    1   /*
    2    *
    3    * Copyright (c) 2004 The Apache Software Foundation. All rights reserved.
    4    *
    5    * Licensed under the Apache License, Version 2.0 (the "License"); you may not
    6    * use this file except in compliance with the License. You may obtain a copy
    7    * of the License at
    8    *
    9    * http://www.apache.org/licenses/LICENSE-2.0
    10   *
    11   * Unless required by applicable law or agreed to in writing, software
    12   * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
    13   * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
    14   * License for the specific language governing permissions and limitations
    15   * under the License.
    16   *
    17   */
    18  package org.apache.commons.math.analysis;
    19
    20  import org.apache.commons.math.MathException;
    21  import org.apache.commons.math.TestUtils;
    22
    23  import junit.framework.Test;
    24  import junit.framework.TestCase;
    25  import junit.framework.TestSuite;
    26
    27  /***
    28   * Test the SplineInterpolator.
    29   *
    30   * @version $Revision: 1.1 $ $Date: 2004/04/02 20:58:59 $
    31   */
    32  public class SplineInterpolatorTest extends TestCase {
    33
    34      /*** error tolerance for spline interpolator value at knot points */
    35      protected double knotTolerance = 1E-12;
    36
    37      /*** error tolerance for interpolating polynomial coefficients */
    38      protected double coefficientTolerance = 1E-6;
    39
    40      /*** error tolerance for interpolated values -- high value is from sin test */
    41      protected double interpolationTolerance = 1E-2;
    42
    43      public SplineInterpolatorTest(String name) {
    44          super(name);
    45      }
    46
    47      public static Test suite() {
    48          TestSuite suite = new TestSuite(SplineInterpolatorTest.class);
    49          suite.setName("UnivariateRealInterpolator Tests");
    50          return suite;
    51      }
    52
    53      public void testInterpolateLinearDegenerateTwoSegment()
    54          throws Exception {
    55          double x[] = { 0.0, 0.5, 1.0 };
    56          double y[] = { 0.0, 0.5, 1.0 };
    57          UnivariateRealInterpolator i = new SplineInterpolator();
    58          UnivariateRealFunction f = i.interpolate(x, y);
    59          verifyInterpolation(f, x, y);
    60          verifyConsistency((PolynomialSplineFunction) f, x);
    61
    62          // Verify coefficients using analytical values
    63          PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
    64          double target[] = {y[0], 1d, 0d, 0d};
    65          TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
    66          target = new double[]{y[1], 1d, 0d, 0d};
    67          TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
    68
    69          // Check interpolation
    70          assertEquals(0.4,f.value(0.4), interpolationTolerance);
    71      }
    72
    73      public void testInterpolateLinearDegenerateThreeSegment()
    74          throws Exception {
    75          double x[] = { 0.0, 0.5, 1.0, 1.5 };
    76          double y[] = { 0.0, 0.5, 1.0, 1.5 };
    77          UnivariateRealInterpolator i = new SplineInterpolator();
    78          UnivariateRealFunction f = i.interpolate(x, y);
    79          verifyInterpolation(f, x, y);
    80
    81          // Verify coefficients using analytical values
    82          PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
    83          double target[] = {y[0], 1d, 0d, 0d};
    84          TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
    85          target = new double[]{y[1], 1d, 0d, 0d};
    86          TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
    87          target = new double[]{y[2], 1d, 0d, 0d};
    88          TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
    89
    90          // Check interpolation
    91          assertEquals(1.4,f.value(1.4), interpolationTolerance);
    92      }
    93
    94      public void testInterpolateLinear() throws Exception {
    95          double x[] = { 0.0, 0.5, 1.0 };
    96          double y[] = { 0.0, 0.5, 0.0 };
    97          UnivariateRealInterpolator i = new SplineInterpolator();
    98          UnivariateRealFunction f = i.interpolate(x, y);
    99          verifyInterpolation(f, x, y);
    100         verifyConsistency((PolynomialSplineFunction) f, x);
    101
    102         // Verify coefficients using analytical values
    103         PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
    104         double target[] = {y[0], 1.5d, 0d, -2d};
    105         TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
    106         target = new double[]{y[1], 0d, -3d, 2d};
    107         TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
    108     }
    109
    110     public void testInterpolateSin() throws Exception {
    111         double x[] =
    112             {
    113                 0.0,
    114                 Math.PI / 6d,
    115                 Math.PI / 2d,
    116                 5d * Math.PI / 6d,
