From aebb93a04afd4916deddce2e6b7e878ea77347ea Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Fri, 20 Dec 2013 21:04:31 +0100
Subject: [PATCH] Interpolation: Differentiate2 instead of DifferentiateAll;
 definite integral; cleanup

---
 .../Interpolation/AkimaSplineInterpolation.cs | 41 +++++------
 .../Interpolation/BarycentricInterpolation.cs | 31 ++++----
 .../BulirschStoerRationalInterpolation.cs     | 31 ++++----
 .../CubicHermiteSplineInterpolation.cs        | 33 ++++-----
 .../Interpolation/CubicSplineInterpolation.cs | 33 ++++-----
 .../EquidistantPolynomialInterpolation.cs     | 31 ++++----
 .../FloaterHormannRationalInterpolation.cs    | 31 ++++----
 src/Numerics/Interpolation/IInterpolation.cs  | 30 ++++----
 src/Numerics/Interpolation/LinearSpline.cs    | 32 ++++++---
 .../NevillePolynomialInterpolation.cs         | 39 ++++++-----
 .../Interpolation/SplineInterpolation.cs      | 70 +++++++++----------
 .../InterpolationTests/AkimaSplineTest.cs     | 16 ++---
 .../BulirschStoerRationalTest.cs              | 12 ++--
 .../InterpolationTests/CubicSplineTest.cs     | 41 ++---------
 .../EquidistantPolynomialTest.cs              | 14 ++--
 .../FloaterHormannRationalTest.cs             | 18 ++---
 .../LinearInterpolationCase.cs                |  8 +--
 .../InterpolationTests/LinearSplineTest.cs    | 70 ++++++++++++-------
 .../NevillePolynomialTest.cs                  | 28 +++-----
 19 files changed, 297 insertions(+), 312 deletions(-)

diff --git a/src/Numerics/Interpolation/AkimaSplineInterpolation.cs b/src/Numerics/Interpolation/AkimaSplineInterpolation.cs
index 91a452d7..40ebae5d 100644
--- a/src/Numerics/Interpolation/AkimaSplineInterpolation.cs
+++ b/src/Numerics/Interpolation/AkimaSplineInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -69,8 +69,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -79,7 +77,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return true; }
@@ -155,11 +152,11 @@ namespace MathNet.Numerics.Interpolation
                 derivatives[i] =
                     weights[i - 1].AlmostEqual(0.0) && weights[i + 1].AlmostEqual(0.0)
                         ? (((samplePoints[i + 1] - samplePoints[i])*differences[i - 1])
-                            + ((samplePoints[i] - samplePoints[i - 1])*differences[i]))
-                            /(samplePoints[i + 1] - samplePoints[i - 1])
+                           + ((samplePoints[i] - samplePoints[i - 1])*differences[i]))
+                          /(samplePoints[i + 1] - samplePoints[i - 1])
                         : ((weights[i + 1]*differences[i - 1])
-                            + (weights[i - 1]*differences[i]))
-                            /(weights[i + 1] + weights[i - 1]);
+                           + (weights[i - 1]*differences[i]))
+                          /(weights[i + 1] + weights[i - 1]);
             }
 
