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From l..@apache.org
Subject svn commit: r735501 - in /commons/proper/math/trunk: ./ src/java/org/apache/commons/math/analysis/minimization/ src/java/org/apache/commons/math/analysis/solvers/ src/java/org/apache/commons/math/ode/ src/java/org/apache/commons/math/transform/ src/jav...
Date Sun, 18 Jan 2009 16:57:30 GMT
Author: luc
Date: Sun Jan 18 08:57:29 2009
New Revision: 735501

URL: http://svn.apache.org/viewvc?rev=735501&view=rev
Log:
fixed various minor bugs identified by checkstyle and findbugs

Modified:
    commons/proper/math/trunk/findbugs-exclude-filter.xml
    commons/proper/math/trunk/pom.xml
    commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/BrentMinimizer.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/UnivariateRealMinimizerImpl.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolverImpl.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/ode/SecondOrderDifferentialEquations.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/transform/FastFourierTransformer.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/util/OpenIntToDoubleHashMap.java
    commons/proper/math/trunk/src/java/org/apache/commons/math/util/ResizableDoubleArray.java
    commons/proper/math/trunk/src/site/xdoc/userguide/index.xml

Modified: commons/proper/math/trunk/findbugs-exclude-filter.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/findbugs-exclude-filter.xml?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/findbugs-exclude-filter.xml (original)
+++ commons/proper/math/trunk/findbugs-exclude-filter.xml Sun Jan 18 08:57:29 2009
@@ -26,6 +26,11 @@
   <!--  the following equality tests are part of the reference algorithms -->
   <!--  which already know about limited precision of the double numbers -->
   <Match>
+    <Class name="org.apache.commons.math.analysis.minimization.BrentMinimizer" />
+    <Method name="localMin" params="double,double,double,double,org.apache.commons.math.analysis.UnivariateRealFunction"
returns="double" />
+    <Bug pattern="FE_FLOATING_POINT_EQUALITY" />
+  </Match>
+  <Match>
     <Class name="org.apache.commons.math.analysis.solvers.BrentSolver" />
     <Method name="solve" params="org.apache.commons.math.analysis.UnivariateRealFunction,double,double,double,double,double,double"
returns="double" />
     <Bug pattern="FE_FLOATING_POINT_EQUALITY" />

Modified: commons/proper/math/trunk/pom.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/pom.xml?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/pom.xml (original)
+++ commons/proper/math/trunk/pom.xml Sun Jan 18 08:57:29 2009
@@ -224,11 +224,10 @@
             </descriptors>
           </configuration>
         </plugin>
-        <!--
         <plugin>
           <groupId>org.codehaus.mojo</groupId>
           <artifactId>cobertura-maven-plugin</artifactId>
-          <version>2.0</version>
+          <version>2.2</version>
           <executions>
             <execution>
               <goals>
@@ -237,7 +236,6 @@
             </execution>
           </executions>
         </plugin>
-        -->
         <plugin>
           <groupId>org.codehaus.mojo</groupId>
           <artifactId>clirr-maven-plugin</artifactId>
@@ -264,13 +262,11 @@
           <excludeFilterFile>${basedir}/findbugs-exclude-filter.xml</excludeFilterFile>
        </configuration>
       </plugin>
-      <!--
       <plugin>
         <groupId>org.codehaus.mojo</groupId>
         <artifactId>cobertura-maven-plugin</artifactId>
-        <version>2.0</version>
+        <version>2.2</version>
       </plugin>
-      -->
       <plugin>
         <groupId>org.apache.maven.plugins</groupId>
         <artifactId>maven-changes-plugin</artifactId>

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/BrentMinimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/BrentMinimizer.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/BrentMinimizer.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/BrentMinimizer.java
Sun Jan 18 08:57:29 2009
@@ -16,7 +16,6 @@
  */
 package org.apache.commons.math.analysis.minimization;
 
