, {3.4, 5.2, 4.3, 1.1, 0.2 },
{1.4, 2.2, 4.1, 1.9, 0.99 } };
for (int k = 0; k < xValuesSet.length; ++k) {
double[] xValues = Arrays.copyOf(xValuesSet[k], xValuesSet[k].length);
double[] yValues = Arrays.copyOf(yValuesSet[k], yValuesSet[k].length);
int nData = xValues.length;
int nKeys = 100;
double interval = (xValues[2] - xValues[0]) / (nKeys - 1.0);
int n = INTERP_SENSE.length;
for (int i = 0; i < n; ++i) {
ProductPiecewisePolynomialInterpolator interp = new ProductPiecewisePolynomialInterpolator(INTERP_SENSE[i]);
PiecewisePolynomialResult result = interp.interpolateWithSensitivity(xValues, yValues);
ReciprocalExtrapolator1D extrap1D = new ReciprocalExtrapolator1D(
new ProductPiecewisePolynomialInterpolator1D(INTERP_SENSE[i]));
Interpolator1DDataBundle data = extrap1D.getDataBundle(xValues, yValues);
InterpolatorTestUtil.assertArrayRelative("notClampedTest", xValues, data.getKeys(), EPS);
InterpolatorTestUtil.assertArrayRelative("notClampedTest", yValues, data.getValues(), EPS);
/* left extrapolation */
double grad = FUNC.differentiate(result, xValues[0]).getEntry(0);
for (int j = 1; j < nKeys; ++j) {
double key = xValues[0] - interval * j;
double ref = grad * (key - xValues[0]) + yValues[0] * xValues[0];
InterpolatorTestUtil.assertRelative("notClampedTest", ref / key, extrap1D.interpolate(data, key), EPS);
double keyUp = key + DELTA;
double keyDw = key - DELTA;
double refDeriv = 0.5 * (extrap1D.interpolate(data, keyUp) - extrap1D.interpolate(data, keyDw)) / DELTA;
InterpolatorTestUtil.assertRelative("notClampedTest", refDeriv,
extrap1D.firstDerivative(data, key), DELTA);
double[] refSense = new double[nData];
for (int l = 0; l < nData; ++l) {
double[] yValuesUp = Arrays.copyOf(yValues, nData);
double[] yValuesDw = Arrays.copyOf(yValues, nData);
yValuesUp[l] += DELTA;
yValuesDw[l] -= DELTA;
Interpolator1DDataBundle dataUp = extrap1D.getDataBundle(xValues, yValuesUp);
Interpolator1DDataBundle dataDw = extrap1D.getDataBundle(xValues, yValuesDw);
refSense[l] = 0.5 * (extrap1D.interpolate(dataUp, key) - extrap1D.interpolate(dataDw, key)) / DELTA;
}
InterpolatorTestUtil.assertArrayRelative("notClampedTest", extrap1D.getNodeSensitivitiesForValue(data, key),
refSense, DELTA * 10.0);
}
/* right extrapolation */
for (int j = 1; j < nKeys; ++j) {
double key = xValues[nData - 1] + interval * j;
InterpolatorTestUtil.assertRelative("notClampedTest", FUNC.evaluate(result, key).getEntry(0) / key,
extrap1D.interpolate(data, key), EPS);
double keyUp = key + DELTA;
double keyDw = key - DELTA;
double refDeriv = 0.5 * (extrap1D.interpolate(data, keyUp) - extrap1D.interpolate(data, keyDw)) / DELTA;
InterpolatorTestUtil.assertRelative("notClampedTest", refDeriv,
extrap1D.firstDerivative(data, key), DELTA);
double[] refSense = new double[nData];
for (int l = 0; l < nData; ++l) {
double[] yValuesUp = Arrays.copyOf(yValues, nData);
double[] yValuesDw = Arrays.copyOf(yValues, nData);
yValuesUp[l] += DELTA;
yValuesDw[l] -= DELTA;
Interpolator1DDataBundle dataUp = extrap1D.getDataBundle(xValues, yValuesUp);
Interpolator1DDataBundle dataDw = extrap1D.getDataBundle(xValues, yValuesDw);
refSense[l] = 0.5 * (extrap1D.interpolate(dataUp, key) - extrap1D.interpolate(dataDw, key)) / DELTA;
}
InterpolatorTestUtil.assertArrayRelative("notClampedTest", extrap1D.getNodeSensitivitiesForValue(data, key),
refSense, DELTA * 10.0);
}
}
}
}
/**
* Clamped points.