             derivatives[0] = DifferentiateThreePoint(samplePoints, sampleValues, 0, 0, 1, 2);
@@ -227,34 +224,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Differentiate twice at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double)"/>
-        public Tuple<double, double, double> DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        public double Differentiate2(double t)
         {
-            return _spline.DifferentiateAll(t);
+            return _spline.Differentiate2(t);
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Indefinite integral at point t.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         public double Integrate(double t)
         {
             return _spline.Integrate(t);
         }
+
+        /// <summary>
+        /// Definite integral between points a and b.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        public double Integrate(double a, double b)
+        {
+            return _spline.Integrate(a, b);
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/BarycentricInterpolation.cs b/src/Numerics/Interpolation/BarycentricInterpolation.cs
index 89cc0ccb..88e01e9e 100644
--- a/src/Numerics/Interpolation/BarycentricInterpolation.cs
+++ b/src/Numerics/Interpolation/BarycentricInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -77,8 +77,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -87,7 +85,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="IInterpolation.Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return false; }
@@ -201,34 +198,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
+        /// Differentiate twice at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        double IInterpolation.Differentiate2(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t. NOT SUPPORTED.
+        /// Indefinite integral at point t. NOT SUPPORTED.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         double IInterpolation.Integrate(double t)
         {
             throw new NotSupportedException();
         }
+
+        /// <summary>
+        /// Definite integral between points a and b. NOT SUPPORTED.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        double IInterpolation.Integrate(double a, double b)
+        {
+            throw new NotSupportedException();
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/BulirschStoerRationalInterpolation.cs b/src/Numerics/Interpolation/BulirschStoerRationalInterpolation.cs
index efce88a4..b97f97e0 100644
--- a/src/Numerics/Interpolation/BulirschStoerRationalInterpolation.cs
+++ b/src/Numerics/Interpolation/BulirschStoerRationalInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -73,8 +73,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -83,7 +81,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="IInterpolation.Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return false; }
@@ -187,34 +184,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
+        /// Differentiate twice at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        double IInterpolation.Differentiate2(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t. NOT SUPPORTED.
+        /// Indefinite integral at point t. NOT SUPPORTED.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         double IInterpolation.Integrate(double t)
         {
             throw new NotSupportedException();
         }
+
+        /// <summary>
+        /// Definite integral between points a and b. NOT SUPPORTED.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        double IInterpolation.Integrate(double a, double b)
+        {
+            throw new NotSupportedException();
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/CubicHermiteSplineInterpolation.cs b/src/Numerics/Interpolation/CubicHermiteSplineInterpolation.cs
index b4b88682..ee54263f 100644
--- a/src/Numerics/Interpolation/CubicHermiteSplineInterpolation.cs
+++ b/src/Numerics/Interpolation/CubicHermiteSplineInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -70,8 +70,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -80,7 +78,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return true; }
@@ -169,34 +166,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Differentiate twice at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double)"/>
-        public Tuple<double, double, double> DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        public double Differentiate2(double t)
         {
-            return _spline.DifferentiateAll(t);
+            return _spline.Differentiate2(t);
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Indefinite integral at point t.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         public double Integrate(double t)
         {
             return _spline.Integrate(t);
         }
+
+        /// <summary>
+        /// Definite integral between points a and b.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        public double Integrate(double a, double b)
+        {
+            return _spline.Integrate(a, b);
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/CubicSplineInterpolation.cs b/src/Numerics/Interpolation/CubicSplineInterpolation.cs
index 725073ed..220d748f 100644
--- a/src/Numerics/Interpolation/CubicSplineInterpolation.cs
+++ b/src/Numerics/Interpolation/CubicSplineInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -91,8 +91,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -101,7 +99,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return true; }
@@ -339,34 +336,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Differentiate twice at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double)"/>
-        public Tuple<double, double, double> DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        public double Differentiate2(double t)
         {
-            return _spline.DifferentiateAll(t);
+            return _spline.Differentiate2(t);
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Indefinite integral at point t.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         public double Integrate(double t)
         {
             return _spline.Integrate(t);
         }
+
+        /// <summary>
+        /// Definite integral between points a and b.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        public double Integrate(double a, double b)
+        {
+            return _spline.Integrate(a, b);
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/EquidistantPolynomialInterpolation.cs b/src/Numerics/Interpolation/EquidistantPolynomialInterpolation.cs
index bf3d155f..72ddb638 100644
--- a/src/Numerics/Interpolation/EquidistantPolynomialInterpolation.cs
+++ b/src/Numerics/Interpolation/EquidistantPolynomialInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -80,8 +80,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -90,7 +88,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="IInterpolation.Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return false; }
@@ -181,34 +178,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
+        /// Differentiate twice at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        double IInterpolation.Differentiate2(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t. NOT SUPPORTED.
+        /// Indefinite integral at point t. NOT SUPPORTED.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         double IInterpolation.Integrate(double t)
         {
             throw new NotSupportedException();
         }
+
+        /// <summary>
+        /// Definite integral between points a and b. NOT SUPPORTED.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        double IInterpolation.Integrate(double a, double b)
+        {
+            throw new NotSupportedException();
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/FloaterHormannRationalInterpolation.cs b/src/Numerics/Interpolation/FloaterHormannRationalInterpolation.cs
index 6ae1573e..586e5852 100644
--- a/src/Numerics/Interpolation/FloaterHormannRationalInterpolation.cs
+++ b/src/Numerics/Interpolation/FloaterHormannRationalInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -83,8 +83,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -93,7 +91,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="IInterpolation.Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return false; }
@@ -250,34 +247,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
+        /// Differentiate twice at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        double IInterpolation.Differentiate2(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t. NOT SUPPORTED.
+        /// Indefinite integral at point t. NOT SUPPORTED.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         double IInterpolation.Integrate(double t)
         {
             throw new NotSupportedException();
         }
+
+        /// <summary>
+        /// Definite integral between points a and b. NOT SUPPORTED.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        double IInterpolation.Integrate(double a, double b)
+        {
+            throw new NotSupportedException();
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/IInterpolation.cs b/src/Numerics/Interpolation/IInterpolation.cs
index d36fb344..7c91e6ff 100644
--- a/src/Numerics/Interpolation/IInterpolation.cs
+++ b/src/Numerics/Interpolation/IInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,8 +28,6 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-using System;
-
 namespace MathNet.Numerics.Interpolation
 {
     /// <summary>
@@ -40,14 +38,11 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         bool SupportsDifferentiation { get; }
 
