From 434de1dd39f9ff05cb0770fdf4b2fa5d81674597 Mon Sep 17 00:00:00 2001 From: Gilles Sadowski Date: Tue, 22 Jun 2010 15:05:51 +0000 Subject: [PATCH] MATH-378 git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@956914 13f79535-47bb-0310-9956-ffa450edef68 --- .../interpolation/LinearInterpolator.java | 73 ++++++++++ .../interpolation/SplineInterpolator.java | 2 +- src/site/xdoc/changes.xml | 3 + .../interpolation/LinearInterpolatorTest.java | 136 ++++++++++++++++++ 4 files changed, 213 insertions(+), 1 deletion(-) create mode 100644 src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java create mode 100644 src/test/java/org/apache/commons/math/analysis/interpolation/LinearInterpolatorTest.java diff --git a/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java b/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java new file mode 100644 index 000000000..f7b6c211c --- /dev/null +++ b/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java @@ -0,0 +1,73 @@ +/* + * 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.math.analysis.interpolation; + +import org.apache.commons.math.MathRuntimeException; +import org.apache.commons.math.analysis.polynomials.PolynomialFunction; +import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; +import org.apache.commons.math.util.LocalizedFormats; + +/** + * Implements a linear function for interpolation of real univariate functions. + */ +public class LinearInterpolator implements UnivariateRealInterpolator { + /** + * Computes a linear interpolating function for the data set. + * @param x the arguments for the interpolation points + * @param y the values for the interpolation points + * @return a function which interpolates the data set + */ + public PolynomialSplineFunction interpolate(double x[], double y[]) { + if (x.length != y.length) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, x.length, y.length); + } + + if (x.length < 2) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.WRONG_NUMBER_OF_POINTS, 2, x.length); + } + + // Number of intervals. The number of data points is n + 1. + int n = x.length - 1; + + for (int i = 0; i < n; i++) { + if (x[i] >= x[i + 1]) { + throw MathRuntimeException.createIllegalArgumentException( + LocalizedFormats.NOT_STRICTLY_INCREASING_NUMBER_OF_POINTS, + i, i+1, x[i], x[i+1]); + } + } + + // Slope of the lines between the datapoints. + final double m[] = new double[n]; + for (int i = 0; i < n; i++) { + m[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]); + } + + PolynomialFunction polynomials[] = new PolynomialFunction[n]; + final double coefficients[] = new double[2]; + for (int i = 0; i < n; i++) { + coefficients[0] = y[i]; + coefficients[1] = m[i]; + polynomials[i] = new PolynomialFunction(coefficients); + } + + return new PolynomialSplineFunction(x, polynomials); + } + +} diff --git a/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java b/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java index 8ed1d9cd6..d90822869 100644 --- a/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java +++ b/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java @@ -71,7 +71,7 @@ public class SplineInterpolator implements UnivariateRealInterpolator { int n = x.length - 1; for (int i = 0; i < n; i++) { - if (x[i] >= x[i + 1]) { + if (x[i] >= x[i + 1]) { throw MathRuntimeException.createIllegalArgumentException( LocalizedFormats.NOT_STRICTLY_INCREASING_NUMBER_OF_POINTS, i, i+1, x[i], x[i+1]); diff --git a/src/site/xdoc/changes.xml b/src/site/xdoc/changes.xml index 913301fbd..1823aee5e 100644 --- a/src/site/xdoc/changes.xml +++ b/src/site/xdoc/changes.xml @@ -52,6 +52,9 @@ The type attribute can be add,update,fix,remove. If the output is not quite correct, check for invisible trailing spaces! --> + + Implementation of linear interpolation. + Improved localization of error messages. diff --git a/src/test/java/org/apache/commons/math/analysis/interpolation/LinearInterpolatorTest.java b/src/test/java/org/apache/commons/math/analysis/interpolation/LinearInterpolatorTest.java new file mode 100644 index 000000000..8ea5a8188 --- /dev/null +++ b/src/test/java/org/apache/commons/math/analysis/interpolation/LinearInterpolatorTest.java @@ -0,0 +1,136 @@ +/* + * 