Christoph Ruegg
17 years ago
5 changed files with 142 additions and 40 deletions
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// <copyright file="Stability.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://mathnet.opensourcedotnet.info
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//
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// Copyright (c) 2009 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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namespace MathNet.Numerics |
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{ |
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using System; |
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public partial class SpecialFunctions |
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{ |
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/// <summary>
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/// Numerically stable exponential minus one, i.e. <code>x -> exp(x)-1</code>
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/// </summary>
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/// <param name="power">A number specifying a power.</param>
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/// <returns>Returns <code>exp(power)-1</code>.</returns>
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public static double ExponentialMinusOne(double power) |
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{ |
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double x = Math.Abs(power); |
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if (x > 0.1) |
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{ |
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return Math.Exp(power) - 1.0; |
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} |
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if (x < Precision.DoubleMachinePrecision) |
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{ |
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return x; |
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} |
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// Series Expansion to x^k / k!
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int k = 0; |
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double term = 1.0; |
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return Series( |
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() => |
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{ |
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k++; |
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term *= power; |
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term /= k; |
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return term; |
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} |
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); |
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} |
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/// <summary>
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/// Numerically stable hypotenuse of a right angle triangle, i.e. <code>(a,b) -> sqrt(a^2 + b^2)</code>
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/// </summary>
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/// <param name="a">The length of side a of the triangle.</param>
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/// <param name="b">The length of side b of the triangle.</param>
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/// <returns>Returns <code>sqrt(a<sup>2</sup> + b<sup>2</sup>)</code> without underflow/overflow.</returns>
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public static double Hypotenuse(double a, double b) |
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{ |
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if (Math.Abs(a) > Math.Abs(b)) |
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{ |
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double r = b / a; |
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return Math.Abs(a) * Math.Sqrt(1 + (r * r)); |
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} |
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if (b != 0.0) |
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{ |
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// NOTE (ruegg): not "!b.AlmostZero()" to avoid convergence issues (e.g. in SVD algorithm)
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double r = a / b; |
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return Math.Abs(b) * Math.Sqrt(1 + (r * r)); |
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} |
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return 0d; |
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} |
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/// <summary>
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/// Numerically stable series summation
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/// </summary>
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/// <param name="nextSummand">provides the summands sequentially</param>
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/// <returns>Sum</returns>
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private static double Series(Func<double> nextSummand) |
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{ |
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double compensation = 0.0; |
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double current; |
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double factor = 1 << 16; |
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double sum = nextSummand(); |
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do |
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{ |
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// Kahan Summation
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// NOTE (ruegg): do NOT optimize. Now, how to tell that the compiler?
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current = nextSummand(); |
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double y = current - compensation; |
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double t = sum + y; |
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compensation = t - sum; |
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compensation -= y; |
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sum = t; |
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} |
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while (Math.Abs(sum) < Math.Abs(factor * current)); |
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return sum; |
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} |
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} |
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} |
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