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="Integrate"/>
         bool SupportsIntegration { get; }
 
         /// <summary>
@@ -62,25 +57,26 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="SupportsDifferentiation"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         double Differentiate(double t);
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Differentiate twice at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double)"/>
-        Tuple<double, double, double> DifferentiateAll(double t);
+        /// <returns>Interpolated second derivative at point t.</returns>
+        double Differentiate2(double t);
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Indefinite integral at point t.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         double Integrate(double t);
+
+        /// <summary>
+        /// Definite integral between points a and b.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        double Integrate(double a, double b);
     }
 }
diff --git a/src/Numerics/Interpolation/LinearSpline.cs b/src/Numerics/Interpolation/LinearSpline.cs
index 8996429f..307252ba 100644
--- a/src/Numerics/Interpolation/LinearSpline.cs
+++ b/src/Numerics/Interpolation/LinearSpline.cs
@@ -44,6 +44,7 @@ namespace MathNet.Numerics.Interpolation
         readonly double[] _x;
         readonly double[] _c0;
         readonly double[] _c1;
+        readonly Lazy<double[]> _indefiniteIntegral;
 
         /// <param name="x">Sample points (N+1), sorted ascending</param>
         /// <param name="c0">Sample values (N or N+1) at the corresponding points; intercept, zero order coefficients</param>
@@ -53,6 +54,7 @@ namespace MathNet.Numerics.Interpolation
             _x = x;
             _c0 = c0;
             _c1 = c1;
+            _indefiniteIntegral = new Lazy<double[]>(ComputeIndefiniteIntegral);
         }
 
         /// <summary>
@@ -132,27 +134,35 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Indefinite integral at point t.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
+        /// <param name="t">Point t to integrate at.</param>
         public double Integrate(double t)
         {
             int k = LeftBracketIndex(t);
             var x = (t - _x[k]);
-            return x*(_c0[k] + x*0.5*_c1[k]);
+            return _indefiniteIntegral.Value[k] + x*(_c0[k] + x*_c1[k]/2);
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Definite integral between points a and b.
         /// </summary>
-        /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        public Tuple<double, double, double> DifferentiateAll(double t)
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        public double Integrate(double a, double b)
         {
-            int k = LeftBracketIndex(t);
-            var x = (t - _x[k]);
-            return new Tuple<double, double, double>(_c0[k] + x*_c1[k], _c1[k], 0d);
+            return Integrate(b) - Integrate(a);
+        }
+
+        double[] ComputeIndefiniteIntegral()
+        {
+            var integral = new double[_c1.Length];
+            for (int i = 0; i < integral.Length - 1; i++)
+            {
+                double w = _x[i + 1] - _x[i];
+                integral[i + 1] = integral[i] + w*(_c0[i] + w*_c1[i]/2);
+            }
+            return integral;
         }
 
         /// <summary>
diff --git a/src/Numerics/Interpolation/NevillePolynomialInterpolation.cs b/src/Numerics/Interpolation/NevillePolynomialInterpolation.cs
index c63ed4ca..d2ee878e 100644
--- a/src/Numerics/Interpolation/NevillePolynomialInterpolation.cs
+++ b/src/Numerics/Interpolation/NevillePolynomialInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -79,8 +79,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -89,7 +87,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="IInterpolation.Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return false; }
@@ -159,8 +156,6 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             var x = new double[_values.Count];
@@ -183,13 +178,11 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Differentiate twice at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double)"/>
-        public Tuple<double, double, double> DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        public double Differentiate2(double t)
         {
             var x = new double[_values.Count];
             var dx = new double[_values.Count];
@@ -203,24 +196,32 @@ namespace MathNet.Numerics.Interpolation
                     double hp = t - _points[i + level];
                     double ho = _points[i] - t;
                     double den = _points[i] - _points[i + level];
-                    ddx[i] = ((hp * ddx[i]) + (ho * ddx[i + 1]) + (2 * dx[i]) - (2 * dx[i + 1])) / den;
-                    dx[i] = ((hp * dx[i]) + x[i] + (ho * dx[i + 1]) - x[i + 1]) / den;
-                    x[i] = ((hp * x[i]) + (ho * x[i + 1])) / den;
+                    ddx[i] = ((hp*ddx[i]) + (ho*ddx[i + 1]) + (2*dx[i]) - (2*dx[i + 1]))/den;
+                    dx[i] = ((hp*dx[i]) + x[i] + (ho*dx[i + 1]) - x[i + 1])/den;
+                    x[i] = ((hp*x[i]) + (ho*x[i + 1]))/den;
                 }
             }
 
