Examples of TrivariateRealFunction

org.apache.commons.math.analysis.TrivariateRealFunction
An interface representing a trivariate real function. @since 2.2 @version $Revision$ $Date$

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

        double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5};
        double[][][] fval = new double[xval.length][yval.length][zval.length];


        TrivariateRealGridInterpolator interpolator = new TricubicSplineInterpolator();
        
        @SuppressWarnings("unused")
        TrivariateRealFunction p = interpolator.interpolate(xval, yval, zval, fval);
        
        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
            p = interpolator.interpolate(wxval, yval, zval, fval);

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

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


        TrivariateRealGridInterpolator interpolator = new TricubicSplineInterpolator();


        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5};
        double[][][] fval = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    fval[i][j][k] = f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        TrivariateRealFunction p = interpolator.interpolate(xval, yval, zval, fval);
        double x, y, z;
        double expected, result;
        
        x = 4;
        y = -3;
        z = 0;
        expected = f.value(x, y, z);
        result = p.value(x, y, z);
        Assert.assertEquals("On sample point", expected, result, 1e-15);


        x = 4.5;
        y = -1.5;
        z = -4.25;
        expected = f.value(x, y, z);
        result = p.value(x, y, z);
        Assert.assertEquals("half-way between sample points (middle of the patch)", expected, result, 0.3);


        x = 3.5;
        y = -3.5;
        z = -10;
        expected = f.value(x, y, z);
        result = p.value(x, y, z);
        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.TrivariateRealFunction

        final double omega = 0.5;
        final double kx = 2;
        final double ky = 1;


        // Function values
        TrivariateRealFunction f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.cos(omega * z - kx * x - ky * y);
                }
            };
        
        double[][][] fval = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    fval[i][j][k] = f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        TrivariateRealGridInterpolator interpolator = new TricubicSplineInterpolator();


        TrivariateRealFunction p = interpolator.interpolate(xval, yval, zval, fval);
        double x, y, z;
        double expected, result;
        
        x = 4;
        y = -3;
        z = 0;
        expected = f.value(x, y, z);
        result = p.value(x, y, z);
        Assert.assertEquals("On sample point",
                            expected, result, 1e-12);


        x = 4.5;
        y = -1.5;
        z = -4.25;
        expected = f.value(x, y, z);
        result = p.value(x, y, z);
        Assert.assertEquals("Half-way between sample points (middle of the patch)",
                            expected, result, 0.1);


        x = 3.5;
        y = -3.5;
        z = -10;
        expected = f.value(x, y, z);
        result = p.value(x, y, z);
        Assert.assertEquals("Half-way between sample points (border of the patch)",
                            expected, result, 0.1);
    }

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

        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2.5};
        double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5};
        double[][][] fval = new double[xval.length][yval.length][zval.length];


        @SuppressWarnings("unused")
        TrivariateRealFunction tcf = new TricubicSplineInterpolatingFunction(xval, yval, zval,
                                                                             fval, fval, fval, fval,
                                                                             fval, fval, fval, fval);
        
        double[] wxval = new double[] {3, 2, 5, 6.5};

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

        double[] xval = new double[] {3, 4, 5, 6.5};
        double[] yval = new double[] {-4, -3, -1, 2, 2.5};
        double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5};


        // Function values
        TrivariateRealFunction f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return 2 * x - 3 * y - 4 * z + 5;
                }
            };


        double[][][] fval = new double[xval.length][yval.length][zval.length];


        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    fval[i][j][k] = f.value(xval[i], yval[j], zval[k]);
                }
            }
        }
        // Partial derivatives with respect to x
        double[][][] dFdX = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    dFdX[i][j][k] = 2;
                }
            }
        }
        // Partial derivatives with respect to y
        double[][][] dFdY = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    dFdY[i][j][k] = -3;
                }
            }
        }


        // Partial derivatives with respect to z
        double[][][] dFdZ = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    dFdZ[i][j][k] = -4;
                }
            }
        }
        // Partial cross-derivatives
        double[][][] d2FdXdY = new double[xval.length][yval.length][zval.length];
        double[][][] d2FdXdZ = new double[xval.length][yval.length][zval.length];
        double[][][] d2FdYdZ = new double[xval.length][yval.length][zval.length];
        double[][][] d3FdXdYdZ = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    d2FdXdY[i][j][k] = 0;
                    d2FdXdZ[i][j][k] = 0;
                    d2FdYdZ[i][j][k] = 0;
                    d3FdXdYdZ[i][j][k] = 0;
                }
            }
        }