-import org.apache.commons.math.ConvergenceException;
 import org.apache.commons.math.FunctionEvaluationException;
 import org.apache.commons.math.MaxIterationsExceededException;
 import org.apache.commons.math.analysis.UnivariateRealFunction;
@@ -56,7 +55,7 @@
      * @param max the upper bound for the interval.
      * @param startValue this parameter is <em>not</em> used at all
      * @return a value where the function is minimum
-     * @throws ConvergenceException if the maximum iteration count is exceeded
+     * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
      * or the minimizer detects convergence problems otherwise.
      * @throws FunctionEvaluationException if an error occurs evaluating the
      * function
@@ -75,7 +74,7 @@
         throws MaxIterationsExceededException, 
         FunctionEvaluationException {
         clearResult();
-        return localmin(min, max, relativeAccuracy, absoluteAccuracy, f);
+        return localMin(min, max, relativeAccuracy, absoluteAccuracy, f);
     }
     
     /**
@@ -101,7 +100,7 @@
      * @throws FunctionEvaluationException if an error occurs evaluating
      * the function. 
      */
-    private double localmin(double a, double b, final double eps,
+    private double localMin(double a, double b, final double eps,
                             final double t, final UnivariateRealFunction f)
         throws MaxIterationsExceededException, FunctionEvaluationException {
         double x = a + c * (b - a);

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/UnivariateRealMinimizerImpl.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/UnivariateRealMinimizerImpl.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/UnivariateRealMinimizerImpl.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/minimization/UnivariateRealMinimizerImpl.java
Sun Jan 18 08:57:29 2009
@@ -33,12 +33,6 @@
     /** Serializable version identifier. */
     private static final long serialVersionUID = 4543031162377070699L;
 
-//    /** Maximum error of function. */
-//    protected double functionValueAccuracy;
-//
-//    /** Default maximum error of function. */
-//    protected double defaultFunctionValueAccuracy;
-
     /** Indicates where a root has been computed. */
     protected boolean resultComputed = false;
 
@@ -59,13 +53,12 @@
     protected UnivariateRealMinimizerImpl(int defaultMaximalIterationCount,
                                           double defaultAbsoluteAccuracy) {
         super(defaultMaximalIterationCount, defaultAbsoluteAccuracy);
-//        this.functionValueAccuracy = defaultFunctionValueAccuracy;
     }
 
     /** Check if a result has been computed.
      * @exception IllegalStateException if no result has been computed
      */
-    protected void checkResultComputed() throws IllegalArgumentException {
+    protected void checkResultComputed() throws IllegalStateException {
         if (!resultComputed) {
             throw MathRuntimeException.createIllegalStateException("no result available",
null);
         }
@@ -83,21 +76,6 @@
         return functionValue;
     }
 
-//    /** {@inheritDoc} */
-//    public void setFunctionValueAccuracy(double accuracy) {
-//        functionValueAccuracy = accuracy;
-//    }
-//
-//    /** {@inheritDoc} */
-//    public double getFunctionValueAccuracy() {
-//        return functionValueAccuracy;
-//    }
-//
-//    /** {@inheritDoc} */
-//    public void resetFunctionValueAccuracy() {
-//        functionValueAccuracy = defaultFunctionValueAccuracy;
-//    }
-    
     /**
      * Convenience function for implementations.
      * 

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.java
Sun Jan 18 08:57:29 2009
@@ -117,7 +117,7 @@
      */
     @Deprecated
     double solve(double min, double max, double startValue)
-        throws ConvergenceException, FunctionEvaluationException;
+        throws ConvergenceException, FunctionEvaluationException, IllegalArgumentException;
 
     /**
      * Solve for a zero in the given interval, start at startValue.
@@ -137,7 +137,7 @@
      * @since 2.0
      */
     double solve(UnivariateRealFunction f, double min, double max, double startValue)
-        throws ConvergenceException, FunctionEvaluationException;
+        throws ConvergenceException, FunctionEvaluationException, IllegalArgumentException;
 
     /**
      * Get the result of the last run of the solver.