-            return new Tuple<double, double, double>(x[0], dx[0], ddx[0]);
+            return ddx[0];
         }
 
         /// <summary>
-        /// Integrate up to point t. NOT SUPPORTED.
+        /// Indefinite integral at point t. NOT SUPPORTED.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         double IInterpolation.Integrate(double t)
         {
             throw new NotSupportedException();
         }
+
+        /// <summary>
+        /// Definite integral between points a and b. NOT SUPPORTED.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        double IInterpolation.Integrate(double a, double b)
+        {
+            throw new NotSupportedException();
+        }
     }
 }
diff --git a/src/Numerics/Interpolation/SplineInterpolation.cs b/src/Numerics/Interpolation/SplineInterpolation.cs
index cca27bbd..537d1117 100644
--- a/src/Numerics/Interpolation/SplineInterpolation.cs
+++ b/src/Numerics/Interpolation/SplineInterpolation.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -77,8 +77,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
-        /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -87,7 +85,6 @@ namespace MathNet.Numerics.Interpolation
         /// <summary>
         /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
         /// </summary>
-        /// <seealso cref="Integrate"/>
         bool IInterpolation.SupportsIntegration
         {
             get { return true; }
@@ -136,16 +133,16 @@ namespace MathNet.Numerics.Interpolation
         /// <returns>Interpolated value x(t).</returns>
         public double Interpolate(double t)
         {
-            int closestLeftIndex = IndexOfClosestPointLeftOf(t);
+            int closestLeftIndex = LeftBracketIndex(t);
 
             // Interpolation
             double offset = t - _points[closestLeftIndex];
             int k = closestLeftIndex << 2;
 
             return _coefficients[k]
-                + (offset*(_coefficients[k + 1]
-                    + (offset*(_coefficients[k + 2]
-                        + (offset*_coefficients[k + 3])))));
+                   + (offset*(_coefficients[k + 1]
+                              + (offset*(_coefficients[k + 2]
+                                         + (offset*_coefficients[k + 3])))));
         }
 
         /// <summary>
@@ -153,49 +150,38 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
-            int closestLeftIndex = IndexOfClosestPointLeftOf(t);
-
-            // Differentiation
+            int closestLeftIndex = LeftBracketIndex(t);
             double offset = t - _points[closestLeftIndex];
             int k = closestLeftIndex << 2;
 
             return _coefficients[k + 1]
-                + (2*offset*_coefficients[k + 2])
-                + (3*offset*offset*_coefficients[k + 3]);
+                   + (2*offset*_coefficients[k + 2])
+                   + (3*offset*offset*_coefficients[k + 3]);
         }
 
         /// <summary>
-        /// Interpolate, differentiate and 2nd differentiate at point t.
+        /// Differentiate twice at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <returns>Interpolated first derivative at point t.</returns>
-        /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double)"/>
-        public Tuple<double, double, double> DifferentiateAll(double t)
+        /// <returns>Interpolated second derivative at point t.</returns>
+        public double Differentiate2(double t)
         {
-            int closestLeftIndex = IndexOfClosestPointLeftOf(t);
+            int closestLeftIndex = LeftBracketIndex(t);
             double offset = t - _points[closestLeftIndex];
             int k = closestLeftIndex << 2;
 
-            return new Tuple<double, double, double>(
-                _coefficients[k] + (offset*(_coefficients[k + 1] + (offset*(_coefficients[k + 2] + (offset*_coefficients[k + 3]))))),
-                _coefficients[k + 1] + (2*offset*_coefficients[k + 2]) + (3*offset*offset*_coefficients[k + 3]),
-                (2*_coefficients[k + 2]) + (6*offset*_coefficients[k + 3]));
+            return (2*_coefficients[k + 2]) + (6*offset*_coefficients[k + 3]);
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Indefinite integral at point t.
         /// </summary>
-        /// <param name="t">Right bound of the integration interval [a,t].</param>
-        /// <returns>Interpolated definite integral over the interval [a,t].</returns>
-        /// <seealso cref="IInterpolation.SupportsIntegration"/>
+        /// <param name="t">Point t to integrate at.</param>
         public double Integrate(double t)
         {
-            int closestLeftIndex = IndexOfClosestPointLeftOf(t);
+            int closestLeftIndex = LeftBracketIndex(t);
 
