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fit.cpp
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fit.cpp
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/***************************************************************************
* Copyright (C) 2020 by Nuno Cardoso *
* nmrcardoso@gmail.com *
* *
* 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. *
* *
* 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., *
* 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. *
***************************************************************************/
#include <iostream>
#include <sstream>
#include <fstream>
#include <string>
#include <limits>
#include <cstdlib>
#include <algorithm>
#include <numeric>
#include <cstring>
#include <cassert>
#include <map>
#include <vector>
#include <cmath>
#include <float.h>
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_multifit_nlinear.h>
#include "fit.h"
#include "log.h"
#include "jackerr.h"
#ifndef uint
#define uint unsigned int
#endif
using namespace std;
struct data {
size_t n;
double * t;
double * y;
};
int expb_f (const gsl_vector * x, void *data, gsl_vector * f);
int expb_df (const gsl_vector * x, void *data, gsl_matrix * J);
void callback(const size_t iter, void *params, const gsl_multifit_nlinear_workspace *w);
GSLfitRes GSLfit1(DataLine data);
int expb_f (const gsl_vector * x, void *data, gsl_vector * f){
size_t n = ((struct data *)data)->n;
double *t = ((struct data *)data)->t;
double *y = ((struct data *)data)->y;
double A = gsl_vector_get (x, 0);
double B = gsl_vector_get (x, 1);
double C = gsl_vector_get (x, 2);
size_t i;
for (i = 0; i < n; i++){
/* Model Yi = A * exp(-lambda * t_i) + b */
double Yi = A + B/t[i] +C*t[i];
gsl_vector_set (f, i, Yi - y[i]);
}
return GSL_SUCCESS;
}
int expb_df (const gsl_vector * x, void *data, gsl_matrix * J){
size_t n = ((struct data *)data)->n;
double *t = ((struct data *)data)->t;
double A = gsl_vector_get (x, 0);
double B = gsl_vector_get (x, 1);
double C = gsl_vector_get (x, 2);
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 * t_i) + b */
/* and the xj are the parameters (A,lambda,b) */
gsl_matrix_set (J, i, 0, 1.0);
gsl_matrix_set (J, i, 1, 1.0/t[i]);
gsl_matrix_set (J, i, 2, t[i]);
}
return GSL_SUCCESS;
}
void callback(const size_t iter, void *params, const gsl_multifit_nlinear_workspace *w){
gsl_vector *f = gsl_multifit_nlinear_residual(w);
gsl_vector *x = gsl_multifit_nlinear_position(w);
double rcond;
// compute reciprocal condition number of J(x)
gsl_multifit_nlinear_rcond(&rcond, w);
qlog << "iter " << iter;
qlog << ": A = " << gsl_vector_get(x, 0);
qlog << ", B = " << gsl_vector_get(x, 1);
qlog << ", C = " << gsl_vector_get(x, 2);
qlog << ", cond(J) = " << 1.0 / rcond;
qlog << ", |f(x)| = " << gsl_blas_dnrm2(f) << endl;
}
GSLfitRes GSLfit1(DataLine data, bool print_info){
const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
gsl_multifit_nlinear_workspace *w;
gsl_multifit_nlinear_fdf fdf;
gsl_multifit_nlinear_parameters fdf_params =
gsl_multifit_nlinear_default_parameters();
const size_t n = data.size();
const size_t p = 3;
gsl_vector *f;
gsl_matrix *J;
gsl_matrix *covar = gsl_matrix_alloc (p, p);
double * t = new double[n];
double * y = new double[n];
double * weights = new double[n];
struct data d = { n, t, y };
double x_init[3] = { 1.0, -0.6, .1 }; /* starting values */
gsl_vector_view x = gsl_vector_view_array (x_init, p);
gsl_vector_view wts = gsl_vector_view_array(weights, n);
gsl_rng * r;
double chisq, chisq0;
int status, info;
size_t i;
const double xtol = 1e-10;
const double gtol = 1e-10;
const double ftol = 0.0;
gsl_rng_env_setup();
r = gsl_rng_alloc(gsl_rng_default);
/* define the function to be minimized */
fdf.f = expb_f;
fdf.df = expb_df; /* set to NULL for finite-difference Jacobian */
fdf.fvv = NULL; /* not using geodesic acceleration */
fdf.n = n;
fdf.p = p;
fdf.params = &d;
/* this is the data to be fitted */
for (i = 0; i < n; i++){
double ti = data[i].x;
double yi = data[i].y;
double si = data[i].error;
double dy = gsl_ran_gaussian(r, si);
t[i] = ti;