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolverImpl.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolverImpl.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolverImpl.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/analysis/solvers/UnivariateRealSolverImpl.java
Sun Jan 18 08:57:29 2009
@@ -102,7 +102,7 @@
     /** Check if a result has been computed.
      * @exception IllegalStateException if no result has been computed
      */
-    protected void checkResultComputed() throws IllegalArgumentException {
+    protected void checkResultComputed() throws IllegalStateException {
         if (!resultComputed) {
             throw MathRuntimeException.createIllegalStateException("no result available",
null);
         }

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/ode/SecondOrderDifferentialEquations.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/ode/SecondOrderDifferentialEquations.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/ode/SecondOrderDifferentialEquations.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/ode/SecondOrderDifferentialEquations.java
Sun Jan 18 08:57:29 2009
@@ -17,6 +17,8 @@
 
 package org.apache.commons.math.ode;
 
+import java.io.Serializable;
+
 /** This interface represents a second order differential equations set.
 
  * <p>This interface should be implemented by all real second order
@@ -44,7 +46,7 @@
  * @since 1.2
  */
 
-public interface SecondOrderDifferentialEquations {
+public interface SecondOrderDifferentialEquations extends Serializable {
 
   /** Get the dimension of the problem.
    * @return dimension of the problem

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/transform/FastFourierTransformer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/transform/FastFourierTransformer.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/transform/FastFourierTransformer.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/transform/FastFourierTransformer.java
Sun Jan 18 08:57:29 2009
@@ -722,9 +722,12 @@
          */
         public Complex set(Complex magnitude, int... vector)
             throws IllegalArgumentException {
-            if (vector == null && dimensionSize.length > 1) {
-                throw MathRuntimeException.createIllegalArgumentException("some dimensions
don't math: {0} != {1}",
-                                                                          new Object[] {
0, dimensionSize.length });
+            if (vector == null) {
+                if (dimensionSize.length > 1) {
+                    throw MathRuntimeException.createIllegalArgumentException("some dimensions
don't math: {0} != {1}",
+                                                                              new Object[]
{ 0, dimensionSize.length });
+                }
+                return null;
             }
             if (vector != null && vector.length != dimensionSize.length) {
                 throw MathRuntimeException.createIllegalArgumentException("some dimensions
don't math: {0} != {1}",
@@ -733,17 +736,15 @@
                                                                               dimensionSize.length
                                                                           });
             }
-            
-            Object lastDimension = multiDimensionalComplexArray;
-            
+
+            Object[] lastDimension = (Object[]) multiDimensionalComplexArray;
             for (int i = 0; i < dimensionSize.length - 1; i++) {
-                lastDimension = ((Object[]) lastDimension)[vector[i]];
+                lastDimension = (Object[]) lastDimension[vector[i]];
             }
-            
-            Complex lastValue = (Complex) ((Object[])
-                    lastDimension)[vector[dimensionSize.length - 1]];
-            ((Object[]) lastDimension)[vector[dimensionSize.length - 1]] =
-                    magnitude;
+
+            Complex lastValue = (Complex) lastDimension[vector[dimensionSize.length - 1]];
+            lastDimension[vector[dimensionSize.length - 1]] = magnitude;
+
             return lastValue;
         }
 

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/util/OpenIntToDoubleHashMap.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/util/OpenIntToDoubleHashMap.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/util/OpenIntToDoubleHashMap.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/util/OpenIntToDoubleHashMap.java
Sun Jan 18 08:57:29 2009
@@ -17,6 +17,8 @@
 
 package org.apache.commons.math.util;
 
+import java.io.IOException;
+import java.io.ObjectInputStream;
 import java.io.Serializable;
 import java.util.ConcurrentModificationException;
 import java.util.NoSuchElementException;
@@ -579,4 +581,17 @@
 
     }
 
+    /**
+     * Read a serialized object.
+     * @param stream input stream
+     * @throws IOException if object cannot be read
+     * @throws ClassNotFoundException if the class corresponding
+     * to the serialized object cannot be found
+     */
+    private void readObject(final ObjectInputStream stream)
+        throws IOException, ClassNotFoundException {
+        stream.defaultReadObject();
+        count = 0;
+    }
+
 }