             // Integration
             double result = 0;
@@ -203,18 +189,28 @@ namespace MathNet.Numerics.Interpolation
             {
                 double w = _points[i + 1] - _points[i];
                 result += w*(_coefficients[j]
-                    + ((w*_coefficients[j + 1]*0.5)
-                        + (w*((_coefficients[j + 2]/3)
-                            + (w*_coefficients[j + 3]*0.25)))));
+                             + ((w*_coefficients[j + 1]*0.5)
+                                + (w*((_coefficients[j + 2]/3)
+                                      + (w*_coefficients[j + 3]*0.25)))));
             }
 
             double offset = t - _points[closestLeftIndex];
             int k = closestLeftIndex << 2;
 
             return result + (offset*(_coefficients[k]
-                + (offset*_coefficients[k + 1]*0.5)
-                + (offset*_coefficients[k + 2]/3)
-                + (offset*_coefficients[k + 3]*0.25)));
+                                     + (offset*_coefficients[k + 1]*0.5)
+                                     + (offset*_coefficients[k + 2]/3)
+                                     + (offset*_coefficients[k + 3]*0.25)));
+        }
+
+        /// <summary>
+        /// Definite integral between points a and b.
+        /// </summary>
+        /// <param name="a">Left bound of the integration interval [a,b].</param>
+        /// <param name="b">Right bound of the integration interval [a,b].</param>
+        public double Integrate(double a, double b)
+        {
+            return Integrate(b) - Integrate(a);
         }
 
         /// <summary>
@@ -222,7 +218,7 @@ namespace MathNet.Numerics.Interpolation
         /// </summary>
         /// <param name="t">The value to look for.</param>
         /// <returns>The sample point index.</returns>
-        int IndexOfClosestPointLeftOf(double t)
+        int LeftBracketIndex(double t)
         {
             // Binary search in the [ t[0], ..., t[n-2] ] (t[n-1] is not included)
             int low = 0;
diff --git a/src/UnitTests/InterpolationTests/AkimaSplineTest.cs b/src/UnitTests/InterpolationTests/AkimaSplineTest.cs
index 9f8c4d1e..acc97113 100644
--- a/src/UnitTests/InterpolationTests/AkimaSplineTest.cs
+++ b/src/UnitTests/InterpolationTests/AkimaSplineTest.cs
@@ -28,11 +28,11 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.Interpolation;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    using Interpolation;
-    using NUnit.Framework;
-
     /// <summary>
     /// AkimaSpline test case.
     /// </summary>
@@ -42,12 +42,12 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// <summary>
         /// Sample points.
         /// </summary>
-        private readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 };
+        readonly double[] _t = { -2.0, -1.0, 0.0, 1.0, 2.0 };
 
         /// <summary>
         /// Sample values.
         /// </summary>
-        private readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 };
+        readonly double[] _x = { 1.0, 2.0, -1.0, 0.0, 1.0 };
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided sample points.
@@ -60,9 +60,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             for (int i = 0; i < _x.Length; i++)
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
-
-                var actual = interpolation.DifferentiateAll(_t[i]);
-                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -87,9 +84,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
 
             // TODO: Verify the expected values (that they are really the expected ones)
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
-
-            var actual = interpolation.DifferentiateAll(t);
-            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
diff --git a/src/UnitTests/InterpolationTests/BulirschStoerRationalTest.cs b/src/UnitTests/InterpolationTests/BulirschStoerRationalTest.cs
index 05ae54e4..3db86cd6 100644
--- a/src/UnitTests/InterpolationTests/BulirschStoerRationalTest.cs
+++ b/src/UnitTests/InterpolationTests/BulirschStoerRationalTest.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2002-2011 Math.NET
+// Copyright (c) 2002-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,11 +28,11 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.Interpolation;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    using Interpolation;
-    using NUnit.Framework;
-
     /// <summary>
     /// BulirschStoerRational test case.
     /// </summary>
@@ -42,12 +42,12 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// <summary>
         /// Sample points.
         /// </summary>
-        private readonly double[] _t = new[] { 0d, 1, 3, 4, 5 };
+        readonly double[] _t = { 0d, 1, 3, 4, 5 };
 
