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Interpolation: migrate cubic spline to CubicSpline class

optimization-3
Christoph Ruegg 13 years ago
parent
fb35625def
commit
94b5c448e6
2 changed files with 173 additions and 34 deletions
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  1. 155
      src/Numerics/Interpolation/CubicSpline.cs
  2. 52
      src/UnitTests/InterpolationTests/CubicSplineTest.cs

155
src/Numerics/Interpolation/CubicSpline.cs
View File

@ -86,6 +86,11 @@ namespace MathNet.Numerics.Interpolation
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (xx.Length < 2)
{
throw new ArgumentOutOfRangeException("x");
}
Sorting.Sort(xx, yy, dd);
var c0 = new double[xx.Length - 1];
@ -122,6 +127,11 @@ namespace MathNet.Numerics.Interpolation
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (xx.Length < 5)
{
throw new ArgumentOutOfRangeException("x");
}
Sorting.Sort(xx, yy);
/* Prepare divided differences (diff) and weights (w) */
@ -160,6 +170,124 @@ namespace MathNet.Numerics.Interpolation
return InterpolateHermite(xx, yy, dd);
}
public static CubicSpline Interpolate(IEnumerable<double> x, IEnumerable<double> y)
{
return InterpolateBoundaries(x, y, SplineBoundaryCondition.SecondDerivative, 0.0, SplineBoundaryCondition.SecondDerivative, 0.0);
}
public static CubicSpline InterpolateBoundaries(IEnumerable<double> x, IEnumerable<double> y,
SplineBoundaryCondition leftBoundaryCondition, double leftBoundary,
SplineBoundaryCondition rightBoundaryCondition, double rightBoundary)
{
var xx = (x as double[]) ?? x.ToArray();
var yy = (y as double[]) ?? y.ToArray();
if (xx.Length != yy.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (xx.Length < 2)
{
throw new ArgumentOutOfRangeException("x");
}
Sorting.Sort(xx, yy);
int n = xx.Length;
// normalize special cases
if ((n == 2)
&& (leftBoundaryCondition == SplineBoundaryCondition.ParabolicallyTerminated)
&& (rightBoundaryCondition == SplineBoundaryCondition.ParabolicallyTerminated))
{
leftBoundaryCondition = SplineBoundaryCondition.SecondDerivative;
leftBoundary = 0d;
rightBoundaryCondition = SplineBoundaryCondition.SecondDerivative;
rightBoundary = 0d;
}
if (leftBoundaryCondition == SplineBoundaryCondition.Natural)
{
leftBoundaryCondition = SplineBoundaryCondition.SecondDerivative;
leftBoundary = 0d;
}
if (rightBoundaryCondition == SplineBoundaryCondition.Natural)
{
rightBoundaryCondition = SplineBoundaryCondition.SecondDerivative;
rightBoundary = 0d;
}
var a1 = new double[n];
var a2 = new double[n];
var a3 = new double[n];
var b = new double[n];
// Left Boundary
switch (leftBoundaryCondition)
{
case SplineBoundaryCondition.ParabolicallyTerminated:
a1[0] = 0;
a2[0] = 1;
a3[0] = 1;
b[0] = 2*(yy[1] - yy[0])/(xx[1] - xx[0]);
break;
case SplineBoundaryCondition.FirstDerivative:
a1[0] = 0;
a2[0] = 1;
a3[0] = 0;
b[0] = leftBoundary;
break;
case SplineBoundaryCondition.SecondDerivative:
a1[0] = 0;
a2[0] = 2;
a3[0] = 1;
b[0] = (3*((yy[1] - yy[0])/(xx[1] - xx[0]))) - (0.5*leftBoundary*(xx[1] - xx[0]));
break;
default:
throw new NotSupportedException(Resources.InvalidLeftBoundaryCondition);
}
// Central Conditions
for (int i = 1; i < xx.Length - 1; i++)
{
a1[i] = xx[i + 1] - xx[i];
a2[i] = 2*(xx[i + 1] - xx[i - 1]);
a3[i] = xx[i] - xx[i - 1];
b[i] = (3*(yy[i] - yy[i - 1])/(xx[i] - xx[i - 1])*(xx[i + 1] - xx[i])) + (3*(yy[i + 1] - yy[i])/(xx[i + 1] - xx[i])*(xx[i] - xx[i - 1]));
}
// Right Boundary
switch (rightBoundaryCondition)
{
case SplineBoundaryCondition.ParabolicallyTerminated:
a1[n - 1] = 1;
a2[n - 1] = 1;
a3[n - 1] = 0;
b[n - 1] = 2*(yy[n - 1] - yy[n - 2])/(xx[n - 1] - xx[n - 2]);
break;
case SplineBoundaryCondition.FirstDerivative:
a1[n - 1] = 0;
a2[n - 1] = 1;
a3[n - 1] = 0;
b[n - 1] = rightBoundary;
break;
case SplineBoundaryCondition.SecondDerivative:
a1[n - 1] = 1;
a2[n - 1] = 2;
a3[n - 1] = 0;
b[n - 1] = (3*(yy[n - 1] - yy[n - 2])/(xx[n - 1] - xx[n - 2])) + (0.5*rightBoundary*(xx[n - 1] - xx[n - 2]));
break;
default:
throw new NotSupportedException(Resources.InvalidRightBoundaryCondition);
}
// Build Spline
double[] dd = SolveTridiagonal(a1, a2, a3, b);
return InterpolateHermite(xx, yy, dd);
}
/// <summary>
/// Three-Point Differentiation Helper.
/// </summary>
@ -185,6 +313,33 @@ namespace MathNet.Numerics.Interpolation
return (2*a*t) + b;
}
/// <summary>
/// Tridiagonal Solve Helper.
/// </summary>
/// <param name="a">The a-vector[n].</param>
/// <param name="b">The b-vector[n], will be modified by this function.</param>
/// <param name="c">The c-vector[n].</param>
/// <param name="d">The d-vector[n], will be modified by this function.</param>
/// <returns>The x-vector[n]</returns>
static double[] SolveTridiagonal(double[] a, double[] b, double[] c, double[] d)
{
for (int k = 1; k < a.Length; k++)
{
double t = a[k]/b[k - 1];
b[k] = b[k] - (t*c[k - 1]);
d[k] = d[k] - (t*d[k - 1]);
}
var x = new double[a.Length];
x[x.Length - 1] = d[d.Length - 1]/b[b.Length - 1];
for (int k = x.Length - 2; k >= 0; k--)
{
x[k] = (d[k] - (c[k]*x[k + 1]))/b[k];
}
return x;
}
/// <summary>
/// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
/// </summary>

