sampling: equidistant, chebyshev

Signed-off-by: Christoph Ruegg <git@cdrnet.ch>

src/MathNet.Numerics.4.5.resharper

@@ -13,7 +13,7 @@
               <UserWords>Wikipedia
 Cholesky
 Bluestein
-</UserWords>
+Chebyshev</UserWords>
             </CustomDictionary>
           </Dictionaries>
         </CustomDictionaries>
@@ -33,7 +33,7 @@ Bluestein
           </CommentMatch>
           <CommentNotMatch />
           <SuppressIfBaseHasComment>false</SuppressIfBaseHasComment>
-          <MaxLineLength>80</MaxLineLength>
+          <MaxLineLength>120</MaxLineLength>
         </CommentsSettings>
         <NamingConventionSettings>
           <Rules>
@@ -790,7 +790,9 @@ Bluestein
         <WRAP_OBJECT_AND_COLLECTION_INITIALIZER_STYLE>CHOP_ALWAYS</WRAP_OBJECT_AND_COLLECTION_INITIALIZER_STYLE>
         <WRAP_PARAMETERS_STYLE>CHOP_IF_LONG</WRAP_PARAMETERS_STYLE>
       </FormatSettings>
-      <UsingsSettings />
+      <UsingsSettings>
+        <AddImportsToDeepestScope>True</AddImportsToDeepestScope>
+      </UsingsSettings>
       <Naming2>
         <ExceptionName IsNull="False">
         </ExceptionName>

src/Numerics/Numerics.csproj

@@ -96,6 +96,8 @@
       <DesignTime>True</DesignTime>
       <DependentUpon>Resources.resx</DependentUpon>
     </Compile>
+    <Compile Include="Sampling\Sample.Chebyshev.cs" />
+    <Compile Include="Sampling\Sample.Equidistant.cs" />
     <Compile Include="SiConstants.cs" />
     <Compile Include="SiPrefixes.cs" />
     <Compile Include="Sorting.cs" />

src/Numerics/Sampling/Sample.Chebyshev.cs

@@ -0,0 +1,126 @@
+// <copyright file="Sample.Chebyshev.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics.Sampling
+{
+    using System;
+
+    /// <summary>
+    /// Generic Function Sampling and Quantization Provider
+    /// </summary>
+    public static partial class Sample
+    {
+        /// <summary>
+        /// Samples a function at the roots of the Chebyshev polynomial of the first kind.
+        /// </summary>
+        /// <param name="function">The real-domain function to sample.</param>
+        /// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
+        /// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>Vector of the function sampled in [a,b] at (b+a)/2+(b-1)/2*cos(pi*(2i-1)/(2n))</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException" />
+        public static T[] ChebyshevNodesFirstKind<T>(
+            Func<double, T> function,
+            double intervalBegin,
+            double intervalEnd,
+            int sampleCount)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 1)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            // transform to map to [-1..1] interval
+            double transformSummand = 0.5 * (intervalBegin + intervalEnd);
+            double transformFactor = 0.5 * (intervalEnd - intervalBegin);
+
+            // evaluate first kind chebyshev nodes
+            double angleFactor = Constants.Pi / (2 * sampleCount);
+
+            var samples = new T[sampleCount];
+
+            for (int i = 0; i < samples.Length; i++)
+            {
+                samples[i] = function(transformSummand + transformFactor * Math.Cos(((2 * i) + 1) * angleFactor));
+            }
+
+            return samples;
+        }
+
+        /// <summary>
+        /// Samples a function at the roots of the Chebyshev polynomial of the second kind.
+        /// </summary>
+        /// <param name="function">The real-domain function to sample.</param>
+        /// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
+        /// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>Vector of the function sampled in [a,b] at (b+a)/2+(b-1)/2*cos(pi*i/(n-1))</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException" />
+        public static T[] ChebyshevNodesSecondKind<T>(
+            Func<double, T> function,
+            double intervalBegin,
+            double intervalEnd,
+            int sampleCount)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 1)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            // transform to map to [-1..1] interval
+            double transformSummand = 0.5 * (intervalBegin + intervalEnd);
+            double transformFactor = 0.5 * (intervalEnd - intervalBegin);
+
+            // evaluate second kind chebyshev nodes
+            double angleFactor = Constants.Pi / (sampleCount + 1);
+
+            var samples = new T[sampleCount];
+
+            for (int i = 0; i < samples.Length; i++)
+            {
+                samples[i] = function(transformSummand + transformFactor * Math.Cos((i + 1) * angleFactor));
+            }
+
+            return samples;
+        }
+    }
+}

