/***************************************************************************
   File                 : fit_gsl.cpp
   Project              : SciDAVis
   Description          : Built-in data fit models for QtiPlot
   --------------------------------------------------------------------
   Copyright            : (C) 2004-2007 Ion Vasilief (ion_vasilief*yahoo.fr)
                          (C) 2008-2009 Knut Franke (knut.franke*gmx.de)
						  (replace * with @ in the email address)
 ***************************************************************************/

/***************************************************************************
 *                                                                         *
 *  This program is free software; you can redistribute it and/or modify   *
 *  it under the terms of the GNU General Public License as published by   *
 *  the Free Software Foundation; either version 2 of the License, or      *
 *  (at your option) any later version.                                    *
 *                                                                         *
 *  As a special exception, you may omit the above copyright notice when   *
 *  distributing modified copies of this file (for instance, when using it *
 *  as a template for your own fit plugin).                                *
 *                                                                         *
 *  This program is distributed in the hope that it will be useful,        *
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of         *
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the          *
 *  GNU General Public License for more details.                           *
 *                                                                         *
 *   You should have received a copy of the GNU General Public License     *
 *   along with this program; if not, write to the Free Software           *
 *   Foundation, Inc., 51 Franklin Street, Fifth Floor,                    *
 *   Boston, MA  02110-1301  USA                                           *
 *                                                                         *
 ***************************************************************************/

#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <stddef.h>

#include <qmessagebox.h>

#include <gsl/gsl_blas.h>
#include <gsl/gsl_math.h>
#include "fit_gsl.h"
#include "Fit.h"

int expd3_f (const gsl_vector * x, void *params,
		gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1=gsl_vector_get(x,0);
	double t1=gsl_vector_get(x,1);
	double A2=gsl_vector_get(x,2);
	double t2=gsl_vector_get(x,3);
	double A3=gsl_vector_get(x,4);
	double t3=gsl_vector_get(x,5);
	double y0=gsl_vector_get(x,6);

	size_t i;
	for (i = 0; i < n; i++)
	{
		double Yi = A1 * exp (-X[i]*t1) + A2 * exp (-X[i]*t2) + A3 * exp (-X[i]*t3) +y0;
		gsl_vector_set (f, i, (Yi - Y[i])/sigma[i]);
	}

	return GSL_SUCCESS;
}

double expd3_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1=gsl_vector_get(x,0);
	double t1=gsl_vector_get(x,1);
	double A2=gsl_vector_get(x,2);
	double t2=gsl_vector_get(x,3);
	double A3=gsl_vector_get(x,4);
	double t3=gsl_vector_get(x,5);
	double y0=gsl_vector_get(x,6);

	size_t i;
	double val=0;
	for (i = 0; i < n; i++)
	{
		double dYi = ((A1 * exp (-X[i]*t1) + A2 * exp (-X[i]*t2) + A3 * exp (-X[i]*t3) +y0)-Y[i])/sigma[i];
		val+=dYi * dYi;
	}

	return val;
}

int expd3_df (const gsl_vector * x, void *params,
		gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1=gsl_vector_get(x,0);
	double l1=gsl_vector_get(x,1);
	double A2=gsl_vector_get(x,2);
	double l2=gsl_vector_get(x,3);
	double A3=gsl_vector_get(x,4);
	double l3=gsl_vector_get(x,5);

	size_t i;
	for (i = 0; i < n; i++)
	{
		/* Jacobian matrix J(i,j) = dfi / dxj, */
		/* where fi = (Yi - yi)/sigma[i],      */
		/*       Yi = A1 * exp(-xi*l1) + A2 * exp(-xi*l2) +y0  */
		/* and the xj are the parameters (A1,l1,A2,l2,y0) */
		double t = X[i];
		double s = sigma[i];
		double e1 = exp(-t*l1)/s;
		double e2 = exp(-t*l2)/s;
		double e3 = exp(-t*l3)/s;

		gsl_matrix_set (J, i, 0, e1);
		gsl_matrix_set (J, i, 1, -t * A1 * e1);
		gsl_matrix_set (J, i, 2, e2);
		gsl_matrix_set (J, i, 3, -t * A2 * e2);
		gsl_matrix_set (J, i, 4, e3);
		gsl_matrix_set (J, i, 5, -t * A3 * e3);
		gsl_matrix_set (J, i, 6, 1/s);
	}
	return GSL_SUCCESS;
}

