From 0234e46518b92148a12aaab11526cfc963b4f9ec Mon Sep 17 00:00:00 2001
From: Luc Maisonobe <luc@apache.org>
Date: Tue, 1 Sep 2009 19:47:46 +0000
Subject: [PATCH] tighten rules for constants naming conventions

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@810196 13f79535-47bb-0310-9956-ffa450edef68
---
 checkstyle.xml                                |   9 +-
 .../commons/math/MessagesResources_fr.java    |   4 +-
 .../apache/commons/math/complex/Complex.java  |   4 +-
 .../commons/math/geometry/Vector3D.java       |   2 +
 .../nonstiff/AdamsNordsieckTransformer.java   |   8 +-
 .../ClassicalRungeKuttaIntegrator.java        |   8 +-
 .../nonstiff/DormandPrince54Integrator.java   |  28 ++--
 .../DormandPrince54StepInterpolator.java      |  26 ++--
 .../nonstiff/DormandPrince853Integrator.java  |  58 ++++----
 .../DormandPrince853StepInterpolator.java     | 128 +++++++++---------
 .../math/ode/nonstiff/EulerIntegrator.java    |   8 +-
 .../math/ode/nonstiff/GillIntegrator.java     |   8 +-
 .../ode/nonstiff/GillStepInterpolator.java    |  12 +-
 .../ode/nonstiff/HighamHall54Integrator.java  |  18 +--
 .../math/ode/nonstiff/MidpointIntegrator.java |   8 +-
 .../ode/nonstiff/ThreeEighthesIntegrator.java |   8 +-
 .../math/ode/sampling/DummyStepHandler.java   |   4 +-
 .../univariate/BrentOptimizer.java            |   6 +-
 .../apache/commons/math/special/Gamma.java    |   8 +-
 .../apache/commons/math/stat/StatUtils.java   |  64 ++++-----
 .../apache/commons/math/util/MathUtils.java   |   4 +-
 21 files changed, 217 insertions(+), 206 deletions(-)

diff --git a/checkstyle.xml b/checkstyle.xml
index b9601dc2a..56c56b33b 100644
--- a/checkstyle.xml
+++ b/checkstyle.xml
@@ -82,8 +82,10 @@
     <module name="FallThrough" />
     <module name="MissingSwitchDefault" />
 
-    <!--
+    <!-- Constant names should obey the traditional all uppercase naming convention -->
     <module name="ConstantName" />
+
+    <!--
     <module name="HiddenField">
         <property name="ignoreConstructorParameter" value="true" />
         <property name="ignoreSetter" value="true" />
@@ -109,6 +111,11 @@
     <property name="onCommentFormat"  value="CHECKSTYLE\: resume JavadocMethodCheck"/>
     <property name="checkFormat"      value="JavadocMethodCheck"/>
   </module>
+  <module name="SuppressionCommentFilter">
+    <property name="offCommentFormat" value="CHECKSTYLE\: stop ConstantName"/>
+    <property name="onCommentFormat"  value="CHECKSTYLE\: resume ConstantName"/>
+    <property name="checkFormat"      value="ConstantName"/>
+  </module>
 
 </module>
 
diff --git a/src/main/java/org/apache/commons/math/MessagesResources_fr.java b/src/main/java/org/apache/commons/math/MessagesResources_fr.java
index 64f750828..bc53d9825 100644
--- a/src/main/java/org/apache/commons/math/MessagesResources_fr.java
+++ b/src/main/java/org/apache/commons/math/MessagesResources_fr.java
@@ -39,11 +39,11 @@ public class MessagesResources_fr
    */
   @Override
   public Object[][] getContents() {
-    return contents.clone();
+    return CONTENTS.clone();
   }
 
   /** Non-translated/translated messages arrays. */
-  private static final Object[][] contents = {
+  private static final Object[][] CONTENTS = {
 
     // org.apache.commons.math.util.MathUtils
     { "must have n >= k for binomial coefficient (n,k), got n = {0}, k = {1}",
diff --git a/src/main/java/org/apache/commons/math/complex/Complex.java b/src/main/java/org/apache/commons/math/complex/Complex.java
index f12e22b11..227489a2e 100644
--- a/src/main/java/org/apache/commons/math/complex/Complex.java
+++ b/src/main/java/org/apache/commons/math/complex/Complex.java
@@ -50,9 +50,11 @@ public class Complex implements FieldElement<Complex>, Serializable  {
 
     /** The square root of -1. A number representing "0.0 + 1.0i" */    
     public static final Complex I = new Complex(0.0, 1.0);
-    
+
+    // CHECKSTYLE: stop ConstantName
     /** A complex number representing "NaN + NaNi" */
     public static final Complex NaN = new Complex(Double.NaN, Double.NaN);
+    // CHECKSTYLE: resume ConstantName
 
     /** A complex number representing "+INF + INFi" */
     public static final Complex INF = new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
diff --git a/src/main/java/org/apache/commons/math/geometry/Vector3D.java b/src/main/java/org/apache/commons/math/geometry/Vector3D.java
index 3f3b67b08..ce62e2ca7 100644
--- a/src/main/java/org/apache/commons/math/geometry/Vector3D.java
+++ b/src/main/java/org/apache/commons/math/geometry/Vector3D.java
@@ -53,8 +53,10 @@ public class Vector3D
   /** Opposite of the third canonical vector (coordinates: 0, 0, -1).  */
   public static final Vector3D MINUS_K = new Vector3D(0, 0, -1);
 
+  // CHECKSTYLE: stop ConstantName
   /** A vector with all coordinates set to NaN. */
   public static final Vector3D NaN = new Vector3D(Double.NaN, Double.NaN, Double.NaN);
+  // CHECKSTYLE: resume ConstantName
 
   /** A vector with all coordinates set to positive infinity. */
   public static final Vector3D POSITIVE_INFINITY =
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsNordsieckTransformer.java b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsNordsieckTransformer.java
index 8e1844972..78ee0d104 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsNordsieckTransformer.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsNordsieckTransformer.java
@@ -133,7 +133,7 @@ import org.apache.commons.math.linear.MatrixUtils;
 public class AdamsNordsieckTransformer {
 
     /** Cache for already computed coefficients. */
-    private static final Map<Integer, AdamsNordsieckTransformer> cache =
+    private static final Map<Integer, AdamsNordsieckTransformer> CACHE =
         new HashMap<Integer, AdamsNordsieckTransformer>();
 
     /** Initialization matrix for the higher order derivatives wrt y'', y''' ... */
@@ -200,11 +200,11 @@ public class AdamsNordsieckTransformer {
      * @return Nordsieck transformer for the specified number of steps
      */
     public static AdamsNordsieckTransformer getInstance(final int nSteps) {
-        synchronized(cache) {
-            AdamsNordsieckTransformer t = cache.get(nSteps);
+        synchronized(CACHE) {
+            AdamsNordsieckTransformer t = CACHE.get(nSteps);
             if (t == null) {
                 t = new AdamsNordsieckTransformer(nSteps);
-                cache.put(nSteps, t);
+                CACHE.put(nSteps, t);
             }
             return t;
         }
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/ClassicalRungeKuttaIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/ClassicalRungeKuttaIntegrator.java
index 533d1b856..39aa8e47b 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/ClassicalRungeKuttaIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/ClassicalRungeKuttaIntegrator.java
@@ -46,19 +46,19 @@ package org.apache.commons.math.ode.nonstiff;
 public class ClassicalRungeKuttaIntegrator extends RungeKuttaIntegrator {
 
