Christoph Ruegg
17 years ago
4 changed files with 501 additions and 3 deletions
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// <copyright file="Sample.Chebyshev.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.Sampling |
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{ |
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using System; |
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/// <summary>
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/// Generic Function Sampling and Quantization Provider
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/// </summary>
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public static partial class Sample |
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{ |
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/// <summary>
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/// Samples a function at the roots of the Chebyshev polynomial of the first kind.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
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/// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>Vector of the function sampled in [a,b] at (b+a)/2+(b-1)/2*cos(pi*(2i-1)/(2n))</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException" />
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public static T[] ChebyshevNodesFirstKind<T>( |
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Func<double, T> function, |
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double intervalBegin, |
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double intervalEnd, |
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int sampleCount) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 1) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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// transform to map to [-1..1] interval
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double transformSummand = 0.5 * (intervalBegin + intervalEnd); |
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double transformFactor = 0.5 * (intervalEnd - intervalBegin); |
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// evaluate first kind chebyshev nodes
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double angleFactor = Constants.Pi / (2 * sampleCount); |
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var samples = new T[sampleCount]; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = function(transformSummand + transformFactor * Math.Cos(((2 * i) + 1) * angleFactor)); |
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} |
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return samples; |
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} |
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/// <summary>
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/// Samples a function at the roots of the Chebyshev polynomial of the second kind.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
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/// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>Vector of the function sampled in [a,b] at (b+a)/2+(b-1)/2*cos(pi*i/(n-1))</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException" />
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public static T[] ChebyshevNodesSecondKind<T>( |
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Func<double, T> function, |
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double intervalBegin, |
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double intervalEnd, |
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int sampleCount) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 1) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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// transform to map to [-1..1] interval
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double transformSummand = 0.5 * (intervalBegin + intervalEnd); |
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double transformFactor = 0.5 * (intervalEnd - intervalBegin); |
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// evaluate second kind chebyshev nodes
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double angleFactor = Constants.Pi / (sampleCount + 1); |
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var samples = new T[sampleCount]; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = function(transformSummand + transformFactor * Math.Cos((i + 1) * angleFactor)); |
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} |
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return samples; |
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} |
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} |
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} |
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@ -0,0 +1,368 @@ |
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// <copyright file="Sample.Equidistant.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.Sampling |
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{ |
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using System; |
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using System.Collections.Generic; |
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/// <summary>
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/// Generic Function Sampling and Quantization Provider
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/// </summary>
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public static partial class Sample |
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{ |
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/// <summary>
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/// Samples a function equidistant within the provided interval.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
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/// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>The generated sample vector.</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException" />
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public static T[] EquidistantInterval<T>( |
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Func<double, T> function, |
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double intervalBegin, |
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double intervalEnd, |
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int sampleCount) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 0) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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if (sampleCount == 0) |
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{ |
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return new T[0]; |
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} |
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if (sampleCount == 1) |
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{ |
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return new T[] { function(0.5 * (intervalBegin + intervalEnd)) }; |
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} |
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var samples = new T[sampleCount]; |
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var step = (intervalEnd - intervalBegin) / (sampleCount - 1); |
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var current = intervalBegin; |
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for (int i = 0; i < samples.Length - 1; i++) |
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{ |
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samples[i] = function(current); |
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current += step; |
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} |
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samples[samples.Length - 1] = function(intervalEnd); |
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return samples; |
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} |
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/// <summary>
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/// Samples a function equidistant within the provided interval.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
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/// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <param name="samplePoints">The real domain points where the samples are taken at.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>The generated sample vector.</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException" />
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public static T[] EquidistantInterval<T>( |
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Func<double, T> function, |
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double intervalBegin, |
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double intervalEnd, |
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int sampleCount, |
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out double[] samplePoints) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 0) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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if (sampleCount == 0) |
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{ |
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samplePoints = new double[0]; |
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return new T[0]; |
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} |
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if (sampleCount == 1) |
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{ |
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samplePoints = new[] { 0.5 * (intervalBegin + intervalEnd) }; |
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return new T[] { function(samplePoints[0]) }; |
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} |
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var samples = new T[sampleCount]; |
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samplePoints = new double[sampleCount]; |
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var step = (intervalEnd - intervalBegin) / (sampleCount - 1); |
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var current = intervalBegin; |
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for (int i = 0; i < samples.Length - 1; i++) |
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{ |
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samplePoints[i] = current; |
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samples[i] = function(current); |
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current += step; |
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} |
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samplePoints[samplePoints.Length - 1] = intervalEnd; |
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samples[samples.Length - 1] = function(intervalEnd); |
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return samples; |
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} |
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/// <summary>
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/// Samples a periodic function equidistant within one period, but omits the last sample such that the sequence
