src/test/java/org/apache/commons/math3/analysis/interpolation/PiecewiseBicubicSplineInterpolatingFunctionTest.java - commons-math - Git at Google

 /*
  * 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.InsufficientDataException;
 import org.apache.commons.math3.exception.NonMonotonicSequenceException;
 import org.apache.commons.math3.exception.NullArgumentException;
 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 piecewise bicubic function.
  */
 public final class PiecewiseBicubicSplineInterpolatingFunctionTest {
     /**
      * Test preconditions.
      */
     @Test
     public void testPreconditions() {
         double[] xval = new double[] { 3, 4, 5, 6.5, 7.5 };
         double[] yval = new double[] { -4, -3, -1, 2.5, 3.5 };
         double[][] zval = new double[xval.length][yval.length];

         @SuppressWarnings("unused")
         PiecewiseBicubicSplineInterpolatingFunction bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval, zval);

         try {
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(null, yval, zval);
             Assert.fail("Failed to detect x null pointer");
         } catch (NullArgumentException iae) {
             // Expected.
         }

         try {
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, null, zval);
             Assert.fail("Failed to detect y null pointer");
         } catch (NullArgumentException iae) {
             // Expected.
         }

         try {
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval, null);
             Assert.fail("Failed to detect z null pointer");
         } catch (NullArgumentException iae) {
             // Expected.
         }

         try {
             double xval1[] = { 0.0, 1.0, 2.0, 3.0 };
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval1, yval, zval);
             Assert.fail("Failed to detect insufficient x data");
         } catch (InsufficientDataException iae) {
             // Expected.
         }

         try {
             double yval1[] = { 0.0, 1.0, 2.0, 3.0 };
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval1, zval);
             Assert.fail("Failed to detect insufficient y data");
         } catch (InsufficientDataException iae) {
             // Expected.
         }

         try {
             double zval1[][] = new double[4][4];
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval, zval1);
             Assert.fail("Failed to detect insufficient z data");
         } catch (InsufficientDataException iae) {
             // Expected.
         }

         try {
             double xval1[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval1, yval, zval);
             Assert.fail("Failed to detect data set array with different sizes.");
         } catch (DimensionMismatchException iae) {
             // Expected.
         }

         try {
             double yval1[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval1, zval);
             Assert.fail("Failed to detect data set array with different sizes.");
         } catch (DimensionMismatchException iae) {
             // Expected.
         }

         // X values not sorted.
         try {
             double xval1[] = { 0.0, 1.0, 0.5, 7.0, 3.5 };
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval1, yval, zval);
             Assert.fail("Failed to detect unsorted x arguments.");
         } catch (NonMonotonicSequenceException iae) {
             // Expected.
         }

         // Y values not sorted.
         try {
             double yval1[] = { 0.0, 1.0, 1.5, 0.0, 3.0 };
             bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval1, zval);
             Assert.fail("Failed to detect unsorted y arguments.");
         } catch (NonMonotonicSequenceException iae) {
             // 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 = 100;

         final double interpolationTolerance = 7e-15;
         final double maxTolerance = 6e-14;

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

         testInterpolation(minimumX,
                           maximumX,
                           minimumY,
                           maximumY,
                           numberOfElements,
                           numberOfSamples,
                           f,
                           interpolationTolerance,
                           maxTolerance);
     }

     /**
      * Interpolating a paraboloid.
      * <p>
      * z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
      */
     @Test
     public void testParabaloid() {
         final int numberOfElements = 10;
         final double minimumX = -10;
         final double maximumX = 10;
         final double minimumY = -10;
         final double maximumY = 10;
         final int numberOfSamples = 100;

         final double interpolationTolerance = 2e-14;
         final double maxTolerance = 6e-14;

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

         testInterpolation(minimumX,
                           maximumX,
                           minimumY,
                           maximumY,
                           numberOfElements,
                           numberOfSamples,
                           f,
                           interpolationTolerance,
                           maxTolerance);
     }

     /**
      * @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 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,
                                    double meanTolerance,
                                    double maxTolerance) {
         double expected;
         double actual;
         double currentX;
         double currentY;
         final double deltaX = (maximumX - minimumX) / ((double) numberOfElements);
         final double deltaY = (maximumY - minimumY) / ((double) numberOfElements);
         final double[] xValues = new double[numberOfElements];
         final double[] yValues = new double[numberOfElements];
         final double[][] zValues = new double[numberOfElements][numberOfElements];

         for (int i = 0; i < numberOfElements; i++) {
             xValues[i] = minimumX + deltaX * (double) i;
             for (int j = 0; j < numberOfElements; j++) {
                 yValues[j] = minimumY + deltaY * (double) j;
                 zValues[i][j] = f.value(xValues[i], yValues[j]);
             }
         }

         final BivariateFunction interpolation
             = new PiecewiseBicubicSplineInterpolatingFunction(xValues,
                                                               yValues,
                                                               zValues);