   /** Time steps Butcher array. */
-  private static final double[] c = {
+  private static final double[] STATIC_C = {
     1.0 / 2.0, 1.0 / 2.0, 1.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] a = {
+  private static final double[][] STATIC_A = {
     { 1.0 / 2.0 },
     { 0.0, 1.0 / 2.0 },
     { 0.0, 0.0, 1.0 }
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] b = {
+  private static final double[] STATIC_B = {
     1.0 / 6.0, 1.0 / 3.0, 1.0 / 3.0, 1.0 / 6.0
   };
 
@@ -68,7 +68,7 @@ public class ClassicalRungeKuttaIntegrator extends RungeKuttaIntegrator {
    * @param step integration step
    */
   public ClassicalRungeKuttaIntegrator(final double step) {
-    super("classical Runge-Kutta", c, a, b,
+    super("classical Runge-Kutta", STATIC_C, STATIC_A, STATIC_B,
           new ClassicalRungeKuttaStepInterpolator(), step);
   }
 
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java
index a9a68d3e4..7ed175a6a 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java
@@ -50,12 +50,12 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
   private static final String METHOD_NAME = "Dormand-Prince 5(4)";
 
   /** Time steps Butcher array. */
-  private static final double[] staticC = {
+  private static final double[] STATIC_C = {
     1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] staticA = {
+  private static final double[][] STATIC_A = {
     {1.0/5.0},
     {3.0/40.0, 9.0/40.0},
     {44.0/45.0, -56.0/15.0, 32.0/9.0},
@@ -65,29 +65,29 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] staticB = {
+  private static final double[] STATIC_B = {
     35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0
   };
 
   /** Error array, element 1. */
-  private static final double e1 =     71.0 / 57600.0;
+  private static final double E1 =     71.0 / 57600.0;
 
   // element 2 is zero, so it is neither stored nor used
 
   /** Error array, element 3. */
-  private static final double e3 =    -71.0 / 16695.0;
+  private static final double E3 =    -71.0 / 16695.0;
 
   /** Error array, element 4. */
-  private static final double e4 =     71.0 / 1920.0;
+  private static final double E4 =     71.0 / 1920.0;
 
   /** Error array, element 5. */
-  private static final double e5 = -17253.0 / 339200.0;
+  private static final double E5 = -17253.0 / 339200.0;
 
   /** Error array, element 6. */
-  private static final double e6 =     22.0 / 525.0;
+  private static final double E6 =     22.0 / 525.0;
 
   /** Error array, element 7. */
-  private static final double e7 =     -1.0 / 40.0;
+  private static final double E7 =     -1.0 / 40.0;
 
   /** Simple constructor.
    * Build a fifth order Dormand-Prince integrator with the given step bounds
@@ -101,7 +101,7 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
   public DormandPrince54Integrator(final double minStep, final double maxStep,
                                    final double scalAbsoluteTolerance,
                                    final double scalRelativeTolerance) {
-    super(METHOD_NAME, true, staticC, staticA, staticB, new DormandPrince54StepInterpolator(),
+    super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(),
           minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
   }
 
@@ -117,7 +117,7 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
   public DormandPrince54Integrator(final double minStep, final double maxStep,
                                    final double[] vecAbsoluteTolerance,
                                    final double[] vecRelativeTolerance) {
-    super(METHOD_NAME, true, staticC, staticA, staticB, new DormandPrince54StepInterpolator(),
+    super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B, new DormandPrince54StepInterpolator(),
           minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
   }
 
@@ -136,9 +136,9 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
     double error = 0;
 
     for (int j = 0; j < y0.length; ++j) {
-        final double errSum = e1 * yDotK[0][j] +  e3 * yDotK[2][j] +
-                              e4 * yDotK[3][j] +  e5 * yDotK[4][j] +
-                              e6 * yDotK[5][j] +  e7 * yDotK[6][j];
+        final double errSum = E1 * yDotK[0][j] +  E3 * yDotK[2][j] +
+                              E4 * yDotK[3][j] +  E5 * yDotK[4][j] +
+                              E6 * yDotK[5][j] +  E7 * yDotK[6][j];
 
         final double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));
         final double tol = (vecAbsoluteTolerance == null) ?
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54StepInterpolator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54StepInterpolator.java
index d77bc873e..d1d917777 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54StepInterpolator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54StepInterpolator.java
@@ -132,10 +132,10 @@ class DormandPrince54StepInterpolator
           final double yDot4 = yDotK[4][i];
           final double yDot5 = yDotK[5][i];
           final double yDot6 = yDotK[6][i];
-          v1[i] = a70 * yDot0 + a72 * yDot2 + a73 * yDot3 + a74 * yDot4 + a75 * yDot5;
+          v1[i] = A70 * yDot0 + A72 * yDot2 + A73 * yDot3 + A74 * yDot4 + A75 * yDot5;
           v2[i] = yDot0 - v1[i];
           v3[i] = v1[i] - v2[i] - yDot6;
-          v4[i] = d0 * yDot0 + d2 * yDot2 + d3 * yDot3 + d4 * yDot4 + d5 * yDot5 + d6 * yDot6;
+          v4[i] = D0 * yDot0 + D2 * yDot2 + D3 * yDot3 + D4 * yDot4 + D5 * yDot5 + D6 * yDot6;
       }
 
       vectorsInitialized = true;
@@ -172,41 +172,41 @@ class DormandPrince54StepInterpolator
   private boolean vectorsInitialized;
 
   /** Last row of the Butcher-array internal weights, element 0. */
-  private static final double a70 =    35.0 /  384.0;
+  private static final double A70 =    35.0 /  384.0;
 
   // element 1 is zero, so it is neither stored nor used
 
   /** Last row of the Butcher-array internal weights, element 2. */
-  private static final double a72 =   500.0 / 1113.0;
+  private static final double A72 =   500.0 / 1113.0;
 
   /** Last row of the Butcher-array internal weights, element 3. */
-  private static final double a73 =   125.0 /  192.0;
+  private static final double A73 =   125.0 /  192.0;
 
   /** Last row of the Butcher-array internal weights, element 4. */
-  private static final double a74 = -2187.0 / 6784.0;
+  private static final double A74 = -2187.0 / 6784.0;
 
   /** Last row of the Butcher-array internal weights, element 5. */
-  private static final double a75 =    11.0 /   84.0;
+  private static final double A75 =    11.0 /   84.0;
 
   /** Shampine (1986) Dense output, element 0. */
-  private static final double d0 =  -12715105075.0 /  11282082432.0;
+  private static final double D0 =  -12715105075.0 /  11282082432.0;
 
   // element 1 is zero, so it is neither stored nor used
 
   /** Shampine (1986) Dense output, element 2. */
-  private static final double d2 =   87487479700.0 /  32700410799.0;
+  private static final double D2 =   87487479700.0 /  32700410799.0;
 