         /// <summary>
         /// Sample values.
         /// </summary>
-        private readonly double[] _x = new[] { 0d, 3, 1000, -1000, 3 };
+        readonly double[] _x = { 0d, 3, 1000, -1000, 3 };
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided sample points.
diff --git a/src/UnitTests/InterpolationTests/CubicSplineTest.cs b/src/UnitTests/InterpolationTests/CubicSplineTest.cs
index 64dd0199..4e1c27af 100644
--- a/src/UnitTests/InterpolationTests/CubicSplineTest.cs
+++ b/src/UnitTests/InterpolationTests/CubicSplineTest.cs
@@ -28,12 +28,11 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.Interpolation;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    using System;
-    using Interpolation;
-    using NUnit.Framework;
-
     /// <summary>
     /// CubicSpline Test case.
     /// </summary>
@@ -43,12 +42,12 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// <summary>
         /// Sample points.
         /// </summary>
-        private readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 };
+        readonly double[] _t = { -2.0, -1.0, 0.0, 1.0, 2.0 };
 
         /// <summary>
         /// Sample values.
         /// </summary>
-        private readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 };
+        readonly double[] _x = { 1.0, 2.0, -1.0, 0.0, 1.0 };
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided sample points.
@@ -61,9 +60,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             for (int i = 0; i < _x.Length; i++)
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
-
-                var actual = interpolation.DifferentiateAll(_t[i]);
-                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -92,9 +88,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             IInterpolation interpolation = new CubicSplineInterpolation(_t, _x);
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
-
-            var actual = interpolation.DifferentiateAll(t);
-            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
@@ -108,9 +101,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             for (int i = 0; i < _x.Length; i++)
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
-
-                var actual = interpolation.DifferentiateAll(_t[i]);
-                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -139,9 +129,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0);
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
-
-            var actual = interpolation.DifferentiateAll(t);
-            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
@@ -155,9 +142,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             for (int i = 0; i < _x.Length; i++)
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
-
-                var actual = interpolation.DifferentiateAll(_t[i]);
-                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -186,9 +170,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0);
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
-
-            var actual = interpolation.DifferentiateAll(t);
-            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
@@ -208,17 +189,5 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
                 Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
             }
         }
-
-        /// <summary>
-        /// Verifies that sample points are required to be sorted in strictly monotonically ascending order.
-        /// </summary>
-        [Test]
-        [ExpectedException(typeof(ArgumentException))]
-        public void Constructor_SamplePointsNotStrictlyAscending_Throws()
-        {
-            var x = new[] { -1.0, 0.0, 1.5, 1.5, 2.5, 4.0 };
-            var y = new[] { 1.0, 0.3, -0.7, -0.6, -0.1, 0.4 };
-            var interpolation = new CubicSplineInterpolation(x, y);
-        }
     }
 }
diff --git a/src/UnitTests/InterpolationTests/EquidistantPolynomialTest.cs b/src/UnitTests/InterpolationTests/EquidistantPolynomialTest.cs
index 1a1c470f..e7c4d618 100644
--- a/src/UnitTests/InterpolationTests/EquidistantPolynomialTest.cs
+++ b/src/UnitTests/InterpolationTests/EquidistantPolynomialTest.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2002-2011 Math.NET
+// Copyright (c) 2002-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,11 +28,11 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.Interpolation;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    using Interpolation;
-    using NUnit.Framework;
-
     /// <summary>
     /// EquidistantPolynomial Test case.
     /// </summary>
@@ -42,17 +42,17 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// <summary>
         /// Left bound;
         /// </summary>
-        private const double Tmin = 0.0;
+        const double Tmin = 0.0;
 
         /// <summary>
         /// Right bound.
         /// </summary>
-        private const double Tmax = 4.0;
+        const double Tmax = 4.0;
 
         /// <summary>
         /// Sample values.
         /// </summary>
-        private readonly double[] _x = new[] { 0.0, 3.0, 2.5, 1.0, 3.0 };
+        readonly double[] _x = { 0.0, 3.0, 2.5, 1.0, 3.0 };
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided sample points.
diff --git a/src/UnitTests/InterpolationTests/FloaterHormannRationalTest.cs b/src/UnitTests/InterpolationTests/FloaterHormannRationalTest.cs
index 987b7ce6..37f7be20 100644
--- a/src/UnitTests/InterpolationTests/FloaterHormannRationalTest.cs
+++ b/src/UnitTests/InterpolationTests/FloaterHormannRationalTest.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2002-2011 Math.NET
+// Copyright (c) 2002-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,11 +28,11 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.Interpolation;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    using Interpolation;
-    using NUnit.Framework;
-
     /// <summary>
     /// FloaterHormannRational test case.
     /// </summary>
@@ -42,12 +42,12 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// <summary>
         /// Sample points.
         /// </summary>
-        private readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 };
+        readonly double[] _t = { -2.0, -1.0, 0.0, 1.0, 2.0 };
 
