@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);
}
}
}
/** Tests below for debugging */
@Test(enabled = false)
public void printTest() {
// double[] x0Values = new double[] {0., 1., 2., 3. };
// double[] x1Values = new double[] {0., 0.000000000001, 2. };
double[] x0Values = new double[] {0., 1., 2., 3.};
double[] x1Values = new double[] {0., 1., 2.};
double[][] yValues =
new double[][] {
{1.e-20, 3.e-120, 5.e-20},
{2.e-20, 3.e-120, 4.e-120},
{1.e-20, 1.e-120, 1.e-20},
{4.e-120, 3.e-20, 2.e-20}
};
// double[] x0Values = new double[] {0., 1., 2. };
// double[] x1Values = new double[] {0., 1., 2., 3. };
// double[][] yValues = new double[][] { {1., 3., 5., 7. }, {2., 3., 4., 5. }, {1., 1., 1.,
// 1. } };
BicubicSplineInterpolator intp = new BicubicSplineInterpolator(new CubicSplineInterpolator());
PiecewisePolynomialResult2D result2D = intp.interpolate(x0Values, x1Values, yValues);
System.out.println(result2D.getCoefs()[0][0]);
System.out.println(result2D.getCoefs()[2][1]);
final int n0Keys = 31;
final int n1Keys = 21;
double[] x0Keys = new double[n0Keys];
double[] x1Keys = new double[n1Keys];
for (int i = 0; i < n0Keys; ++i) {
x0Keys[i] = 0. + 3. * i / (n0Keys - 1);
}
for (int i = 0; i < n1Keys; ++i) {
x1Keys[i] = 0. + 2. * i / (n1Keys - 1);
}
// final int n0Keys = 61;
// final int n1Keys = 101;
// double[] x0Keys = new double[n0Keys];
// double[] x1Keys = new double[n1Keys];
// for (int i = 0; i < n0Keys; ++i) {
// x0Keys[i] = -1. + 4. * i / (n0Keys - 1);
// }
// for (int i = 0; i < n1Keys; ++i) {
// x1Keys[i] = -1. + 5. * i / (n1Keys - 1);
// }
PiecewisePolynomialFunction2D func = new PiecewisePolynomialFunction2D();
final double[][] values = func.evaluate(result2D, x0Keys, x1Keys).getData();
for (int i = 0; i < n0Keys; ++i) {
System.out.print("\t" + x0Keys[i]);
}
System.out.print("\n");
for (int j = 0; j < n1Keys; ++j) {
System.out.print(x1Keys[j]);
for (int i = 0; i < n0Keys; ++i) {
System.out.print("\t" + values[i][j]);
}
System.out.print("\n");
}
System.out.print("\n");
for (int i = 0; i < x0Values.length; ++i) {
System.out.print("\t" + x0Values[i]);
}
System.out.print("\n");
for (int j = 0; j < x1Values.length; ++j) {
System.out.print(x1Values[j]);
for (int i = 0; i < x0Values.length; ++i) {
System.out.print("\t" + yValues[i][j]);
}
System.out.print("\n");
}
System.out.print("\n");
}
@Test
public void linearTest() {
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[n0Data][n1Data];
for (int i = 0; i < n0Data; ++i) {
for (int j = 0; j < n1Data; ++j) {
yValues[i][j] = (x0Values[i] + 2.) * (x1Values[j] + 5.);
}
}
// System.out.println(new DoubleMatrix2D(yValues));
CubicSplineInterpolator method = new CubicSplineInterpolator();
PiecewisePolynomialInterpolator2D interp =
new BicubicSplineInterpolator(new CubicSplineInterpolator[] {method, method});
PiecewisePolynomialResult2D result = interp.interpolate(x0Values, x1Values, yValues);
final int n0IntExp = n0Data - 1;
final int n1IntExp = n1Data - 1;
final int orderExp = 4;
DoubleMatrix2D[][] coefsExp = new DoubleMatrix2D[n0Data - 1][n1Data - 1];
for (int i = 0; i < n0Data - 1; ++i) {
for (int j = 0; j < n1Data - 1; ++j) {
coefsExp[i][j] =
new DoubleMatrix2D(
new double[][] {
{
0., 0., 0., 0.,
},
{
0., 0., 0., 0.,
},
{0., 0., 1., (5. + x1Values[j])},
{0., 0., (2. + x0Values[i]), (2. + x0Values[i]) * (5. + x1Values[j])}
});
}
}
assertEquals(result.getNumberOfIntervals()[0], n0IntExp);
assertEquals(result.getNumberOfIntervals()[1], n1IntExp);
assertEquals(result.getOrder()[0], orderExp);
assertEquals(result.getOrder()[1], orderExp);
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);
}
// PiecewisePolynomialFunction2D func = new PiecewisePolynomialFunction2D();
// final double[][] values = func.evaluate(result, x0Keys, x1Keys).getData();
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) {
for (int k = 0; k < orderExp; ++k) {
for (int l = 0; l < orderExp; ++l) {
final double ref =
Math.abs(coefsExp[i][j].getData()[k][l]) == 0.
? 1.
: Math.abs(coefsExp[i][j].getData()[k][l]);
assertEquals(
result.getCoefs()[i][j].getData()[k][l], coefsExp[i][j].getData()[k][l], ref * EPS);
}
}
}
}
double[][] resValues =
interp.interpolate(x0Values, x1Values, yValues, x0Keys, x1Keys).getData();
for (int i = 0; i < n0Keys; ++i) {
for (int j = 0; j < n1Keys; ++j) {
final double expVal = (x0Keys[i] + 2.) * (x1Keys[j] + 5.);
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(resValues[i][j], expVal, ref * EPS);
}
}
// final PiecewisePolynomialFunction2D func = new PiecewisePolynomialFunction2D();
for (int i = 0; i < n0Keys; ++i) {
for (int j = 0; j < n1Keys; ++j) {
final double expVal = (x0Keys[i] + 2.) * (x1Keys[j] + 5.);
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(resValues[i][j], expVal, ref * EPS);
// assertEquals(resValues[i][j], func.evaluate(result, x0Keys[i], x1Keys[j]), ref *
// EPS);
}
}
{
final double expVal = (x0Keys[1] + 2.) * (x1Keys[2] + 5.);
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(
interp.interpolate(x0Values, x1Values, yValues, x0Keys[1], x1Keys[2]), expVal, ref * EPS);
}
{
final double expVal = (x0Keys[23] + 2.) * (x1Keys[20] + 5.);
final double ref = Math.abs(expVal) == 0. ? 1. : Math.abs(expVal);
assertEquals(
interp.interpolate(x0Values, x1Values, yValues, x0Keys[23], x1Keys[20]),
expVal,
ref * EPS);
}
// for (int i = 0; i < n0Keys; ++i) {
// System.out.print("\t" + x0Keys[i]);
// }
// System.out.print("\n");
// for (int j = 0; j < n1Keys; ++j) {
// System.out.print(x1Keys[j]);
// for (int i = 0; i < n0Keys; ++i) {
// System.out.print("\t" + values[i][j]);
// }
// System.out.print("\n");
// }
//
// System.out.print("\n");
}
