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Java example source code file (BicubicSplineInterpolatingFunctionTest.java)

This example Java source code file (BicubicSplineInterpolatingFunctionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

bicubicsplinefunction, bicubicsplineinterpolatingfunction, bicubicsplineinterpolatingfunctiontest, bivariatefunction, dimensionmismatchexception, half-way, ignore@test, mathillegalargumentexception, outofrangeexception, randomgenerator, suppresswarnings, test, uniformrealdistribution, well19937c

The BicubicSplineInterpolatingFunctionTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.analysis.interpolation;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.analysis.BivariateFunction;
import org.apache.commons.math3.distribution.UniformRealDistribution;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.junit.Assert;
import org.junit.Test;
import org.junit.Ignore;

/**
 * Test case for the bicubic function.
 *
 * @deprecated as of 3.4 replaced by
 * {@link org.apache.commons.math3.analysis.interpolation.PiecewiseBicubicSplineInterpolatingFunction}
 */
@Deprecated
public final class BicubicSplineInterpolatingFunctionTest {
    /**
     * Test preconditions.
     */
    @Test
    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 {
            bcf = new BicubicSplineInterpolatingFunction(wxval, yval, zval, zval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException e) {
            // Expected
        }
        double[] wyval = new double[] {-4, -1, -1, 2.5};
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, wyval, zval, zval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException e) {
            // Expected
        }
        double[][] wzval = new double[xval.length][yval.length - 1];
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }

        wzval = new double[xval.length - 1][yval.length];
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
    }

    /**
     * Test for a plane.
     * <p>
     * z = 2 x - 3 y + 5
     */
    @Ignore@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);
    }

    /**
     * Test for a paraboloid.
     * <p>
     * z = 2 x<sup>2 - 3 y2 + 4 x y - 5
     */
    @Ignore@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);
    }

    /**
     * Test for partial derivatives of {@link BicubicSplineFunction}.
     * <p>
     * f(x, y) = Σ<sub>iΣj (i+1) (j+2) xi yj
     */
    @Ignore@Test
    public void testSplinePartialDerivatives() {
        final int N = 4;
        final double[] coeff = new double[16];

        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                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);
    }

    /**
     * Test that the partial derivatives computed from a
     * {@link BicubicSplineInterpolatingFunction} match the input data.
     * <p>
     * f(x, y) = 5
     *           - 3 x + 2 y
     *           - x y + 2 x<sup>2 - 3 y2
     *           + 4 x<sup>2 y - x y2 - 3 x3 + y3
     */
    @Ignore@Test
    public void testMatchingPartialDerivatives() {
        final int sz = 21;
        double[] val = new double[sz];
        // Coordinate values
        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);
            }
        }
    }

    /**
     * Interpolating a plane.
     * <p>
     * z = 2 x - 3 y + 5
     */
    @Test
    public void testInterpolation1() {
        final int sz = 21;
        double[] xval = new double[sz];
        double[] yval = new double[sz];
        // Coordinate values
        final double delta = 1d / (sz - 1);
        for (int i = 0; i < sz; i++) {
            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 - 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;
            }
        }

        final BivariateFunction bcf
            = new BicubicSplineInterpolatingFunction(xval, yval, zval,
                                                     dZdX, dZdY, dZdXdY);
        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 = 6;
        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) + " " + bcf.value(x, y));
                Assert.assertEquals(f.value(x, y),  bcf.value(x, y), tol);
            }
//             System.out.println();
        }
    }

    /**
     * Interpolating a paraboloid.
     * <p>
     * z = 2 x<sup>2 - 3 y2 + 4 x y - 5
     */
    @Test
    public void testInterpolation2() {
        final int sz = 21;
        double[] xval = new double[sz];
        double[] yval = new double[sz];
        // Coordinate values
        final double delta = 1d / (sz - 1);
        for (int i = 0; i < sz; i++) {
            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]);
            }
        }
        // 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;

        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 double tol = 224;
        for (int i = 0; i < sz; i++) {
            x = distX.sample();
            for (int j = 0; j < sz; j++) {
                y = distY.sample();
//                 System.out.println(x + " " + y + " " + f.value(x, y) + " " + bcf.value(x, y));
                Assert.assertEquals(f.value(x, y),  bcf.value(x, y), tol);
            }
//             System.out.println();
        }
    }

    @Test
    public void testIsValidPoint() {
        final double xMin = -12;
        final double xMax = 34;
        final double yMin = 5;
        final double yMax = 67;
        final double[] xval = new double[] { xMin, xMax };
        final double[] yval = new double[] { yMin, yMax };
        final double[][] f = new double[][] { { 1, 2 },
                                              { 3, 4 } };
        final double[][] dFdX = f;
        final double[][] dFdY = f;
        final double[][] dFdXdY = f;

        final BicubicSplineInterpolatingFunction bcf
            = new BicubicSplineInterpolatingFunction(xval, yval, f,
                                                     dFdX, dFdY, dFdXdY);

        double x, y;

        x = xMin;
        y = yMin;
        Assert.assertTrue(bcf.isValidPoint(x, y));
        // Ensure that no exception is thrown.
        bcf.value(x, y);

        x = xMax;
        y = yMax;
        Assert.assertTrue(bcf.isValidPoint(x, y));
        // Ensure that no exception is thrown.
        bcf.value(x, y);

        final double xRange = xMax - xMin;
        final double yRange = yMax - yMin;
        x = xMin + xRange / 3.4;
        y = yMin + yRange / 1.2;
        Assert.assertTrue(bcf.isValidPoint(x, y));
        // Ensure that no exception is thrown.
        bcf.value(x, y);

        final double small = 1e-8;
        x = xMin - small;
        y = yMax;
        Assert.assertFalse(bcf.isValidPoint(x, y));
        // Ensure that an exception would have been thrown.
        try {
            bcf.value(x, y);
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException expected) {}

        x = xMin;
        y = yMax + small;
        Assert.assertFalse(bcf.isValidPoint(x, y));
        // Ensure that an exception would have been thrown.
        try {
            bcf.value(x, y);
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException expected) {}
    }
}

Other Java examples (source code examples)

Here is a short list of links related to this Java BicubicSplineInterpolatingFunctionTest.java source code file:



my book on functional programming

 

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