int expd3_fdf (const gsl_vector * x, void *params,
		gsl_vector * f, gsl_matrix * J)
{
	expd3_f (x, params, f);
	expd3_df (x, params, J);

	return GSL_SUCCESS;
}

int expd2_f (const gsl_vector * x, void *params,
		gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1=gsl_vector_get(x,0);
	double t1=gsl_vector_get(x,1);
	double A2=gsl_vector_get(x,2);
	double t2=gsl_vector_get(x,3);
	double y0=gsl_vector_get(x,4);

	size_t i;
	for (i = 0; i < n; i++)
	{
		double Yi = A1 * exp (-X[i]*t1) + A2 * exp (-X[i]*t2) + y0;
		gsl_vector_set (f, i, (Yi - Y[i])/sigma[i]);
	}

	return GSL_SUCCESS;
}

double expd2_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1=gsl_vector_get(x,0);
	double t1=gsl_vector_get(x,1);
	double A2=gsl_vector_get(x,2);
	double t2=gsl_vector_get(x,3);
	double y0=gsl_vector_get(x,4);

	size_t i;
	double val=0;
	for (i = 0; i < n; i++)
	{
		double dYi = ((A1 * exp (-X[i]*t1) + A2 * exp (-X[i]*t2) + y0)-Y[i])/sigma[i];
		val+=dYi * dYi;
	}

	return val;
}

int expd2_df (const gsl_vector * x, void *params,
		gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1=gsl_vector_get(x,0);
	double l1=gsl_vector_get(x,1);
	double A2=gsl_vector_get(x,2);
	double l2=gsl_vector_get(x,3);

	size_t i;

	for (i = 0; i < n; i++)
	{
		/* Jacobian matrix J(i,j) = dfi / dxj, */
		/* where fi = (Yi - yi)/sigma[i],      */
		/*       Yi = A1 * exp(-xi*l1) + A2 * exp(-xi*l2) +y0  */
		/* and the xj are the parameters (A1,l1,A2,l2,y0) */
		double s = sigma[i];
		double t = X[i];
		double e1 = exp(-t*l1)/s;
		double e2 = exp(-t*l2)/s;

		gsl_matrix_set (J, i, 0, e1);
		gsl_matrix_set (J, i, 1, -t * A1 * e1);
		gsl_matrix_set (J, i, 2, e2);
		gsl_matrix_set (J, i, 3, -t * A2 * e2);
		gsl_matrix_set (J, i, 4, 1/s);
	}
	return GSL_SUCCESS;
}

int expd2_fdf (const gsl_vector * x, void *params,
		gsl_vector * f, gsl_matrix * J)
{
	expd2_f (x, params, f);
	expd2_df (x, params, J);
	return GSL_SUCCESS;
}

int exp_f (const gsl_vector * x, void *params,
		gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A = gsl_vector_get (x, 0);
	double lambda = gsl_vector_get (x, 1);
	double b = gsl_vector_get (x, 2);
	size_t i;
	for (i = 0; i < n; i++)
	{
		double Yi = A * exp (-lambda * X[i]) + b;
		gsl_vector_set (f, i, (Yi - Y[i])/sigma[i]);
	}
	return GSL_SUCCESS;
}

double exp_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A = gsl_vector_get (x, 0);
	double lambda = gsl_vector_get (x, 1);
	double b = gsl_vector_get (x, 2);
	size_t i;
	double val=0;
	for (i = 0; i < n; i++)
	{
		double dYi = ((A * exp (-lambda * X[i]) + b)-Y[i])/sigma[i];
		val+=dYi * dYi;
	}
	return val;
}

int exp_df (const gsl_vector * x, void *params,
		gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	double A = gsl_vector_get (x, 0);
	double lambda = gsl_vector_get (x, 1);
	size_t i;
	for (i = 0; i < n; i++)
	{
		/* Jacobian matrix J(i,j) = dfi / dxj, */
		/* where fi = (Yi - yi)/sigma[i],      */
		/*       Yi = A * exp(-lambda * i) + b  */
		/* and the xj are the parameters (A,lambda,b) */

		double t = X[i];
		double s = sigma[i];
		double e = exp(-lambda * t);
		gsl_matrix_set (J, i, 0, e/s); 
		gsl_matrix_set (J, i, 1, -t * A * e/s);
		gsl_matrix_set (J, i, 2, 1/s);
	}
	return GSL_SUCCESS;
}

