Examples of BivariateRealFunction

Examples of org.apache.commons.math.analysis.BivariateRealFunction

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    public void testPreconditions() throws MathException {
        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")
        BivariateRealFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval,
                                                                           zval, zval, zval);
       
        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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    @Test
    public void testPlane() throws MathException {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        // Function values
        BivariateRealFunction f = new BivariateRealFunction() {
                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;
            }
        }

        BivariateRealFunction 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);
    }
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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    @Test
    public void testParaboloid() throws MathException {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        // Function values
        BivariateRealFunction f = new BivariateRealFunction() {
                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];
        BivariateRealFunction dfdX = new BivariateRealFunction() {
                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];
        BivariateRealFunction dfdY = new BivariateRealFunction() {
                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;
            }
        }

        BivariateRealFunction 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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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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

        BivariateRealGridInterpolator interpolator = new SmoothingBicubicSplineInterpolator();
       
        @SuppressWarnings("unused")
        BivariateRealFunction p = interpolator.interpolate(xval, yval, zval);
       
        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
            p = interpolator.interpolate(wxval, yval, zval);
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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

        BivariateRealGridInterpolator interpolator = new SmoothingBicubicSplineInterpolator();

        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]);
            }
        }

        BivariateRealFunction 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);
    }
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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

        BivariateRealGridInterpolator interpolator = new SmoothingBicubicSplineInterpolator();

        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]);
            }
        }

        BivariateRealFunction 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);
    }
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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                aYY[i][j] = (j - 1) * aY[i][j];
                aXY[i][j] = j * aX[i][j];
            }
        }

        partialDerivativeX = new BivariateRealFunction() {
                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 BivariateRealFunction() {
                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 BivariateRealFunction() {
                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 BivariateRealFunction() {
                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 BivariateRealFunction() {
                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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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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    public void testPreconditions() throws MathException {
        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")
        BivariateRealFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval,
                                                                           zval, zval, zval);
       
        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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    @Test
    public void testPlane() throws MathException {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        // Function values
        BivariateRealFunction f = new BivariateRealFunction() {
                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;
            }
        }

        BivariateRealFunction 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);
    }
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Examples of org.apache.commons.math.analysis.BivariateRealFunction

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    @Test
    public void testParaboloid() throws MathException {
        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        // Function values
        BivariateRealFunction f = new BivariateRealFunction() {
                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];
        BivariateRealFunction dfdX = new BivariateRealFunction() {
                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];
        BivariateRealFunction dfdY = new BivariateRealFunction() {
                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;
            }
        }

        BivariateRealFunction 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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