   /** Shampine (1986) Dense output, element 3. */
-  private static final double d3 =  -10690763975.0 /   1880347072.0;
+  private static final double D3 =  -10690763975.0 /   1880347072.0;
 
   /** Shampine (1986) Dense output, element 4. */
-  private static final double d4 =  701980252875.0 / 199316789632.0;
+  private static final double D4 =  701980252875.0 / 199316789632.0;
 
   /** Shampine (1986) Dense output, element 5. */
-  private static final double d5 =   -1453857185.0 /    822651844.0;
+  private static final double D5 =   -1453857185.0 /    822651844.0;
 
   /** Shampine (1986) Dense output, element 6. */
-  private static final double d6 =      69997945.0 /     29380423.0;
+  private static final double D6 =      69997945.0 /     29380423.0;
 
   /** Serializable version identifier */
   private static final long serialVersionUID = 4104157279605906956L;
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java
index 2ea773389..2d6b17e29 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java
@@ -58,14 +58,14 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
   private static final String METHOD_NAME = "Dormand-Prince 8 (5, 3)";
 
   /** Time steps Butcher array. */
-  private static final double[] staticC = {
+  private static final double[] STATIC_C = {
     (12.0 - 2.0 * Math.sqrt(6.0)) / 135.0, (6.0 - Math.sqrt(6.0)) / 45.0, (6.0 - Math.sqrt(6.0)) / 30.0,
     (6.0 + Math.sqrt(6.0)) / 30.0, 1.0/3.0, 1.0/4.0, 4.0/13.0, 127.0/195.0, 3.0/5.0,
     6.0/7.0, 1.0, 1.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] staticA = {
+  private static final double[][] STATIC_A = {
 
     // k2
     {(12.0 - 2.0 * Math.sqrt(6.0)) / 135.0},
@@ -132,7 +132,7 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] staticB = {
+  private static final double[] STATIC_B = {
       104257.0/1920240.0,
       0.0,
       0.0,
@@ -149,57 +149,57 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
   };
 
   /** First error weights array, element 1. */
-  private static final double e1_01 =         116092271.0 / 8848465920.0;
+  private static final double E1_01 =         116092271.0 / 8848465920.0;
 
   // elements 2 to 5 are zero, so they are neither stored nor used
 
   /** First error weights array, element 6. */
-  private static final double e1_06 =          -1871647.0 / 1527680.0;
+  private static final double E1_06 =          -1871647.0 / 1527680.0;
 
   /** First error weights array, element 7. */
-  private static final double e1_07 =         -69799717.0 / 140793660.0;
+  private static final double E1_07 =         -69799717.0 / 140793660.0;
 
   /** First error weights array, element 8. */
-  private static final double e1_08 =     1230164450203.0 / 739113984000.0;
+  private static final double E1_08 =     1230164450203.0 / 739113984000.0;
 
   /** First error weights array, element 9. */
-  private static final double e1_09 = -1980813971228885.0 / 5654156025964544.0;
+  private static final double E1_09 = -1980813971228885.0 / 5654156025964544.0;
 
   /** First error weights array, element 10. */
-  private static final double e1_10 =         464500805.0 / 1389975552.0;
+  private static final double E1_10 =         464500805.0 / 1389975552.0;
 
   /** First error weights array, element 11. */
-  private static final double e1_11 =     1606764981773.0 / 19613062656000.0;
+  private static final double E1_11 =     1606764981773.0 / 19613062656000.0;
 
   /** First error weights array, element 12. */
-  private static final double e1_12 =           -137909.0 / 6168960.0;
+  private static final double E1_12 =           -137909.0 / 6168960.0;
 
 
   /** Second error weights array, element 1. */
-  private static final double e2_01 =           -364463.0 / 1920240.0;
+  private static final double E2_01 =           -364463.0 / 1920240.0;
 
   // elements 2 to 5 are zero, so they are neither stored nor used
 
   /** Second error weights array, element 6. */
-  private static final double e2_06 =           3399327.0 / 763840.0;
+  private static final double E2_06 =           3399327.0 / 763840.0;
 
   /** Second error weights array, element 7. */
-  private static final double e2_07 =          66578432.0 / 35198415.0;
+  private static final double E2_07 =          66578432.0 / 35198415.0;
 
   /** Second error weights array, element 8. */
-  private static final double e2_08 =       -1674902723.0 / 288716400.0;
+  private static final double E2_08 =       -1674902723.0 / 288716400.0;
 
   /** Second error weights array, element 9. */
-  private static final double e2_09 =   -74684743568175.0 / 176692375811392.0;
+  private static final double E2_09 =   -74684743568175.0 / 176692375811392.0;
 
   /** Second error weights array, element 10. */
-  private static final double e2_10 =           -734375.0 / 4826304.0;
+  private static final double E2_10 =           -734375.0 / 4826304.0;
 
   /** Second error weights array, element 11. */
-  private static final double e2_11 =         171414593.0 / 851261400.0;
+  private static final double E2_11 =         171414593.0 / 851261400.0;
 
   /** Second error weights array, element 12. */
-  private static final double e2_12 =             69869.0 / 3084480.0;
+  private static final double E2_12 =             69869.0 / 3084480.0;
 
   /** Simple constructor.
    * Build an eighth order Dormand-Prince integrator with the given step bounds
@@ -213,7 +213,7 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
   public DormandPrince853Integrator(final double minStep, final double maxStep,
                                     final double scalAbsoluteTolerance,
                                     final double scalRelativeTolerance) {
-    super(METHOD_NAME, true, staticC, staticA, staticB,
+    super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B,
           new DormandPrince853StepInterpolator(),
           minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
   }
@@ -230,7 +230,7 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
   public DormandPrince853Integrator(final double minStep, final double maxStep,
                                     final double[] vecAbsoluteTolerance,
                                     final double[] vecRelativeTolerance) {
-    super(METHOD_NAME, true, staticC, staticA, staticB,
+    super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B,
           new DormandPrince853StepInterpolator(),
           minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
   }
@@ -250,14 +250,14 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
     double error2 = 0;
 
     for (int j = 0; j < y0.length; ++j) {
-      final double errSum1 = e1_01 * yDotK[0][j]  + e1_06 * yDotK[5][j] +
-                             e1_07 * yDotK[6][j]  + e1_08 * yDotK[7][j] +
-                             e1_09 * yDotK[8][j]  + e1_10 * yDotK[9][j] +
-                             e1_11 * yDotK[10][j] + e1_12 * yDotK[11][j];
-      final double errSum2 = e2_01 * yDotK[0][j]  + e2_06 * yDotK[5][j] +
-                             e2_07 * yDotK[6][j]  + e2_08 * yDotK[7][j] +
-                             e2_09 * yDotK[8][j]  + e2_10 * yDotK[9][j] +
-                             e2_11 * yDotK[10][j] + e2_12 * yDotK[11][j];
+      final double errSum1 = E1_01 * yDotK[0][j]  + E1_06 * yDotK[5][j] +
+                             E1_07 * yDotK[6][j]  + E1_08 * yDotK[7][j] +
+                             E1_09 * yDotK[8][j]  + E1_10 * yDotK[9][j] +
+                             E1_11 * yDotK[10][j] + E1_12 * yDotK[11][j];
+      final double errSum2 = E2_01 * yDotK[0][j]  + E2_06 * yDotK[5][j] +
+                             E2_07 * yDotK[6][j]  + E2_08 * yDotK[7][j] +
+                             E2_09 * yDotK[8][j]  + E2_10 * yDotK[9][j] +
+                             E2_11 * yDotK[10][j] + E2_12 * yDotK[11][j];
 
