Init(
IList <double> t,
IList <double> x
)
{
if (null == t)
{
throw new ArgumentNullException("t");
}
if (null == x)
{
throw new ArgumentNullException("x");
}
if (t.Count < 5)
{
throw new ArgumentOutOfRangeException("t");
}
if (t.Count != x.Count)
{
throw new ArgumentException(Properties.Resources.ArgumentVectorsSameLengths, "x");
}
int n = t.Count;
double[] tt = new double[n];
t.CopyTo(tt, 0);
double[] xx = new double[n];
x.CopyTo(xx, 0);
Sorting.Sort(tt, xx);
// Prepare W (weights), Diff (divided differences)
double[] w = new double[n - 1];
double[] diff = new double[n - 1];
for (int i = 0; i < diff.Length; i++)
{
diff[i] = (xx[i + 1] - xx[i]) / (tt[i + 1] - tt[i]);
}
for (int i = 1; i < w.Length; i++)
{
w[i] = Math.Abs(diff[i] - diff[i - 1]);
}
// Prepare Hermite interpolation scheme
double[] d = new double[n];
for (int i = 2; i < d.Length - 2; i++)
{
if (!Number.AlmostZero(w[i - 1]) || !Number.AlmostZero(w[i + 1]))
{
d[i] = (w[i + 1] * diff[i - 1] + w[i - 1] * diff[i]) / (w[i + 1] + w[i - 1]);
}
else
{
d[i] = ((tt[i + 1] - tt[i]) * diff[i - 1] + (tt[i] - tt[i - 1]) * diff[i]) / (tt[i + 1] - tt[i - 1]);
}
}
d[0] = DifferentiateThreePoint(tt[0], tt[0], xx[0], tt[1], xx[1], tt[2], xx[2]);
d[1] = DifferentiateThreePoint(tt[1], tt[0], xx[0], tt[1], xx[1], tt[2], xx[2]);
d[n - 2] = DifferentiateThreePoint(tt[n - 2], tt[n - 3], xx[n - 3], tt[n - 2], xx[n - 2], tt[n - 1], xx[n - 1]);
d[n - 1] = DifferentiateThreePoint(tt[n - 1], tt[n - 3], xx[n - 3], tt[n - 2], xx[n - 2], tt[n - 1], xx[n - 1]);
// Build Akima spline using Hermite interpolation scheme
_hermiteSpline.InitInternal(tt, xx, d);
}
Init(
IList <double> t,
IList <double> x,
SplineBoundaryCondition leftBoundaryCondition,
double leftBoundary,
SplineBoundaryCondition rightBoundaryCondition,
double rightBoundary
)
{
if (null == t)
{
throw new ArgumentNullException("t");
}
if (null == x)
{
throw new ArgumentNullException("x");
}
if (t.Count < 2)
{
throw new ArgumentOutOfRangeException("t");
}
if (t.Count != x.Count)
{
throw new ArgumentException(Properties.Resources.ArgumentVectorsSameLengths, "x");
}
int n = t.Count;
double[] tt = new double[n];
t.CopyTo(tt, 0);
double[] xx = new double[n];
x.CopyTo(xx, 0);
Sorting.Sort(tt, xx);
// 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;
}
double[] a1 = new double[n];
double[] a2 = new double[n];
double[] a3 = new double[n];
double[] b = new double[n];
// Left Boundary
switch (leftBoundaryCondition)
{
case SplineBoundaryCondition.ParabolicallyTerminated:
a1[0] = 0;
a2[0] = 1;
a3[0] = 1;
b[0] = 2 * (xx[1] - xx[0]) / (tt[1] - tt[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 * (xx[1] - xx[0]) / (tt[1] - tt[0]) - 0.5 * leftBoundary * (tt[1] - tt[0]);
break;
default:
throw new NotSupportedException(Properties.Resources.InvalidLeftBoundaryCondition);
}
// Central Conditions
for (int i = 1; i < tt.Length - 1; i++)
{
a1[i] = tt[i + 1] - tt[i];
a2[i] = 2 * (tt[i + 1] - tt[i - 1]);
a3[i] = tt[i] - tt[i - 1];
b[i] = 3 * (xx[i] - xx[i - 1]) / (tt[i] - tt[i - 1]) * (tt[i + 1] - tt[i]) + 3 * (xx[i + 1] - xx[i]) / (tt[i + 1] - tt[i]) * (tt[i] - tt[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 * (xx[n - 1] - xx[n - 2]) / (tt[n - 1] - tt[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 * (xx[n - 1] - xx[n - 2]) / (tt[n - 1] - tt[n - 2]) + 0.5 * rightBoundary * (tt[n - 1] - tt[n - 2]);
break;
default:
throw new NotSupportedException(Properties.Resources.InvalidRightBoundaryCondition);
}
// Build Spline
double[] dd = SolveTridiagonal(a1, a2, a3, b);
_hermiteSpline.InitInternal(tt, xx, dd);
}