int exp_fdf (const gsl_vector * x, void *params,
		gsl_vector * f, gsl_matrix * J)
{
	exp_f (x, params, f);
	exp_df (x, params, J);
	return GSL_SUCCESS;
}

int gauss_f (const gsl_vector * x, void *params,
		gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double Y0 = gsl_vector_get (x, 0);
	double A = gsl_vector_get (x, 1);
	double C = gsl_vector_get (x, 2);
	double w = gsl_vector_get (x, 3);

	size_t i;

	for (i = 0; i < n; i++)
	{
		double diff=X[i]-C;
		double Yi = A*exp(-0.5*diff*diff/(w*w))+Y0;
		gsl_vector_set (f, i, (Yi - Y[i])/sigma[i]);
	}
	return GSL_SUCCESS;
}

double gauss_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double Y0 = gsl_vector_get (x, 0);
	double A = gsl_vector_get (x, 1);
	double C = gsl_vector_get (x, 2);
	double w = gsl_vector_get (x, 3);

	size_t i;
	double val=0;

	for (i = 0; i < n; i++)
	{
		double diff=X[i]-C;
		double dYi = ((A*exp(-0.5*diff*diff/(w*w))+Y0)-Y[i])/sigma[i];
		val+=dYi * dYi;
	}
	return val;
}

int gauss_df (const gsl_vector * x, void *params,
		gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	double A = gsl_vector_get (x, 1);
	double C = gsl_vector_get (x, 2);
	double w = gsl_vector_get (x, 3);

	size_t i;
	for (i = 0; i < n; i++)
	{
		/* Jacobian matrix J(i,j) = dfi / dxj,	 */
		/* where fi = Yi - yi,					*/
		/* Yi = y=A*exp[-(Xi-xc)^2/(2*w*w)]+B		*/
		/* and the xj are the parameters (B,A,C,w) */

		double s = sigma[i];
		double diff = X[i]-C;
		double e = exp(-0.5*diff*diff/(w*w))/s;

		gsl_matrix_set (J, i, 0, 1/s);
		gsl_matrix_set (J, i, 1, e);
		gsl_matrix_set (J, i, 2, diff*A*e/(w*w));
		gsl_matrix_set (J, i, 3, diff*diff*A*e/(w*w*w));
	}
	return GSL_SUCCESS;
}

int gauss_fdf (const gsl_vector * x, void *params,
		gsl_vector * f, gsl_matrix * J)
{
	gauss_f (x, params, f);
	gauss_df (x, params, J);

	return GSL_SUCCESS;
}

int gauss_multi_peak_f (const gsl_vector * x, void *params, gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	size_t p = ((struct FitData *)params)->p;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	size_t peaks = (p-1)/3;
	double *a = new double[peaks]; 
	double *xc = new double[peaks];
	double *w2 = new double[peaks];
	double offset = gsl_vector_get (x, p-1);

	size_t i,j;
	for (i = 0; i < peaks; i++)
	{
		xc[i] = gsl_vector_get(x, 3*i+1);
		double wi = gsl_vector_get(x, 3*i+2);
		a[i] = sqrt(M_2_PI)*gsl_vector_get(x, 3*i)/wi;
		w2[i] = wi*wi;
	}
	for (i = 0; i < n; i++)
	{
		double res = 0;
		for (j = 0; j < peaks; j++)
		{
			double diff=X[i]-xc[j];
			res+= a[j]*exp(-2*diff*diff/w2[j]);
		}
		gsl_vector_set(f, i, (res + offset - Y[i])/sigma[i]);
	}
	delete[] a;
	delete[] xc;
	delete[] w2;
	return GSL_SUCCESS;
}

double gauss_multi_peak_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	size_t p = ((struct FitData *)params)->p;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	size_t peaks = (p-1)/3;
	double *a = new double[peaks]; 
	double *xc = new double[peaks];
	double *w2 = new double[peaks];
	double offset = gsl_vector_get (x, p-1);

	size_t i,j;
	double val=0;
	for (i = 0; i < peaks; i++)
	{
		xc[i] = gsl_vector_get(x, 3*i+1);
		double wi = gsl_vector_get(x, 3*i+2);
		a[i] = sqrt(M_2_PI)*gsl_vector_get(x, 3*i)/wi;
		w2[i] = wi*wi;
	}
	double t;
	for (i = 0; i < n; i++)
	{
		double res = 0;
		for (j = 0; j < peaks; j++)
		{
			double diff=X[i]-xc[j];
			res+= a[j]*exp(-2*diff*diff/w2[j]);
		}
		t = (res+offset-Y[i])/sigma[i];
		val += t*t;
	}
	delete[] a;
	delete[] xc;
	delete[] w2;
	return val;
}

