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Generate: port signal generation routines from neodym

optimization-3
Christoph Ruegg 13 years ago
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  1. 361
      src/Numerics/Generate.cs
  2. 1
      src/Numerics/Numerics.csproj
  3. 161
      src/UnitTests/GenerateTests.cs
  4. 1
      src/UnitTests/UnitTests.csproj

361
src/Numerics/Generate.cs
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@ -0,0 +1,361 @@
// <copyright file="Generate.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
// Copyright (c) 2009-2013 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>
using System;
using System.Collections.Generic;
using System.Linq;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.Random;
namespace MathNet.Numerics
{
public static class Generate
{
/// <summary>
/// Generate a linearly spaced sample vector of the given length between the specified values (inclusive).
/// Equivalent to MATLAB linspace but with the length as first instead of last argument.
/// </summary>
public static double[] LinearSpaced(int length, double start, double stop)
{
if (length <= 0) return new double[0];
if (length == 1) return new[] { stop };
double step = (stop - start)/(length - 1);
var data = new double[length];
for (int i = 0; i < data.Length; i++)
{
data[i] = start + i*step;
}
data[data.Length - 1] = stop;
return data;
}
/// <summary>
/// Generate a base 10 logarithmically spaced sample vector of the given length between the specified decade exponents (inclusive).
/// Equivalent to MATLAB logspace but with the length as first instead of last argument.
/// </summary>
public static double[] LogSpaced(int length, double startExponent, double stopExponent)
{
if (length <= 0) return new double[0];
if (length == 1) return new[] { Math.Pow(10, stopExponent) };
double step = (stopExponent - startExponent)/(length - 1);
var data = new double[length];
for (int i = 0; i < data.Length; i++)
{
data[i] = Math.Pow(10, startExponent + i*step);
}
data[data.Length - 1] = Math.Pow(10, stopExponent);
return data;
}
/// <summary>
/// Generate a linearly spaced sample vector within the inclusive interval (start, stop) and step 1.
/// Equivalent to MATLAB colon operator (:).
/// </summary>
public static double[] LinearRange(int start, int stop)
{
if (start == stop) return new double[] { start };
if (start < stop)
{
var data = new double[stop - start + 1];
for (int i = 0; i < data.Length; i++)
{
data[i] = start + i;
}
return data;
}
else
{
var data = new double[start - stop + 1];
for (int i = 0; i < data.Length; i++)
{
data[i] = start - i;
}
return data;
}
}
/// <summary>
/// Generate a linearly spaced sample vector within the inclusive interval (start, stop) and the provide step.
/// The start value is aways included as first value, but stop is only included if it stop-start is a multiple of step.
/// Equivalent to MATLAB double colon operator (::).
/// </summary>
public static double[] LinearRange(int start, int step, int stop)
{
if (start == stop) return new double[] { start };
if (start < stop && step < 0 || start > stop && step > 0 || step == 0d)
{
return new double[0];
}
var data = new double[(stop - start)/step + 1];
for (int i = 0; i < data.Length; i++)
{
data[i] = start + i*step;
}
return data;
}
/// <summary>
/// Generate a linearly spaced sample vector within the inclusive interval (start, stop) and the provide step.
/// The start value is aways included as first value, but stop is only included if it stop-start is a multiple of step.
/// Equivalent to MATLAB double colon operator (::).
/// </summary>
public static double[] LinearRange(double start, double step, double stop)
{
if (start == stop) return new double[] { start };
if (start < stop && step < 0 || start > stop && step > 0 || step == 0d)
{
return new double[0];
}
var data = new double[(int)Math.Floor((stop - start)/step + 1d)];
for (int i = 0; i < data.Length; i++)
{
data[i] = start + i*step;
}
return data;
}
/// <summary>
/// Create a Sine sample vector.
