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Java example source code file (BicubicInterpolatingFunctionTest.java)

This example Java source code file (BicubicInterpolatingFunctionTest.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.

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Java - Java tags/keywords

bicubicinterpolatingfunction, bicubicinterpolatingfunctiontest, bivariatefunction, dimensionmismatchexception, mathillegalargumentexception, outofrangeexception, randomgenerator, suppresswarnings, test, uniformrealdistribution, well19937c

The BicubicInterpolatingFunctionTest.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.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test case for the bicubic function.
 */
public final class BicubicInterpolatingFunctionTest {
    /**
     * 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 BicubicInterpolatingFunction(xval, yval, zval,
                                                                 zval, zval, zval);

        double[] wxval = new double[] {3, 2, 5, 6.5};
        try {
            bcf = new BicubicInterpolatingFunction(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 BicubicInterpolatingFunction(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 BicubicInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicInterpolatingFunction(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 BicubicInterpolatingFunction(xval, yval, wzval, zval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicInterpolatingFunction(xval, yval, zval, wzval, zval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, wzval, zval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
        try {
            bcf = new BicubicInterpolatingFunction(xval, yval, zval, zval, zval, wzval);
            Assert.fail("an exception should have been thrown");
        } catch (DimensionMismatchException e) {
            // Expected
        }
    }

    @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 BicubicInterpolatingFunction bcf
            = new BicubicInterpolatingFunction(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) {}
    }

    /**
     * Interpolating a plane.
     * <p>
     * z = 2 x - 3 y + 5
     */
    @Test
    public void testPlane() {
        final int numberOfElements = 10;
        final double minimumX = -10;
        final double maximumX = 10;
        final double minimumY = -10;
        final double maximumY = 10;
        final int numberOfSamples = 1000;

        final double interpolationTolerance = 1e-15;
        final double maxTolerance = 1e-14;

        // Function values
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x - 3 * y + 5;
                }
            };
        BivariateFunction dfdx = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2;
                }
            };
        BivariateFunction dfdy = new BivariateFunction() {
                public double value(double x, double y) {
                    return -3;
                }
            };
        BivariateFunction d2fdxdy = new BivariateFunction() {
                public double value(double x, double y) {
                    return 0;
                }
            };

        testInterpolation(minimumX,
                          maximumX,
                          minimumY,
                          maximumY,
                          numberOfElements,
                          numberOfSamples,
                          f,
                          dfdx,
                          dfdy,
                          d2fdxdy,
                          interpolationTolerance,
                          maxTolerance,
                          false);
    }

    /**
     * Interpolating a paraboloid.
     * <p>
     * z = 2 x<sup>2 - 3 y2 + 4 x y - 5
     */
    @Test
    public void testParaboloid() {
        final int numberOfElements = 10;
        final double minimumX = -10;
        final double maximumX = 10;
        final double minimumY = -10;
        final double maximumY = 10;
        final int numberOfSamples = 1000;

        final double interpolationTolerance = 2e-14;
        final double maxTolerance = 1e-12;

        // Function values
        BivariateFunction f = new BivariateFunction() {
                public double value(double x, double y) {
                    return 2 * x * x - 3 * y * y + 4 * x * y - 5;
                }
            };
        BivariateFunction dfdx = new BivariateFunction() {
                public double value(double x, double y) {
                    return 4 * (x + y);
                }
            };
        BivariateFunction dfdy = new BivariateFunction() {
                public double value(double x, double y) {
                    return 4 * x - 6 * y;
                }
            };
        BivariateFunction d2fdxdy = new BivariateFunction() {
                public double value(double x, double y) {
                    return 4;
                }
            };

        testInterpolation(minimumX,
                          maximumX,
                          minimumY,
                          maximumY,
                          numberOfElements,
                          numberOfSamples,
                          f,
                          dfdx,
                          dfdy,
                          d2fdxdy,
                          interpolationTolerance,
                          maxTolerance,
                          false);
    }