int gauss_multi_peak_df (const gsl_vector * x, void *params, gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	size_t p = ((struct FitData *)params)->p;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	size_t peaks = (p-1)/3;
	double *a = new double[peaks]; 
	double *xc = new double[peaks];
	double *w = new double[peaks];

	size_t i,j;
	for (i = 0; i<peaks; i++)
	{
		a[i] = gsl_vector_get (x, 3*i);
		xc[i] = gsl_vector_get (x, 3*i+1);
		w[i] = gsl_vector_get (x, 3*i+2);	
	}
	for (i = 0; i<n; i++)
	{   
		double s = sigma[i];
		for (j = 0; j<peaks; j++)
		{
			double diff = X[i]-xc[j];
			double w2 = w[j]*w[j];
			double e = sqrt(M_2_PI)/s*exp(-2*diff*diff/w2);

			gsl_matrix_set (J, i, 3*j, e/w[j]);
			gsl_matrix_set (J, i, 3*j+1, 4*diff*a[j]*e/(w2*w[j]));
			gsl_matrix_set (J, i, 3*j+2, a[j]/w2*e*(4*diff*diff/w2 - 1));
		}
		gsl_matrix_set (J, i, p-1, 1.0/s);
	}
	delete[] a;
	delete[] xc;
	delete[] w;
	return GSL_SUCCESS;
}

int gauss_multi_peak_fdf (const gsl_vector * x, void *params, gsl_vector * f, gsl_matrix * J)
{
	gauss_multi_peak_f (x, params, f);
	gauss_multi_peak_df (x, params, J);
	return GSL_SUCCESS;
}

int lorentz_multi_peak_f (const gsl_vector * x, void *params, gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	size_t p = ((struct FitData *)params)->p;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	size_t peaks = (p-1)/3;
	double *a = new double[peaks]; 
	double *xc = new double[peaks];
	double *w = new double[peaks];
	double offset = gsl_vector_get (x, p-1);

	size_t i,j;
	for (i = 0; i < peaks; i++)
	{
		a[i] = gsl_vector_get(x, 3*i);
		xc[i] = gsl_vector_get(x, 3*i+1);
		w[i] = gsl_vector_get(x, 3*i+2);
	}
	for (i = 0; i < n; i++)
	{
		double res = 0;
		for (j = 0; j < peaks; j++)
		{
			double diff=X[i]-xc[j];
			res+= a[j]*w[j]/(4*diff*diff+w[j]*w[j]);
		}
		gsl_vector_set(f, i, (res + offset - Y[i])/sigma[i]);
	}
	delete[] a;
	delete[] xc;
	delete[] w;
	return GSL_SUCCESS;
}

double lorentz_multi_peak_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	size_t p = ((struct FitData *)params)->p;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	size_t peaks = (p-1)/3;
	double *a = new double[peaks]; 
	double *xc = new double[peaks];
	double *w = new double[peaks];
	double offset = gsl_vector_get (x, p-1);

	size_t i,j;
	double val=0,t;
	for (i = 0; i < peaks; i++)
	{
		a[i] = gsl_vector_get(x, 3*i);
		xc[i] = gsl_vector_get(x, 3*i+1);
		w[i] = gsl_vector_get(x, 3*i+2);
	}
	for (i = 0; i < n; i++)
	{
		double res = 0;
		for (j = 0; j < peaks; j++)
		{
			double diff=X[i]-xc[j];
			res+= a[j]*w[j]/(4*diff*diff+w[j]*w[j]);
		}
		t=(res+offset-Y[i])/sigma[i];
		val+=t*t;
	}
	delete[] a;
	delete[] xc;
	delete[] w;
	return GSL_SUCCESS;
}

int lorentz_multi_peak_df (const gsl_vector * x, void *params, gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	size_t p = ((struct FitData *)params)->p;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	size_t peaks = (p-1)/3;
	double *a = new double[peaks]; 
	double *xc = new double[peaks];
	double *w = new double[peaks];

	size_t i,j;
	for (i = 0; i<peaks; i++)
	{
		a[i] = gsl_vector_get (x, 3*i);
		xc[i] = gsl_vector_get (x, 3*i+1);
		w[i] = gsl_vector_get (x, 3*i+2);	
	}
	for (i = 0; i<n; i++)
	{    
		double s = sigma[i];
		for (j = 0; j<peaks; j++)
		{
			double diff = X[i]-xc[j];
			double w2 = w[j]*w[j];
			double num = 1.0/(4*diff*diff+w2);
			double den = 4*diff*diff-w2;