/// </summary>
/// <param name="length">The number of samples to generate.</param>
/// <param name="samplingRate">Samples per unit.</param>
/// <param name="frequency">Frequency in samples per unit.</param>
/// <param name="amplitude">The maximal reached peak.</param>
/// <param name="mean">The mean, or dc part, of the signal.</param>
/// <param name="phase">Optional phase offset.</param>
/// <param name="delay">Optional delay, relative to the phase.</param>
public static double[] Sinusoidal(int length, double samplingRate, double frequency, double amplitude, double mean = 0.0, double phase = 0.0, int delay = 0)
{
double step = frequency/samplingRate*Constants.Pi2;
phase = (phase - delay*step)%Constants.Pi2;
var data = new double[length];
for (int i = 0; i < length; i++)
{
data[i] = mean + amplitude*Math.Sin(phase + i*step);
}
return data;
}
/// <summary>
/// Create an infinite Sine sample sequence.
/// </summary>
/// <param name="samplingRate">Samples per unit.</param>
/// <param name="frequency">Frequency in samples per unit.</param>
/// <param name="amplitude">The maximal reached peak.</param>
/// <param name="mean">The mean, or dc part, of the signal.</param>
/// <param name="phase">Optional phase offset.</param>
/// <param name="delay">Optional delay, relative to the phase.</param>
public static IEnumerable<double> SinusoidalSequence(double samplingRate, double frequency, double amplitude, double mean = 0.0, double phase = 0.0, int delay = 0)
{
double step = frequency/samplingRate*Constants.Pi2;
phase = (phase - delay*step)%Constants.Pi2;
while (true)
{
for (int i = 0; i < 1000; i++)
{
yield return mean + amplitude*Math.Sin(phase + i*step);
}
phase = (phase + 1000*step)%Constants.Pi2;
}
}
/// <summary>
/// Create a Heaviside Step sample vector.
/// </summary>
/// <param name="length">The number of samples to generate.</param>
/// <param name="amplitude">The maximal reached peak.</param>
/// <param name="delay">Offset to the time axis.</param>
public static double[] Step(int length, double amplitude, int delay)
{
var data = new double[length];
for (int i = Math.Max(0, delay); i < data.Length; i++)
{
data[i] = amplitude;
}
return data;
}
/// <summary>
/// Create an infinite Heaviside Step sample sequence.
/// </summary>
/// <param name="amplitude">The maximal reached peak.</param>
/// <param name="delay">Offset to the time axis.</param>
public static IEnumerable<double> StepSequence(double amplitude, int delay)
{
for (int i = 0; i < delay; i++)
{
yield return 0d;
}
while (true)
{
yield return amplitude;
}
}
/// <summary>
/// Create a Dirac Delta Impulse sample vector.
/// </summary>
/// <param name="length">The number of samples to generate.</param>
/// <param name="period">impulse sequence period. -1 for single impulse only.</param>
/// <param name="amplitude">The maximal reached peak.</param>
/// <param name="delay">Offset to the time axis. Zero or positive.</param>
public static double[] Impulse(int length, int period, double amplitude, int delay)
{
var data = new double[length];
if (period <= 0)
{
if (delay >= 0 && delay < length)
{
data[delay] = amplitude;
}
}
else
{
delay = ((delay%period) + period)%period;
while (delay < length)
{
data[delay] = amplitude;
delay += period;
}
}
return data;
}
/// <summary>
/// Create a Dirac Delta Impulse sample vector.
/// </summary>
/// <param name="period">impulse sequence period. -1 for single impulse only.</param>
/// <param name="amplitude">The maximal reached peak.</param>
/// <param name="delay">Offset to the time axis. Zero or positive.</param>
public static IEnumerable<double> ImpulseSequence(int period, double amplitude, int delay)
{
if (period <= 0)
{
for (int i = 0; i < delay; i++)
{
yield return 0d;
}
yield return amplitude;
while (true)
{
yield return 0d;
}
}
else
{
delay = ((delay%period) + period)%period;
for (int i = 0; i < delay; i++)
{
yield return 0d;
}
while (true)
{
yield return amplitude;
for (int i = 1; i < period; i++)
{
yield return 0d;
}
}
}
}
/// <summary>
/// Create random samples.
