| /* |
| * 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 static org.junit.Assert.assertEquals; |
| import static org.junit.Assert.assertTrue; |
| |
| import org.apache.commons.math4.legacy.analysis.UnivariateFunction; |
| 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.NonMonotonicSequenceException; |
| import org.apache.commons.math4.legacy.exception.NullArgumentException; |
| import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException; |
| import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialSplineFunction; |
| 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; |
| import org.junit.Ignore; |
| |
| public class AkimaSplineInterpolatorTest { |
| @Test |
| public void testIllegalArguments() { |
| // Data set arrays of different size. |
| UnivariateInterpolator i = new AkimaSplineInterpolator(); |
| |
| try { |
| double yval[] = {0.0, 1.0, 2.0, 3.0, 4.0}; |
| i.interpolate(null, yval); |
| Assert.fail("Failed to detect x null pointer"); |
| } catch (NullArgumentException iae) { |
| // Expected. |
| } |
| |
| try { |
| double xval[] = {0.0, 1.0, 2.0, 3.0, 4.0}; |
| i.interpolate(xval, null); |
| Assert.fail("Failed to detect y null pointer"); |
| } catch (NullArgumentException iae) { |
| // Expected. |
| } |
| |
| try { |
| double xval[] = {0.0, 1.0, 2.0, 3.0}; |
| double yval[] = {0.0, 1.0, 2.0, 3.0}; |
| i.interpolate(xval, yval); |
| Assert.fail("Failed to detect insufficient data"); |
| } catch (NumberIsTooSmallException iae) { |
| // Expected. |
| } |
| |
| try { |
| double xval[] = {0.0, 1.0, 2.0, 3.0, 4.0}; |
| double yval[] = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0}; |
| i.interpolate(xval, yval); |
| Assert.fail("Failed to detect data set array with different sizes."); |
| } catch (DimensionMismatchException iae) { |
| // Expected. |
| } |
| |
| // X values not sorted. |
| try { |
| double xval[] = {0.0, 1.0, 0.5, 7.0, 3.5, 2.2, 8.0}; |
| double yval[] = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0}; |
| i.interpolate(xval, yval); |
| Assert.fail("Failed to detect unsorted arguments."); |
| } catch (NonMonotonicSequenceException iae) { |
| // Expected. |
| } |
| } |
| |
| /* |
| * Interpolate a straight line. <p> y = 2 x - 5 <p> Tolerances determined by performing same calculation using |
| * Math.NET over ten runs of 100 random number draws for the same function over the same span with the same number |
| * of elements |
| */ |
| @Test |
| public void testInterpolateLine() { |
| final int numberOfElements = 10; |
| final double minimumX = -10; |
| final double maximumX = 10; |
| final int numberOfSamples = 100; |
| final double interpolationTolerance = 1e-15; |
| final double maxTolerance = 1e-15; |
| |
| UnivariateFunction f = new UnivariateFunction() { |
| @Override |
| public double value(double x) { |
| return 2 * x - 5; |
| } |
| }; |
| |
| testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance, |
| maxTolerance ); |
| } |
| |
| /* |
| * Interpolate a straight line. <p> y = 3 x<sup>2</sup> - 5 x + 7 <p> Tolerances determined by performing same |
| * calculation using Math.NET over ten runs of 100 random number draws for the same function over the same span with |
| * the same number of elements |
| */ |
| |
| @Test |
| public void testInterpolateParabola() { |
| final int numberOfElements = 10; |
| final double minimumX = -10; |
| final double maximumX = 10; |
| final int numberOfSamples = 100; |
| final double interpolationTolerance = 7e-15; |
| final double maxTolerance = 6e-14; |
| |
| UnivariateFunction f = new UnivariateFunction() { |
| @Override |
| public double value(double x) { |
| return (3 * x * x) - (5 * x) + 7; |
| } |
| }; |
| |
| testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance, |
| maxTolerance ); |
| } |
| |
| /* |
| * Interpolate a straight line. <p> y = 3 x<sup>3</sup> - 0.5 x<sup>2</sup> + x - 1 <p> Tolerances determined by |
| * performing same calculation using Math.NET over ten runs of 100 random number draws for the same function over |
| * the same span with the same number of elements |
| */ |
| @Test |
| public void testInterpolateCubic() { |
