@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"); }