* checking agreement with the extrapolation done by the underlying interpolation
*/
@Test
public void clampedTest() {
double[] xValues = new double[] {-5.0, -1.4, 3.2, 3.5, 7.6 };
double[] yValues = new double[] {-2.2, 1.1, 1.9, 2.3, -0.1 };
double[][] xValuesClampedSet = new double[][] { {0.0 }, {-4.2, -2.5, 7.45 }, {} };
double[][] yValuesClampedSet = new double[][] { {0.0 }, {-1.2, -1.4, 2.2 }, {} };
for (int k = 0; k < xValuesClampedSet.length; ++k) {
double[] xValuesClamped = Arrays.copyOf(xValuesClampedSet[k], xValuesClampedSet[k].length);
double[] yValuesClamped = Arrays.copyOf(yValuesClampedSet[k], yValuesClampedSet[k].length);
int nData = xValues.length;
int nKeys = 100;
double interval = (xValues[2] - xValues[0]) / (nKeys - 1.0);
int n = INTERP_SENSE.length;
for (int i = 0; i < n; ++i) {
ProductPiecewisePolynomialInterpolator interp = new ProductPiecewisePolynomialInterpolator(INTERP_SENSE[i],
xValuesClamped, yValuesClamped);
PiecewisePolynomialResultsWithSensitivity result = interp.interpolateWithSensitivity(xValues, yValues);
ReciprocalExtrapolator1D extrap1D = new ReciprocalExtrapolator1D(
new ProductPiecewisePolynomialInterpolator1D(INTERP_SENSE[i], xValuesClamped, yValuesClamped));
Interpolator1DDataBundle data = extrap1D.getDataBundleFromSortedArrays(xValues, yValues);
InterpolatorTestUtil.assertArrayRelative("notClampedTest", xValues, data.getKeys(), EPS);
InterpolatorTestUtil.assertArrayRelative("notClampedTest", yValues, data.getValues(), EPS);
double grad = FUNC.differentiate(result, xValues[0]).getEntry(0);
/* left extrapolation */
for (int j = 1; j < nKeys; ++j) {
double key = xValues[0] - interval * j;
double ref = grad * (key - xValues[0]) + yValues[0] * xValues[0];
InterpolatorTestUtil.assertRelative("notClampedTest", ref / key, extrap1D.interpolate(data, key), EPS);
double keyUp = key + DELTA;
double keyDw = key - DELTA;
double refDeriv = 0.5 * (extrap1D.interpolate(data, keyUp) - extrap1D.interpolate(data, keyDw)) / DELTA;
InterpolatorTestUtil.assertRelative("notClampedTest", refDeriv,
extrap1D.firstDerivative(data, key), DELTA * 10.0);
double[] refSense = new double[nData];
for (int l = 0; l < nData; ++l) {
double[] yValuesUp = Arrays.copyOf(yValues, nData);
double[] yValuesDw = Arrays.copyOf(yValues, nData);
yValuesUp[l] += DELTA;
yValuesDw[l] -= DELTA;
Interpolator1DDataBundle dataUp = extrap1D.getDataBundle(xValues, yValuesUp);
Interpolator1DDataBundle dataDw = extrap1D.getDataBundle(xValues, yValuesDw);
refSense[l] = 0.5 * (extrap1D.interpolate(dataUp, key) - extrap1D.interpolate(dataDw, key)) / DELTA;
}
InterpolatorTestUtil.assertArrayRelative("notClampedTest", extrap1D.getNodeSensitivitiesForValue(data, key),
refSense, DELTA * 10.0);
}
/* right extrapolation */
for (int j = 1; j < nKeys; ++j) {
double key = xValues[nData - 1] + interval * j;
InterpolatorTestUtil.assertRelative("notClampedTest " + k, FUNC.evaluate(result, key).getEntry(0) / key,
extrap1D.interpolate(data, key), EPS);
double keyUp = key + DELTA;
double keyDw = key - DELTA;
double refDeriv = 0.5 * (extrap1D.interpolate(data, keyUp) - extrap1D.interpolate(data, keyDw)) / DELTA;
InterpolatorTestUtil.assertRelative("notClampedTest", refDeriv,
extrap1D.firstDerivative(data, key), DELTA * 10.0);
double[] refSense = new double[nData];
for (int l = 0; l < nData; ++l) {
double[] yValuesUp = Arrays.copyOf(yValues, nData);
double[] yValuesDw = Arrays.copyOf(yValues, nData);
yValuesUp[l] += DELTA;
yValuesDw[l] -= DELTA;
Interpolator1DDataBundle dataUp = extrap1D.getDataBundle(xValues, yValuesUp);
Interpolator1DDataBundle dataDw = extrap1D.getDataBundle(xValues, yValuesDw);
refSense[l] = 0.5 * (extrap1D.interpolate(dataUp, key) - extrap1D.interpolate(dataDw, key)) / DELTA;
}
