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MATH-378
git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@956914 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Gilles Sadowski
parent
3f15fc7c1a
commit
434de1dd39
@ -0,0 +1,73 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math.analysis.interpolation;
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import org.apache.commons.math.MathRuntimeException;
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import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
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import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
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import org.apache.commons.math.util.LocalizedFormats;
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/**
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* Implements a linear function for interpolation of real univariate functions.
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*/
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public class LinearInterpolator implements UnivariateRealInterpolator {
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/**
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* Computes a linear interpolating function for the data set.
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* @param x the arguments for the interpolation points
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* @param y the values for the interpolation points
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* @return a function which interpolates the data set
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*/
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public PolynomialSplineFunction interpolate(double x[], double y[]) {
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if (x.length != y.length) {
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throw MathRuntimeException.createIllegalArgumentException(
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LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, x.length, y.length);
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}
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if (x.length < 2) {
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throw MathRuntimeException.createIllegalArgumentException(
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LocalizedFormats.WRONG_NUMBER_OF_POINTS, 2, x.length);
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}
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// Number of intervals. The number of data points is n + 1.
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int n = x.length - 1;
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for (int i = 0; i < n; i++) {
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if (x[i] >= x[i + 1]) {
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throw MathRuntimeException.createIllegalArgumentException(
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LocalizedFormats.NOT_STRICTLY_INCREASING_NUMBER_OF_POINTS,
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i, i+1, x[i], x[i+1]);
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}
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}
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// Slope of the lines between the datapoints.
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final double m[] = new double[n];
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for (int i = 0; i < n; i++) {
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m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
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}
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PolynomialFunction polynomials[] = new PolynomialFunction[n];
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final double coefficients[] = new double[2];
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for (int i = 0; i < n; i++) {
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coefficients[0] = y[i];
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coefficients[1] = m[i];
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polynomials[i] = new PolynomialFunction(coefficients);
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}
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return new PolynomialSplineFunction(x, polynomials);
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}
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}
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@ -71,7 +71,7 @@ public class SplineInterpolator implements UnivariateRealInterpolator {
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int n = x.length - 1;
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for (int i = 0; i < n; i++) {
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if (x[i] >= x[i + 1]) {
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if (x[i] >= x[i + 1]) {
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throw MathRuntimeException.createIllegalArgumentException(
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LocalizedFormats.NOT_STRICTLY_INCREASING_NUMBER_OF_POINTS,
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i, i+1, x[i], x[i+1]);
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@ -52,6 +52,9 @@ The <action> type attribute can be add,update,fix,remove.
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If the output is not quite correct, check for invisible trailing spaces!
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-->
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<release version="2.2" date="TBD" description="TBD">
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<action dev="erans" type="add" issue="MATH-378" due-to="Matthew Rowles">
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Implementation of linear interpolation.
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</action>
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<action dev="luc" type="fix" issue="MATH-361">
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Improved localization of error messages.
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</action>
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@ -0,0 +1,136 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math.analysis.interpolation;
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import org.apache.commons.math.MathException;
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import org.apache.commons.math.TestUtils;
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import org.apache.commons.math.analysis.UnivariateRealFunction;
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import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
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import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
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import org.junit.Assert;
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import org.junit.Test;
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/**
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* Test the LinearInterpolator.
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*/
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public class LinearInterpolatorTest {
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/** error tolerance for spline interpolator value at knot points */
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protected double knotTolerance = 1E-12;
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/** error tolerance for interpolating polynomial coefficients */
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protected double coefficientTolerance = 1E-6;
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/** error tolerance for interpolated values */
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protected double interpolationTolerance = 1E-12;
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@Test
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public void testInterpolateLinearDegenerateTwoSegment()
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throws Exception {
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double x[] = { 0.0, 0.5, 1.0 };
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double y[] = { 0.0, 0.5, 1.0 };
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UnivariateRealInterpolator i = new LinearInterpolator();
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UnivariateRealFunction f = i.interpolate(x, y);
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verifyInterpolation(f, x, y);
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// Verify coefficients using analytical values
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PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
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double target[] = {y[0], 1d};
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TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
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target = new double[]{y[1], 1d};
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TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
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// Check interpolation
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Assert.assertEquals(0.0,f.value(0.0), interpolationTolerance);
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Assert.assertEquals(0.4,f.value(0.4), interpolationTolerance);
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Assert.assertEquals(1.0,f.value(1.0), interpolationTolerance);
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}
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@Test
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public void testInterpolateLinearDegenerateThreeSegment()
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throws Exception {
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double x[] = { 0.0, 0.5, 1.0, 1.5 };
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double y[] = { 0.0, 0.5, 1.0, 1.5 };
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UnivariateRealInterpolator i = new LinearInterpolator();
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UnivariateRealFunction f = i.interpolate(x, y);
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verifyInterpolation(f, x, y);
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// Verify coefficients using analytical values
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PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
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double target[] = {y[0], 1d};
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TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
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target = new double[]{y[1], 1d};
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TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
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target = new double[]{y[2], 1d};
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TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance);
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// Check interpolation
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Assert.assertEquals(0,f.value(0), interpolationTolerance);
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Assert.assertEquals(1.4,f.value(1.4), interpolationTolerance);
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Assert.assertEquals(1.5,f.value(1.5), interpolationTolerance);
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}
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@Test
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public void testInterpolateLinear() throws Exception {
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double x[] = { 0.0, 0.5, 1.0 };
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double y[] = { 0.0, 0.5, 0.0 };
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UnivariateRealInterpolator i = new LinearInterpolator();
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UnivariateRealFunction f = i.interpolate(x, y);
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verifyInterpolation(f, x, y);
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// Verify coefficients using analytical values
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PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials();
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double target[] = {y[0], 1d};
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TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance);
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target = new double[]{y[1], -1d};
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TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance);
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}
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@Test
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public void testIllegalArguments() throws MathException {
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// Data set arrays of different size.
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UnivariateRealInterpolator i = new LinearInterpolator();
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try {
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double xval[] = { 0.0, 1.0 };
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double yval[] = { 0.0, 1.0, 2.0 };
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i.interpolate(xval, yval);
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Assert.fail("Failed to detect data set array with different sizes.");
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} catch (IllegalArgumentException iae) {
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// Expected.
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}
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// X values not sorted.
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try {
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double xval[] = { 0.0, 1.0, 0.5 };
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double yval[] = { 0.0, 1.0, 2.0 };
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i.interpolate(xval, yval);
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Assert.fail("Failed to detect unsorted arguments.");
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} catch (IllegalArgumentException iae) {
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// Expected.
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}
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}
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/**
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* verifies that f(x[i]) = y[i] for i = 0..n-1 where n is common length.
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*/
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protected void verifyInterpolation(UnivariateRealFunction f, double x[], double y[])
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throws Exception{
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for (int i = 0; i < x.length; i++) {
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Assert.assertEquals(f.value(x[i]), y[i], knotTolerance);
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}
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}
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}
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