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/// can be concatenated together.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="periodLength">The real domain full period length.</param>
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/// <param name="periodOffset">The real domain offset where to start the sampling period.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>The generated sample vector.</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException"/>
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public static T[] EquidistantPeriodic<T>( |
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Func<double, T> function, |
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double periodLength, |
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double periodOffset, |
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int sampleCount) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 1) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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var samples = new T[sampleCount]; |
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var step = periodLength / sampleCount; |
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var current = periodOffset; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = function(current); |
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current += step; |
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} |
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return samples; |
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} |
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/// <summary>
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/// Samples a periodic function equidistant within one period, but omits the last sample such that the sequence
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/// can be concatenated together.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="periodLength">The real domain full period length.</param>
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/// <param name="periodOffset">The real domain offset where to start the sampling period.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <param name="samplePoints">The real domain points where the samples are taken at.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>The generated sample vector.</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException"/>
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public static T[] EquidistantPeriodic<T>( |
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Func<double, T> function, |
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double periodLength, |
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double periodOffset, |
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int sampleCount, |
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out double[] samplePoints) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 1) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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var samples = new T[sampleCount]; |
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samplePoints = new double[sampleCount]; |
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var step = periodLength / sampleCount; |
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var current = periodOffset; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samplePoints[i] = current; |
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samples[i] = function(current); |
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current += step; |
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} |
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return samples; |
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} |
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/// <summary>
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/// Samples a function equidistant starting from the provided location with a fixed step length.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="start">The real domain location offset where to start sampling.</param>
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/// <param name="step">The real domain step length between the equidistant samples.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>The generated sample vector.</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException"/>
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public static T[] EquidistantStartingAt<T>( |
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Func<double, T> function, |
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double start, |
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double step, |
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int sampleCount) |
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{ |
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if (ReferenceEquals(function, null)) |
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{ |
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throw new ArgumentNullException("function"); |
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} |
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if (sampleCount < 0) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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var samples = new T[sampleCount]; |
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var current = start; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = function(current); |
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current += step; |
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} |
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return samples; |
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} |
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/// <summary>
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/// Samples a function equidistant starting from the provided location with a fixed step length.
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/// </summary>
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/// <param name="function">The real-domain function to sample.</param>
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/// <param name="start">The real domain location offset where to start sampling.</param>
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/// <param name="step">The real domain step length between the equidistant samples.</param>
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/// <param name="sampleCount">The number of samples to generate.</param>
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/// <param name="samplePoints">The real domain points where the samples are taken at.</param>
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/// <typeparam name="T">The value type of the function to sample.</typeparam>
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/// <returns>The generated sample vector.</returns>
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/// <exception cref="ArgumentNullException" />
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/// <exception cref="ArgumentOutOfRangeException"/>
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public static T[] EquidistantStartingAt<T>( |
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Func<double, T> function, |
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double start, |
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double step, |
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int sampleCount, |
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out double[] samplePoints) |
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|
{ |
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|
if (ReferenceEquals(function, null)) |
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|
{ |
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|
throw new ArgumentNullException("function"); |
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} |
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|
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|
if (sampleCount < 0) |
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{ |
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throw new ArgumentOutOfRangeException("sampleCount"); |
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} |
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|
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var samples = new T[sampleCount]; |
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samplePoints = new double[sampleCount]; |
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var current = start; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samplePoints[i] = current; |
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samples[i] = function(current); |
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current += step; |
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} |
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return samples; |
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} |
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|
/// <summary>
|
||||
|
/// Samples a function equidistant continuously starting from the provided location with a fixed step length.
|
||||
|
/// </summary>
|
||||
|
/// <param name="function">The real-domain function to sample.</param>
|
||||
|
/// <param name="start">The real domain location offset where to start sampling.</param>
|
||||
|
/// <param name="step">The real domain step length between the equidistant samples.</param>
|
||||
|
/// <typeparam name="T">The value type of the function to sample.</typeparam>
|
||||
|
/// <returns>The generated sample enumerator.</returns>
|
||||
|
/// <exception cref="ArgumentNullException" />
|
||||
|
public static IEnumerable<T> EquidistantContinuous<T>( |
||||
|
Func<double, T> function, |
||||
|
double start, |
||||
|
double step) |
||||
|
{ |
||||
|
if (ReferenceEquals(function, null)) |
||||
|
{ |
||||
|
throw new ArgumentNullException("function"); |
||||
|
} |
||||
|
|
||||
|
var current = start; |
||||
|
|
||||
|
while (true) |
||||
|
{ |
||||
|
yield return function(current); |
||||
|
current += step; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Samples a function equidistant with the provided start and step length to an integer-domain function
|
||||
|
/// </summary>
|
||||
|
/// <param name="function">The real-domain function to sample.</param>
|
||||
|
/// <param name="start">The real domain location where to start sampling.</param>
|
||||
|
/// <param name="step">The real domain step length between the equidistant samples.</param>
|
||||
|
/// <typeparam name="T">The value type of the function to sample.</typeparam>
|
||||
|
/// <returns>The generated samples integer-domain function.</returns>
|
||||
|
/// <exception cref="ArgumentNullException" />
|
||||
|
public static Func<int, T> EquidistantToFunction<T>( |
||||
|
Func<double, T> function, |
||||
|
double start, |
||||
|
double step) |
||||
|
{ |
||||
|
if (ReferenceEquals(function, null)) |
||||
|
{ |
||||
|
throw new ArgumentNullException("function"); |
||||
|
} |
||||
|
|
||||
|
return k => function(start + k * step); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
Loading…
Reference in new issue