       final double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));
       final double tol = (vecAbsoluteTolerance == null) ?
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853StepInterpolator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853StepInterpolator.java
index 6e859ad5e..31d561457 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853StepInterpolator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853StepInterpolator.java
@@ -161,16 +161,16 @@ class DormandPrince853StepInterpolator
           final double yDot14 = yDotKLast[0][i];
           final double yDot15 = yDotKLast[1][i];
           final double yDot16 = yDotKLast[2][i];
-          v[0][i] = b_01 * yDot1  + b_06 * yDot6 + b_07 * yDot7 +
-                    b_08 * yDot8  + b_09 * yDot9 + b_10 * yDot10 +
-                    b_11 * yDot11 + b_12 * yDot12;
+          v[0][i] = B_01 * yDot1  + B_06 * yDot6 + B_07 * yDot7 +
+                    B_08 * yDot8  + B_09 * yDot9 + B_10 * yDot10 +
+                    B_11 * yDot11 + B_12 * yDot12;
           v[1][i] = yDot1 - v[0][i];
           v[2][i] = v[0][i] - v[1][i] - yDotK[12][i];
-          for (int k = 0; k < d.length; ++k) {
-              v[k+3][i] = d[k][0] * yDot1  + d[k][1]  * yDot6  + d[k][2]  * yDot7  +
-                          d[k][3] * yDot8  + d[k][4]  * yDot9  + d[k][5]  * yDot10 +
-                          d[k][6] * yDot11 + d[k][7]  * yDot12 + d[k][8]  * yDot13 +
-                          d[k][9] * yDot14 + d[k][10] * yDot15 + d[k][11] * yDot16;
+          for (int k = 0; k < D.length; ++k) {
+              v[k+3][i] = D[k][0] * yDot1  + D[k][1]  * yDot6  + D[k][2]  * yDot7  +
+                          D[k][3] * yDot8  + D[k][4]  * yDot9  + D[k][5]  * yDot10 +
+                          D[k][6] * yDot11 + D[k][7]  * yDot12 + D[k][8]  * yDot13 +
+                          D[k][9] * yDot14 + D[k][10] * yDot15 + D[k][11] * yDot16;
           }
       }
 
@@ -219,32 +219,32 @@ class DormandPrince853StepInterpolator
 
     // k14
     for (int j = 0; j < currentState.length; ++j) {
-      s = k14_01 * yDotK[0][j]  + k14_06 * yDotK[5][j]  + k14_07 * yDotK[6][j] +
-          k14_08 * yDotK[7][j]  + k14_09 * yDotK[8][j]  + k14_10 * yDotK[9][j] +
-          k14_11 * yDotK[10][j] + k14_12 * yDotK[11][j] + k14_13 * yDotK[12][j];
+      s = K14_01 * yDotK[0][j]  + K14_06 * yDotK[5][j]  + K14_07 * yDotK[6][j] +
+          K14_08 * yDotK[7][j]  + K14_09 * yDotK[8][j]  + K14_10 * yDotK[9][j] +
+          K14_11 * yDotK[10][j] + K14_12 * yDotK[11][j] + K14_13 * yDotK[12][j];
       yTmp[j] = currentState[j] + h * s;
     }
-    integrator.computeDerivatives(previousTime + c14 * h, yTmp, yDotKLast[0]);
+    integrator.computeDerivatives(previousTime + C14 * h, yTmp, yDotKLast[0]);
 
     // k15
     for (int j = 0; j < currentState.length; ++j) {
-     s = k15_01 * yDotK[0][j]  + k15_06 * yDotK[5][j]  + k15_07 * yDotK[6][j] +
-         k15_08 * yDotK[7][j]  + k15_09 * yDotK[8][j]  + k15_10 * yDotK[9][j] +
-         k15_11 * yDotK[10][j] + k15_12 * yDotK[11][j] + k15_13 * yDotK[12][j] +
-         k15_14 * yDotKLast[0][j];
+     s = K15_01 * yDotK[0][j]  + K15_06 * yDotK[5][j]  + K15_07 * yDotK[6][j] +
+         K15_08 * yDotK[7][j]  + K15_09 * yDotK[8][j]  + K15_10 * yDotK[9][j] +
+         K15_11 * yDotK[10][j] + K15_12 * yDotK[11][j] + K15_13 * yDotK[12][j] +
+         K15_14 * yDotKLast[0][j];
      yTmp[j] = currentState[j] + h * s;
     }
-    integrator.computeDerivatives(previousTime + c15 * h, yTmp, yDotKLast[1]);
+    integrator.computeDerivatives(previousTime + C15 * h, yTmp, yDotKLast[1]);
 
     // k16
     for (int j = 0; j < currentState.length; ++j) {
-      s = k16_01 * yDotK[0][j]  + k16_06 * yDotK[5][j]  + k16_07 * yDotK[6][j] +
-          k16_08 * yDotK[7][j]  + k16_09 * yDotK[8][j]  + k16_10 * yDotK[9][j] +
-          k16_11 * yDotK[10][j] + k16_12 * yDotK[11][j] + k16_13 * yDotK[12][j] +
-          k16_14 * yDotKLast[0][j] +  k16_15 * yDotKLast[1][j];
+      s = K16_01 * yDotK[0][j]  + K16_06 * yDotK[5][j]  + K16_07 * yDotK[6][j] +
+          K16_08 * yDotK[7][j]  + K16_09 * yDotK[8][j]  + K16_10 * yDotK[9][j] +
+          K16_11 * yDotK[10][j] + K16_12 * yDotK[11][j] + K16_13 * yDotK[12][j] +
+          K16_14 * yDotKLast[0][j] +  K16_15 * yDotKLast[1][j];
       yTmp[j] = currentState[j] + h * s;
     }
-    integrator.computeDerivatives(previousTime + c16 * h, yTmp, yDotKLast[2]);
+    integrator.computeDerivatives(previousTime + C16 * h, yTmp, yDotKLast[2]);
 
   }
 
@@ -305,142 +305,142 @@ class DormandPrince853StepInterpolator
   private boolean vectorsInitialized;
 
   /** Propagation weights, element 1. */
-  private static final double b_01 =         104257.0 / 1920240.0;
+  private static final double B_01 =         104257.0 / 1920240.0;
 
   // elements 2 to 5 are zero, so they are neither stored nor used
 
   /** Propagation weights, element 6. */
-  private static final double b_06 =        3399327.0 / 763840.0;
+  private static final double B_06 =        3399327.0 / 763840.0;
 
   /** Propagation weights, element 7. */
-  private static final double b_07 =       66578432.0 / 35198415.0;
+  private static final double B_07 =       66578432.0 / 35198415.0;
 
