Package org.apache.commons.math3.analysis

Examples of org.apache.commons.math3.analysis.BivariateFunction


            xval[i] = -1 + 15 * i * delta;
            yval[i] = -20 + 30 * i * delta;
        }

        // Function values
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x * x - 3 * y * y + 4 * x * y - 5;
                }
            };
        double[][] zval = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                zval[i][j] = f.value(xval[i], yval[j]);
            }
        }

        BivariateGridInterpolator interpolator = new BicubicSplineInterpolator();
        BivariateFunction p = interpolator.interpolate(xval, yval, zval);
        double x, y;

        final RandomGenerator rng = new Well19937c(1234567L); // "tol" depends on the seed.
        final UniformRealDistribution distX
            = new UniformRealDistribution(rng, xval[0], xval[xval.length - 1]);
        final UniformRealDistribution distY
            = new UniformRealDistribution(rng, yval[0], yval[yval.length - 1]);

        final int numSamples = 50;
        final double tol = 251;
        for (int i = 0; i < numSamples; i++) {
            x = distX.sample();
            for (int j = 0; j < numSamples; j++) {
                y = distY.sample();
//                 System.out.println(x + " " + y + " " + f.value(x, y) + " " + p.value(x, y));
                Assert.assertEquals(f.value(x, y),  p.value(x, y), tol);
            }
//             System.out.println();
        }
    }
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                aYY[i][j] = (j - 1) * aY[i][j];
                aXY[i][j] = j * aX[i][j];
            }
        }

        partialDerivativeX = new BivariateFunction() {
                public double value(double x, double y)  {
                    final double x2 = x * x;
                    final double[] pX = {0, 1, x, x2};

                    final double y2 = y * y;
                    final double y3 = y2 * y;
                    final double[] pY = {1, y, y2, y3};

                    return apply(pX, pY, aX);
                }
            };
        partialDerivativeY = new BivariateFunction() {
                public double value(double x, double y)  {
                    final double x2 = x * x;
                    final double x3 = x2 * x;
                    final double[] pX = {1, x, x2, x3};

                    final double y2 = y * y;
                    final double[] pY = {0, 1, y, y2};

                    return apply(pX, pY, aY);
                }
            };
        partialDerivativeXX = new BivariateFunction() {
                public double value(double x, double y)  {
                    final double[] pX = {0, 0, 1, x};

                    final double y2 = y * y;
                    final double y3 = y2 * y;
                    final double[] pY = {1, y, y2, y3};

                    return apply(pX, pY, aXX);
                }
            };
        partialDerivativeYY = new BivariateFunction() {
                public double value(double x, double y)  {
                    final double x2 = x * x;
                    final double x3 = x2 * x;
                    final double[] pX = {1, x, x2, x3};

                    final double[] pY = {0, 0, 1, y};

                    return apply(pX, pY, aYY);
                }
            };
        partialDerivativeXY = new BivariateFunction() {
                public double value(double x, double y)  {
                    final double x2 = x * x;
                    final double[] pX = {0, 1, x, x2};

                    final double y2 = y * y;
 
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    public void testPreconditions() {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2.5};
        double[][] zval = new double[xval.length][yval.length];

        @SuppressWarnings("unused")
        BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval,
                                                                           zval, zval, zval);
       
        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
View Full Code Here

    @Test
    public void testPlane() {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        // Function values
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x - 3 * y + 5;
                }
            };
        double[][] zval = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                zval[i][j] = f.value(xval[i], yval[j]);
            }
        }
        // Partial derivatives with respect to x
        double[][] dZdX = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                dZdX[i][j] = 2;
            }
        }
        // Partial derivatives with respect to y
        double[][] dZdY = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                dZdY[i][j] = -3;
            }
        }
        // Partial cross-derivatives
        double[][] dZdXdY = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                dZdXdY[i][j] = 0;
            }
        }

        BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval,
                                                                           dZdX, dZdY, dZdXdY);
        double x, y;
        double expected, result;

        x = 4;
        y = -3;
        expected = f.value(x, y);
        result = bcf.value(x, y);
        Assert.assertEquals("On sample point",
                            expected, result, 1e-15);

        x = 4.5;
        y = -1.5;
        expected = f.value(x, y);
        result = bcf.value(x, y);
        Assert.assertEquals("Half-way between sample points (middle of the patch)",
                            expected, result, 0.3);

        x = 3.5;
        y = -3.5;
        expected = f.value(x, y);
        result = bcf.value(x, y);
        Assert.assertEquals("Half-way between sample points (border of the patch)",
                            expected, result, 0.3);
    }
View Full Code Here