			gsl_matrix_set (J, i, 3*j, w[j]*num/s);
			gsl_matrix_set (J, i, 3*j+1, 8*diff*a[j]*w[j]*num*sqrt(num)/s);
			gsl_matrix_set (J, i, 3*j+2, den*a[j]*num*num/s);
		}
		gsl_matrix_set (J, i, p-1, 1.0/s);
	}
	delete[] a;
	delete[] xc;
	delete[] w;
	return GSL_SUCCESS;
}

int lorentz_multi_peak_fdf (const gsl_vector * x, void *params, gsl_vector * f, gsl_matrix * J)
{
	lorentz_multi_peak_f (x, params, f);
	lorentz_multi_peak_df (x, params, J);
	return GSL_SUCCESS;
}

int user_f(const gsl_vector * x, void *params, gsl_vector * f)
{
  return static_cast<struct FitData*>(params)->fit->evaluate_f(x, f);
}

double user_d(const gsl_vector * x, void *params)
{
        return static_cast<struct FitData*>(params)->fit->evaluate_d(x);
}

int user_df(const gsl_vector *x, void *params, gsl_matrix *J)
{
    return static_cast<struct FitData*>(params)->fit->evaluate_df(x, J);
}

int user_fdf(const gsl_vector * x, void *params, gsl_vector * f, gsl_matrix * J)
{
	user_f (x, params, f);
	user_df (x, params, J);
	return GSL_SUCCESS;
}

int boltzmann_f (const gsl_vector * x, void *params, gsl_vector * f)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1 = gsl_vector_get (x, 0);
	double A2 = gsl_vector_get (x, 1);
	double x0 = gsl_vector_get (x, 2);
	double dx = gsl_vector_get (x, 3);
	size_t i;
	for (i = 0; i < n; i++)
	{
		double Yi = (A1-A2)/(1+exp((X[i]-x0)/dx))+A2;
		gsl_vector_set (f, i, (Yi - Y[i])/sigma[i]);
	}

	return GSL_SUCCESS;
}

double boltzmann_d (const gsl_vector * x, void *params)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *Y = ((struct FitData *)params)->Y;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1 = gsl_vector_get (x, 0);
	double A2 = gsl_vector_get (x, 1);
	double x0 = gsl_vector_get (x, 2);
	double dx = gsl_vector_get (x, 3);
	size_t i;
	double val=0;
	for (i = 0; i < n; i++)
	{
		double dYi = ((A1-A2)/(1+exp((X[i]-x0)/dx)) + A2 - Y[i])/sigma[i];
		val+=dYi * dYi;
	}
	return val;
}

int boltzmann_df (const gsl_vector * x, void *params, gsl_matrix * J)
{
	size_t n = ((struct FitData *)params)->n;
	double *X = ((struct FitData *)params)->X;
	double *sigma = ((struct FitData *)params)->sigma;

	double A1 = gsl_vector_get (x, 0);
	double A2 = gsl_vector_get (x, 1);
	double x0 = gsl_vector_get (x, 2);
	double dx = gsl_vector_get (x, 3);
	size_t i;
	for (i = 0; i < n; i++)
	{
		/* Jacobian matrix J(i,j) = dfi / dxj,		*/
		/* where fi = Yi - yi,						*/
		/* Yi = (A1-A2)/(1+exp((X[i]-x0)/dx)) + A2	*/
		/* and the xj are the parameters (A1,A2,x0,dx)*/
		double s = sigma[i];
		double diff = X[i]-x0;
		double e = exp(diff/dx);
		double r = 1/(1+e);
		double aux = (A1 - A2)*e*r*r/(dx*s);
		gsl_matrix_set (J, i, 0, r/s);
		gsl_matrix_set (J, i, 1, (1-r)/s);
		gsl_matrix_set (J, i, 2, aux);
		gsl_matrix_set (J, i, 3, aux*diff/dx);
	}
	return GSL_SUCCESS;
}

int boltzmann_fdf (const gsl_vector * x, void *params, gsl_vector * f, gsl_matrix * J)
{
	boltzmann_f (x, params, f);
	boltzmann_df (x, params, J);
	return GSL_SUCCESS;
}