52
src/UnitTests/InterpolationTests/CubicSplineTest.cs
View File

@ -33,21 +33,11 @@ using NUnit.Framework;
namespace MathNet.Numerics.UnitTests.InterpolationTests
{
/// <summary>
/// CubicSpline Test case.
/// </summary>
[TestFixture, Category("Interpolation")]
public class CubicSplineTest
{
/// <summary>
/// Sample points.
/// </summary>
readonly double[] _t = { -2.0, -1.0, 0.0, 1.0, 2.0 };
/// <summary>
/// Sample values.
/// </summary>
readonly double[] _x = { 1.0, 2.0, -1.0, 0.0, 1.0 };
readonly double[] _y = { 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.
@ -55,11 +45,10 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
[Test]
public void NaturalFitsAtSamplePoints()
{
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x);
for (int i = 0; i < _x.Length; i++)
IInterpolation it = CubicSpline.Interpolate(_t, _y);
for (int i = 0; i < _y.Length; i++)
{
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
Assert.AreEqual(_y[i], it.Interpolate(_t[i]), "A Exact Point " + i);
}
}
@ -85,9 +74,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
[TestCase(-10.0, 677, 1e-12)]
public void NaturalFitsAtArbitraryPointsWithMaple(double t, double x, double maxAbsoluteError)
{
IInterpolation interpolation = new CubicSplineInterpolation(_t, _x);
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
IInterpolation it = CubicSpline.Interpolate(_t, _y);
Assert.AreEqual(x, it.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
}
/// <summary>
@ -96,11 +84,10 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
[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++)
IInterpolation it = CubicSpline.InterpolateBoundaries(_t, _y, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0);
for (int i = 0; i < _y.Length; i++)
{
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
Assert.AreEqual(_y[i], it.Interpolate(_t[i]), "A Exact Point " + i);
}
}
@ -126,9 +113,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
[TestCase(-10.0, 1330.1428571428571429, 1e-12)]
public void FixedFirstDerivativeFitsAtArbitraryPointsWithMaple(double t, double x, 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);
IInterpolation it = CubicSpline.InterpolateBoundaries(_t, _y, SplineBoundaryCondition.FirstDerivative, 1.0, SplineBoundaryCondition.FirstDerivative, -1.0);
Assert.AreEqual(x, it.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
}
/// <summary>
@ -137,11 +123,10 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
[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++)
IInterpolation it = CubicSpline.InterpolateBoundaries(_t, _y, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0);
for (int i = 0; i < _y.Length; i++)
{
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
Assert.AreEqual(_y[i], it.Interpolate(_t[i]), "A Exact Point " + i);
}
}
@ -167,9 +152,8 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
[TestCase(-10.0, -37, 1e-12)]
public void FixedSecondDerivativeFitsAtArbitraryPointsWithMaple(double t, double x, 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);
IInterpolation it = CubicSpline.InterpolateBoundaries(_t, _y, SplineBoundaryCondition.SecondDerivative, -5.0, SplineBoundaryCondition.SecondDerivative, -1.0);
Assert.AreEqual(x, it.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
}
/// <summary>
@ -183,10 +167,10 @@ namespace MathNet.Numerics.UnitTests.InterpolationTests
{
double[] x, y, xtest, ytest;
LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples);
IInterpolation interpolation = new CubicSplineInterpolation(x, y);
IInterpolation it = CubicSpline.Interpolate(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);
Assert.AreEqual(ytest[i], it.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
}
}
}

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