/// <summary>
/// Fits the data to the specified function. The function is meant to have <b>p</b>+<b>v</b> parameters, the first <b>p</b> of which are to be fitted,
/// whereas the remaining <b>v</b> are assumed to be independent variables, whose values are picked from the lists for the independent variables.
/// </summary>
/// <param name="f">the function to be fitted. First derivatives w.r.t. the fit parameters are needed.</param>
/// <param name="fitparameters">the number of parameters to be fitted. They must be the first parameters to be passed to the function.</param>
/// <param name="indep">the list of values for the independent variables.</param>
/// <param name="dep">the list of values for the dependent variable.</param>
/// <param name="deperr">the list of errors for the dependent variable.</param>
/// <param name="maxiterations">maximum number of iterations to find the minimum.</param>
/// <returns>the parameters of the fit.</returns>
public double[] Fit(NumericalTools.Minimization.ITargetFunction f, int fitparameters, double[][] indep, double[] dep, double[] deperr, int maxiterations)
{
m_DegreesOfFreedom = dep.Length - fitparameters;
if (m_DegreesOfFreedom < 0)
{
throw new NumericalTools.Minimization.MinimizationException("Degrees of freedom = " + m_DegreesOfFreedom + ". Aborting.");
}
NumericalTools.Minimization.NewtonMinimizer MA = new NumericalTools.Minimization.NewtonMinimizer();
MA.Logger = m_TW;
Chi2F chi2 = new Chi2F(f, fitparameters, indep, dep, deperr);
MA.FindMinimum(chi2, maxiterations);
m_EstimatedVariance = MA.Value / m_DegreesOfFreedom;
m_BestFit = MA.Point;
Minimization.ITargetFunction[] g = new NumericalTools.Minimization.ITargetFunction[fitparameters];
double[,] hessian = new double[fitparameters, fitparameters];
int i, j;
for (i = 0; i < fitparameters; i++)
{
g[i] = chi2.Derive(i);
for (j = 0; j < fitparameters; j++)
{
hessian[i, j] = g[i].Derive(j).Evaluate(m_BestFit);
}
}
m_CorrelationMatrix = new double[fitparameters, fitparameters];
double[][] c = new Cholesky(hessian, 0.0).Inverse(0.0);
for (i = 0; i < fitparameters; i++)
{
for (j = 0; j < i; j++)
{
m_CorrelationMatrix[j, i] = m_CorrelationMatrix[i, j] = c[i][j] / (Math.Sqrt(c[i][i]) * Math.Sqrt(c[j][j]));
}
m_CorrelationMatrix[i, j] = 1.0;
}
m_StandardErrors = new double[fitparameters];
for (i = 0; i < fitparameters; i++)
{
m_StandardErrors[i] = Math.Sqrt(m_EstimatedVariance * c[i][i]);
}
return(m_BestFit);
}
/// <summary>
/// Fits the data to the specified function. The function is meant to have <b>p</b>+<b>v</b> parameters, the first <b>p</b> of which are to be fitted,
/// whereas the remaining <b>v</b> are assumed to be independent variables, whose values are picked from the lists for the independent variables.