    /**
     * @param minimumX Lower bound of interpolation range along the x-coordinate.
     * @param maximumX Higher bound of interpolation range along the x-coordinate.
     * @param minimumY Lower bound of interpolation range along the y-coordinate.
     * @param maximumY Higher bound of interpolation range along the y-coordinate.
     * @param numberOfElements Number of data points (along each dimension).
     * @param numberOfSamples Number of test points.
     * @param f Function to test.
     * @param dfdx Partial derivative w.r.t. x of the function to test.
     * @param dfdy Partial derivative w.r.t. y of the function to test.
     * @param d2fdxdy Second partial cross-derivative of the function to test.
     * @param meanTolerance Allowed average error (mean error on all interpolated values).
     * @param maxTolerance Allowed error on each interpolated value.
     */
    private void testInterpolation(double minimumX,
                                   double maximumX,
                                   double minimumY,
                                   double maximumY,
                                   int numberOfElements,
                                   int numberOfSamples,
                                   BivariateFunction f,
                                   BivariateFunction dfdx,
                                   BivariateFunction dfdy,
                                   BivariateFunction d2fdxdy,
                                   double meanTolerance,
                                   double maxTolerance,
                                   boolean print) {
        double expected;
        double actual;
        double currentX;
        double currentY;
        final double deltaX = (maximumX - minimumX) / numberOfElements;
        final double deltaY = (maximumY - minimumY) / numberOfElements;
        final double[] xValues = new double[numberOfElements];
        final double[] yValues = new double[numberOfElements];
        final double[][] zValues = new double[numberOfElements][numberOfElements];
        final double[][] dzdx = new double[numberOfElements][numberOfElements];
        final double[][] dzdy = new double[numberOfElements][numberOfElements];
        final double[][] d2zdxdy = new double[numberOfElements][numberOfElements];

        for (int i = 0; i < numberOfElements; i++) {
            xValues[i] = minimumX + deltaX * i;
            final double x = xValues[i];
            for (int j = 0; j < numberOfElements; j++) {
                yValues[j] = minimumY + deltaY * j;
                final double y = yValues[j];
                zValues[i][j] = f.value(x, y);
                dzdx[i][j] = dfdx.value(x, y);
                dzdy[i][j] = dfdy.value(x, y);
                d2zdxdy[i][j] = d2fdxdy.value(x, y);
            }
        }

        final BivariateFunction interpolation
            = new BicubicInterpolatingFunction(xValues,
                                               yValues,
                                               zValues,
                                               dzdx,
                                               dzdy,
                                               d2zdxdy);

        for (int i = 0; i < numberOfElements; i++) {
            currentX = xValues[i];
            for (int j = 0; j < numberOfElements; j++) {
                currentY = yValues[j];
                expected = f.value(currentX, currentY);
                actual = interpolation.value(currentX, currentY);
                Assert.assertTrue("On data point: " + expected + " != " + actual,
                                  Precision.equals(expected, actual));
            }
        }

        final RandomGenerator rng = new Well19937c(1234567L);
        final UniformRealDistribution distX = new UniformRealDistribution(rng, xValues[0], xValues[xValues.length - 1]);
        final UniformRealDistribution distY = new UniformRealDistribution(rng, yValues[0], yValues[yValues.length - 1]);

        double sumError = 0;
        for (int i = 0; i < numberOfSamples; i++) {
            currentX = distX.sample();
            currentY = distY.sample();
            expected = f.value(currentX, currentY);

            if (print) {
                System.out.println(currentX + " " + currentY + " -> ");
            }

            actual = interpolation.value(currentX, currentY);
            sumError += FastMath.abs(actual - expected);

            if (print) {
                System.out.println(actual + " (diff=" + (expected - actual) + ")");
            }

            Assert.assertEquals(expected, actual, maxTolerance);
        }

        final double meanError = sumError / numberOfSamples;
        Assert.assertEquals(0, meanError, meanTolerance);
    }
}

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