   /** Propagation weights, element 8. */
-  private static final double b_08 =    -1674902723.0 / 288716400.0;
+  private static final double B_08 =    -1674902723.0 / 288716400.0;
 
   /** Propagation weights, element 9. */
-  private static final double b_09 = 54980371265625.0 / 176692375811392.0;
+  private static final double B_09 = 54980371265625.0 / 176692375811392.0;
 
   /** Propagation weights, element 10. */
-  private static final double b_10 =        -734375.0 / 4826304.0;
+  private static final double B_10 =        -734375.0 / 4826304.0;
 
   /** Propagation weights, element 11. */
-  private static final double b_11 =      171414593.0 / 851261400.0;
+  private static final double B_11 =      171414593.0 / 851261400.0;
 
   /** Propagation weights, element 12. */
-  private static final double b_12 =         137909.0 / 3084480.0;
+  private static final double B_12 =         137909.0 / 3084480.0;
 
   /** Time step for stage 14 (interpolation only). */
-  private static final double c14    = 1.0 / 10.0;
+  private static final double C14    = 1.0 / 10.0;
 
   /** Internal weights for stage 14, element 1. */
-  private static final double k14_01 =       13481885573.0 / 240030000000.0      - b_01;
+  private static final double K14_01 =       13481885573.0 / 240030000000.0      - B_01;
 
   // elements 2 to 5 are zero, so they are neither stored nor used
 
   /** Internal weights for stage 14, element 6. */
-  private static final double k14_06 =                 0.0                       - b_06;
+  private static final double K14_06 =                 0.0                       - B_06;
 
   /** Internal weights for stage 14, element 7. */
-  private static final double k14_07 =      139418837528.0 / 549975234375.0      - b_07;
+  private static final double K14_07 =      139418837528.0 / 549975234375.0      - B_07;
 
   /** Internal weights for stage 14, element 8. */
-  private static final double k14_08 =   -11108320068443.0 / 45111937500000.0    - b_08;
+  private static final double K14_08 =   -11108320068443.0 / 45111937500000.0    - B_08;
 
   /** Internal weights for stage 14, element 9. */
-  private static final double k14_09 = -1769651421925959.0 / 14249385146080000.0 - b_09;
+  private static final double K14_09 = -1769651421925959.0 / 14249385146080000.0 - B_09;
 
   /** Internal weights for stage 14, element 10. */
-  private static final double k14_10 =          57799439.0 / 377055000.0         - b_10;
+  private static final double K14_10 =          57799439.0 / 377055000.0         - B_10;
 
   /** Internal weights for stage 14, element 11. */
-  private static final double k14_11 =      793322643029.0 / 96734250000000.0    - b_11;
+  private static final double K14_11 =      793322643029.0 / 96734250000000.0    - B_11;
 
   /** Internal weights for stage 14, element 12. */
-  private static final double k14_12 =        1458939311.0 / 192780000000.0      - b_12;
+  private static final double K14_12 =        1458939311.0 / 192780000000.0      - B_12;
 
   /** Internal weights for stage 14, element 13. */
-  private static final double k14_13 =             -4149.0 / 500000.0;
+  private static final double K14_13 =             -4149.0 / 500000.0;
 
   /** Time step for stage 15 (interpolation only). */
-  private static final double c15    = 1.0 / 5.0;
+  private static final double C15    = 1.0 / 5.0;
 
 
   /** Internal weights for stage 15, element 1. */
-  private static final double k15_01 =     1595561272731.0 / 50120273500000.0    - b_01;
+  private static final double K15_01 =     1595561272731.0 / 50120273500000.0    - B_01;
 
   // elements 2 to 5 are zero, so they are neither stored nor used
 
   /** Internal weights for stage 15, element 6. */
-  private static final double k15_06 =      975183916491.0 / 34457688031250.0    - b_06;
+  private static final double K15_06 =      975183916491.0 / 34457688031250.0    - B_06;
 
   /** Internal weights for stage 15, element 7. */
-  private static final double k15_07 =    38492013932672.0 / 718912673015625.0   - b_07;
+  private static final double K15_07 =    38492013932672.0 / 718912673015625.0   - B_07;
 
   /** Internal weights for stage 15, element 8. */
-  private static final double k15_08 = -1114881286517557.0 / 20298710767500000.0 - b_08;
+  private static final double K15_08 = -1114881286517557.0 / 20298710767500000.0 - B_08;
 
   /** Internal weights for stage 15, element 9. */
-  private static final double k15_09 =                 0.0                       - b_09;
+  private static final double K15_09 =                 0.0                       - B_09;
 
   /** Internal weights for stage 15, element 10. */
-  private static final double k15_10 =                 0.0                       - b_10;
+  private static final double K15_10 =                 0.0                       - B_10;
 
   /** Internal weights for stage 15, element 11. */
-  private static final double k15_11 =    -2538710946863.0 / 23431227861250000.0 - b_11;
+  private static final double K15_11 =    -2538710946863.0 / 23431227861250000.0 - B_11;
 
   /** Internal weights for stage 15, element 12. */
-  private static final double k15_12 =        8824659001.0 / 23066716781250.0    - b_12;
+  private static final double K15_12 =        8824659001.0 / 23066716781250.0    - B_12;
 
   /** Internal weights for stage 15, element 13. */
-  private static final double k15_13 =      -11518334563.0 / 33831184612500.0;
+  private static final double K15_13 =      -11518334563.0 / 33831184612500.0;
 
   /** Internal weights for stage 15, element 14. */
-  private static final double k15_14 =        1912306948.0 / 13532473845.0;
+  private static final double K15_14 =        1912306948.0 / 13532473845.0;
 
   /** Time step for stage 16 (interpolation only). */
-  private static final double c16    = 7.0 / 9.0;
+  private static final double C16    = 7.0 / 9.0;
 
 
   /** Internal weights for stage 16, element 1. */
-  private static final double k16_01 =      -13613986967.0 / 31741908048.0       - b_01;
+  private static final double K16_01 =      -13613986967.0 / 31741908048.0       - B_01;
 
   // elements 2 to 5 are zero, so they are neither stored nor used
 
   /** Internal weights for stage 16, element 6. */
-  private static final double k16_06 =       -4755612631.0 / 1012344804.0        - b_06;
+  private static final double K16_06 =       -4755612631.0 / 1012344804.0        - B_06;
 
   /** Internal weights for stage 16, element 7. */
-  private static final double k16_07 =    42939257944576.0 / 5588559685701.0     - b_07;
+  private static final double K16_07 =    42939257944576.0 / 5588559685701.0     - B_07;
 
   /** Internal weights for stage 16, element 8. */
-  private static final double k16_08 =    77881972900277.0 / 19140370552944.0    - b_08;
+  private static final double K16_08 =    77881972900277.0 / 19140370552944.0    - B_08;
 
   /** Internal weights for stage 16, element 9. */
-  private static final double k16_09 =    22719829234375.0 / 63689648654052.0    - b_09;
+  private static final double K16_09 =    22719829234375.0 / 63689648654052.0    - B_09;
 
   /** Internal weights for stage 16, element 10. */
-  private static final double k16_10 =                 0.0                       - b_10;
+  private static final double K16_10 =                 0.0                       - B_10;
 