    @Test
    public void testParaboloid() {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        // Function values
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x * x - 3 * y * y + 4 * x * y - 5;
                }
            };
        double[][] zval = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                zval[i][j] = f.value(xval[i], yval[j]);
            }
        }
        // Partial derivatives with respect to x
        double[][] dZdX = new double[xval.length][yval.length];
        BivariateFunction dfdX = new BivariateFunction() {
                public double value(double x, double y) {
                    return 4 * (x + y);
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                dZdX[i][j] = dfdX.value(xval[i], yval[j]);
            }
        }
        // Partial derivatives with respect to y
        double[][] dZdY = new double[xval.length][yval.length];
        BivariateFunction dfdY = new BivariateFunction() {
                public double value(double x, double y) {
                    return 4 * x - 6 * y;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                dZdY[i][j] = dfdY.value(xval[i], yval[j]);
            }
        }
        // Partial cross-derivatives
        double[][] dZdXdY = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                dZdXdY[i][j] = 4;
            }
        }

        BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval,
                                                                           dZdX, dZdY, dZdXdY);
        double x, y;
        double expected, result;
       
        x = 4;
        y = -3;
        expected = f.value(x, y);
        result = bcf.value(x, y);
        Assert.assertEquals("On sample point",
                            expected, result, 1e-15);

        x = 4.5;
        y = -1.5;
        expected = f.value(x, y);
        result = bcf.value(x, y);
        Assert.assertEquals("Half-way between sample points (middle of the patch)",
                            expected, result, 2);

        x = 3.5;
        y = -3.5;
        expected = f.value(x, y);
        result = bcf.value(x, y);
        Assert.assertEquals("Half-way between sample points (border of the patch)",
                            expected, result, 2);
    }
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                coeff[i + N * j] = (i + 1) * (j + 2);
            }
        }

        final BicubicSplineFunction f = new BicubicSplineFunction(coeff);
        BivariateFunction derivative;
        final double x = 0.435;
        final double y = 0.776;
        final double tol = 1e-13;

        derivative = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double y2 = y * y;
                    final double y3 = y2 * y;
                    final double yFactor = 2 + 3 * y + 4 * y2 + 5 * y3;
                    return yFactor * (2 + 6 * x + 12 * x2);
                }
            };
        Assert.assertEquals("dFdX", derivative.value(x, y),
                            f.partialDerivativeX().value(x, y), tol);
       
        derivative = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double x3 = x2 * x;
                    final double y2 = y * y;
                    final double xFactor = 1 + 2 * x + 3 * x2 + 4 * x3;
                    return xFactor * (3 + 8 * y + 15 * y2);
                }
            };
        Assert.assertEquals("dFdY", derivative.value(x, y),
                            f.partialDerivativeY().value(x, y), tol);

        derivative = new BivariateFunction() {
                public double value(double x, double y) {
                    final double y2 = y * y;
                    final double y3 = y2 * y;
                    final double yFactor = 2 + 3 * y + 4 * y2 + 5 * y3;
                    return yFactor * (6 + 24 * x);
                }
            };
        Assert.assertEquals("d2FdX2", derivative.value(x, y),
                            f.partialDerivativeXX().value(x, y), tol);

        derivative = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double x3 = x2 * x;
                    final double xFactor = 1 + 2 * x + 3 * x2 + 4 * x3;
                    return xFactor * (8 + 30 * y);
                }
            };
        Assert.assertEquals("d2FdY2", derivative.value(x, y),
                            f.partialDerivativeYY().value(x, y), tol);

        derivative = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double y2 = y * y;
                    final double yFactor = 3 + 8 * y + 15 * y2;
                    return yFactor * (2 + 6 * x + 12 * x2);
                }
            };
        Assert.assertEquals("d2FdXdY", derivative.value(x, y),
                            f.partialDerivativeXY().value(x, y), tol);
    }
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        final double delta = 1d / (sz - 1);
        for (int i = 0; i < sz; i++) {
            val[i] = i * delta;
        }
        // Function values
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double x3 = x2 * x;
                    final double y2 = y * y;
                    final double y3 = y2 * y;