/// </summary>
public static double[] Random(int length, IContinuousDistribution distribution)
{
return distribution.Samples().Take(length).ToArray();
}
/// <summary>
/// Create an infinite random sample sequence.
/// </summary>
public static IEnumerable<double> Random(IContinuousDistribution distribution)
{
return distribution.Samples();
}
/// <summary>
/// Create samples with independent amplitudes of normal distribution and a flat spectral density.
/// </summary>
public static double[] WhiteGaussianNoise(int length, double mean, double standardDeviation)
{
return Normal.Samples(MersenneTwister.Default, mean, standardDeviation).Take(length).ToArray();
}
/// <summary>
/// Create an infinite sample sequence with independent amplitudes of normal distribution and a flat spectral density.
/// </summary>
public static IEnumerable<double> WhiteGaussianNoiseSequence(double mean, double standardDeviation)
{
return Normal.Samples(MersenneTwister.Default, mean, standardDeviation);
}
/// <summary>
/// Create skew alpha stable samples.
/// </summary>
/// <param name="length">The number of samples to generate.</param>
/// <param name="alpha">Stability alpha-parameter of the stable distribution</param>
/// <param name="beta">Skewness beta-parameter of the stable distribution</param>
/// <param name="scale">Scale c-parameter of the stable distribution</param>
/// <param name="location">Location mu-parameter of the stable distribution</param>
public static double[] StableNoise(int length, double alpha, double beta, double scale, double location)
{
return Stable.Samples(MersenneTwister.Default, alpha, beta, scale, location).Take(length).ToArray();
}
/// <summary>
/// Create skew alpha stable samples.
/// </summary>
/// <param name="alpha">Stability alpha-parameter of the stable distribution</param>
/// <param name="beta">Skewness beta-parameter of the stable distribution</param>
/// <param name="scale">Scale c-parameter of the stable distribution</param>
/// <param name="location">Location mu-parameter of the stable distribution</param>
public static IEnumerable<double> StableNoiseSequence(double alpha, double beta, double scale, double location)
{
return Stable.Samples(MersenneTwister.Default, alpha, beta, scale, location);
}
}
}

1
src/Numerics/Numerics.csproj
View File

@ -87,6 +87,7 @@
<Reference Include="System.Xml" />
</ItemGroup>
<ItemGroup>
<Compile Include="Generate.cs" />
<Compile Include="GoodnessOfFit.cs" />
<Compile Include="Precision.Comparison.cs" />
<Compile Include="Precision.Equality.cs" />

161
src/UnitTests/GenerateTests.cs
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@ -0,0 +1,161 @@
// <copyright file="GenerateTests.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
// Copyright (c) 2009-2013 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>
using System;
using System.Linq;
using NUnit.Framework;
namespace MathNet.Numerics.UnitTests
{
[TestFixture]
public class GenerateTests
{
[Test]
public void LinearSpaced()
{
Assert.That(Generate.LinearSpaced(0, 0d, 2d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearSpaced(1, 0d, 2d), Is.EqualTo(new[] { 2d }).AsCollection);
Assert.That(Generate.LinearSpaced(2, 0d, 2d), Is.EqualTo(new[] { 0d, 2d }).AsCollection);
