/** 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);
}
}
/**
* 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);
}
}
}
}