         /// <summary>
         /// Sample values.
         /// </summary>
-        private readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 };
+        readonly double[] _x = { 1.0, 2.0, -1.0, 0.0, 1.0 };
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided polynomial sample points.
@@ -99,12 +99,12 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             var t = new double[40];
             var x = new double[40];
 
-            const double Step = 10.0 / 39.0;
+            const double Step = 10.0/39.0;
             for (int i = 0; i < t.Length; i++)
             {
-                double tt = -5 + (i * Step);
+                double tt = -5 + (i*Step);
                 t[i] = tt;
-                x[i] = 1.0 / (1.0 + (tt * tt));
+                x[i] = 1.0/(1.0 + (tt*tt));
             }
 
             IInterpolation interpolation = new FloaterHormannRationalInterpolation(t, x);
diff --git a/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs b/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs
index c6301b10..4e989c90 100644
--- a/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs
+++ b/src/UnitTests/InterpolationTests/LinearInterpolationCase.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2002-2011 Math.NET
+// Copyright (c) 2002-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -60,7 +60,7 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             for (int i = 0; i < x.Length; i++)
             {
                 x[i] = i + sampleOffset;
-                y[i] = (x[i] * slope) + intercept;
+                y[i] = (x[i]*slope) + intercept;
             }
 
             // build linear test vectors randomly between the sample points
@@ -71,14 +71,14 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
                 // y = const
                 xtest[0] = sampleOffset - uniform.Sample();
                 xtest[1] = sampleOffset + uniform.Sample();
-                ytest[0] = ytest[1] = (sampleOffset * slope) + intercept;
+                ytest[0] = ytest[1] = (sampleOffset*slope) + intercept;
             }
             else
             {
                 for (int i = 0; i < xtest.Length; i++)
                 {
                     xtest[i] = (i - 1) + sampleOffset + uniform.Sample();
-                    ytest[i] = (xtest[i] * slope) + intercept;
+                    ytest[i] = (xtest[i]*slope) + intercept;
                 }
             }
         }
diff --git a/src/UnitTests/InterpolationTests/LinearSplineTest.cs b/src/UnitTests/InterpolationTests/LinearSplineTest.cs
index fea52514..44e07b20 100644
--- a/src/UnitTests/InterpolationTests/LinearSplineTest.cs
+++ b/src/UnitTests/InterpolationTests/LinearSplineTest.cs
@@ -33,21 +33,46 @@ using NUnit.Framework;
 
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    /// <summary>
-    /// LinearSpline test case
-    /// </summary>
     [TestFixture, Category("Interpolation")]
     public class LinearSplineTest
     {
-        /// <summary>
-        /// Sample points.
-        /// </summary>
         readonly double[] _t = { -2.0, -1.0, 0.0, 1.0, 2.0 };
+        readonly double[] _y = { 1.0, 2.0, -1.0, 0.0, 1.0 };
 
