Added "derivative".

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1183776 13f79535-47bb-0310-9956-ffa450edef68

src/main/java/org/apache/commons/math/analysis/function/Sqrt.java

@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Sqrt implements UnivariateRealFunction {
+public class Sqrt implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.sqrt(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / (2 * FastMath.sqrt(x));
+            }
+        };
+    }
 }

src/test/java/org/apache/commons/math/analysis/function/SqrtTest.java

@@ -0,0 +1,56 @@
+/*
+ * 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.function;
+
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+
+import org.junit.Test;
+import org.junit.Assert;
+
+public class SqrtTest {
+   @Test
+   public void testComparison() {
+       final Sqrt s = new Sqrt();
+       final UnivariateRealFunction f = new UnivariateRealFunction() {
+               public double value(double x) {
+                   return Math.sqrt(x);
+               }
+           };
+
+       for (double x = 1e-30; x < 1e10; x *= 2) {
+           final double fX = f.value(x);
+           final double sX = s.value(x);
+           Assert.assertEquals("x=" + x, fX, sX, 0);
+       }
+   }
+
+   @Test
+   public void testDerivativeComparison() {
+       final UnivariateRealFunction sPrime = (new Sqrt()).derivative();
+       final UnivariateRealFunction f = new UnivariateRealFunction() {
+               public double value(double x) {
+                   return 1 / (2 * Math.sqrt(x));
+               }
+           };
+
+       for (double x = 1e-30; x < 1e10; x *= 2) {
+           final double fX = f.value(x);
+           final double sX = sPrime.value(x);
+           Assert.assertEquals("x=" + x, fX, sX, 0);
+       }
+   }
+}