Christoph Ruegg
14 years ago
10 changed files with 272 additions and 209 deletions
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// <copyright file="SpecialFunctions.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2011 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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// <contribution>
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// Cephes Math Library, Stephen L. Moshier
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// ALGLIB 2.0.1, Sergey Bochkanov
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// </contribution>
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namespace MathNet.Numerics |
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{ |
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using System; |
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using Properties; |
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/// <summary>
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/// This class implements a collection of special function evaluations for double precision. This class
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/// has a static constructor which will precompute a small number of values for faster runtime computations.
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/// </summary>
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public static partial class SpecialFunctions |
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{ |
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/// <summary>
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/// Initializes static members of the SpecialFunctions class.
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/// </summary>
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static SpecialFunctions() |
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{ |
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InitializeFactorial(); |
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} |
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/// <summary>
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/// Computes the <paramref name="t"/>'th Harmonic number.
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/// </summary>
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/// <param name="t">The Harmonic number which needs to be computed.</param>
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/// <returns>The t'th Harmonic number.</returns>
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public static double Harmonic(int t) |
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{ |
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return Constants.EulerMascheroni + DiGamma(t + 1.0); |
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} |
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/// <summary>
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/// Compute the generalized harmonic number of order n of m. (1 + 1/2^m + 1/3^m + ... + 1/n^m)
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/// </summary>
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/// <param name="n">The order parameter.</param>
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/// <param name="m">The power parameter.</param>
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/// <returns>General Harmonic number.</returns>
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public static double GeneralHarmonic(int n, double m) |
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{ |
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double sum = 0; |
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for (int i = 0; i < n; i++) |
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{ |
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sum += Math.Pow(i + 1, -m); |
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} |
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return sum; |
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} |
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/// <summary>
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/// Computes the Digamma function which is mathematically defined as the derivative of the logarithm of the gamma function.
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/// This implementation is based on
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/// Jose Bernardo
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/// Algorithm AS 103:
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/// Psi ( Digamma ) Function,
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/// Applied Statistics,
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/// Volume 25, Number 3, 1976, pages 315-317.
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/// Using the modifications as in Tom Minka's lightspeed toolbox.
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/// </summary>
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/// <param name="x">The argument of the digamma function.</param>
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/// <returns>The value of the DiGamma function at <paramref name="x"/>.</returns>
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public static double DiGamma(double x) |
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{ |
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const double C = 12.0; |
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const double D1 = -0.57721566490153286; |
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const double D2 = 1.6449340668482264365; |
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const double S = 1e-6; |
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const double S3 = 1.0 / 12.0; |
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const double S4 = 1.0 / 120.0; |
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const double S5 = 1.0 / 252.0; |
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const double S6 = 1.0 / 240.0; |
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const double S7 = 1.0 / 132.0; |
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if (Double.IsNegativeInfinity(x) || Double.IsNaN(x)) |
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{ |
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return Double.NaN; |
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} |
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// Handle special cases.
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if (x <= 0 && Math.Floor(x) == x) |
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{ |
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return Double.NegativeInfinity; |
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} |
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// Use inversion formula for negative numbers.
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if (x < 0) |
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{ |
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return DiGamma(1.0 - x) + (Math.PI / Math.Tan(-Math.PI * x)); |
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} |
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if (x <= S) |
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{ |
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return D1 - (1 / x) + (D2 * x); |
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} |
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double result = 0; |
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while (x < C) |
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{ |
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result -= 1 / x; |
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x++; |
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} |
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if (x >= C) |
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{ |
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var r = 1 / x; |
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result += Math.Log(x) - (0.5 * r); |
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r *= r; |
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result -= r * (S3 - (r * (S4 - (r * (S5 - (r * (S6 - (r * S7)))))))); |
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} |
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return result; |
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} |
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/// <summary>
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/// <para>Computes the inverse Digamma function: this is the inverse of the logarithm of the gamma function. This function will
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/// only return solutions that are positive.</para>
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/// <para>This implementation is based on the bisection method.</para>
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/// </summary>
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/// <param name="p">The argument of the inverse digamma function.</param>
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/// <returns>The positive solution to the inverse DiGamma function at <paramref name="p"/>.</returns>
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public static double DiGammaInv(double p) |
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{ |
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if (Double.IsNaN(p)) |
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{ |
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return Double.NaN; |
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} |
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if (Double.IsNegativeInfinity(p)) |
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{ |
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return 0.0; |
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} |
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if (Double.IsPositiveInfinity(p)) |
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{ |
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return Double.PositiveInfinity; |
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} |
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var x = Math.Exp(p); |
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for (var d = 1.0; d > 1.0e-15; d /= 2.0) |
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{ |
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x += d * Math.Sign(p - DiGamma(x)); |
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} |
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return x; |
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} |
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/// <summary>
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/// Computes the logit function. see: http://en.wikipedia.org/wiki/Logit
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/// </summary>
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/// <param name="p">The parameter for which to compute the logit function. This number should be
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/// between 0 and 1.</param>
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/// <returns>The logarithm of <paramref name="p"/> divided by 1.0 - <paramref name="p"/>.</returns>
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public static double Logit(double p) |
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{ |
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if (p < 0.0 || p > 1.0) |
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{ |
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throw new ArgumentOutOfRangeException(Resources.ArgumentBetween0And1); |
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} |
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return Math.Log(p / (1.0 - p)); |
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} |
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/// <summary>
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/// Computes the logistic function. see: http://en.wikipedia.org/wiki/Logistic
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/// </summary>
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/// <param name="p">The parameter for which to compute the logistic function.</param>
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/// <returns>The logistic function of <paramref name="p"/>.</returns>
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public static double Logistic(double p) |
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{ |
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return 1.0 / (Math.Exp(-p) + 1.0); |
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} |
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} |
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} |
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@ -0,0 +1,74 @@ |
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// <copyright file="Harmonic.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2011 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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|
// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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|
// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
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// OTHER DEALINGS IN THE SOFTWARE.