   /** Internal weights for stage 16, element 11. */
-  private static final double k16_11 =                 0.0                       - b_11;
+  private static final double K16_11 =                 0.0                       - B_11;
 
   /** Internal weights for stage 16, element 12. */
-  private static final double k16_12 =                 0.0                       - b_12;
+  private static final double K16_12 =                 0.0                       - B_12;
 
   /** Internal weights for stage 16, element 13. */
-  private static final double k16_13 =       -1199007803.0 / 857031517296.0;
+  private static final double K16_13 =       -1199007803.0 / 857031517296.0;
 
   /** Internal weights for stage 16, element 14. */
-  private static final double k16_14 =      157882067000.0 / 53564469831.0;
+  private static final double K16_14 =      157882067000.0 / 53564469831.0;
 
   /** Internal weights for stage 16, element 15. */
-  private static final double k16_15 =     -290468882375.0 / 31741908048.0;
+  private static final double K16_15 =     -290468882375.0 / 31741908048.0;
 
   /** Interpolation weights.
    * (beware that only the non-null values are in the table)
    */
-  private static final double[][] d = {
+  private static final double[][] D = {
 
     {        -17751989329.0 / 2106076560.0,               4272954039.0 / 7539864640.0,
             -118476319744.0 / 38604839385.0,            755123450731.0 / 316657731600.0,
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/EulerIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/EulerIntegrator.java
index 84ce30669..0a9269b2c 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/EulerIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/EulerIntegrator.java
@@ -49,15 +49,15 @@ package org.apache.commons.math.ode.nonstiff;
 public class EulerIntegrator extends RungeKuttaIntegrator {
 
   /** Time steps Butcher array. */
-  private static final double[] c = {
+  private static final double[] STATIC_C = {
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] a = {
+  private static final double[][] STATIC_A = {
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] b = {
+  private static final double[] STATIC_B = {
     1.0
   };
 
@@ -66,7 +66,7 @@ public class EulerIntegrator extends RungeKuttaIntegrator {
    * @param step integration step
    */
   public EulerIntegrator(final double step) {
-    super("Euler", c, a, b, new EulerStepInterpolator(), step);
+    super("Euler", STATIC_C, STATIC_A, STATIC_B, new EulerStepInterpolator(), step);
   }
 
 }
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/GillIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/GillIntegrator.java
index 678fc8cd7..631e87fd3 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/GillIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/GillIntegrator.java
@@ -45,19 +45,19 @@ package org.apache.commons.math.ode.nonstiff;
 public class GillIntegrator extends RungeKuttaIntegrator {
 
   /** Time steps Butcher array. */
-  private static final double[] c = {
+  private static final double[] STATIC_C = {
     1.0 / 2.0, 1.0 / 2.0, 1.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] a = {
+  private static final double[][] STATIC_A = {
     { 1.0 / 2.0 },
     { (Math.sqrt(2.0) - 1.0) / 2.0, (2.0 - Math.sqrt(2.0)) / 2.0 },
     { 0.0, -Math.sqrt(2.0) / 2.0, (2.0 + Math.sqrt(2.0)) / 2.0 }
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] b = {
+  private static final double[] STATIC_B = {
     1.0 / 6.0, (2.0 - Math.sqrt(2.0)) / 6.0, (2.0 + Math.sqrt(2.0)) / 6.0, 1.0 / 6.0
   };
 
@@ -66,7 +66,7 @@ public class GillIntegrator extends RungeKuttaIntegrator {
    * @param step integration step
    */
   public GillIntegrator(final double step) {
-    super("Gill", c, a, b, new GillStepInterpolator(), step);
+    super("Gill", STATIC_C, STATIC_A, STATIC_B, new GillStepInterpolator(), step);
   }
 
 }
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/GillStepInterpolator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/GillStepInterpolator.java
index f3d529556..7b4d771a8 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/GillStepInterpolator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/GillStepInterpolator.java
@@ -90,13 +90,13 @@ class GillStepInterpolator
     final double soMt      = s * oMt;
     final double c23       = soMt * (1 + twoTheta);
     final double coeff1    = soMt * (1 - fourTheta);
-    final double coeff2    = c23  * tMq;
-    final double coeff3    = c23  * tPq;
+    final double coeff2    = c23  * TWO_MINUS_SQRT_2;
+    final double coeff3    = c23  * TWO_PLUS_SQRT_2;
     final double coeff4    = s * (1 + theta * (1 + fourTheta));
     final double coeffDot1 = theta * (twoTheta - 3) + 1;
     final double cDot23    = theta * oMt;
-    final double coeffDot2 = cDot23  * tMq;
-    final double coeffDot3 = cDot23  * tPq;
+    final double coeffDot2 = cDot23  * TWO_MINUS_SQRT_2;
+    final double coeffDot3 = cDot23  * TWO_PLUS_SQRT_2;
     final double coeffDot4 = theta * (twoTheta - 1);
 
     for (int i = 0; i < interpolatedState.length; ++i) {
@@ -113,10 +113,10 @@ class GillStepInterpolator
   }
 
   /** First Gill coefficient. */
-  private static final double tMq = 2 - Math.sqrt(2.0);
+  private static final double TWO_MINUS_SQRT_2 = 2 - Math.sqrt(2.0);
 
   /** Second Gill coefficient. */
-  private static final double tPq = 2 + Math.sqrt(2.0);
+  private static final double TWO_PLUS_SQRT_2 = 2 + Math.sqrt(2.0);
 
   /** Serializable version identifier */
   private static final long serialVersionUID = -107804074496313322L;
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java
index ca9674a8a..c78afeadd 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java
@@ -38,12 +38,12 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
   private static final String METHOD_NAME = "Higham-Hall 5(4)";
 
   /** Time steps Butcher array. */
-  private static final double[] staticC = {
+  private static final double[] STATIC_C = {
     2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] staticA = {
+  private static final double[][] STATIC_A = {
     {2.0/9.0},
     {1.0/12.0, 1.0/4.0},
     {1.0/8.0, 0.0, 3.0/8.0},
@@ -53,12 +53,12 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] staticB = {
+  private static final double[] STATIC_B = {
     1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
   };
 
   /** Error weights Butcher array. */
-  private static final double[] staticE = {
+  private static final double[] STATIC_E = {
     -1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
   };
 
@@ -74,7 +74,7 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
   public HighamHall54Integrator(final double minStep, final double maxStep,
                                 final double scalAbsoluteTolerance,
                                 final double scalRelativeTolerance) {
-    super(METHOD_NAME, false, staticC, staticA, staticB, new HighamHall54StepInterpolator(),
+    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
           minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
   }
 
@@ -90,7 +90,7 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
   public HighamHall54Integrator(final double minStep, final double maxStep,
                                 final double[] vecAbsoluteTolerance,
                                 final double[] vecRelativeTolerance) {
-    super(METHOD_NAME, false, staticC, staticA, staticB, new HighamHall54StepInterpolator(),
+    super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
           minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
   }
 