-        /// <summary>
-        /// Sample values.
-        /// </summary>
-        readonly double[] _x = { 1.0, 2.0, -1.0, 0.0, 1.0 };
+        [Test]
+        public void FirstDerivative()
+        {
+            IInterpolation ip = LinearSpline.Interpolate(_t, _y);
+            Assert.That(ip.Differentiate(-3.0), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(-2.0), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(-1.5), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(-1.0), Is.EqualTo(-3.0));
+            Assert.That(ip.Differentiate(-0.5), Is.EqualTo(-3.0));
+            Assert.That(ip.Differentiate(0.0), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(0.5), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(1.0), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(2.0), Is.EqualTo(1.0));
+            Assert.That(ip.Differentiate(3.0), Is.EqualTo(1.0));
+        }
+
+        [Test]
+        public void DefiniteIntegral()
+        {
+            IInterpolation ip = LinearSpline.Interpolate(_t, _y);
+            Assert.That(ip.Integrate(-4.0, -3.0), Is.EqualTo(-0.5));
+            Assert.That(ip.Integrate(-3.0, -2.0), Is.EqualTo(0.5));
+            Assert.That(ip.Integrate(-2.0, -1.0), Is.EqualTo(1.5));
+            Assert.That(ip.Integrate(-1.0, 0.0), Is.EqualTo(0.5));
+            Assert.That(ip.Integrate(0.0, 1.0), Is.EqualTo(-0.5));
+            Assert.That(ip.Integrate(1.0, 2.0), Is.EqualTo(0.5));
+            Assert.That(ip.Integrate(2.0, 3.0), Is.EqualTo(1.5));
+            Assert.That(ip.Integrate(3.0, 4.0), Is.EqualTo(2.5));
+            Assert.That(ip.Integrate(0.0, 4.0), Is.EqualTo(4.0));
+            Assert.That(ip.Integrate(-3.0, -1.0), Is.EqualTo(2.0));
+            Assert.That(ip.Integrate(-3.0, 4.0), Is.EqualTo(6.5));
+            Assert.That(ip.Integrate(0.5, 1.5), Is.EqualTo(0.0));
+            Assert.That(ip.Integrate(-2.5, -1.0), Is.EqualTo(1.875));
+        }
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided sample points.
@@ -55,14 +80,10 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         [Test]
         public void FitsAtSamplePoints()
         {
-            IInterpolation interpolation = LinearSpline.Interpolate(_t, _x);
-
-            for (int i = 0; i < _x.Length; i++)
+            IInterpolation ip = LinearSpline.Interpolate(_t, _y);
+            for (int i = 0; i < _y.Length; i++)
             {
-                Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
-
-                var actual = interpolation.DifferentiateAll(_t[i]);
-                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
+                Assert.AreEqual(_y[i], ip.Interpolate(_t[i]), "A Exact Point " + i);
             }
         }
 
@@ -86,14 +107,10 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         [TestCase(1.2, .2, 1e-15)]
         [TestCase(10.0, 9.0, 1e-15)]
         [TestCase(-10.0, -7.0, 1e-15)]
-        public void FitsAtArbitraryPointsWithMaple(double t, double x, double maxAbsoluteError)
+        public void FitsAtArbitraryPoints(double t, double x, double maxAbsoluteError)
         {
-            IInterpolation interpolation = LinearSpline.Interpolate(_t, _x);
-
-            Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
-
-            var actual = interpolation.DifferentiateAll(t);
-            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            IInterpolation ip = LinearSpline.Interpolate(_t, _y);
+            Assert.AreEqual(x, ip.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
         }
 
         /// <summary>
@@ -107,10 +124,11 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         {
             double[] x, y, xtest, ytest;
             LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples);
-            IInterpolation interpolation = LinearSpline.Interpolate(x, y);
+
+            IInterpolation ip = LinearSpline.Interpolate(x, y);
             for (int i = 0; i < xtest.Length; i++)
             {
-                Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
+                Assert.AreEqual(ytest[i], ip.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
             }
         }
     }
diff --git a/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs b/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs
index b6cfa7e9..2f7d19e3 100644
--- a/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs
+++ b/src/UnitTests/InterpolationTests/NevillePolynomialTest.cs
@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2002-2011 Math.NET
+// Copyright (c) 2002-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -28,15 +28,15 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
+using System.Globalization;
+using System.IO;
+using System.Linq;
+using MathNet.Numerics.Interpolation;
+using NUnit.Framework;
+
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
-    using System;
-    using System.Globalization;
-    using System.IO;
-    using System.Linq;
-    using Interpolation;
-    using NUnit.Framework;
-
     /// <summary>
     /// NevillePolynomial test case.
     /// </summary>
@@ -46,12 +46,12 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// <summary>
         /// Sample points.
         /// </summary>
-        private readonly double[] _t = new[] { 0.0, 1.0, 3.0, 4.0 };
+        readonly double[] _t = { 0.0, 1.0, 3.0, 4.0 };
 
         /// <summary>
         /// Sample values.
         /// </summary>
-        private readonly double[] _x = new[] { 0.0, 3.0, 1.0, 3.0 };
+        readonly double[] _x = { 0.0, 3.0, 1.0, 3.0 };
 
         /// <summary>
         /// Verifies that the interpolation matches the given value at all the provided sample points.
@@ -64,9 +64,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             for (int i = 0; i < _x.Length; i++)
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
-
-                var actual = interpolation.DifferentiateAll(_t[i]);
-                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -93,9 +90,6 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
-
-            var actual = interpolation.DifferentiateAll(t);
-            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
@@ -120,7 +114,7 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
         /// Verifies that all sample points must be unique.
         /// </summary>
         [Test]
-        [ExpectedException(typeof(ArgumentException))]
+        [ExpectedException(typeof (ArgumentException))]
         public void Constructor_SamplePointsNotUnique_Throws()
         {
             var x = new[] { -1.0, 0.0, 1.5, 1.5, 2.5, 4.0 };