Taylor Series, Dissimilarity functions.

Sources/Accord.Math/TaylorSeries.cs

@@ -0,0 +1,206 @@
+// Accord Math Library
+// The Accord.NET Framework
+// http://accord-framework.net
+//
+// Copyright © Diego Catalano, 2014
+// diego.catalano at live.com
+//
+//    This library is free software; you can redistribute it and/or
+//    modify it under the terms of the GNU Lesser General Public
+//    License as published by the Free Software Foundation; either
+//    version 2.1 of the License, or (at your option) any later version.
+//
+//    This library is distributed in the hope that it will be useful,
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+//    Lesser General Public License for more details.
+//
+//    You should have received a copy of the GNU Lesser General Public
+//    License along with this library; if not, write to the Free Software
+//    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
+//
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+
+namespace Accord.Math
+{
+
+    /// <summary>
+    /// Taylor Series Expansions.
+    /// 
+    /// <para>In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from
+    /// the values of the function's derivatives at a single point.</para>
+    /// 
+    /// </summary>
+    /// <remarks>
+    ///   http://www.haverford.edu/physics/MathAppendices/Taylor_Series.pdf
+    /// </remarks>
+    public static class TaylorSeries
+    {
+
+        /// <summary>
+        /// Compute Sin using Taylor Series.
+        /// </summary>
+        /// <param name="x">An angle, in radians.</param>
+        /// <param name="nTerms">Number of terms.</param>
+        /// <returns>Sin of the x.</returns>
+        public static double Sin(double x, int nTerms)
+        {
+            if (nTerms < 2) return x;
+            if (nTerms == 2)
+            {
+                return x - (x * x * x) / 6D;
+            }
+            else
+            {
+
+                double mult = x * x * x;
+                double fact = 6;
+                double sign = 1;
+                int factS = 5;
+                double result = x - mult / fact;
+                for (int i = 3; i <= nTerms; i++)
+                {
+                    mult *= x * x;
+                    fact *= factS * (factS - 1);
+                    factS += 2;
+                    result += sign * (mult / fact);
+                    sign *= -1;
+                }
+
+                return result;
+            }
+        }
+
+        /// <summary>
+        /// Compute Cos using Taylor Series.
+        /// </summary>
+        /// <param name="x">An angle, in radians.</param>
+        /// <param name="nTerms">Number of terms.</param>
+        /// <returns>Cos of the x.</returns>
+        public static double Cos(double x, int nTerms)
+        {
+            if (nTerms < 2) return 1;
+            if (nTerms == 2)
+            {
+                return 1 - (x * x) / 2D;
+            }
+            else
+            {
+
+                double mult = x * x;
+                double fact = 2;
+                double sign = 1;
+                int factS = 4;
+                double result = 1 - mult / fact;
+                for (int i = 3; i <= nTerms; i++)
+                {
+                    mult *= x * x;
+                    fact *= factS * (factS - 1);
+                    factS += 2;
+                    result += sign * (mult / fact);
+                    sign *= -1;
+                }
+
+                return result;
+            }
+        }
+
+        /// <summary>
+        /// Compute Hiperbolic Sin using Taylor Series.
+        /// </summary>
+        /// <param name="x">An angle, in radians.</param>
+        /// <param name="nTerms">Number of terms.</param>
+        /// <returns>Hiperbolic sin of the x.</returns>
+        public static double Sinh(double x, int nTerms)
+        {
+            if (nTerms < 2) return x;
+            if (nTerms == 2)
+            {
+                return x + (x * x * x) / 6D;
+            }
+            else
+            {
+
+                double mult = x * x * x;
+                double fact = 6;
+                int factS = 5;
+                double result = x + mult / fact;
+                for (int i = 3; i <= nTerms; i++)
+                {
+                    mult *= x * x;
+                    fact *= factS * (factS - 1);
+                    factS += 2;
+                    result += mult / fact;
+                }
+
+                return result;
+            }
+        }
+
+        /// <summary>
+        /// Compute Hiperbolic Cos using Taylor Series.
+        /// </summary>
+        /// <param name="x">An angle, in radians.</param>
+        /// <param name="nTerms">Number of terms.</param>
+        /// <returns>Hiperbolic cos of the x.</returns>
+        public static double Cosh(double x, int nTerms)
+        {
+            if (nTerms < 2) return x;
+            if (nTerms == 2)
+            {
+                return 1 + (x * x) / 2D;
+            }
+            else
+            {
+
+                double mult = x * x;
+                double fact = 2;
+                int factS = 4;
+                double result = 1 + mult / fact;
+                for (int i = 3; i <= nTerms; i++)
+                {
+                    mult *= x * x;
+                    fact *= factS * (factS - 1);
+                    factS += 2;
+                    result += mult / fact;
+                }
+
+                return result;
+            }
+        }
+
+        /// <summary>
+        /// Compute Exp using Taylor Series.
+        /// </summary>
+        /// <param name="x">An angle, in radians.</param>
+        /// <param name="nTerms">Number of terms.</param>
+        /// <returns>Exp of the x.</returns>
+        public static double Exp(double x, int nTerms)
+        {
+            if (nTerms < 2) return 1 + x;
+            if (nTerms == 2)
+            {
+                return 1 + x + (x * x) / 2;
+            }
+            else
+            {
+
+                double mult = x * x;
+                double fact = 2;
+                double result = 1 + x + mult / fact;
+                for (int i = 3; i <= nTerms; i++)
+                {
+                    mult *= x;
+                    fact *= i;
+                    result += mult / fact;
+                }
+
+                return result;
+            }
+        }
+    }
+}

Sources/Accord.Math/Tools.cs

@@ -150,6 +150,24 @@ public static int Direction(IntPoint previous, IntPoint next)
             return code;
         }
 
+        /// <summary>
+        /// Gets the greatest common divisor between two integers.
+        /// </summary>
+        /// <param name="a">First value.</param>
+        /// <param name="b">Second value.</param>
+        /// <returns>The greatest common divisor.</returns>
+        public static int GreatestCommonDivisor(int a, int b)
+        {
+            int x = a - b * (int)Math.Floor((double)(a / b));
+            while (x != 0)
+            {
+                a = b;
+                b = x;
+                x = a - b * (int)Math.Floor((double)(a / b));
+            }
+            return b;
+        }
+
         /// <summary>
         ///   Returns the next power of 2 after the input value x.
         /// </summary>
@@ -185,8 +203,8 @@ public static int PreviousPowerOf2(int x)
         ///   Hypotenuse calculus without overflow/underflow
         /// </summary>
         /// 
-        /// <param name="a">first value</param>
-        /// <param name="b">second value</param>
+        /// <param name="a">First value</param>
+        /// <param name="b">Second value</param>
         /// <returns>The hypotenuse Sqrt(a^2 + b^2)</returns>
         /// 
         public static double Hypotenuse(double a, double b)

Sources/Accord.Statistics/Accord.Statistics.csproj

@@ -152,6 +152,7 @@
     <Compile Include="Analysis\Performance\ReceiverOperatingCharacteristic.cs" />
     <Compile Include="Analysis\StepwiseLogisticRegressionAnalysis.cs" />
     <Compile Include="Circular.cs" />
+    <Compile Include="Dissimilarity.cs" />
     <Compile Include="Distributions\Accord.Statistics.Distributions.cs" />
     <Compile Include="Distributions\Density Kernels\Accord.Statistics.Distributions.DensityKernels.cs" />
     <Compile Include="Distributions\Density Kernels\IDensityKernel.cs" />