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.math.analysis.interpolation; + +import org.apache.commons.math.MathException; +import org.apache.commons.math.TestUtils; +import org.apache.commons.math.analysis.UnivariateRealFunction; +import org.apache.commons.math.analysis.polynomials.PolynomialFunction; +import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction; +import org.junit.Assert; +import org.junit.Test; + +/** + * Test the LinearInterpolator. + */ +public class LinearInterpolatorTest { + + /** error tolerance for spline interpolator value at knot points */ + protected double knotTolerance = 1E-12; + + /** error tolerance for interpolating polynomial coefficients */ + protected double coefficientTolerance = 1E-6; + + /** error tolerance for interpolated values */ + protected double interpolationTolerance = 1E-12; + + @Test + public void testInterpolateLinearDegenerateTwoSegment() + throws Exception { + double x[] = { 0.0, 0.5, 1.0 }; + double y[] = { 0.0, 0.5, 1.0 }; + UnivariateRealInterpolator i = new LinearInterpolator(); + UnivariateRealFunction f = i.interpolate(x, y); + verifyInterpolation(f, x, y); + + // Verify coefficients using analytical values + PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials(); + double target[] = {y[0], 1d}; + TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance); + target = new double[]{y[1], 1d}; + TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance); + + // Check interpolation + Assert.assertEquals(0.0,f.value(0.0), interpolationTolerance); + Assert.assertEquals(0.4,f.value(0.4), interpolationTolerance); + Assert.assertEquals(1.0,f.value(1.0), interpolationTolerance); + } + + @Test + public void testInterpolateLinearDegenerateThreeSegment() + throws Exception { + double x[] = { 0.0, 0.5, 1.0, 1.5 }; + double y[] = { 0.0, 0.5, 1.0, 1.5 }; + UnivariateRealInterpolator i = new LinearInterpolator(); + UnivariateRealFunction f = i.interpolate(x, y); + verifyInterpolation(f, x, y); + + // Verify coefficients using analytical values + PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials(); + double target[] = {y[0], 1d}; + TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance); + target = new double[]{y[1], 1d}; + TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance); + target = new double[]{y[2], 1d}; + TestUtils.assertEquals(polynomials[2].getCoefficients(), target, coefficientTolerance); + + // Check interpolation + Assert.assertEquals(0,f.value(0), interpolationTolerance); + Assert.assertEquals(1.4,f.value(1.4), interpolationTolerance); + Assert.assertEquals(1.5,f.value(1.5), interpolationTolerance); + } + + @Test + public void testInterpolateLinear() throws Exception { + double x[] = { 0.0, 0.5, 1.0 }; + double y[] = { 0.0, 0.5, 0.0 }; + UnivariateRealInterpolator i = new LinearInterpolator(); + UnivariateRealFunction f = i.interpolate(x, y); + verifyInterpolation(f, x, y); + + // Verify coefficients using analytical values + PolynomialFunction polynomials[] = ((PolynomialSplineFunction) f).getPolynomials(); + double target[] = {y[0], 1d}; + TestUtils.assertEquals(polynomials[0].getCoefficients(), target, coefficientTolerance); + target = new double[]{y[1], -1d}; + TestUtils.assertEquals(polynomials[1].getCoefficients(), target, coefficientTolerance); + } + + @Test + public void testIllegalArguments() throws MathException { + // Data set arrays of different size. + UnivariateRealInterpolator i = new LinearInterpolator(); + try { + double xval[] = { 0.0, 1.0 }; + double yval[] = { 0.0, 1.0, 2.0 }; + i.interpolate(xval, yval); + Assert.fail("Failed to detect data set array with different sizes."); + } catch (IllegalArgumentException iae) { + // Expected. + } + // X values not sorted. + try { + double xval[] = { 0.0, 1.0, 0.5 }; + double yval[] = { 0.0, 1.0, 2.0 }; + i.interpolate(xval, yval); + Assert.fail("Failed to detect unsorted arguments."); + } catch (IllegalArgumentException iae) { + // Expected. + } + } + + /** + * verifies that f(x[i]) = y[i] for i = 0..n-1 where n is common length. + */ + protected void verifyInterpolation(UnivariateRealFunction f, double x[], double y[]) + throws Exception{ + for (int i = 0; i < x.length; i++) { + Assert.assertEquals(f.value(x[i]), y[i], knotTolerance); + } + } + +}