Assert.That(Generate.LinearSpaced(3, 0d, 2d), Is.EqualTo(new[] { 0d, 1d, 2d }).AsCollection);
Assert.That(Generate.LinearSpaced(4, 0d, 2d), Is.EqualTo(new[] { 0d, 2d/3d, 4d/3d, 2d }).Within(1e-12).AsCollection);
Assert.That(Generate.LinearSpaced(0, 2d, 0d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearSpaced(1, 2d, 0d), Is.EqualTo(new[] { 0d }).AsCollection);
Assert.That(Generate.LinearSpaced(2, 2d, 0d), Is.EqualTo(new[] { 2d, 0d }).AsCollection);
Assert.That(Generate.LinearSpaced(3, 2d, 0d), Is.EqualTo(new[] { 2d, 1d, 0d }).AsCollection);
Assert.That(Generate.LinearSpaced(4, 2d, 0d), Is.EqualTo(new[] { 2d, 4d/3d, 2d/3d, 0d }).Within(1e-12).AsCollection);
}
[Test]
public void LogSpaced()
{
Assert.That(Generate.LogSpaced(0, 0d, 2d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LogSpaced(1, 0d, 2d), Is.EqualTo(new[] { 100.0 }).AsCollection);
Assert.That(Generate.LogSpaced(2, 0d, 2d), Is.EqualTo(new[] { 1.0, 100.0 }).AsCollection);
Assert.That(Generate.LogSpaced(3, 0d, 2d), Is.EqualTo(new[] { 1.0, 10.0, 100.0 }).AsCollection);
Assert.That(Generate.LogSpaced(4, 0d, 2d), Is.EqualTo(new[] { 1.0, Math.Pow(10.0, 2.0/3.0), Math.Pow(10.0, 4.0/3.0), 100.0 }).Within(1e-12).AsCollection);
Assert.That(Generate.LogSpaced(0, 2d, 0d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LogSpaced(1, 2d, 0d), Is.EqualTo(new[] { 1.0 }).AsCollection);
Assert.That(Generate.LogSpaced(2, 2d, 0d), Is.EqualTo(new[] { 100.0, 1.0 }).AsCollection);
Assert.That(Generate.LogSpaced(3, 2d, 0d), Is.EqualTo(new[] { 100.0, 10.0, 1.0 }).AsCollection);
Assert.That(Generate.LogSpaced(4, 2d, 0d), Is.EqualTo(new[] { 100.0, Math.Pow(10.0, 4.0/3.0), Math.Pow(10, 2.0/3.0), 1.0 }).Within(1e-12).AsCollection);
Assert.That(Generate.LogSpaced(5, -2d, 2d), Is.EqualTo(new[] { 0.01, 0.1, 1.0, 10.0, 100.0 }).AsCollection);
Assert.That(Generate.LogSpaced(5, 2d, -2d), Is.EqualTo(new[] { 100.0, 10.0, 1.0, 0.1, 0.01 }).AsCollection);
}
[Test]
public void LinearRange()
{
Assert.That(Generate.LinearRange(1, 1), Is.EqualTo(new[] { 1d }).AsCollection);
Assert.That(Generate.LinearRange(1, 3), Is.EqualTo(new[] { 1d, 2d, 3d }).AsCollection);
Assert.That(Generate.LinearRange(-1, -3), Is.EqualTo(new[] { -1d, -2d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(-3, -1), Is.EqualTo(new[] { -3d, -2d, -1d }).AsCollection);
Assert.That(Generate.LinearRange(1, -2), Is.EqualTo(new[] { 1d, 0d, -1d, -2d }).AsCollection);
}
[Test]
public void LinearRangeStep()
{
Assert.That(Generate.LinearRange(1, 1, 1), Is.EqualTo(new[] { 1d }).AsCollection);
Assert.That(Generate.LinearRange(1, -1, 2), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(2, 1, 1), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(1, 0, 2), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(2, 0, 1), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(1, 1, 5), Is.EqualTo(new[] { 1d, 2d, 3d, 4d, 5d }).AsCollection);
Assert.That(Generate.LinearRange(1, 2, 5), Is.EqualTo(new[] { 1d, 3d, 5d }).AsCollection);
Assert.That(Generate.LinearRange(1, 2, 6), Is.EqualTo(new[] { 1d, 3d, 5d }).AsCollection);
Assert.That(Generate.LinearRange(1, 2, 4), Is.EqualTo(new[] { 1d, 3d }).AsCollection);