| final int numberOfElements = 10; |
| final double minimumX = -3; |
| final double maximumX = 3; |
| final int numberOfSamples = 100; |
| final double interpolationTolerance = 0.37; |
| final double maxTolerance = 3.8; |
| |
| UnivariateFunction f = new UnivariateFunction() { |
| @Override |
| public double value(double x) { |
| return (3 * x * x * x) - (0.5 * x * x) + (1 * x) - 1; |
| } |
| }; |
| |
| testInterpolation( minimumX, maximumX, numberOfElements, numberOfSamples, f, interpolationTolerance, |
| maxTolerance ); |
| } |
| |
| // Test currently fails but it is not clear whether |
| // https://issues.apache.org/jira/browse/MATH-1635 |
| // actually describes a bug, or a limitation of the algorithm. |
| @Ignore |
| @Test |
| public void testMath1635() { |
| final double[] x = { |
| 5994, 6005, 6555, 6588, 6663, |
| 6760, 6770, 6792, 6856, 6964, |
| 7028, 7233, 7426, 7469, 7619, |
| 7910, 8038, 8178, 8414, 8747, |
| 8983, 9316, 9864, 9875 |
| }; |
| |
| final double[] y = { |
| 3.0, 2.0, 2.0, 2.0, 2.0, |
| 2.0, 2.0, 2.0, 2.0, 2.0, |
| 2.0, 2.0, 2.0, 2.0, 2.0, |
| 2.0, 2.0, 2.0, 2.0, 2.0, |
| 2.0, 2.0, 2.0, 3.0 |
| }; |
| |
| final AkimaSplineInterpolator interpolator = new AkimaSplineInterpolator(true); |
| final PolynomialSplineFunction interpolate = interpolator.interpolate(x, y); |
| final double value = interpolate.value(9584); |
| final double expected = 2; |
| Assert.assertEquals(expected, value, 1e-4); |
| } |
| |
| @Test |
| public void testOriginalVsModified() { |
| final UnivariateFunction f = new UnivariateFunction() { |
| @Override |
| public double value(double x) { |
| return x < -1 ? -1 : |
| x < 1 ? x : 1; |
| } |
| }; |
| |
| final double[] xS = new double[] {-1, 0, 1, 2, 3 }; |
| final double[] yS = new double[xS.length]; |
| |
| for (int i = 0; i < xS.length; i++) { |
| yS[i] = f.value(xS[i]); |
| } |
| |
| final UnivariateFunction iOriginal = new AkimaSplineInterpolator(false).interpolate(xS, yS); |
| final UnivariateFunction iModified = new AkimaSplineInterpolator(true).interpolate(xS, yS); |
| |
| final int n = 100; |
| final double delta = 1d / n; |
| for (int i = 1; i < n - 1; i++) { |
| final double x = 2 - i * delta; |
| |
| final double value = f.value(x); |
| final double diffOriginal = Math.abs(iOriginal.value(x) - value); |
| final double diffModified = Math.abs(iModified.value(x) - value); |
| |
| // In interval (1, 2), the modified algorithm eliminates interpolation artefacts. |
| Assert.assertTrue(diffOriginal > 0); |
| Assert.assertEquals(0d, diffModified, 0d); |
| } |
| } |
| |
| private void testInterpolation( double minimumX, double maximumX, int numberOfElements, int numberOfSamples, |
| UnivariateFunction f, double tolerance, double maxTolerance ) { |
| double expected; |
| double actual; |
| double currentX; |
| final double delta = ( maximumX - minimumX ) / ( (double) numberOfElements ); |
| double xValues[] = new double[numberOfElements]; |
| double yValues[] = new double[numberOfElements]; |
| |
| for (int i = 0; i < numberOfElements; i++) { |
| xValues[i] = minimumX + delta * (double) i; |
| yValues[i] = f.value(xValues[i]); |
| } |
| |
| UnivariateFunction interpolation = new AkimaSplineInterpolator().interpolate( xValues, yValues ); |
| |
| for (int i = 0; i < numberOfElements; i++) { |
| currentX = xValues[i]; |
| expected = f.value(currentX); |
| actual = interpolation.value( currentX ); |
| assertTrue( Precision.equals( expected, actual ) ); |
| } |
| |
| final UniformRandomProvider rng = RandomSource.WELL_19937_C.create(1234567L); // "tol" depends on the seed. |
| final ContinuousDistribution.Sampler distX = |
| UniformContinuousDistribution.of(xValues[0], xValues[xValues.length - 1]).createSampler(rng); |
| |
| double sumError = 0; |
| for (int i = 0; i < numberOfSamples; i++) { |
| currentX = distX.sample(); |
| expected = f.value(currentX); |
| actual = interpolation.value( currentX ); |
| sumError += JdkMath.abs( actual - expected ); |
| assertEquals( expected, actual, maxTolerance ); |
| } |
| |
| assertEquals( 0.0, sumError / (double) numberOfSamples, tolerance ); |
| } |
| } |