/// <summary>
/// Perform a SVD fit.
/// </summary>
/// <param name="x">The X matrix.</param>
/// <param name="y">The Y matrix.</param>
/// <param name="a">The A matrix.</param>
/// <param name="funcs">The RBF functions.</param>
/// <returns>The fit.</returns>
public static double Svdfit(double[][] x, double[][] y, double[][] a,
IRadialBasisFunction[] funcs)
{
int i, j, k;
double wmax, tmp, thresh, sum, TOL = 1e-13d;
//Allocated memory for svd matrices
double[][] u = EngineArray.AllocateDouble2D(x.Length, funcs.Length);
double[][] v = EngineArray.AllocateDouble2D(funcs.Length, funcs.Length);
var w = new double[funcs.Length];
//Fill input matrix with values based on fitting functions and input coordinates
for (i = 0; i < x.Length; i++)
{
for (j = 0; j < funcs.Length; j++)
{
u[i][j] = funcs[j].Calculate(x[i]);
}
}
//Perform decomposition
Svdcmp(u, w, v);
//Check for w values that are close to zero and replace them with zeros such that they are ignored in backsub
wmax = 0;
for (j = 0; j < funcs.Length; j++)
{
if (w[j] > wmax)
{
wmax = w[j];
}
}
thresh = TOL * wmax;
for (j = 0; j < funcs.Length; j++)
{
if (w[j] < thresh)
{
w[j] = 0;
}
}
//Perform back substitution to get result
Svdbksb(u, w, v, y, a);
//Calculate chi squared for the fit
double chisq = 0;
for (k = 0; k < y[0].Length; k++)
{
for (i = 0; i < y.Length; i++)
{
sum = 0.0d;
for (j = 0; j < funcs.Length; j++)
{
sum += a[j][k] * funcs[j].Calculate(x[i]);
}
tmp = (y[i][k] - sum);
chisq += tmp * tmp;
}
}
return(Math.Sqrt(chisq / (y.Length * y[0].Length)));
}
