| /* |
| * 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.math4.legacy.analysis.interpolation; |
| |
| import org.apache.commons.math4.legacy.analysis.BivariateFunction; |
| import org.apache.commons.statistics.distribution.ContinuousDistribution; |
| import org.apache.commons.statistics.distribution.UniformContinuousDistribution; |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.math4.legacy.exception.InsufficientDataException; |
| import org.apache.commons.math4.legacy.exception.NonMonotonicSequenceException; |
| import org.apache.commons.math4.legacy.exception.NullArgumentException; |
| import org.apache.commons.rng.UniformRandomProvider; |
| import org.apache.commons.rng.simple.RandomSource; |
| import org.apache.commons.math4.core.jdkmath.JdkMath; |
| import org.apache.commons.numbers.core.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() { |
| @Override |
| 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 = 1e-13; |
| final double maxTolerance = 6e-14; |
| |
| // Function values |
| BivariateFunction f = new BivariateFunction() { |
| @Override |
| 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 UniformRandomProvider rng = RandomSource.WELL_19937_C.create(1234567L); |
| final ContinuousDistribution.Sampler distX = UniformContinuousDistribution.of(xValues[0], xValues[xValues.length - 1]).createSampler(rng); |
| final ContinuousDistribution.Sampler distY = UniformContinuousDistribution.of(yValues[0], yValues[yValues.length - 1]).createSampler(rng); |
| |
| 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 += JdkMath.abs(actual - expected); |
| Assert.assertEquals(expected, actual, maxTolerance); |
| } |
| |
| final double meanError = sumError / numberOfSamples; |
| Assert.assertEquals(0, meanError, meanTolerance); |
| } |
| } |