InterpolatorTestUtil.assertArrayRelative("notClampedTest", extrap1D.getNodeSensitivitiesForValue(data, key),
refSense, DELTA * 10.0);
}
}
}
}
/**
* Check Math.abs(value) < SMALL is smoothly connected to general cases
*/
@Test
public void closeToZeroTest() {
double[] xValues = new double[] {0.1, 0.2, 0.3, 0.4 };
double[] yValues = new double[] {0.1, 0.2, 0.3, 0.4 };
int n = INTERP_SENSE.length;
for (int i = 0; i < n; ++i) {
ReciprocalExtrapolator1D extrap1D = new ReciprocalExtrapolator1D(
new ProductPiecewisePolynomialInterpolator1D(INTERP_SENSE[i], new double[] {0.0 }, new double[] {0.0 }));
Interpolator1DDataBundle data = extrap1D.getDataBundle(xValues, yValues);
double eps = 1.0e-5;
InterpolatorTestUtil.assertRelative("closeToZeroTest", extrap1D.interpolate(data, eps),
extrap1D.interpolate(data, 0.0), eps);
InterpolatorTestUtil.assertRelative("closeToZeroTest", extrap1D.firstDerivative(data, eps),
extrap1D.firstDerivative(data, 0.0), eps);
}
}
/**
* value is within the data range
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void insideRangeTest() {
double[] xValues = new double[] {2.4, 3.2, 3.5, 7.6 };
double[] yValues = new double[] {1.1, 1.9, 2.3, -0.1 };
ReciprocalExtrapolator1D extrap1D = new ReciprocalExtrapolator1D(
new ProductPiecewisePolynomialInterpolator1D(INTERP_SENSE[1]));
Interpolator1DDataBundle data = extrap1D.getDataBundle(xValues, yValues);
extrap1D.interpolate(data, 5.2);
}
/**
* value is within the data range
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void insideRangeDerivativeTest() {
double[] xValues = new double[] {2.4, 3.2, 3.5, 7.6 };
double[] yValues = new double[] {1.1, 1.9, 2.3, -0.1 };
ReciprocalExtrapolator1D extrap1D = new ReciprocalExtrapolator1D(
new ProductPiecewisePolynomialInterpolator1D(INTERP_SENSE[1]));
Interpolator1DDataBundle data = extrap1D.getDataBundle(xValues, yValues);
extrap1D.firstDerivative(data, 5.2);
}
/**
* value is within the data range
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void insideRangeSenseTest() {
double[] xValues = new double[] {2.4, 3.2, 3.5, 7.6 };
double[] yValues = new double[] {1.1, 1.9, 2.3, -0.1 };
ReciprocalExtrapolator1D extrap1D = new ReciprocalExtrapolator1D(
new ProductPiecewisePolynomialInterpolator1D(INTERP_SENSE[1]));
Interpolator1DDataBundle data = extrap1D.getDataBundle(xValues, yValues);
extrap1D.getNodeSensitivitiesForValue(data, 5.2);
}
private static final double[] S_ARR = new double[] {1., 2., 3., 4. };
private static final ProductPiecewisePolynomialInterpolator1D S_INTERP = new ProductPiecewisePolynomialInterpolator1D(
INTERP_SENSE[0]);
private static final ReciprocalExtrapolator1D S_EXTRAP = new ReciprocalExtrapolator1D(S_INTERP);
private static final Interpolator1DDataBundle S_DATA = S_EXTRAP.getDataBundle(S_ARR, S_ARR);
/**
* interpolator is null
*/
@SuppressWarnings("unused")
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullInterpTest1() {
new ReciprocalExtrapolator1D(null);
}
/**
* data bundle is null
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullDataInterpTest() {
S_EXTRAP.interpolate(null, 5.0);
}
/**
* Double value is null
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullValueInterpTest() {
S_EXTRAP.interpolate(S_DATA, null);
}
/**
* data bundle is null
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullDataDerivTest() {
S_EXTRAP.firstDerivative(null, 5.0);
}
/**
* Double value is null
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullValueDerivTest() {
S_EXTRAP.firstDerivative(S_DATA, null);
}
/**
* data bundle is null
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullDataSenseTest() {
S_EXTRAP.getNodeSensitivitiesForValue(null, 5.0);
}
/**
* Double value is null
*/
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullValueSenseTest() {
S_EXTRAP.getNodeSensitivitiesForValue(S_DATA, null);
}
}