public void CalculateHessian(Multiplet exp, out Matrix <double> Hess, out Matrix <double> Grad)
{
int i, size;
//MathNet.Numerics.LinearAlgebra.Matrix<double> Hessian;
double ro2, ro4, ro6, res, delta;
size = exp.u2.Count;
Matrix <double> Res = Matrix <double> .Build.Dense(size, 1);
delta = 1e-26;
Matrix <double> Jaco = Matrix <double> .Build.Dense(size, 3);
//cout <<"Debug " <<o2<<" "<<o4<<" "<<o6<<std::endl;
for (i = 0; i < size; i++)
{
res = Residue(exp.fexp[i], exp.o2, exp.o4, exp.o6, exp.u2[i], exp.u4[i], exp.u6[i], exp.lambda0[i], exp.n, exp.TwoJPlusOne);
ro2 = Residue(exp.fexp[i], exp.o2 + delta, exp.o4, exp.o6, exp.u2[i], exp.u4[i], exp.u6[i], exp.lambda0[i], exp.n, exp.TwoJPlusOne);
ro4 = Residue(exp.fexp[i], exp.o2, exp.o4 + delta, exp.o6, exp.u2[i], exp.u4[i], exp.u6[i], exp.lambda0[i], exp.n, exp.TwoJPlusOne);
ro6 = Residue(exp.fexp[i], exp.o2, exp.o4, exp.o6 + delta, exp.u2[i], exp.u4[i], exp.u6[i], exp.lambda0[i], exp.n, exp.TwoJPlusOne);
Jaco[i, 0] = (ro2 - res) / delta;
Jaco[i, 1] = (ro4 - res) / delta;
Jaco[i, 2] = (ro6 - res) / delta;
Res[i, 0] = res;
}
;
//Console.WriteLine("Jacobian");
//Console.WriteLine(Jaco.ToString());
Hess = Jaco.Transpose() * Jaco;
Grad = Jaco.Transpose() * Res;
/* std::cout <<"_________________________________"<<std::endl;
* std::cout << Hess<<std::endl;
* std::cout <<"_________________________________"<<std::endl;*/
}
public double Chi2new(Multiplet exp, double no2, double no4, double no6)
{
double to2 = exp.o2;
double to4 = exp.o4;
double to6 = exp.o6;
double rv;
exp.o2 = no2;
exp.o4 = no4;
exp.o6 = no6;
rv = Chi2(exp);
exp.o2 = to2;
exp.o4 = to4;
exp.o6 = to6;
return(rv);
}
public double Chi2(Multiplet exp)
{
int size;
double tempchi2 = 0;
//Console.WriteLine(exp.o2 + " " + exp.o4 + " " + exp.o6);
size = exp.u2.Count;
for (int i = 0; i < size; i++)
{
double tf = F(exp.u2[i], exp.u4[i], exp.u6[i], exp.lambda0[i], exp.n, exp.TwoJPlusOne, exp.o2, exp.o4, exp.o6);
//Console.WriteLine(tf.ToString("G4")+" "+exp.fexp[i].ToString("G4"));
//Console.WriteLine(tf/1.488E-07);
tempchi2 += Pow(tf - exp.fexp[i], 2);
}
;
return(tempchi2);
}
private void DumpFitResult(Multiplet exp, ref string MSG, ref string LATEX, System.Diagnostics.Stopwatch sw, Matrix <double> Hessiandiag, ref double sumfexp, ref double sumdfexp, double chi2n)
{
Vector <double> error;
int size = exp.u2.Count;
error = (Hessiandiag.Inverse().Diagonal() * chi2n / (size - 3));
for (int i = 0; i < 3; i++)
{
error[i] = Abs(Sqrt(error[i]));
}
Console.WriteLine("Errors " + error[0].ToString("F3") + " " + error[1].ToString("F3") + " " + error[2].ToString("F3"));
MSG += "Parameters\t o2=" + exp.o2.ToString("G4") + "\t o4=" + exp.o4.ToString("G4") + "\t o6=" + exp.o6.ToString("G4") + "\r\n";
MSG += "Errors \t do2=" + error[0].ToString("G2") + "\t do4=" + error[1].ToString("G2") + "\t do6=" + error[2].ToString("G2") + "\r\n";
//LATEX+="$\\Omega_2$ ="+mantissa(o2).ToString("G4")+"$\\cdot$ 10$^{"+exponent(o2)+"}$ $\\Omega_4$ ="+mantissa(o4).ToString("G4")+"$\\cdot$ 10$^{"+exponent(o4)+"}$ $\\Omega_6$ ="+mantissa(o6).ToString("G4")+"$\\cdot$ 10$^{"+exponent(o6)+"}$ \\\\ \r\n";
LATEX += "$\\Omega_2$ =" + Lf(exp.o2) + " $\\Omega_4$ =" + Lf(exp.o4) + " $\\Omega_6$ =" + Lf(exp.o6) + "\\\\ \r\n";
LATEX += "$\\Delta\\Omega_2$ =" + Lf(error[0]) + " $\\Delta\\Omega_4$ =" + Lf(error[1]) + " $\\Delta\\Omega_6$ =" + Lf(error[2]) + " \\\\ \r\n";
Console.WriteLine("Relative errors " + (100 * error[0] / exp.o2).ToString("G3") + "% " + (100 * error[1] / exp.o4).ToString("G3") + "% " + (100 * error[2] / exp.o6).ToString("G3") + "%");
MSG += "Relative errors \t" + (100 * error[0] / exp.o2).ToString("G3") + "%\t" + (100 * error[1] / exp.o4).ToString("G3") + "%\t" + (100 * error[2] / exp.o6).ToString("G3") + "% \r\n";
