forked from tsai/mathnet-numerics
Christoph Ruegg
16 years ago
4 changed files with 388 additions and 0 deletions
@ -0,0 +1,97 @@ |
|||||
|
// <copyright file="AkimaSplineTest.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) 2002-2011 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.UnitTests.InterpolationTests |
||||
|
{ |
||||
|
using Interpolation; |
||||
|
using Interpolation.Algorithms; |
||||
|
using NUnit.Framework; |
||||
|
|
||||
|
[TestFixture] |
||||
|
public class AkimaSplineTest |
||||
|
{ |
||||
|
readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 }; |
||||
|
readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 }; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation matches the given value at all the provided sample points.
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void FitsAtSamplePoints() |
||||
|
{ |
||||
|
IInterpolation interpolation = new AkimaSplineInterpolation(_t, _x); |
||||
|
|
||||
|
for (int i = 0; i < _x.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
|
||||
|
/// </summary>
|
||||
|
[Test, Sequential] |
||||
|
public void FitsAtArbitraryPointsWithMaple( |
||||
|
[Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t, |
||||
|
[Values(-0.52, 1.826, 0.25, -1.006, -0.9, -0.6, 0.2, 9, -151)] double x, |
||||
|
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15)] double maxAbsoluteError) |
||||
|
{ |
||||
|
IInterpolation interpolation = new AkimaSplineInterpolation(_t, _x); |
||||
|
|
||||
|
// TODO: Verify the expected values (that they are really the expected ones)
|
||||
|
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation supports the linear case appropriately
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void SupportsLinearCase([Values(5, 7, 15)] int samples) |
||||
|
{ |
||||
|
double[] x, y, xtest, ytest; |
||||
|
LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples); |
||||
|
IInterpolation interpolation = new AkimaSplineInterpolation(x, y); |
||||
|
for (int i = 0; i < xtest.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,187 @@ |
|||||
|
// <copyright file="CubicSplineTest.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) 2002-2011 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.UnitTests.InterpolationTests |
||||
|
{ |
||||
|
using Interpolation; |
||||
|
using Interpolation.Algorithms; |
||||
|
using NUnit.Framework; |
||||
|
|
||||
|
[TestFixture] |
||||
|
public class CubicSplineTest |
||||
|
{ |
||||
|
readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 }; |
||||
|
readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 }; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation matches the given value at all the provided sample points.
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void NaturalFitsAtSamplePoints() |
||||
|
{ |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x); |
||||
|
|
||||
|
for (int i = 0; i < _x.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
|
||||
|
/// </summary>
|
||||
|
/// <remarks>
|
||||
|
/// Maple:
|
||||
|
/// with(CurveFitting);
|
||||
|
/// evalf(subs({x=-2.4},Spline([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x, degree=3, endpoints='natural')),20);
|
||||
|
/// </remarks>
|
||||
|
[Test, Sequential] |
||||
|
public void NaturalFitsAtArbitraryPointsWithMaple( |
||||
|
[Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t, |
||||
|
[Values(.144, 1.7906428571428571429, .47321428571428571431, -.80992857142857142857, -1.1089285714285714286, -1.0285714285714285714, .30285714285714285716, 189, 677)] double x, |
||||
|
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12)] double maxAbsoluteError) |
||||
|
{ |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x); |
||||
|
|
||||
|
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation matches the given value at all the provided sample points.
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void FixedFirstDerivativeFitsAtSamplePoints() |
||||
|
{ |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0); |
||||
|
|
||||
|
for (int i = 0; i < _x.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
|
||||
|
/// </summary>
|
||||
|
/// <remarks>
|
||||
|
/// Maple:
|
||||
|
/// with(CurveFitting);
|
||||
|
/// evalf(subs({x=-2.4},Spline([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x, degree=3, endpoints=[1,-1])),20);
|
||||
|
/// </remarks>
|
||||
|
[Test, Sequential] |
||||
|
public void FixedFirstDerivativeFitsAtArbitraryPointsWithMaple( |
||||
|
[Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t, |
||||
|
[Values(1.12, 1.8243928571428571428, .54910714285714285715, -.78903571428571428572, -1.1304642857142857143, -1.1040000000000000000, .4148571428571428571, -608.14285714285714286, 1330.1428571428571429)] double x, |
||||
|
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12, 1e-12)] double maxAbsoluteError) |
||||
|
{ |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0); |
||||
|
|
||||
|
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation matches the given value at all the provided sample points.