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

         final double meanError = sumError / numberOfSamples;
         Assert.assertEquals(0, meanError, meanTolerance);
     }
 }
	/*
	* 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.InsufficientDataException;
	import org.apache.commons.math3.exception.NonMonotonicSequenceException;
	import org.apache.commons.math3.exception.NullArgumentException;
	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 piecewise bicubic function.
	*/
	public final class PiecewiseBicubicSplineInterpolatingFunctionTest {
	/**
	* Test preconditions.
	*/
	@Test
	public void testPreconditions() {
	double[] xval = new double[] { 3, 4, 5, 6.5, 7.5 };
	double[] yval = new double[] { -4, -3, -1, 2.5, 3.5 };
	double[][] zval = new double[xval.length][yval.length];

	@SuppressWarnings("unused")
	PiecewiseBicubicSplineInterpolatingFunction bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval, zval);

	try {
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(null, yval, zval);
	Assert.fail("Failed to detect x null pointer");
	} catch (NullArgumentException iae) {
	// Expected.
	}

	try {
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, null, zval);
	Assert.fail("Failed to detect y null pointer");
	} catch (NullArgumentException iae) {
	// Expected.
	}

	try {
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval, null);
	Assert.fail("Failed to detect z null pointer");
	} catch (NullArgumentException iae) {
	// Expected.
	}

	try {
	double xval1[] = { 0.0, 1.0, 2.0, 3.0 };
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval1, yval, zval);
	Assert.fail("Failed to detect insufficient x data");
	} catch (InsufficientDataException iae) {
	// Expected.
	}

	try {
	double yval1[] = { 0.0, 1.0, 2.0, 3.0 };
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval1, zval);
	Assert.fail("Failed to detect insufficient y data");
	} catch (InsufficientDataException iae) {
	// Expected.
	}

	try {
	double zval1[][] = new double[4][4];
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval, zval1);
	Assert.fail("Failed to detect insufficient z data");
	} catch (InsufficientDataException iae) {
	// Expected.
	}

	try {
	double xval1[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval1, yval, zval);
	Assert.fail("Failed to detect data set array with different sizes.");
	} catch (DimensionMismatchException iae) {
	// Expected.
	}

	try {
	double yval1[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval1, zval);
	Assert.fail("Failed to detect data set array with different sizes.");
	} catch (DimensionMismatchException iae) {
	// Expected.
	}

	// X values not sorted.
	try {
	double xval1[] = { 0.0, 1.0, 0.5, 7.0, 3.5 };
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval1, yval, zval);
	Assert.fail("Failed to detect unsorted x arguments.");
	} catch (NonMonotonicSequenceException iae) {
	// Expected.
	}

	// Y values not sorted.
	try {
	double yval1[] = { 0.0, 1.0, 1.5, 0.0, 3.0 };
	bcf = new PiecewiseBicubicSplineInterpolatingFunction(xval, yval1, zval);
	Assert.fail("Failed to detect unsorted y arguments.");
	} catch (NonMonotonicSequenceException iae) {
	// 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 = 100;

	final double interpolationTolerance = 7e-15;
	final double maxTolerance = 6e-14;

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

	testInterpolation(minimumX,
	maximumX,
	minimumY,
	maximumY,
	numberOfElements,
	numberOfSamples,
	f,
	interpolationTolerance,
	maxTolerance);
	}

	/**
	* Interpolating a paraboloid.
	* <p>
	* z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
	*/
	@Test
	public void testParabaloid() {
	final int numberOfElements = 10;
	final double minimumX = -10;
	final double maximumX = 10;
	final double minimumY = -10;
	final double maximumY = 10;
	final int numberOfSamples = 100;

	final double interpolationTolerance = 2e-14;
	final double maxTolerance = 6e-14;

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

	testInterpolation(minimumX,
	maximumX,
	minimumY,
	maximumY,
	numberOfElements,
	numberOfSamples,
	f,
	interpolationTolerance,
	maxTolerance);
	}

	/**
	* @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 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,
	double meanTolerance,
	double maxTolerance) {
	double expected;
	double actual;
	double currentX;
	double currentY;
	final double deltaX = (maximumX - minimumX) / ((double) numberOfElements);
	final double deltaY = (maximumY - minimumY) / ((double) numberOfElements);
	final double[] xValues = new double[numberOfElements];
	final double[] yValues = new double[numberOfElements];
	final double[][] zValues = new double[numberOfElements][numberOfElements];

	for (int i = 0; i < numberOfElements; i++) {
	xValues[i] = minimumX + deltaX * (double) i;
	for (int j = 0; j < numberOfElements; j++) {
	yValues[j] = minimumY + deltaY * (double) j;
	zValues[i][j] = f.value(xValues[i], yValues[j]);
	}
	}

	final BivariateFunction interpolation
	= new PiecewiseBicubicSplineInterpolatingFunction(xValues,
	yValues,
	zValues);

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

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