MATH-378

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@956914 13f79535-47bb-0310-9956-ffa450edef68

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);
+    }
+
+}

src/site/xdoc/changes.xml

@@ -52,6 +52,9 @@ The <action> type attribute can be add,update,fix,remove.
     If the output is not quite correct, check for invisible trailing spaces!
      -->
     <release version="2.2" date="TBD" description="TBD">
+      <action dev="erans" type="add" issue="MATH-378" due-to="Matthew Rowles">
+        Implementation of linear interpolation.
+      </action>
       <action dev="luc" type="fix" issue="MATH-361">
         Improved localization of error messages.
       </action>      

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);
+        }
+    }
+
+}