/// <summary>
/// Main interpolation process (first way)
/// Applying both direct and backtrack cubic interpolation
/// </summary>
/// <param name="f0">The new F-value</param>
/// <returns>The new G-value</returns>
public double Interpolate(double f0)
{
if (!isValid)
{
return(double.NaN);
}
// filtering data in order to apply back interpolation
// remember that the second array (sourceF) has ordering type.
Filter.Process(1E-5, ref sourceF);
// Step 1. Operator F^-1 (backtrack process)
var engine = new Spline(sourceX, sourceF);
double value = engine.BackInterpolate(f0);
engine = null;
// Step 2. Operator G (direct process)
engine = new Spline(sourceX, sourceG);
double g0 = engine.Interpolate(value);
engine = null;
return(g0);
}
static void Main(string[] args)
{
long N = 37;
double[] srcX = new double[N],
srcY = new double[N];
for (long i = 0; i < N; i++)
{
srcX[i] = Math.Pow((double)i / (N - 1), 2.0);
srcY[i] = F(srcX[i]);
}
double testX = 0.54812;
var machine = new Spline(srcX, srcY);
double interpolatedY = machine.Interpolate(testX),
realY = F(testX);
double backInpterpolatedY = machine.BackInterpolate(interpolatedY);
double absErrorX = 100.0 * Math.Abs((testX - backInpterpolatedY) / testX),
absErrorY = 100.0 * Math.Abs((realY - interpolatedY) / realY);
Console.WriteLine("Source X: {0}\nInterpolated X: {1}\nAbsolute error X: {2} percents.\n",
testX, backInpterpolatedY, absErrorX);
Console.WriteLine("Source Y: {0}\nInterpolated Y: {1}\nAbsolute error Y: {2} percents.",
realY, interpolatedY, absErrorY);
Console.ReadLine();
}
/// <summary>
/// Interpolation with constant axis X and given new axis Y
/// Solution of problem:
/// F(x, y = y0) => G(x, y = y0) as F(x) => G(x)
/// </summary>
/// <param name="newY"></param>
/// <returns></returns>
public double[] Interpolate(double[] f)
{
if (!isValid)
{
return(null);
}
// First step: find the line y = f(x)
var exactFY = new double[sizeX];
for (long i = 0; i < sizeX; i++)
{
var tmpF = GetYByX(i, srcF); // X = x[i] = const, F(x) changes
var spline = new Spline(srcY, tmpF);
exactFY[i] = spline.BackInterpolate(f[i]); // get the correct point (Y[i], X[i])
spline = null;
}
// Second step: find the line y = g(x)
var newG = new double[sizeX];
for (long i = 0; i < sizeX; i++)
{
var tmpG = GetYByX(i, srcG); // X = x[i] = const, G(x) changes
var spline = new Spline(srcY, tmpG);
newG[i] = spline.Interpolate(exactFY[i]);
spline = null;
}
return(newG);
}
static void Main(string[] args)
{
#region Generate source
long NF = 10, NG = 17;
// Generate pairs ( x, f(x) )
double[] orgX = new double[NF];
double[] orgF = new double[NF];
orgX[0] = 0;
orgF[0] = f(orgX[0]);
for (long i = 1; i < orgX.LongLength; i++)
{
orgX[i] = orgX[i - 1] + Generate(0.1, 0.3);
orgF[i] = f(orgX[i]);
}
// Generate pairs ( x, g(x) )
double[] newX = new double[NG];
double[] newG = new double[NG];
double node = (orgX[orgX.LongLength - 1] - orgX[0]) / (newX.LongLength);
for (long i = 0; i < newX.LongLength; i++)
{
newX[i] = i * node + Generate(node) * Generate(0.5, 1);
newG[i] = g(newX[i]);
}
// Show source data
Console.WriteLine("\torgX\t\torgF\n ---------------------------");
for (long i = 0; i < orgX.LongLength; i++)
{
Console.WriteLine("\t{0:F4}\t{1}", orgX[i], orgF[i]);
}
Console.WriteLine("\n\tnewX\t\tnewG\n ---------------------------");
for (long i = 0; i < newX.LongLength; i++)
{
Console.WriteLine("\t{0:F4}\t{1}", newX[i], newG[i]);
}
#endregion
#region OperationTest
// Custom test
double testX = 0.572326;
double testF = f(testX);
double testG = g(testX);
// Mixing method
var orgFX = new Spline(orgX, orgF);
var newGX = new Spline(newX, newG);
double backtrackX = orgFX.BackInterpolate(testF);
double resultG = newGX.Interpolate(backtrackX);
double error = Math.Abs((testG - resultG) / testG);
Console.WriteLine("\n- Custom test #1: F(x) = {0}", testF);
Console.WriteLine("\n- Original X: {0}\n- Interpolated X: {1}", testX, backtrackX);
Console.WriteLine("\n- Original G(x): {0}\n- Interpolated G(x): {1}\n- Absolute error: {2}",
testG, resultG, error);
testF = (orgF[0] + orgF[orgF.LongLength - 1]) / 3 * 2;
resultG = newGX.Interpolate(orgFX.BackInterpolate(testF));
Console.WriteLine("\n\n- Custom test #2: F(x) = {0} -> G(x) = {1}", testF, resultG);
#endregion
Console.ReadKey();
}