@@ -109,9 +109,9 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
     double error = 0;
 
     for (int j = 0; j < y0.length; ++j) {
-      double errSum = staticE[0] * yDotK[0][j];
-      for (int l = 1; l < staticE.length; ++l) {
-        errSum += staticE[l] * yDotK[l][j];
+      double errSum = STATIC_E[0] * yDotK[0][j];
+      for (int l = 1; l < STATIC_E.length; ++l) {
+        errSum += STATIC_E[l] * yDotK[l][j];
       }
 
       final double yScale = Math.max(Math.abs(y0[j]), Math.abs(y1[j]));
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/MidpointIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/MidpointIntegrator.java
index 9e348db1e..b0074fcb5 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/MidpointIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/MidpointIntegrator.java
@@ -43,17 +43,17 @@ package org.apache.commons.math.ode.nonstiff;
 public class MidpointIntegrator extends RungeKuttaIntegrator {
 
   /** Time steps Butcher array. */
-  private static final double[] c = {
+  private static final double[] STATIC_C = {
     1.0 / 2.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] a = {
+  private static final double[][] STATIC_A = {
     { 1.0 / 2.0 }
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] b = {
+  private static final double[] STATIC_B = {
     0.0, 1.0
   };
 
@@ -62,7 +62,7 @@ public class MidpointIntegrator extends RungeKuttaIntegrator {
    * @param step integration step
    */
   public MidpointIntegrator(final double step) {
-    super("midpoint", c, a, b, new MidpointStepInterpolator(), step);
+    super("midpoint", STATIC_C, STATIC_A, STATIC_B, new MidpointStepInterpolator(), step);
   }
 
 }
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/ThreeEighthesIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/ThreeEighthesIntegrator.java
index 613340f58..69ec98db2 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/ThreeEighthesIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/ThreeEighthesIntegrator.java
@@ -45,19 +45,19 @@ package org.apache.commons.math.ode.nonstiff;
 public class ThreeEighthesIntegrator extends RungeKuttaIntegrator {
 
   /** Time steps Butcher array. */
-  private static final double[] c = {
+  private static final double[] STATIC_C = {
     1.0 / 3.0, 2.0 / 3.0, 1.0
   };
 
   /** Internal weights Butcher array. */
-  private static final double[][] a = {
+  private static final double[][] STATIC_A = {
     {  1.0 / 3.0 },
     { -1.0 / 3.0, 1.0 },
     {  1.0, -1.0, 1.0 }
   };
 
   /** Propagation weights Butcher array. */
-  private static final double[] b = {
+  private static final double[] STATIC_B = {
     1.0 / 8.0, 3.0 / 8.0, 3.0 / 8.0, 1.0 / 8.0
   };
 
@@ -66,7 +66,7 @@ public class ThreeEighthesIntegrator extends RungeKuttaIntegrator {
    * @param step integration step
    */
   public ThreeEighthesIntegrator(final double step) {
-    super("3/8", c, a, b, new ThreeEighthesStepInterpolator(), step);
+    super("3/8", STATIC_C, STATIC_A, STATIC_B, new ThreeEighthesStepInterpolator(), step);
   }
 
 }
diff --git a/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java b/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java
index 6178365d0..4b63efc5d 100644
--- a/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java
+++ b/src/main/java/org/apache/commons/math/ode/sampling/DummyStepHandler.java
@@ -48,7 +48,7 @@ public class DummyStepHandler implements StepHandler {
    * @return the only instance
    */
   public static DummyStepHandler getInstance() {
-    return instance;
+    return INSTANCE;
   }
 
   /** Determines whether this handler needs dense output.
@@ -82,6 +82,6 @@ public class DummyStepHandler implements StepHandler {
   }
 
   /** The only instance. */
-  private static final DummyStepHandler instance = new DummyStepHandler();
+  private static final DummyStepHandler INSTANCE = new DummyStepHandler();
 
 }
diff --git a/src/main/java/org/apache/commons/math/optimization/univariate/BrentOptimizer.java b/src/main/java/org/apache/commons/math/optimization/univariate/BrentOptimizer.java
index 8a383cc83..71a059c7b 100644
--- a/src/main/java/org/apache/commons/math/optimization/univariate/BrentOptimizer.java
+++ b/src/main/java/org/apache/commons/math/optimization/univariate/BrentOptimizer.java
@@ -34,7 +34,7 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
     /**
      * Golden section.
      */
-    private static final double c = 0.5 * (3 - Math.sqrt(5));
+    private static final double GOLDEN_SECTION = 0.5 * (3 - Math.sqrt(5));
 
     /**
      * Construct a solver.
@@ -85,7 +85,7 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
     private double localMin(final UnivariateRealFunction f, final GoalType goalType,
                             double a, double b, final double eps, final double t)
         throws MaxIterationsExceededException, FunctionEvaluationException {
-        double x = a + c * (b - a);
+        double x = a + GOLDEN_SECTION * (b - a);
         double v = x;
         double w = x;
         double e = 0;
@@ -137,7 +137,7 @@ public class BrentOptimizer extends AbstractUnivariateRealOptimizer {
                     }
                 } else { // Golden section step.
                     e = ((x < m) ? b : a) - x;
-                    d = c * e;
+                    d = GOLDEN_SECTION * e;
                 }
 
                 // f must not be evaluated too close to a or b.
diff --git a/src/main/java/org/apache/commons/math/special/Gamma.java b/src/main/java/org/apache/commons/math/special/Gamma.java
index 10c537774..ad850ab46 100644
--- a/src/main/java/org/apache/commons/math/special/Gamma.java
+++ b/src/main/java/org/apache/commons/math/special/Gamma.java
@@ -38,7 +38,7 @@ public class Gamma {
     private static final double DEFAULT_EPSILON = 10e-15;
 
     /** Lanczos coefficients */
-    private static final double[] lanczos =
+    private static final double[] LANCZOS =
     {
         0.99999999999999709182,
         57.156235665862923517,
@@ -94,10 +94,10 @@ public class Gamma {
             double g = 607.0 / 128.0;
             
             double sum = 0.0;
-            for (int i = lanczos.length - 1; i > 0; --i) {
-                sum = sum + (lanczos[i] / (x + i));
+            for (int i = LANCZOS.length - 1; i > 0; --i) {
+                sum = sum + (LANCZOS[i] / (x + i));
             }
-            sum = sum + lanczos[0];
+            sum = sum + LANCZOS[0];
 
             double tmp = x + g + .5;
             ret = ((x + .5) * Math.log(tmp)) - tmp +
diff --git a/src/main/java/org/apache/commons/math/stat/StatUtils.java b/src/main/java/org/apache/commons/math/stat/StatUtils.java
index 389013d35..c43581435 100644
--- a/src/main/java/org/apache/commons/math/stat/StatUtils.java
+++ b/src/main/java/org/apache/commons/math/stat/StatUtils.java
@@ -38,34 +38,34 @@ import org.apache.commons.math.stat.descriptive.summary.SumOfSquares;
 public final class StatUtils {
 
     /** sum */
-    private static final UnivariateStatistic sum = new Sum();
+    private static final UnivariateStatistic SUM = new Sum();
 
     /** sumSq */
-    private static final UnivariateStatistic sumSq = new SumOfSquares();
+    private static final UnivariateStatistic SUM_OF_SQUARES = new SumOfSquares();
 
