Interpolation: computing interpolation 1st/2nd derivative at once should use tuple type instead of out parameters

src/Numerics/Interpolate.cs

@@ -69,7 +69,7 @@ namespace MathNet.Numerics
             IList<double> points,
             IList<double> values)
         {
-            LinearSplineInterpolation method = new LinearSplineInterpolation();
+            var method = new LinearSplineInterpolation();
             method.Initialize(points, values);
             return method;
         }
@@ -88,7 +88,7 @@ namespace MathNet.Numerics
             IList<double> points,
             IList<double> values)
         {
-            FloaterHormannRationalInterpolation method = new FloaterHormannRationalInterpolation();
+            var method = new FloaterHormannRationalInterpolation();
             method.Initialize(points, values);
             return method;
         }
@@ -107,7 +107,7 @@ namespace MathNet.Numerics
             IList<double> points,
             IList<double> values)
         {
-            BulirschStoerRationalInterpolation method = new BulirschStoerRationalInterpolation();
+            var method = new BulirschStoerRationalInterpolation();
             method.Initialize(points, values);
             return method;
         }

src/Numerics/Interpolation/AkimaSplineInterpolation.cs

@@ -72,7 +72,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -249,27 +249,22 @@ namespace MathNet.Numerics.Interpolation
         /// <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, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        public double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        public Tuple<double, double, double> DifferentiateAll(double t)
         {
-            return _spline.Differentiate(t, out interpolatedValue, out secondDerivative);
+            return _spline.DifferentiateAll(t);
         }
 
         /// <summary>

src/Numerics/Interpolation/BarycentricInterpolation.cs

@@ -81,7 +81,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.Differentiate(double, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -203,36 +203,31 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Differentiate 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, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        double IInterpolation.Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Integrate up to 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>

src/Numerics/Interpolation/BulirschStoerRationalInterpolation.cs

@@ -76,7 +76,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.Differentiate(double, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -187,36 +187,31 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Differentiate 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, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        double IInterpolation.Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Integrate up to 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>

src/Numerics/Interpolation/CubicHermiteSplineInterpolation.cs

@@ -74,7 +74,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -183,27 +183,22 @@ namespace MathNet.Numerics.Interpolation
         /// <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, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        public double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        public Tuple<double, double, double> DifferentiateAll(double t)
         {
-            return _spline.Differentiate(t, out interpolatedValue, out secondDerivative);
+            return _spline.DifferentiateAll(t);
         }
 
         /// <summary>

src/Numerics/Interpolation/CubicSplineInterpolation.cs

@@ -103,7 +103,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -383,27 +383,22 @@ namespace MathNet.Numerics.Interpolation
         /// <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, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        public double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        public Tuple<double, double, double> DifferentiateAll(double t)
         {
-            return _spline.Differentiate(t, out interpolatedValue, out secondDerivative);
+            return _spline.DifferentiateAll(t);
         }
 
         /// <summary>

src/Numerics/Interpolation/EquidistantPolynomialInterpolation.cs

@@ -86,7 +86,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.Differentiate(double, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -189,36 +189,31 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Differentiate 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, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        double IInterpolation.Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Integrate up to 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>

src/Numerics/Interpolation/FloaterHormannRationalInterpolation.cs

@@ -89,7 +89,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        /// <seealso cref="IInterpolation.Differentiate(double, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return false; }
@@ -266,36 +266,31 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Differentiate 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, out double, out double)"/>
+        /// <seealso cref="IInterpolation.DifferentiateAll(double)"/>
         double IInterpolation.Differentiate(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t. NOT SUPPORTED.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="IInterpolation.Differentiate(double)"/>
-        double IInterpolation.Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        Tuple<double, double, double> IInterpolation.DifferentiateAll(double t)
         {
             throw new NotSupportedException();
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Integrate up to 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>

src/Numerics/Interpolation/IInterpolation.cs

@@ -28,6 +28,8 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
+
 namespace MathNet.Numerics.Interpolation
 {
     /// <summary>
@@ -39,7 +41,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool SupportsDifferentiation { get; }
 
         /// <summary>
@@ -61,22 +63,17 @@ namespace MathNet.Numerics.Interpolation
         /// <param name="t">Point t to interpolate at.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="SupportsDifferentiation"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         double Differentiate(double t);
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative);
+        Tuple<double, double, double> DifferentiateAll(double t);
 
         /// <summary>
         /// Integrate up to point t.

src/Numerics/Interpolation/LinearSplineInterpolation.cs

@@ -72,7 +72,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -167,27 +167,22 @@ namespace MathNet.Numerics.Interpolation
         /// <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, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             return _spline.Differentiate(t);
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        public double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        public Tuple<double, double, double> DifferentiateAll(double t)
         {
-            return _spline.Differentiate(t, out interpolatedValue, out secondDerivative);
+            return _spline.DifferentiateAll(t);
         }
 
         /// <summary>

src/Numerics/Interpolation/NevillePolynomialInterpolation.cs

@@ -82,7 +82,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -164,7 +164,7 @@ namespace MathNet.Numerics.Interpolation
         /// <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, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             double[] x = new double[_values.Count];
@@ -187,22 +187,17 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        public double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        public Tuple<double, double, double> DifferentiateAll(double t)
         {
-            double[] x = new double[_values.Count];
-            double[] dx = new double[_values.Count];
-            double[] ddx = new double[_values.Count];
+            var x = new double[_values.Count];
+            var dx = new double[_values.Count];
+            var ddx = new double[_values.Count];
             _values.CopyTo(x, 0);
 
             for (int level = 1; level < x.Length; level++)
@@ -212,19 +207,17 @@ 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;
                 }
             }
 