Modified: commons/proper/math/trunk/src/java/org/apache/commons/math/util/ResizableDoubleArray.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/java/org/apache/commons/math/util/ResizableDoubleArray.java?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/java/org/apache/commons/math/util/ResizableDoubleArray.java
(original)
+++ commons/proper/math/trunk/src/java/org/apache/commons/math/util/ResizableDoubleArray.java
Sun Jan 18 08:57:29 2009
@@ -873,13 +873,15 @@
      */
     public int hashCode() {
         int[] hashData = new int[7];
-        hashData[0] = Arrays.hashCode(internalArray);
-        hashData[1] = new Float(expansionFactor).hashCode();
-        hashData[2] = new Float(contractionCriteria).hashCode();
-        hashData[3] = initialCapacity;
-        hashData[4] = expansionMode;
-        hashData[5] = numElements;
-        hashData[6] = startIndex;
+        hashData[0] = new Float(expansionFactor).hashCode();
+        hashData[1] = new Float(contractionCriteria).hashCode();
+        hashData[2] = expansionMode;
+        synchronized(this) {
+            hashData[3] = Arrays.hashCode(internalArray);
+            hashData[4] = initialCapacity;
+            hashData[5] = numElements;
+            hashData[6] = startIndex;
+        }
         return Arrays.hashCode(hashData);
     }
          

Modified: commons/proper/math/trunk/src/site/xdoc/userguide/index.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/xdoc/userguide/index.xml?rev=735501&r1=735500&r2=735501&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/xdoc/userguide/index.xml (original)
+++ commons/proper/math/trunk/src/site/xdoc/userguide/index.xml Sun Jan 18 08:57:29 2009
@@ -30,107 +30,108 @@
         <ul>
             <li><a href="overview.html">0. Overview</a>
             <ul>
-              <li><a href="overview.html#0.1 About the User Guide">0.1 About
the User Guide</a></li>
-              <li><a href="overview.html#0.2 What&amp;apos;s in commons-math">0.2
What's in commons-math</a></li>
-              <li><a href="overview.html#0.3 How commons-math is organized">0.3
How commons-math is organized</a></li>
-              <li><a href="overview.html#0.4 How interface contracts are specified
in commons-math javadoc">0.4 How interface contracts are specified in commons-math javadoc</a></li>
-              <li><a href="overview.html#0.5 Dependencies">0.5 Dependencies</a></li>
+              <li><a href="overview.html#a0.1_About_the_User_Guide">0.1 About
the User Guide</a></li>
+              <li><a href="overview.html#a0.2_Whats_in_commons-math">0.2 What's
in commons-math</a></li>
+              <li><a href="overview.html#a0.3_How_commons-math_is_organized">0.3
How commons-math is organized</a></li>
+              <li><a href="overview.html#a0.4_How_interface_contracts_are_specified_in_commons-math_javadoc">0.4
How interface contracts are specified in commons-math javadoc</a></li>
+              <li><a href="overview.html#a0.5_Dependencies">0.5 Dependencies</a></li>
             </ul></li>
 