                    return 5
                        - 3 * x + 2 * y
                        - x * y + 2 * x2 - 3 * y2
                        + 4 * x2 * y - x * y2 - 3 * x3 + y3;
                }
            };
        double[][] fval = new double[sz][sz];
        for (int i = 0; i < sz; i++) {
            for (int j = 0; j < sz; j++) {
                fval[i][j] = f.value(val[i], val[j]);
            }
        }
        // Partial derivatives with respect to x
        double[][] dFdX = new double[sz][sz];
        BivariateFunction dfdX = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double y2 = y * y;                   
                    return - 3 - y + 4 * x + 8 * x * y - y2 - 9 * x2;
                }
            };
        for (int i = 0; i < sz; i++) {
            for (int j = 0; j < sz; j++) {
                dFdX[i][j] = dfdX.value(val[i], val[j]);
            }
        }
        // Partial derivatives with respect to y
        double[][] dFdY = new double[sz][sz];
        BivariateFunction dfdY = new BivariateFunction() {
                public double value(double x, double y) {
                    final double x2 = x * x;
                    final double y2 = y * y;                   
                    return 2 - x - 6 * y + 4 * x2 - 2 * x * y + 3 * y2;
                }
            };
        for (int i = 0; i < sz; i++) {
            for (int j = 0; j < sz; j++) {
                dFdY[i][j] = dfdY.value(val[i], val[j]);
            }
        }
        // Partial cross-derivatives
        double[][] d2FdXdY = new double[sz][sz];
        BivariateFunction d2fdXdY = new BivariateFunction() {
                public double value(double x, double y) {
                    return -1 + 8 * x - 2 * y;
                }
            };
        for (int i = 0; i < sz; i++) {
            for (int j = 0; j < sz; j++) {
                d2FdXdY[i][j] = d2fdXdY.value(val[i], val[j]);
            }
        }

        BicubicSplineInterpolatingFunction bcf
            = new BicubicSplineInterpolatingFunction(val, val, fval, dFdX, dFdY, d2FdXdY);

        double x, y;
        double expected, result;

        final double tol = 1e-12;
        for (int i = 0; i < sz; i++) {
            x = val[i];
            for (int j = 0; j < sz; j++) {
                y = val[j];
               
                expected = dfdX.value(x, y);
                result = bcf.partialDerivativeX(x, y);
                Assert.assertEquals(x + " " + y + " dFdX", expected, result, tol);

                expected = dfdY.value(x, y);
                result = bcf.partialDerivativeY(x, y);
                Assert.assertEquals(x + " " + y + " dFdY", expected, result, tol);
               
                expected = d2fdXdY.value(x, y);
                result = bcf.partialDerivativeXY(x, y);
                Assert.assertEquals(x + " " + y + " d2FdXdY", expected, result, tol);
            }
        }
    }
View Full Code Here

        double[] yval = new double[] {-4, -3, -1, 2.5};
        double[][] zval = new double[xval.length][yval.length];

        BivariateGridInterpolator interpolator = new BicubicSplineInterpolator();
       
        @SuppressWarnings("unused")
        BivariateFunction p = interpolator.interpolate(xval, yval, zval);
       
        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
            p = interpolator.interpolate(wxval, yval, zval);
View Full Code Here

     * <p>
     * z = 2 x - 3 y + 5
     */
    @Test
    public void testPlane() {
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x - 3 * y + 5;
                }
            };

        BivariateGridInterpolator interpolator = new BicubicSplineInterpolator();

        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        double[][] zval = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                zval[i][j] = f.value(xval[i], yval[j]);
            }
        }

        BivariateFunction p = interpolator.interpolate(xval, yval, zval);
        double x, y;
        double expected, result;
       
        x = 4;
        y = -3;
        expected = f.value(x, y);
        result = p.value(x, y);
        Assert.assertEquals("On sample point", expected, result, 1e-15);

        x = 4.5;
        y = -1.5;
        expected = f.value(x, y);
        result = p.value(x, y);
        Assert.assertEquals("half-way between sample points (middle of the patch)", expected, result, 0.3);

        x = 3.5;
        y = -3.5;
        expected = f.value(x, y);
        result = p.value(x, y);
        Assert.assertEquals("half-way between sample points (border of the patch)", expected, result, 0.3);
    }
View Full Code Here

     * <p>
     * z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
     */
    @Test
    public void testParaboloid() {
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x * x - 3 * y * y + 4 * x * y - 5;
                }
            };

        BivariateGridInterpolator interpolator = new BicubicSplineInterpolator();

        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -2, -1, 0.5, 2.5};
        double[][] zval = new double[xval.length][yval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                zval[i][j] = f.value(xval[i], yval[j]);
            }
        }

        BivariateFunction p = interpolator.interpolate(xval, yval, zval);
        double x, y;
        double expected, result;
       
        x = 5;
        y = 0.5;
        expected = f.value(x, y);
        result = p.value(x, y);
        Assert.assertEquals("On sample point", expected, result, 1e-13);

        x = 4.5;
        y = -1.5;
        expected = f.value(x, y);
        result = p.value(x, y);
        Assert.assertEquals("half-way between sample points (middle of the patch)", expected, result, 0.2);

        x = 3.5;
        y = -3.5;
        expected = f.value(x, y);
        result = p.value(x, y);
        Assert.assertEquals("half-way between sample points (border of the patch)", expected, result, 0.2);
    }
View Full Code Here

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