-            interpolatedValue = x[0];
-            secondDerivative = ddx[0];
-            return dx[0];
+            return new Tuple<double, double, double>(x[0], dx[0], ddx[0]);
         }
 
         /// <summary>
-        /// Integrate up to point t.
+        /// Integrate up to 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>

src/Numerics/Interpolation/SplineInterpolation.cs

@@ -80,7 +80,7 @@ namespace MathNet.Numerics.Interpolation
         /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
         /// </summary>
         /// <seealso cref="Differentiate(double)"/>
-        /// <seealso cref="Differentiate(double, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         bool IInterpolation.SupportsDifferentiation
         {
             get { return true; }
@@ -158,7 +158,7 @@ namespace MathNet.Numerics.Interpolation
         /// <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, out double, out double)"/>
+        /// <seealso cref="DifferentiateAll(double)"/>
         public double Differentiate(double t)
         {
             int closestLeftIndex = IndexOfClosestPointLeftOf(t);
@@ -173,36 +173,22 @@ namespace MathNet.Numerics.Interpolation
         }
 
         /// <summary>
-        /// Differentiate at point t.
+        /// Interpolate, differentiate and 2nd differentiate at point t.
         /// </summary>
         /// <param name="t">Point t to interpolate at.</param>
-        /// <param name="interpolatedValue">Interpolated value x(t)</param>
-        /// <param name="secondDerivative">Interpolated second derivative at point t.</param>
         /// <returns>Interpolated first derivative at point t.</returns>
         /// <seealso cref="IInterpolation.SupportsDifferentiation"/>
         /// <seealso cref="Differentiate(double)"/>
-        public double Differentiate(
-            double t,
-            out double interpolatedValue,
-            out double secondDerivative)
+        public Tuple<double, double, double> DifferentiateAll(double t)
         {
             int closestLeftIndex = IndexOfClosestPointLeftOf(t);
-
-            // Differentiation
             double offset = t - _points[closestLeftIndex];
             int k = closestLeftIndex << 2;
 
-            interpolatedValue = _coefficients[k]
-                + (offset*(_coefficients[k + 1]
-                    + (offset*(_coefficients[k + 2]
-                        + (offset*_coefficients[k + 3])))));
-
-            secondDerivative = (2*_coefficients[k + 2])
-                + (6*offset*_coefficients[k + 3]);
-
-            return _coefficients[k + 1]
-                + (2*offset*_coefficients[k + 2])
-                + (3*offset*offset*_coefficients[k + 3]);
+            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]));
         }
 
         /// <summary>

src/UnitTests/InterpolationTests/AkimaSplineTest.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
@@ -61,10 +61,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
 
-                double interpolatedValue;
-                double secondDerivative;
-                interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
-                Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
+                var actual = interpolation.DifferentiateAll(_t[i]);
+                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -90,10 +88,8 @@ 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);
 
-            double interpolatedValue;
-            double secondDerivative;
-            interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
-            Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            var actual = interpolation.DifferentiateAll(t);
+            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>

src/UnitTests/InterpolationTests/CubicSplineTest.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
@@ -31,9 +31,6 @@
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
     using System;
-    using System.Globalization;
-    using System.IO;
-    using System.Linq;
     using Interpolation;
     using NUnit.Framework;
 
@@ -65,10 +62,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
 
-                double interpolatedValue;
-                double secondDerivative;
-                interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
-                Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
+                var actual = interpolation.DifferentiateAll(_t[i]);
+                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -98,10 +93,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
 
-            double interpolatedValue;
-            double secondDerivative;
-            interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
-            Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            var actual = interpolation.DifferentiateAll(t);
+            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
@@ -116,10 +109,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
 
-                double interpolatedValue;
-                double secondDerivative;
-                interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
-                Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
+                var actual = interpolation.DifferentiateAll(_t[i]);
+                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -149,10 +140,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
 
-            double interpolatedValue;
-            double secondDerivative;
-            interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
-            Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            var actual = interpolation.DifferentiateAll(t);
+            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>
@@ -167,10 +156,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
 
-                double interpolatedValue;
-                double secondDerivative;
-                interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
-                Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
+                var actual = interpolation.DifferentiateAll(_t[i]);
+                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -200,10 +187,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
 
-            double interpolatedValue;
-            double secondDerivative;
-            interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
-            Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            var actual = interpolation.DifferentiateAll(t);
+            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>

src/UnitTests/InterpolationTests/LinearSplineTest.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
@@ -31,9 +31,6 @@
 namespace MathNet.Numerics.UnitTests.InterpolationTests
 {
     using System;
-    using System.Globalization;
-    using System.IO;
-    using System.Linq;
     using Interpolation;
     using NUnit.Framework;
 
@@ -65,10 +62,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
 
-                double interpolatedValue;
-                double secondDerivative;
-                interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
-                Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
+                var actual = interpolation.DifferentiateAll(_t[i]);
+                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -98,10 +93,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
 
-            double interpolatedValue;
-            double secondDerivative;
-            interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
-            Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            var actual = interpolation.DifferentiateAll(t);
+            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>

src/UnitTests/InterpolationTests/NevillePolynomialTest.cs

@@ -65,10 +65,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
             {
                 Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
 
-                double interpolatedValue;
-                double secondDerivative;
-                interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
-                Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
+                var actual = interpolation.DifferentiateAll(_t[i]);
+                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
             }
         }
 
@@ -96,10 +94,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
 
             Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
 
-            double interpolatedValue;
-            double secondDerivative;
-            interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
-            Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
+            var actual = interpolation.DifferentiateAll(t);
+            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
         }
 
         /// <summary>