            <li><a href="stat.html">1. Statistics</a>
                 <ul>
-                <li><a href="stat.html#1.1 Overview">1.1 Overview</a></li>
-                <li><a href="stat.html#1.2 Descriptive statistics">1.2 Descriptive
statistics</a></li>
-                <li><a href="stat.html#1.3 Frequency distributions">1.3 Frequency
distributions</a></li>
-                <li><a href="stat.html#1.4 Simple regression">1.4 Simple regression</a></li>
-                <li><a href="stat.html#1.5 Statistical tests">1.5 Statistical
tests</a></li>
+                <li><a href="stat.html#a1.1_Overview">1.1 Overview</a></li>
+                <li><a href="stat.html#a1.2_Descriptive_statistics">1.2 Descriptive
statistics</a></li>
+                <li><a href="stat.html#a1.3_Frequency_distributions">1.3 Frequency
distributions</a></li>
+                <li><a href="stat.html#a1.4_Simple_regression">1.4 Simple regression</a></li>
+                <li><a href="stat.html#a1.5_Statistical_tests">1.5 Statistical
tests</a></li>
                 </ul></li>
             <li><a href="random.html">2. Data Generation</a>
                 <ul>
-                <li><a href="random.html#2.1 Overview">2.1 Overview</a></li>
-                <li><a href="random.html#2.2 Random numbers">2.2 Random numbers</a></li>
-                <li><a href="random.html#2.3 Random Strings">2.3 Random Strings</a></li>
-                <li><a href="random.html#2.4 Random permutations, combinations,
sampling">2.4 Random permutations, combinations, sampling</a></li>
-                <li><a href="random.html#2.5 Generating data 'like' an input file">2.5
Generating data 'like' an input file</a></li>
-                <li><a href="random.html#2.6 PRNG Pluggability">2.6 PRNG Pluggability</a></li>
+                <li><a href="random.html#a2.1_Overview">2.1 Overview</a></li>
+                <li><a href="random.html#a2.2_Random_numbers">2.2 Random numbers</a></li>
+                <li><a href="random.html#a2.3_Random_Vectors">2.3 Random Vectors</a></li>
+                <li><a href="random.html#a2.4_Random_Strings">2.4 Random Strings</a></li>
+                <li><a href="random.html#a2.5_Random_permutations_combinations_sampling">2.5
Random permutations, combinations, sampling</a></li>
+                <li><a href="random.html#a2.6_Generating_data_like_an_input_file">2.6
Generating data 'like' an input file</a></li>
+                <li><a href="random.html#a2.7_PRNG_Pluggability">2.7 PRNG Pluggability</a></li>
                 </ul></li>
             <li><a href="linear.html">3. Linear Algebra</a>
                 <ul>
-                <li><a href="linear.html#3.1 Overview">3.1 Overview</a></li>
-                <li><a href="linear.html#3.2 Real matrices">3.2 Real matrices</a></li>
-                <li><a href="linear.html#3.3 Real vectors">3.3 Real vectors</a></li>
-                <li><a href="linear.html#3.4 Solving linear systems">3.4 Solving
linear systems</a></li> 
-                <li><a href="linear.html#3.5 Eigenvalues/eigenvectors and singular
values/singular vectors">3.5 Eigenvalues/eigenvectors and singular values/singular vectors</a></li>
+                <li><a href="linear.html#a3.1_Overview">3.1 Overview</a></li>
+                <li><a href="linear.html#a3.2_Real_matrices">3.2 Real matrices</a></li>
+                <li><a href="linear.html#a3.3_Real_vectors">3.3 Real vectors</a></li>
+                <li><a href="linear.html#a3.4_Solving_linear_systems">3.4 Solving
linear systems</a></li> 
+                <li><a href="linear.html#a3.5_Eigenvalueseigenvectors_and_singular_valuessingular_vectors">3.5
Eigenvalues/eigenvectors and singular values/singular vectors</a></li>
                 </ul></li>             
             <li><a href="analysis.html">4. Numerical Analysis</a>
                 <ul>
-                <li><a href="analysis.html#4.1 Overview">4.1 Overview</a></li>
-                <li><a href="analysis.html#4.2 Root-finding">4.2 Root-finding</a></li>
               
-                <li><a href="analysis.html#4.3 Minimization">4.3 Minimization</a></li>
-                <li><a href="analysis.html#4.4 Interpolation">4.4 Interpolation</a></li>
-                <li><a href="analysis.html#4.5 Integration">4.5 Integration</a></li>
-                <li><a href="analysis.html#4.6 Polynomials">4.6 Polynomials</a></li>
+                <li><a href="analysis.html#a4.1_Overview">4.1 Overview</a></li>
+                <li><a href="analysis.html#a4.2_Root-finding">4.2 Root-finding</a></li>
               