y[i] = yi;
weights[i] = 1.0 / (si * si);
//printf ("data: %g %g %g\n", ti, y[i], si);
}
/* allocate workspace with default parameters */
w = gsl_multifit_nlinear_alloc (T, &fdf_params, n, p);
/* initialize solver with starting point and weights */
gsl_multifit_nlinear_winit (&x.vector, &wts.vector, &fdf, w);
/* compute initial cost function */
f = gsl_multifit_nlinear_residual(w);
gsl_blas_ddot(f, f, &chisq0);
/* solve the system with a maximum of 100 iterations */
if(print_info) status = gsl_multifit_nlinear_driver(100, xtol, gtol, ftol, callback, NULL, &info, w);
else status = gsl_multifit_nlinear_driver(100, xtol, gtol, ftol, NULL, NULL, &info, w);
/* compute covariance of best fit parameters */
J = gsl_multifit_nlinear_jac(w);
gsl_multifit_nlinear_covar (J, 0.0, covar);
/* compute final cost */
gsl_blas_ddot(f, f, &chisq);
#define FIT(i) gsl_vector_get(w->x, i)
#define ERR(i) sqrt(gsl_matrix_get(covar,i,i))
if(print_info){
qlog << "summary from method '" << gsl_multifit_nlinear_name(w) << "/" << gsl_multifit_nlinear_trs_name(w) << "'" << endl;
qlog << "number of iterations: " << gsl_multifit_nlinear_niter(w) << endl;
qlog << "function evaluations: " << fdf.nevalf << endl;
qlog << "Jacobian evaluations: " << fdf.nevaldf << endl;
qlog << "reason for stopping: " << ((info == 1) ? "small step size" : "small gradient") << endl;
qlog << "initial |f(x)| = " << sqrt(chisq0) << endl;
qlog << "final |f(x)| = " << sqrt(chisq) << endl;
}
GSLfitRes res;
{
double dof = n - p;
double c = GSL_MAX_DBL(1, sqrt(chisq / dof));
if(print_info) {
qlog << "GSL info (not jackknife errors)" << endl;
qlog << "chisq/dof = " << chisq / dof << endl;
qlog << "A = " << FIT(0) << " ± " << c*ERR(0) << endl;
qlog << "B = " << FIT(1) << " ± " << c*ERR(1) << endl;
qlog << "C = " << FIT(2) << " ± " << c*ERR(2) << endl;
}
for(int i=0;i<3;++i){
res.val[i] = FIT(i);
res.error[i] = c*ERR(i);
}
res.chi2_dof = chisq / dof;
}
gsl_strerror (status);
if(print_info) qlog << "status = " << gsl_strerror (status) << endl;
gsl_multifit_nlinear_free (w);
gsl_matrix_free (covar);
gsl_rng_free (r);
delete[] t,y,weights;
return res;
}
GSLfitRes GSLfit(DataLine data, bool err_mean_main_fit){
qlog << "------------------- GSL Fit -------------------" << endl;
//Fit data
GSLfitRes res = GSLfit1(data, true);
//Jackknife fit error
vector<GSLfitRes> err;
vector<double> r0_jack;
for( uint ii = 0; ii < data.size(); ++ii ) {
DataLine data1;
for( uint i = 0; i < data.size(); ++i ) {
if ( ii != i )
data1.push_back(data[i]);
}
GSLfitRes res1 = GSLfit1(data1, false);
err.push_back(res1);
double r0 = std::sqrt( (1.65 + res1.val[1]) / res1.val[2] );
r0_jack.push_back(r0);
//qlog << ii << "\t" << res1.val[0] << "\t" << res1.val[1] << "\t" << res1.val[2] << endl;
}
double err_mean[3];
double errJ_mean[3];
for( uint i = 0; i < 3; ++i ){
vector<double> vals;
for(int j = 0; j < err.size(); ++j)
vals.push_back(err[j].val[i]);
if( err_mean_main_fit ) res.errorJ[i] = jackerr(vals, res.val[i]);
else res.errorJ[i] = jackerr(vals);
//qlog << jackerr(vals) << "::" << jackerr(vals, res.val[i]) << endl;
}
//chi2/dof
double qui = 0.0;
for( uint i = 0; i < data.size(); ++i ) {
double yy = res.val[0] + res.val[1] / data[i].x + res.val[2] * data[i].x;
double dif = data[i].y - yy;
double inverr2 = 1.0 / (data[i].error * data[i].error);
qui += dif * dif * inverr2;
}
//qlog << "qui: " << qui << endl;
res.chi2_dofJ = qui /(data.size() - 3);
double r0 = std::sqrt( (1.65 + res.val[1]) / res.val[2] );
double r0_error = 0.0;
if( err_mean_main_fit ) r0_error = jackerr(r0_jack, r0);
else r0_error = jackerr(r0_jack);
qlog << "Using jackknife:" << endl;
qlog << "r0 = " << r0 << " ± " << r0_error << endl;
//qlog << "r0 = " << r0 << " ± " << jackerr(r0_jack, r0) << endl;
double eb = res.errorJ[1] / (2.0 * res.val[2] * r0);
double ec = res.errorJ[2] * r0 / (2.0 * res.val[2]);
double roerr = std::sqrt( eb * eb + ec * ec);
qlog << "Using propagation error:" << endl;
qlog << "r0 = " << r0 << " ± " << roerr << endl;
qlog << "-----------------------------------------------" << endl;
return res;
}