LATEX += "$\\frac{\\Delta\\Omega_2}{\\Omega_2}=$" + (100 * error[0] / exp.o2).ToString("G3") + "\\% $\\frac{\\Delta\\Omega_4}{\\Omega_4}=$" + (100 * error[1] / exp.o4).ToString("G3") + "\\% $\\frac{\\Delta\\Omega_6}{\\Omega_6}=$" + (100 * error[2] / exp.o6).ToString("G3") + " \\% \\\\\r\n";
Console.WriteLine("Effective relative error " + (100 * (error[0] / exp.o2 + error[1] / exp.o4 + error[2] / exp.o6)).ToString("G3") + "%");
LATEX += "$\\frac{\\Delta f}{f}=$ " + (100 * (error[0] / exp.o2 + error[1] / exp.o4 + error[2] / exp.o6)).ToString("G3") + "\\% \r\n";
MSG += "Wavenumber\tPexp\tPtheor\t(Pexp-Ptheor)/Pexp \r\n";
for (int i = 0; i < size; i++)
{
double ftheor;
ftheor = F(exp.u2[i], exp.u4[i], exp.u6[i], exp.lambda0[i], exp.n, exp.TwoJPlusOne, exp.o2, exp.o4, exp.o6);
sumdfexp += Abs(Pow((exp.fexp[i] - ftheor), 2));
sumfexp += exp.fexp[i] / size;
Console.WriteLine(exp.fexp[i].ToString("G3") + " " + ftheor.ToString("G3") + " " + ((exp.fexp[i] - ftheor) / exp.fexp[i]).ToString("G3"));
MSG += (1.0 / exp.lambda0[i]).ToString() + "\t" + exp.fexp[i].ToString("G4") + "\t" + ftheor.ToString("G4") + "\t" + (Abs(100 * (exp.fexp[i] - ftheor) / exp.fexp[i])).ToString("G4") + "%\r\n";
}
MSG += "-----------------------------------------------\r\n";
Console.WriteLine("-----------------------------------------------");
Console.WriteLine("RMS = " + Sqrt(sumdfexp / (size - 3)) + " RMS/avg f " + 100 * Sqrt(sumdfexp / (size - 3)) / sumfexp + "%");
LATEX += "RMS = " + Lf(Sqrt(sumdfexp / (size - 3))) + "$\\frac{RMS}{\\underline{f}}$= " + (100 * Sqrt(sumdfexp / (size - 3)) / sumfexp).ToString("G3") + "\\%\r\n\r\n";
MSG += "RMS = " + Sqrt(sumdfexp / (size - 3)).ToString("G4") + " RMS/avg f = " + (100 * Sqrt(sumdfexp / (size - 3)) / sumfexp).ToString("G3") + "% \r\n";
Console.WriteLine("Fitting procedure took " + sw.ElapsedMilliseconds / 1000.0 + " seconds");
return;
}
public void FitLM(Multiplet exp, out string MSG, out string LATEX)
{
System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
sw.Start();
//Matrix<double> Grad;
Matrix <double> Hessiandiag;
Matrix <double> parameters = Matrix <double> .Build.Dense(3, 1);
Matrix <double> newparams;// = Matrix<double>.Build.Dense(3, 1);
//Vector<double> error;// = Vector<double>.Build.Dense(3);
LATEX = "";
parameters[0, 0] = exp.o2;
parameters[1, 0] = exp.o4;
parameters[2, 0] = exp.o6;
double no2, no4, no6, sumfexp, sumdfexp;
double lambda, chi2s, chi2n;
lambda = 1 / 1024.0;
sumdfexp = 0;
sumfexp = 0;
// chi2s = 0;
chi2n = 0;
Hessiandiag = Matrix <double> .Build.Dense(3, 3, 1);
MSG = "Num.\tChi2\tO2\tO4\tO6\r\n";
Console.WriteLine("Beginnig fitting procedure.");
for (int i = 1; i < 10; i++)
{
chi2s = Chi2(exp);
CalculateHessian(exp, out Matrix <double> Hessian, out Matrix <double> Grad);
/*Console.WriteLine("gradient");
* Console.WriteLine(Grad.ToString());
* Console.WriteLine("hessian");
* Console.WriteLine(Hessian.ToString());
*/
Hessiandiag = Matrix <double> .Build.DiagonalOfDiagonalVector(Hessian.Diagonal());
//Console.WriteLine(Hessiandiag.ToString());
newparams = parameters - ((Hessian + lambda * Hessiandiag).Inverse() * Grad);
//Console.WriteLine(newparams.ToString());
no2 = (newparams[0, 0]);
no4 = (newparams[1, 0]);
no6 = (newparams[2, 0]);
chi2n = Chi2new(exp, no2, no4, no6);
Console.WriteLine(i + " " + chi2s.ToString("G6") + " " + no2.ToString("G6") + " " + no4.ToString("G6") + " " + no6.ToString("G6"));
MSG += i.ToString() + "\t" + chi2s.ToString("G6") + "\t" + no2.ToString("G6") + "\t" + no4.ToString("G6") + "\t" + no6.ToString("G6") + "\r\n";
if (chi2n < chi2s)
{
parameters = newparams;
exp.o2 = no2;
exp.o4 = no4;
exp.o6 = no6;
lambda *= 1.1;
}
else
{
lambda *= 1 / 1.1;
}
}
Console.WriteLine("Fitting finished");
MSG += "Fitting finished \r\n";
DumpFitResult(exp, ref MSG, ref LATEX, sw, Hessiandiag, ref sumfexp, ref sumdfexp, chi2n);
}
public void GetOmegas(Multiplet donor)
{
o2 = donor.o2;
o4 = donor.o4;
o6 = donor.o6;
}