+                <li><a href="analysis.html#a4.3_Minimization">4.3 Minimization</a></li>
+                <li><a href="analysis.html#a4.4_Interpolation">4.4 Interpolation</a></li>
+                <li><a href="analysis.html#a4.5_Integration">4.5 Integration</a></li>
+                <li><a href="analysis.html#a4.6_Polynomials">4.6 Polynomials</a></li>
                 </ul></li>     
             <li><a href="special.html">5. Special Functions</a>
                 <ul>
-                <li><a href="special.html#5.1 Overview">5.1 Overview</a></li>
-                <li><a href="special.html#5.2 Erf functions">5.2 Erf functions</a></li>
-                <li><a href="special.html#5.3 Gamma functions">5.3 Gamma functions</a></li>
-                <li><a href="special.html#5.4 Beta funtions">5.4 Beta funtions</a></li>
+                <li><a href="special.html#a5.1_Overview">5.1 Overview</a></li>
+                <li><a href="special.html#a5.2_Erf_functions">5.2 Erf functions</a></li>
+                <li><a href="special.html#a5.3_Gamma_functions">5.3 Gamma functions</a></li>
+                <li><a href="special.html#a5.4_Beta_funtions">5.4 Beta funtions</a></li>
                 </ul></li>   
         <li><a href="utilities.html">6. Utilities</a>
                 <ul>
-                <li><a href="utilities.html#6.1 Overview">6.1 Overview</a></li>
-                <li><a href="utilities.html#6.2 Double array utilities">6.2 Double
array utilities</a></li>
-                <li><a href="utilities.html#6.3 int/double hash map">6.3 int/double
hash map</a></li>
-                <li><a href="utilities.html#6.4 Continued Fractions">6.4 Continued
Fractions</a></li>
-                <li><a href="utilities.html#6.5 binomial coefficients, factorials
and other common math functions">6.5 binomial coefficients, factorials and other common
math functions</a></li>
+                <li><a href="utilities.html#a6.1_Overview">6.1 Overview</a></li>
+                <li><a href="utilities.html#a6.2_Double_array_utilities">6.2
Double array utilities</a></li>
+                <li><a href="utilities.html#a6.3_intdouble_hash_map">6.3 int/double
hash map</a></li>
+                <li><a href="utilities.html#a6.4_Continued_Fractions">6.4 Continued
Fractions</a></li>
+                <li><a href="utilities.html#a6.5_binomial_coefficients,_factorials_and_other_common_math_functions">6.5
binomial coefficients, factorials and other common math functions</a></li>
                 </ul></li>                                 
         <li><a href="complex.html">7. Complex Numbers</a>
                 <ul>
-                <li><a href="complex.html#7.1 Overview">7.1 Overview</a></li>
-                <li><a href="complex.html#7.2 Complex Numbers">7.2 Complex Numbers</a></li>
-                <li><a href="complex.html#7.3 Complex Transcendental Functions">7.3
Complex Transcendental Functions</a></li>
-                <li><a href="complex.html#7.4 Complex Formatting and Parsing">7.4
Complex Formatting and Parsing</a></li>
+                <li><a href="complex.html#a7.1_Overview">7.1 Overview</a></li>
+                <li><a href="complex.html#a7.2_Complex_Numbers">7.2 Complex Numbers</a></li>
+                <li><a href="complex.html#a7.3_Complex_Transcendental_Functions">7.3
Complex Transcendental Functions</a></li>
+                <li><a href="complex.html#a7.4_Complex_Formatting_and_Parsing">7.4
Complex Formatting and Parsing</a></li>
                 </ul></li>                                 
         <li><a href="distribution.html">8. Probability Distributions</a>
                 <ul>
-                <li><a href="distribution.html#8.1 Overview">8.1 Overview</a></li>
-                <li><a href="distribution.html#8.2 Distribution Framework">8.2
Distribution Framework</a></li>
-                <li><a href="distribution.html#8.3 User Defined Distributions">8.3
User Defined Distributions</a></li>
+                <li><a href="distribution.html#a8.1_Overview">8.1 Overview</a></li>
+                <li><a href="distribution.html#a8.2_Distribution_Framework">8.2
Distribution Framework</a></li>
+                <li><a href="distribution.html#a8.3_User_Defined_Distributions">8.3
User Defined Distributions</a></li>
                 </ul></li>                                 
         <li><a href="fraction.html">9. Fractions</a>
                 <ul>
-                <li><a href="fraction.html#9.1 Overview">9.1 Overview</a></li>
-                <li><a href="fraction.html#9.2 Fraction Numbers">9.2 Fraction
Numbers</a></li>
-                <li><a href="fraction.html#9.3 Fraction Formatting and Parsing">9.3
Fraction Formatting and Parsing</a></li>
+                <li><a href="fraction.html#a9.1_Overview">9.1 Overview</a></li>
+                <li><a href="fraction.html#a9.2_Fraction_Numbers">9.2 Fraction
Numbers</a></li>
+                <li><a href="fraction.html#a9.3_Fraction_Formatting_and_Parsing">9.3
Fraction Formatting and Parsing</a></li>
                 </ul></li>                                 
         <li><a href="transform.html">10. Transform methods</a></li>
                                