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void FixedSecondDerivativeFitsAtSamplePoints() |
||||
|
{ |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0); |
||||
|
|
||||
|
for (int i = 0; i < _x.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
|
||||
|
/// </summary>
|
||||
|
/// <remarks>
|
||||
|
/// Maple:
|
||||
|
/// with(CurveFitting);
|
||||
|
/// evalf(subs({x=-2.4},Spline([[-2,1],[-1,2],[0,-1],[1,0],[2,1]], x, degree=3, endpoints=Matrix(2,13,{(1,3)=1,(1,13)=-5,(2,10)=1,(2,13)=-1}))),20);
|
||||
|
/// </remarks>
|
||||
|
[Test, Sequential] |
||||
|
public void FixedSecondDerivativeFitsAtArbitraryPointsWithMaple( |
||||
|
[Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t, |
||||
|
[Values(-.8999999999999999993, 1.7590357142857142857, .41517857142857142854, -.82010714285714285714, -1.1026071428571428572, -1.0211428571428571429, .31771428571428571421, 39, -37)] double x, |
||||
|
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-13, 1e-12)] double maxAbsoluteError) |
||||
|
{ |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0); |
||||
|
|
||||
|
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation supports the linear case appropriately
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void NaturalSupportsLinearCase([Values(2, 4, 12)] int samples) |
||||
|
{ |
||||
|
double[] x, y, xtest, ytest; |
||||
|
LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples); |
||||
|
IInterpolation interpolation = new CubicSplineInterpolation(x, y); |
||||
|
for (int i = 0; i < xtest.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,101 @@ |
|||||
|
// <copyright file="LinearSplineTest.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) 2002-2011 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.UnitTests.InterpolationTests |
||||
|
{ |
||||
|
using Interpolation; |
||||
|
using Interpolation.Algorithms; |
||||
|
using NUnit.Framework; |
||||
|
|
||||
|
[TestFixture] |
||||
|
public class LinearSplineTest |
||||
|
{ |
||||
|
readonly double[] _t = new[] { -2.0, -1.0, 0.0, 1.0, 2.0 }; |
||||
|
readonly double[] _x = new[] { 1.0, 2.0, -1.0, 0.0, 1.0 }; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation matches the given value at all the provided sample points.
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void FitsAtSamplePoints() |
||||
|
{ |
||||
|
IInterpolation interpolation = new LinearSplineInterpolation(_t, _x); |
||||
|
|
||||
|
for (int i = 0; i < _x.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
|
||||
|
/// </summary>
|
||||
|
/// <remarks>
|
||||
|
/// Maple:
|
||||
|
/// f := x -> piecewise(x<-1,3+x,x<0,-1-3*x,x<1,-1+x,-1+x);
|
||||
|
/// f(x)
|
||||
|
/// </remarks>
|
||||
|
[Test, Sequential] |
||||
|
public void FitsAtArbitraryPointsWithMaple( |
||||
|
[Values(-2.4, -0.9, -0.5, -0.1, 0.1, 0.4, 1.2, 10.0, -10.0)] double t, |
||||
|
[Values(.6, 1.7, .5, -.7, -.9, -.6, .2, 9.0, -7.0)] double x, |
||||
|
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15)] double maxAbsoluteError) |
||||
|
{ |
||||
|
IInterpolation interpolation = new LinearSplineInterpolation(_t, _x); |
||||
|
|
||||
|
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t); |
||||
|
|
||||
|
double interpolatedValue; |
||||
|
double secondDerivative; |
||||
|
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative); |
||||
|
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t); |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Verifies that the interpolation supports the linear case appropriately
|
||||
|
/// </summary>
|
||||
|
[Test] |
||||
|
public void SupportsLinearCase([Values(2, 4, 12)] int samples) |
||||
|
{ |
||||
|
double[] x, y, xtest, ytest; |
||||
|
LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples); |
||||
|
IInterpolation interpolation = new LinearSplineInterpolation(x, y); |
||||
|
for (int i = 0; i < xtest.Length; i++) |
||||
|
{ |
||||
|
Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
} |
||||
Loading…
Reference in new issue