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||||
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// </copyright>
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||||
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||||
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// <contribution>
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// Cephes Math Library, Stephen L. Moshier
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// ALGLIB 2.0.1, Sergey Bochkanov
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// </contribution>
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// ReSharper disable CheckNamespace
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namespace MathNet.Numerics |
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// ReSharper restore CheckNamespace
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{ |
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using System; |
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/// <summary>
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/// This partial implementation of the SpecialFunctions class contains all methods related to the harmonic function.
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/// </summary>
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public static partial class SpecialFunctions |
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{ |
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/// <summary>
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/// Computes the <paramref name="t"/>'th Harmonic number.
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/// </summary>
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/// <param name="t">The Harmonic number which needs to be computed.</param>
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/// <returns>The t'th Harmonic number.</returns>
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public static double Harmonic(int t) |
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{ |
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return Constants.EulerMascheroni + DiGamma(t + 1.0); |
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} |
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/// <summary>
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/// Compute the generalized harmonic number of order n of m. (1 + 1/2^m + 1/3^m + ... + 1/n^m)
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/// </summary>
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/// <param name="n">The order parameter.</param>
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/// <param name="m">The power parameter.</param>
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/// <returns>General Harmonic number.</returns>
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public static double GeneralHarmonic(int n, double m) |
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{ |
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double sum = 0; |
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for (int i = 0; i < n; i++) |
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{ |
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sum += Math.Pow(i + 1, -m); |
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} |
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return sum; |
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} |
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} |
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} |
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@ -0,0 +1,74 @@ |
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// <copyright file="Logistic.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2011 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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||||
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// obtaining a copy of this software and associated documentation
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||||
|
// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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||||
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
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// copies of the Software, and to permit persons to whom the
|
||||
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// Software is furnished to do so, subject to the following
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||||
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// conditions:
|
||||
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//
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||||
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
|
||||
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//
|
||||
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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||||
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
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// OTHER DEALINGS IN THE SOFTWARE.
|
||||
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// </copyright>
|
||||
|
|
||||
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// <contribution>
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||||
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// Cephes Math Library, Stephen L. Moshier
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// ALGLIB 2.0.1, Sergey Bochkanov
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// </contribution>
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// ReSharper disable CheckNamespace
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namespace MathNet.Numerics |
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// ReSharper restore CheckNamespace
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{ |
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using System; |
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using Properties; |
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/// <summary>
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/// This partial implementation of the SpecialFunctions class contains all methods related to the logistic function.
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/// </summary>
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public static partial class SpecialFunctions |
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{ |
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/// <summary>
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/// Computes the logistic function. see: http://en.wikipedia.org/wiki/Logistic
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/// </summary>
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/// <param name="p">The parameter for which to compute the logistic function.</param>
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/// <returns>The logistic function of <paramref name="p"/>.</returns>
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public static double Logistic(double p) |
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{ |
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return 1.0 / (Math.Exp(-p) + 1.0); |
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} |
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/// <summary>
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/// Computes the logit function, the inverse of the sigmoid logistic function. see: http://en.wikipedia.org/wiki/Logit
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/// </summary>
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/// <param name="p">The parameter for which to compute the logit function. This number should be
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/// between 0 and 1.</param>
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/// <returns>The logarithm of <paramref name="p"/> divided by 1.0 - <paramref name="p"/>.</returns>
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public static double Logit(double p) |
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{ |
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if (p < 0.0 || p > 1.0) |
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{ |
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throw new ArgumentOutOfRangeException(Resources.ArgumentBetween0And1); |
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} |
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return Math.Log(p / (1.0 - p)); |
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} |
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} |
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} |
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