public void positivityClampedTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5.};
final double[] yValues = new double[] {0., 0.1, 1., 1., 20., 5., 0.};
PiecewisePolynomialInterpolator interp = new CubicSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
assertEquals(resultPos.getDimensions(), result.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), result.getOrder());
final int nPts = 101;
for (int i = 0; i < 101; ++i) {
final double key = 1. + 4. / (nPts - 1) * i;
assertTrue(function.evaluate(resultPos, key).get(0) >= 0.);
}
final int nData = xValues.length;
for (int i = 1; i < nData - 2; ++i) {
final double tau = Math.signum(resultPos.getCoefMatrix().get(i, 3));
assertTrue(
resultPos.getCoefMatrix().get(i, 2) * tau
>= -3. * yValues[i + 1] * tau / (xValues[i + 1] - xValues[i]));
assertTrue(
resultPos.getCoefMatrix().get(i, 2) * tau
<= 3. * yValues[i + 1] * tau / (xValues[i] - xValues[i - 1]));
}
}
/** PiecewiseCubicHermiteSplineInterpolator is not modified for positive data */
public void noModificationTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5.};
final double[][] yValues = new double[][] {{0.1, 1., 1., 20., 5.}, {1., 2., 3., 0., 0.}};
PiecewisePolynomialInterpolator interp = new PiecewiseCubicHermiteSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
assertEquals(resultPos.getDimensions(), result.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), result.getOrder());
for (int i = 1; i < xValues.length - 1; ++i) {
for (int j = 0; j < 4; ++j) {
final double ref =
result.getCoefMatrix().get(i, j) == 0.
? 1.
: Math.abs(result.getCoefMatrix().get(i, j));
assertEquals(
resultPos.getCoefMatrix().get(i, j), result.getCoefMatrix().get(i, j), ref * EPS);
}
}
}
public void flipTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6.};
final double[] yValues = new double[] {3., 0.1, 0.01, 0.01, 0.1, 3.};
final double[] xValuesFlip = new double[] {6., 2., 3., 5., 4., 1.};
final double[] yValuesFlip = new double[] {3., 0.1, 0.01, 0.1, 0.01, 3.};
PiecewisePolynomialInterpolator interp = new NaturalSplineInterpolator();
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
PiecewisePolynomialResult resultPosFlip = interpPos.interpolate(xValuesFlip, yValuesFlip);
assertEquals(resultPos.getDimensions(), resultPosFlip.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), resultPosFlip.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), resultPosFlip.getOrder());
final int nPts = 101;
for (int i = 0; i < 101; ++i) {
final double key = 1. + 5. / (nPts - 1) * i;
assertTrue(function.evaluate(resultPos, key).get(0) >= 0.);
}
final int nData = xValues.length;
for (int i = 0; i < nData - 1; ++i) {
for (int k = 0; k < 4; ++k)
assertEquals(resultPos.getCoefMatrix().get(i, k), resultPosFlip.getCoefMatrix().get(i, k));
}
}
public void positivityEndIntervalsTest() {
final double[] xValues = new double[] {1., 2., 3., 4., 5., 6.};
final double[][] yValues =
new double[][] {{0.01, 0.01, 0.01, 10., 20., 1.}, {0.01, 0.01, 10., 10., 0.01, 0.01}};
PiecewisePolynomialInterpolator interp = new NaturalSplineInterpolator();
PiecewisePolynomialResult result = interp.interpolate(xValues, yValues);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialInterpolator interpPos =
new NonnegativityPreservingCubicSplineInterpolator(interp);
PiecewisePolynomialResult resultPos = interpPos.interpolate(xValues, yValues);
assertEquals(resultPos.getDimensions(), result.getDimensions());
assertEquals(resultPos.getNumberOfIntervals(), result.getNumberOfIntervals());
assertEquals(resultPos.getOrder(), result.getOrder());
final int nPts = 101;
for (int i = 0; i < 101; ++i) {
final double key = 1. + 5. / (nPts - 1) * i;
assertTrue(function.evaluate(resultPos, key).get(0) >= 0.);
}
int dim = yValues.length;
int nData = xValues.length;
for (int j = 0; j < dim; ++j) {
for (int i = 1; i < nData - 2; ++i) {
DoubleMatrix coefMatrix = resultPos.getCoefMatrix();
double tau = Math.signum(coefMatrix.get(dim * i + j, 3));
assertTrue(
coefMatrix.get(dim * i + j, 2) * tau
>= -3. * yValues[j][i] * tau / (xValues[i + 1] - xValues[i]));
assertTrue(
coefMatrix.get(dim * i + j, 2) * tau
<= 3. * yValues[j][i] * tau / (xValues[i] - xValues[i - 1]));
}
}
}