@Test
public void crossDerivativeTest() {
double[] x0Values = new double[] {1., 2., 3., 4.};
double[] x1Values = new double[] {-1., 0., 1., 2., 3.};
final int n0Data = x0Values.length;
final int n1Data = x1Values.length;
double[][] yValues =
new double[][] {
{
1.0, -1.0, 0.0, 1.0, 0.0,
},
{1.0, -1.0, 0.0, 1.0, -2.0},
{1.0, -2.0, 0.0, -2.0, -2.0},
{-1.0, -1.0, -2.0, -2.0, -1.0}
};
NaturalSplineInterpolator method = new NaturalSplineInterpolator();
PiecewisePolynomialInterpolator2D interp = new BicubicSplineInterpolator(method);
PiecewisePolynomialResult2D result = interp.interpolate(x0Values, x1Values, yValues);
final int n0IntExp = n0Data - 1;
final int n1IntExp = n1Data - 1;
final int orderExp = 4;
final int n0Keys = 51;
final int n1Keys = 61;
double[] x0Keys = new double[n0Keys];
double[] x1Keys = new double[n1Keys];
for (int i = 0; i < n0Keys; ++i) {
x0Keys[i] = 0. + 5. * i / (n0Keys - 1);
}
for (int i = 0; i < n1Keys; ++i) {
x1Keys[i] = -2. + 6. * i / (n1Keys - 1);
}
assertEquals(result.getNumberOfIntervals()[0], n0IntExp);
assertEquals(result.getNumberOfIntervals()[1], n1IntExp);
assertEquals(result.getOrder()[0], orderExp);
assertEquals(result.getOrder()[1], orderExp);
for (int i = 0; i < n0Data; ++i) {
final double ref = Math.abs(x0Values[i]) == 0. ? 1. : Math.abs(x0Values[i]);
assertEquals(result.getKnots0().getData()[i], x0Values[i], ref * EPS);
assertEquals(result.getKnots2D().get(0).getData()[i], x0Values[i], ref * EPS);
}
for (int i = 0; i < n1Data; ++i) {
final double ref = Math.abs(x1Values[i]) == 0. ? 1. : Math.abs(x1Values[i]);
assertEquals(result.getKnots1().getData()[i], x1Values[i], ref * EPS);
assertEquals(result.getKnots2D().get(1).getData()[i], x1Values[i], ref * EPS);
}
for (int i = 0; i < n0Data - 1; ++i) {
for (int j = 0; j < n1Data - 1; ++j) {
final double ref = Math.abs(yValues[i][j]) == 0. ? 1. : Math.abs(yValues[i][j]);
assertEquals(
result.getCoefs()[i][j].getData()[orderExp - 1][orderExp - 1],
yValues[i][j],
ref * EPS);
}
}
double[][] resValues =
interp.interpolate(x0Values, x1Values, yValues, x0Values, x1Values).getData();
final PiecewisePolynomialFunction2D func2D = new PiecewisePolynomialFunction2D();
double[][] resDiffX0 = func2D.differentiateX0(result, x0Values, x1Values).getData();
double[][] resDiffX1 = func2D.differentiateX1(result, x0Values, x1Values).getData();
final PiecewisePolynomialFunction1D func1D = new PiecewisePolynomialFunction1D();
double[][] expDiffX0 =
func1D
.differentiate(
method.interpolate(
x0Values, OG_ALGEBRA.getTranspose(new DoubleMatrix2D(yValues)).getData()),
x0Values)
.getData();
double[][] expDiffX1 =
func1D.differentiate(method.interpolate(x1Values, yValues), x1Values).getData();
for (int i = 0; i < n0Data; ++i) {
for (int j = 0; j < n1Data; ++j) {
final double expVal = expDiffX1[i][j];
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(resDiffX1[i][j], expVal, ref * EPS);
}
}
// System.out.println(new DoubleMatrix2D(expDiffX0));
// System.out.println(new DoubleMatrix2D(resDiffX0));
for (int i = 0; i < n0Data; ++i) {
for (int j = 0; j < n1Data; ++j) {
final double expVal = expDiffX0[j][i];
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(resDiffX0[i][j], expVal, ref * EPS);
}
}
for (int i = 0; i < n0Data; ++i) {
for (int j = 0; j < n1Data; ++j) {
final double expVal = yValues[i][j];
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(resValues[i][j], expVal, ref * EPS);
}
}
}
@Override
public Double evaluate(final Double lambda) {
final DoubleMatrix1D x = (DoubleMatrix1D) OG_ALGEBRA.add(_x0, OG_ALGEBRA.scale(_p, lambda));
return _f.evaluate(x);
}