        TrivariateRealFunction tcf = new TricubicSplineInterpolatingFunction(xval, yval, zval,
                                                                             fval, dFdX, dFdY, dFdZ,
                                                                             d2FdXdY, d2FdXdZ, d2FdYdZ,
                                                                             d3FdXdYdZ);
        double x, y, z;
        double expected, result;


        x = 4;
        y = -3;
        z = 0;
        expected = f.value(x, y, z);
        result = tcf.value(x, y, z);
        Assert.assertEquals("On sample point",
                            expected, result, 1e-15);


        x = 4.5;
        y = -1.5;
        z = -4.25;
        expected = f.value(x, y, z);
        result = tcf.value(x, y, z);
        Assert.assertEquals("Half-way between sample points (middle of the patch)",
                            expected, result, 0.3);


        x = 3.5;
        y = -3.5;
        z = -10;
        expected = f.value(x, y, z);
        result = tcf.value(x, y, z);
        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.TrivariateRealFunction

        final double omega = 0.5;
        final double kx = 2;
        final double ky = 1;
        
        // Function values
        TrivariateRealFunction f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.cos(omega * z - kx * x - ky * y);
                }
            };
        
        double[][][] fval = new double[xval.length][yval.length][zval.length];
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    fval[i][j][k] = f.value(xval[i], yval[j], zval[k]);
                }
            }
        }
        
        // Partial derivatives with respect to x
        double[][][] dFdX = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction dFdX_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.sin(omega * z - kx * x - ky * y) * kx;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    dFdX[i][j][k] = dFdX_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }
            
        // Partial derivatives with respect to y
        double[][][] dFdY = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction dFdY_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.sin(omega * z - kx * x - ky * y) * ky;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    dFdY[i][j][k] = dFdY_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        // Partial derivatives with respect to z
        double[][][] dFdZ = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction dFdZ_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return -a * FastMath.sin(omega * z - kx * x - ky * y) * omega;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    dFdZ[i][j][k] = dFdZ_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        // Partial second derivatives w.r.t. (x, y)
        double[][][] d2FdXdY = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction d2FdXdY_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return -a * FastMath.cos(omega * z - kx * x - ky * y) * kx * ky;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    d2FdXdY[i][j][k] = d2FdXdY_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        // Partial second derivatives w.r.t. (x, z)
        double[][][] d2FdXdZ = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction d2FdXdZ_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.cos(omega * z - kx * x - ky * y) * kx * omega;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    d2FdXdZ[i][j][k] = d2FdXdZ_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        // Partial second derivatives w.r.t. (y, z)
        double[][][] d2FdYdZ = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction d2FdYdZ_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.cos(omega * z - kx * x - ky * y) * ky * omega;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    d2FdYdZ[i][j][k] = d2FdYdZ_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        // Partial third derivatives
        double[][][] d3FdXdYdZ = new double[xval.length][yval.length][zval.length];
        TrivariateRealFunction d3FdXdYdZ_f = new TrivariateRealFunction() {
                public double value(double x, double y, double z) {
                    return a * FastMath.sin(omega * z - kx * x - ky * y) * kx * ky * omega;
                }
            };
        for (int i = 0; i < xval.length; i++) {
            for (int j = 0; j < yval.length; j++) {
                for (int k = 0; k < zval.length; k++) {
                    d3FdXdYdZ[i][j][k] = d3FdXdYdZ_f.value(xval[i], yval[j], zval[k]);
                }
            }
        }


        TrivariateRealFunction tcf = new TricubicSplineInterpolatingFunction(xval, yval, zval,
                                                                             fval, dFdX, dFdY, dFdZ,
                                                                             d2FdXdY, d2FdXdZ, d2FdYdZ,
                                                                             d3FdXdYdZ);
        double x, y, z;
        double expected, result;
        
        x = 4;
        y = -3;
        z = 0;
        expected = f.value(x, y, z);
        result = tcf.value(x, y, z);
        Assert.assertEquals("On sample point",
                            expected, result, 1e-14);


        x = 4.5;
        y = -1.5;
        z = -4.25;
        expected = f.value(x, y, z);
        result = tcf.value(x, y, z);
        Assert.assertEquals("Half-way between sample points (middle of the patch)",
                            expected, result, 0.1);


        x = 3.5;
        y = -3.5;
        z = -10;
        expected = f.value(x, y, z);
        result = tcf.value(x, y, z);
        Assert.assertEquals("Half-way between sample points (border of the patch)",
                            expected, result, 0.1);
    }

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