    117                 Math.PI,
    118                 7d * Math.PI / 6d,
    119                 3d * Math.PI / 2d,
    120                 11d * Math.PI / 6d,
    121                 2.d * Math.PI };
    122         double y[] = { 0d, 0.5d, 1d, 0.5d, 0d, -0.5d, -1d, -0.5d, 0d };
    123         UnivariateRealInterpolator i = new SplineInterpolator();
    124         UnivariateRealFunction f = i.interpolate(x, y);
    125         verifyInterpolation(f, x, y);
    126         verifyConsistency((PolynomialSplineFunction) f, x);
    127
    128         /* Check coefficients against values computed using R (version 1.8.1, Red Hat Linux 9)
    129          *
    130          * To replicate in R:
    131          *     x[1] <- 0
    132          *     x[2] <- pi / 6, etc, same for y[] (could use y <- scan() for y values)
    133          *     g <- splinefun(x, y, "natural")
    134          *     splinecoef <- eval(expression(z), envir = environment(g))
    135          *     print(splinecoef)
    136          */
    137         PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
    138         double target[] = {y[0], 1.002676d, 0d, -0.17415829d};
    139         TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
    140         target = new double[]{y[1], 8.594367e-01, -2.735672e-01, -0.08707914};
    141         TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
    142         target = new double[]{y[2], 1.471804e-17,-5.471344e-01, 0.08707914};
    143         TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
    144         target = new double[]{y[3], -8.594367e-01, -2.735672e-01, 0.17415829};
    145         TestUtils.assertEquals(polynomials[3].getCoefficients(), target, coefficientTolerance);
    146         target = new double[]{y[4], -1.002676, 6.548562e-17, 0.17415829};
    147         TestUtils.assertEquals(polynomials[4].getCoefficients(), target, coefficientTolerance);
    148         target = new double[]{y[5], -8.594367e-01, 2.735672e-01, 0.08707914};
    149         TestUtils.assertEquals(polynomials[5].getCoefficients(), target, coefficientTolerance);
    150         target = new double[]{y[6], 3.466465e-16, 5.471344e-01, -0.08707914};
    151         TestUtils.assertEquals(polynomials[6].getCoefficients(), target, coefficientTolerance);
    152         target = new double[]{y[7], 8.594367e-01, 2.735672e-01, -0.17415829};
    153         TestUtils.assertEquals(polynomials[7].getCoefficients(), target, coefficientTolerance);
    154
    155         //Check interpolation
    156         assertEquals(Math.sqrt(2d) / 2d,f.value(Math.PI/4d),interpolationTolerance);
    157         assertEquals(Math.sqrt(2d) / 2d,f.value(3d*Math.PI/4d),interpolationTolerance);
    158     }
    159
    160
    161     public void testIllegalArguments() throws MathException {
    162         // Data set arrays of different size.
    163         UnivariateRealInterpolator i = new SplineInterpolator();
    164         try {
    165             double xval[] = { 0.0, 1.0 };
    166             double yval[] = { 0.0, 1.0, 2.0 };
    167             i.interpolate(xval, yval);
    168             fail("Failed to detect data set array with different sizes.");
    169         } catch (IllegalArgumentException iae) {
    170         }
    171         // X values not sorted.
    172         try {
    173             double xval[] = { 0.0, 1.0, 0.5 };
    174             double yval[] = { 0.0, 1.0, 2.0 };
    175             i.interpolate(xval, yval);
    176             fail("Failed to detect unsorted arguments.");
    177         } catch (IllegalArgumentException iae) {
    178         }
    179     }
    180
    181     /***
    182      * verifies that f(x[i]) = y[i] for i = 0..n -1 where n is common length -- skips last point.
    183      */
    184     protected void verifyInterpolation(UnivariateRealFunction f, double x[], double y[])
    185     	throws Exception{
    186         for (int i = 0; i < x.length - 1; i++) {
    187             assertEquals(f.value(x[i]), y[i], knotTolerance);
    188         }
    189     }
    190
    191     /***
    192      * Verifies that interpolating polynomials satisfy consistency requirement:
    193      *    adjacent polynomials must agree through two derivatives at knot points
    194      */
    195     protected void verifyConsistency(PolynomialSplineFunction f, double x[])
    196     	throws Exception {
    197         PolynomialFunction polynomials[] = f.getPolynomials();
    198         for (int i = 1; i < x.length - 2; i++) {
    199             // evaluate polynomials and derivatives at x[i + 1]
    200             assertEquals(polynomials[i].value(x[i +1] - x[i]), polynomials[i + 1].value(0), 0.1);
    201             assertEquals(polynomials[i].derivative().value(x[i +1] - x[i]),
    202                     polynomials[i + 1].derivative().value(0), 0.5);
    203             assertEquals(polynomials[i].polynomialDerivative().derivative().value(x[i +1] - x[i]),
    204                     polynomials[i + 1].polynomialDerivative().derivative().value(0), 0.5);
    205         }
    206     }
    207
    208 }