src/Numerics/Sampling/Sample.Equidistant.cs

@@ -0,0 +1,368 @@
+// <copyright file="Sample.Equidistant.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics.Sampling
+{
+    using System;
+    using System.Collections.Generic;
+
+    /// <summary>
+    /// Generic Function Sampling and Quantization Provider
+    /// </summary>
+    public static partial class Sample
+    {
+        /// <summary>
+        /// Samples a function equidistant within the provided interval.
+        /// </summary>
+        /// <param name="function">The real-domain function to sample.</param>
+        /// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
+        /// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>The generated sample vector.</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException" />
+        public static T[] EquidistantInterval<T>(
+            Func<double, T> function,
+            double intervalBegin,
+            double intervalEnd,
+            int sampleCount)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 0)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            if (sampleCount == 0)
+            {
+                return new T[0];
+            }
+
+            if (sampleCount == 1)
+            {
+                return new T[] { function(0.5 * (intervalBegin + intervalEnd)) };
+            }
+
+            var samples = new T[sampleCount];
+            var step = (intervalEnd - intervalBegin) / (sampleCount - 1);
+            var current = intervalBegin;
+
+            for (int i = 0; i < samples.Length - 1; i++)
+            {
+                samples[i] = function(current);
+                current += step;
+            }
+
+            samples[samples.Length - 1] = function(intervalEnd);
+
+            return samples;
+        }
+
+        /// <summary>
+        /// Samples a function equidistant within the provided interval.
+        /// </summary>
+        /// <param name="function">The real-domain function to sample.</param>
+        /// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
+        /// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <param name="samplePoints">The real domain points where the samples are taken at.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>The generated sample vector.</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException" />
+        public static T[] EquidistantInterval<T>(
+            Func<double, T> function,
+            double intervalBegin,
+            double intervalEnd,
+            int sampleCount,
+            out double[] samplePoints)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 0)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+            
+            if (sampleCount == 0)
+            {
+                samplePoints = new double[0];
+                return new T[0];
+            }
+
+            if (sampleCount == 1)
+            {
+                samplePoints = new[] { 0.5 * (intervalBegin + intervalEnd) };
+                return new T[] { function(samplePoints[0]) };
+            }
+
+            var samples = new T[sampleCount];
+            samplePoints = new double[sampleCount];
+            var step = (intervalEnd - intervalBegin) / (sampleCount - 1);
+            var current = intervalBegin;
+
+            for (int i = 0; i < samples.Length - 1; i++)
+            {
+                samplePoints[i] = current;
+                samples[i] = function(current);
+                current += step;
+            }
+
+            samplePoints[samplePoints.Length - 1] = intervalEnd;
+            samples[samples.Length - 1] = function(intervalEnd);
+
+            return samples;
+        }
+
+        /// <summary>
+        /// Samples a periodic function equidistant within one period, but omits the last sample such that the sequence
+        /// can be concatenated together.
+        /// </summary>
+        /// <param name="function">The real-domain function to sample.</param>
+        /// <param name="periodLength">The real domain full period length.</param>
+        /// <param name="periodOffset">The real domain offset where to start the sampling period.</param>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>The generated sample vector.</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException"/>
+        public static T[] EquidistantPeriodic<T>(
+            Func<double, T> function,
+            double periodLength,
+            double periodOffset,
+            int sampleCount)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 1)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            var samples = new T[sampleCount];
+            var step = periodLength / sampleCount;
+            var current = periodOffset;
+
+            for (int i = 0; i < samples.Length; i++)
+            {
+                samples[i] = function(current);
+                current += step;
+            }
+
+            return samples;
+        }
+
+        /// <summary>
+        /// Samples a periodic function equidistant within one period, but omits the last sample such that the sequence
+        /// can be concatenated together.
+        /// </summary>
+        /// <param name="function">The real-domain function to sample.</param>
+        /// <param name="periodLength">The real domain full period length.</param>
+        /// <param name="periodOffset">The real domain offset where to start the sampling period.</param>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <param name="samplePoints">The real domain points where the samples are taken at.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>The generated sample vector.</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException"/>
+        public static T[] EquidistantPeriodic<T>(
+            Func<double, T> function,
+            double periodLength,
+            double periodOffset,
+            int sampleCount,
+            out double[] samplePoints)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 1)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            var samples = new T[sampleCount];
+            samplePoints = new double[sampleCount];
+            var step = periodLength / sampleCount;
+            var current = periodOffset;
+
+            for (int i = 0; i < samples.Length; i++)
+            {
+                samplePoints[i] = current;
+                samples[i] = function(current);
+                current += step;
+            }
+
+            return samples;
+        }
+
+        /// <summary>
+        /// Samples a function equidistant 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>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>The generated sample vector.</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException"/>
+        public static T[] EquidistantStartingAt<T>(
+            Func<double, T> function,
+            double start,
+            double step,
+            int sampleCount)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 0)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            var samples = new T[sampleCount];
+            var current = start;
+
+            for (int i = 0; i < samples.Length; i++)
+            {
+                samples[i] = function(current);
+                current += step;
+            }
+
+            return samples;
+        }
+
+        /// <summary>
+        /// Samples a function equidistant 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>
+        /// <param name="sampleCount">The number of samples to generate.</param>
+        /// <param name="samplePoints">The real domain points where the samples are taken at.</param>
+        /// <typeparam name="T">The value type of the function to sample.</typeparam>
+        /// <returns>The generated sample vector.</returns>
+        /// <exception cref="ArgumentNullException" />
+        /// <exception cref="ArgumentOutOfRangeException"/>
+        public static T[] EquidistantStartingAt<T>(
+            Func<double, T> function,
+            double start,
+            double step,
+            int sampleCount,
+            out double[] samplePoints)
+        {
+            if (ReferenceEquals(function, null))
+            {
+                throw new ArgumentNullException("function");
+            }
+
+            if (sampleCount < 0)
+            {
+                throw new ArgumentOutOfRangeException("sampleCount");
+            }
+
+            var samples = new T[sampleCount];
+            samplePoints = new double[sampleCount];
+            var current = start;
+
+            for (int i = 0; i < samples.Length; i++)
+            {
+                samplePoints[i] = current;
+                samples[i] = function(current);
+                current += step;
+            }
+
+            return samples;
+        }
+
+        /// <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);
+        }
+    }
+}