         <li><a href="geometry.html">11. Geometry</a>
                 <ul>
-                <li><a href="geometry.html#11.1 Overview">11.1 Overview</a></li>
-                <li><a href="geometry.html#11.2 Vectors">11.2 Vectors</a></li>
-                <li><a href="geometry.html#11.3 Rotations">11.3 Rotations</a></li>
+                <li><a href="geometry.html#a11.1_Overview">11.1 Overview</a></li>
+                <li><a href="geometry.html#a11.2_Vectors">11.2 Vectors</a></li>
+                <li><a href="geometry.html#a11.3_Rotations">11.3 Rotations</a></li>
                 </ul></li>                                 
         <li><a href="estimation.html">12. Parametric Estimation</a>
                 <ul>
-                <li><a href="estimation.html#12.1 Overview">12.1 Overview</a></li>
-                <li><a href="estimation.html#12.2 Models">12.2 Models</a></li>
-                <li><a href="estimation.html#12.3 Parameters">12.3 Parameters</a></li>
-                <li><a href="estimation.html#12.4 Measurements">12.4 Measurements</a></li>
-                <li><a href="estimation.html#12.5 Solvers">12.5 Solvers</a></li>
+                <li><a href="estimation.html#a12.1_Overview">12.1 Overview</a></li>
+                <li><a href="estimation.html#a12.2_Models">12.2 Models</a></li>
+                <li><a href="estimation.html#a12.3_Parameters">12.3 Parameters</a></li>
+                <li><a href="estimation.html#a12.4_Measurements">12.4 Measurements</a></li>
+                <li><a href="estimation.html#a12.5_Solvers">12.5 Solvers</a></li>
                 </ul></li>                                 
         <li><a href="optimization.html">13. Optimization</a>
                 <ul>
-                <li><a href="optimization.html#13.1 Overview">13.1 Overview</a></li>
-                <li><a href="optimization.html#13.2 Direct Methods">13.2 Direct
Methods</a></li>
+                <li><a href="optimization.html#a13.1_Overview">13.1 Overview</a></li>
+                <li><a href="optimization.html#a13.2_Direct_Methods">13.2 Direct
Methods</a></li>
                 </ul></li>                                 
         <li><a href="ode.html">14. Ordinary Differential Equations Integration</a>
                 <ul>
-                <li><a href="ode.html#14.1 Overview">14.1 Overview</a></li>
-                <li><a href="ode.html#14.2 Discrete Events Handling">14.2 Discrete
Events Handling</a></li>
-                <li><a href="ode.html#14.3 ODE Problems">14.3 ODE Problems</a></li>
-                <li><a href="ode.html#14.4 Integrators">14.4 Integrators</a></li>
+                <li><a href="ode.html#a14.1_Overview">14.1 Overview</a></li>
+                <li><a href="ode.html#a14.2_Discrete_Events_Handling">14.2 Discrete
Events Handling</a></li>
+                <li><a href="ode.html#a14.3_ODE_Problems">14.3 ODE Problems</a></li>
+                <li><a href="ode.html#a14.4_Integrators">14.4 Integrators</a></li>
                 </ul></li>                                 
         </ul>
       </section>



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