Assert.That(Generate.LinearRange(1, -1, -3), Is.EqualTo(new[] { 1d, 0d, -1d, -2d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(1, -2, -3), Is.EqualTo(new[] { 1d, -1d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(1, -2, -4), Is.EqualTo(new[] { 1d, -1d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(1, -2, -2), Is.EqualTo(new[] { 1d, -1d }).AsCollection);
}
[Test]
public void LinearRangeFloatingPoint()
{
Assert.That(Generate.LinearRange(1d, 1d, 1d), Is.EqualTo(new[] { 1d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -1d, 2d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(2d, 1d, 1d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(1d, 0d, 2d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(2d, 0d, 1d), Is.EqualTo(new double[0]).AsCollection);
Assert.That(Generate.LinearRange(1d, 1d, 5d), Is.EqualTo(new[] { 1d, 2d, 3d, 4d, 5d }).AsCollection);
Assert.That(Generate.LinearRange(1d, 2d, 5d), Is.EqualTo(new[] { 1d, 3d, 5d }).AsCollection);
Assert.That(Generate.LinearRange(1d, 2d, 6d), Is.EqualTo(new[] { 1d, 3d, 5d }).AsCollection);
Assert.That(Generate.LinearRange(1d, 2d, 4d), Is.EqualTo(new[] { 1d, 3d }).AsCollection);
Assert.That(Generate.LinearRange(1d, 1.5d, 5d), Is.EqualTo(new[] { 1d, 2.5d, 4d }).AsCollection);
Assert.That(Generate.LinearRange(1d, 1.5d, 6.5d), Is.EqualTo(new[] { 1d, 2.5d, 4d, 5.5d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -1d, -3d), Is.EqualTo(new[] { 1d, 0d, -1d, -2d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -2d, -3d), Is.EqualTo(new[] { 1d, -1d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -2d, -4d), Is.EqualTo(new[] { 1d, -1d, -3d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -2d, -2d), Is.EqualTo(new[] { 1d, -1d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -1.5d, -3d), Is.EqualTo(new[] { 1d, -0.5d, -2d }).AsCollection);
Assert.That(Generate.LinearRange(1d, -1.5d, -3.5d), Is.EqualTo(new[] { 1d, -0.5d, -2d, -3.5 }).AsCollection);
Assert.That(Generate.LinearRange(1d, -1.5d, -4d), Is.EqualTo(new[] { 1d, -0.5d, -2d, -3.5 }).AsCollection);
}
[Test]
public void SinusoidalConsistentWithSequence()
{
Assert.That(
Generate.SinusoidalSequence(32, 2, 5, 1, 0.5, -6).Take(1000).ToArray(),
Is.EqualTo(Generate.Sinusoidal(1000, 32, 2, 5, 1, 0.5, -6)).AsCollection);
}
[Test]
public void StepConsistentWithSequence()
{
Assert.That(
Generate.StepSequence(5, 40).Take(1000).ToArray(),
Is.EqualTo(Generate.Step(1000, 5, 40)).AsCollection);
}
[Test]
public void ImpulseConsistentWithSequence()
{
Assert.That(
Generate.ImpulseSequence(0, 5, 40).Take(1000).ToArray(),
Is.EqualTo(Generate.Impulse(1000, 0, 5, 40)).AsCollection);
Assert.That(
Generate.ImpulseSequence(100, 5, 40).Take(1000).ToArray(),
Is.EqualTo(Generate.Impulse(1000, 100, 5, 40)).AsCollection);
}
}
}

1
src/UnitTests/UnitTests.csproj
View File

@ -133,6 +133,7 @@
<Compile Include="FinancialTests\GainMeanTests.cs" />
<Compile Include="FinancialTests\LossStandardDeviationTests.cs" />
<Compile Include="FinancialTests\SemiDeviationTests.cs" />
<Compile Include="GenerateTests.cs" />
<Compile Include="GoodnessOfFit\RSquaredTest.cs" />
<Compile Include="IntegralTransformsTests\FourierTest.cs" />
<Compile Include="IntegralTransformsTests\HartleyTest.cs" />

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