     /** prod */
-    private static final UnivariateStatistic prod = new Product();
+    private static final UnivariateStatistic PRODUCT = new Product();
 
     /** sumLog */
-    private static final UnivariateStatistic sumLog = new SumOfLogs();
+    private static final UnivariateStatistic SUM_OF_LOGS = new SumOfLogs();
 
     /** min */
-    private static final UnivariateStatistic min = new Min();
+    private static final UnivariateStatistic MIN = new Min();
 
     /** max */
-    private static final UnivariateStatistic max = new Max();
+    private static final UnivariateStatistic MAX = new Max();
 
     /** mean */
-    private static final UnivariateStatistic mean = new Mean();
+    private static final UnivariateStatistic MEAN = new Mean();
 
     /** variance */
-    private static final Variance variance = new Variance();
+    private static final Variance VARIANCE = new Variance();
 
     /** percentile */
-    private static final Percentile percentile = new Percentile();
+    private static final Percentile PERCENTILE = new Percentile();
     
     /** geometric mean */
-    private static final GeometricMean geometricMean = new GeometricMean();
+    private static final GeometricMean GEOMETRIC_MEAN = new GeometricMean();
 
     /**
      * Private Constructor
@@ -86,7 +86,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double sum(final double[] values) {
-        return sum.evaluate(values);
+        return SUM.evaluate(values);
     }
 
     /**
@@ -105,7 +105,7 @@ public final class StatUtils {
      */
     public static double sum(final double[] values, final int begin, 
             final int length) {
-        return sum.evaluate(values, begin, length);
+        return SUM.evaluate(values, begin, length);
     }
 
     /**
@@ -120,7 +120,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double sumSq(final double[] values) {
-        return sumSq.evaluate(values);
+        return SUM_OF_SQUARES.evaluate(values);
     }
 
     /**
@@ -139,7 +139,7 @@ public final class StatUtils {
      */
     public static double sumSq(final double[] values, final int begin,
             final int length) {
-        return sumSq.evaluate(values, begin, length);
+        return SUM_OF_SQUARES.evaluate(values, begin, length);
     }
 
     /**
@@ -153,7 +153,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double product(final double[] values) {
-        return prod.evaluate(values);
+        return PRODUCT.evaluate(values);
     }
 
     /**
@@ -172,7 +172,7 @@ public final class StatUtils {
      */
     public static double product(final double[] values, final int begin,
             final int length) {
-        return prod.evaluate(values, begin, length);
+        return PRODUCT.evaluate(values, begin, length);
     }
 
     /**
@@ -190,7 +190,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double sumLog(final double[] values) {
-        return sumLog.evaluate(values);
+        return SUM_OF_LOGS.evaluate(values);
     }
 
     /**
@@ -213,7 +213,7 @@ public final class StatUtils {
      */
     public static double sumLog(final double[] values, final int begin,
             final int length) {
-        return sumLog.evaluate(values, begin, length);
+        return SUM_OF_LOGS.evaluate(values, begin, length);
     }
 
     /**
@@ -230,7 +230,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double mean(final double[] values) {
-        return mean.evaluate(values);
+        return MEAN.evaluate(values);
     }
 
     /**
@@ -252,7 +252,7 @@ public final class StatUtils {
      */
     public static double mean(final double[] values, final int begin,
             final int length) {
-        return mean.evaluate(values, begin, length);
+        return MEAN.evaluate(values, begin, length);
     }
     
     /**
@@ -269,7 +269,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double geometricMean(final double[] values) {
-        return geometricMean.evaluate(values);
+        return GEOMETRIC_MEAN.evaluate(values);
     }
 
     /**
@@ -291,7 +291,7 @@ public final class StatUtils {
      */
     public static double geometricMean(final double[] values, final int begin,
             final int length) {
-        return geometricMean.evaluate(values, begin, length);
+        return GEOMETRIC_MEAN.evaluate(values, begin, length);
     }
     
 
@@ -311,7 +311,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double variance(final double[] values) {
-        return variance.evaluate(values);
+        return VARIANCE.evaluate(values);
     }
 
     /**
@@ -336,7 +336,7 @@ public final class StatUtils {
      */
     public static double variance(final double[] values, final int begin,
             final int length) {
-        return variance.evaluate(values, begin, length);
+        return VARIANCE.evaluate(values, begin, length);
     }
     
     /**
@@ -367,7 +367,7 @@ public final class StatUtils {
      */
     public static double variance(final double[] values, final double mean, 
             final int begin, final int length) {
-        return variance.evaluate(values, mean, begin, length);    
+        return VARIANCE.evaluate(values, mean, begin, length);    
     }
     
     /**
@@ -393,7 +393,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double variance(final double[] values, final double mean) {
-        return variance.evaluate(values, mean);    
+        return VARIANCE.evaluate(values, mean);    
     }
 
     /**
@@ -414,7 +414,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double max(final double[] values) {
-        return max.evaluate(values);
+        return MAX.evaluate(values);
     }
 
     /**
@@ -441,7 +441,7 @@ public final class StatUtils {
      */
     public static double max(final double[] values, final int begin,
             final int length) {
-        return max.evaluate(values, begin, length);
+        return MAX.evaluate(values, begin, length);
     }
 
      /**
@@ -462,7 +462,7 @@ public final class StatUtils {
      * @throws IllegalArgumentException if the array is null
      */
     public static double min(final double[] values) {
-        return min.evaluate(values);
+        return MIN.evaluate(values);
     }
 
      /**
@@ -489,7 +489,7 @@ public final class StatUtils {
      */
     public static double min(final double[] values, final int begin,
             final int length) {
-        return min.evaluate(values, begin, length);
+        return MIN.evaluate(values, begin, length);
     }
     
     /**
@@ -516,7 +516,7 @@ public final class StatUtils {
      * or p is invalid
      */
     public static double percentile(final double[] values, final double p) {
-            return percentile.evaluate(values,p);
+            return PERCENTILE.evaluate(values,p);
     }
 
      /**
@@ -548,7 +548,7 @@ public final class StatUtils {
      */
     public static double percentile(final double[] values, final int begin, 
             final int length, final double p) {
-        return percentile.evaluate(values, begin, length, p);
+        return PERCENTILE.evaluate(values, begin, length, p);
     }   
     
     /**
diff --git a/src/main/java/org/apache/commons/math/util/MathUtils.java b/src/main/java/org/apache/commons/math/util/MathUtils.java
index d8fe14386..7f2f5a135 100644
--- a/src/main/java/org/apache/commons/math/util/MathUtils.java
+++ b/src/main/java/org/apache/commons/math/util/MathUtils.java
@@ -470,7 +470,7 @@ public final class MathUtils {
     }
     
     /** All long-representable factorials */
-    private static final long[] factorials = new long[] 
+    private static final long[] FACTORIALS = new long[] 
        {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,
         479001600, 6227020800l, 87178291200l, 1307674368000l, 20922789888000l,
         355687428096000l, 6402373705728000l, 121645100408832000l,
@@ -508,7 +508,7 @@ public final class MathUtils {
             throw new ArithmeticException(
                     "factorial value is too large to fit in a long");
         }
-        return factorials[n];
+        return FACTORIALS[n];
     }
 
     /**