/// </summary>
/// <param name="f">the function to be fitted. First derivatives w.r.t. the fit parameters are needed.</param>
/// <param name="fitparameters">the number of parameters to be fitted. They must be the first parameters to be passed to the function.</param>
/// <param name="indep">the list of values for the independent variables.</param>
/// <param name="indeperr">the list of errors for the independent variable.</param>
/// <param name="dep">the list of values for the dependent variable.</param>
/// <param name="deperr">the list of errors for the dependent variable.</param>
/// <param name="maxiterations">maximum number of iterations to find the minimum.</param>
/// <returns>the parameters of the fit.</returns>
/// <remarks>The method of effective variance is used to take errors on the independent variables into account. </remarks>
public double[] Fit(NumericalTools.Minimization.ITargetFunction f, int fitparameters, double[][] indep, double[] dep, double [][] indeperr, double[] deperr, int maxiterations)
{
m_DegreesOfFreedom = dep.Length - fitparameters;
if (m_DegreesOfFreedom < 0)
{
throw new NumericalTools.Minimization.MinimizationException("Degrees of freedom = " + m_DegreesOfFreedom + ". Aborting.");
}
NumericalTools.Minimization.NewtonMinimizer MA = new NumericalTools.Minimization.NewtonMinimizer();
MA.Logger = m_TW;
NumericalTools.Minimization.ITargetFunction[] f_d = new NumericalTools.Minimization.ITargetFunction[f.CountParams - fitparameters];
int i, j;
for (i = 0; i < f_d.Length; i++)
{
f_d[i] = f.Derive(i + fitparameters);
}
double [] c_deperr = new double[deperr.Length];
double [] xp = new double[f.CountParams];
double [] xfp = new double[fitparameters];
double dfx;
for (i = 0; i < f_d.Length; i++)
{
xfp[i] = f.Start[i];
}
int maxouteriter = maxiterations;
if (maxouteriter <= 0)
{
maxouteriter = -1;
}
double f0, f1, dxchange;
do
{
if (m_TW != null)
{
m_TW.WriteLine("Starting with derivative guess - remaining iterations: " + maxouteriter);
}
for (i = 0; i < f_d.Length; i++)
{
xp[i] = xfp[i];
}
for (i = 0; i < c_deperr.Length; i++)
{
for (j = 0; j < f_d.Length; j++)
{
xp[j + fitparameters] = indep[i][j];
}
c_deperr[i] = deperr[i] * deperr[i];
for (j = 0; j < f_d.Length; j++)
{
dfx = f_d[j].Evaluate(xp) * indeperr[i][j];
c_deperr[i] += dfx * dfx;
}
c_deperr[i] = Math.Sqrt(c_deperr[i]);
}
Chi2F chi2 = new Chi2F(f, fitparameters, indep, dep, c_deperr);
chi2.SetStart(xfp);
f0 = chi2.Evaluate(xfp);
MA.FindMinimum(chi2, maxiterations);
m_EstimatedVariance = MA.Value / m_DegreesOfFreedom;
m_BestFit = MA.Point;
Minimization.ITargetFunction[] g = new NumericalTools.Minimization.ITargetFunction[fitparameters];
double[,] hessian = new double[fitparameters, fitparameters];
for (i = 0; i < fitparameters; i++)
{
g[i] = chi2.Derive(i);
for (j = 0; j < fitparameters; j++)
{
hessian[i, j] = g[i].Derive(j).Evaluate(m_BestFit);
}
}
m_CorrelationMatrix = new double[fitparameters, fitparameters];
double[][] c = new Cholesky(hessian, 0.0).Inverse(0.0);
for (i = 0; i < fitparameters; i++)
{
for (j = 0; j < i; j++)
{
m_CorrelationMatrix[j, i] = m_CorrelationMatrix[i, j] = c[i][j] / (Math.Sqrt(c[i][i]) * Math.Sqrt(c[j][j]));
}
m_CorrelationMatrix[i, j] = 1.0;
}
m_StandardErrors = new double[fitparameters];
for (i = 0; i < fitparameters; i++)
{
m_StandardErrors[i] = Math.Sqrt(m_EstimatedVariance * c[i][i]);
}
dxchange = 0.0;
for (i = 0; i < f_d.Length; i++)
{
dxchange += (xfp[i] - m_BestFit[i]) * (xfp[i] - m_BestFit[i]);
}
f1 = chi2.Evaluate(m_BestFit);
for (i = 0; i < xfp.Length; i++)
{
xfp[i] = m_BestFit[i];
}
if (m_TW != null)
{
m_TW.WriteLine("End with derivative guess - remaining iterations: " + maxouteriter);
}
if (--maxouteriter < 0)
{
maxouteriter = -1;
}
}while (maxouteriter != 0 && f.StopMinimization(f1, f0, dxchange) == false);
return(m_BestFit);
}