gsl_multifit_fdfsolver * Fit::fitGSL(gsl_multifit_function_fdf f, int &iterations, int &status) { const gsl_multifit_fdfsolver_type *T; if (d_solver) T = gsl_multifit_fdfsolver_lmder; else T = gsl_multifit_fdfsolver_lmsder; gsl_set_error_handler_off(); gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc (T, d_n, d_p); status = gsl_multifit_fdfsolver_set (s, &f, d_param_init); size_t iter = 0; bool inRange = true; for (int i=0; i<d_p; i++){ double p = gsl_vector_get(d_param_init, i); d_results[i] = p; if (p < d_param_range_left[i] || p > d_param_range_right[i]){ inRange = false; break; } } if (status){ gsl_multifit_covar (s->J, 0.0, covar); iterations = 0; return s; } do{ iter++; status = gsl_multifit_fdfsolver_iterate (s); if (status) break; for (int i=0; i<d_p; i++){ double p = gsl_vector_get(s->x, i); if (p < d_param_range_left[i] || p > d_param_range_right[i]){ inRange = false; break; } } if (!inRange) break; for (int i = 0; i < d_p; i++) d_results[i] = gsl_vector_get(s->x, i); status = gsl_multifit_test_delta (s->dx, s->x, d_tolerance, d_tolerance); } while (inRange && status == GSL_CONTINUE && (int)iter < d_max_iterations); gsl_multifit_covar (s->J, 0.0, covar); iterations = iter; return s; }
gsl_multifit_fdfsolver *Fit::fitGSL(gsl_multifit_function_fdf f, int &iterations, int &status) { const gsl_multifit_fdfsolver_type *T; if (d_solver) T = gsl_multifit_fdfsolver_lmder; else T = gsl_multifit_fdfsolver_lmsder; gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc(T, d_n, d_p); gsl_multifit_fdfsolver_set(s, &f, d_param_init); size_t iter = 0; bool inRange = true; for (int i = 0; i < d_p; i++) { double p = gsl_vector_get(d_param_init, i); d_results[i] = p; if (p < d_param_range_left[i] || p > d_param_range_right[i]) { inRange = false; break; } } do { iter++; status = gsl_multifit_fdfsolver_iterate(s); if (status) break; for (int i = 0; i < d_p; i++) { double p = gsl_vector_get(s->x, i); if (p < d_param_range_left[i] || p > d_param_range_right[i]) { inRange = false; break; } } if (!inRange) break; for (int i = 0; i < d_p; i++) d_results[i] = gsl_vector_get(s->x, i); status = gsl_multifit_test_delta(s->dx, s->x, d_tolerance, d_tolerance); } while (inRange && status == GSL_CONTINUE && (int)iter < d_max_iterations); #if GSL_MAJOR_VERSION < 2 gsl_multifit_covar(s->J, 0.0, covar); #else gsl_matrix *J = gsl_matrix_alloc(d_n, d_p); gsl_multifit_fdfsolver_jac(s, J); gsl_multifit_covar(J, 0.0, covar); gsl_matrix_free(J); #endif iterations = static_cast<int>(iter); return s; }
/* Calculates covariance matrix * * @param epsrel :: Is used to remove linear-dependent columns * @param covar :: Returned covariance matrix, here as */ void LevenbergMarquardtMinimizer::calCovarianceMatrix(double epsrel, gsl_matrix *covar) { #if GSL_MAJOR_VERSION < 2 gsl_multifit_covar(m_gslSolver->J, epsrel, covar); #else gsl_matrix *J = gsl_matrix_alloc(gslContainer.n, gslContainer.p); gsl_multifit_fdfsolver_jac(m_gslSolver, J); gsl_multifit_covar(J, epsrel, covar); gsl_matrix_free(J); #endif }
//Test fitting result using error estimation from covariance matrix, not reliable. tol is the relative tolerance of error. int covar_rel_test(const gsl_matrix* J, const gsl_vector* x, double tol) { //Check if some parameters become NAN or INF. for (int iter = 0; iter < numOfPara; ++iter) { if (!isfinite(x->data[iter])) { return GSL_EOVRFLW; } } gsl_matrix* covar = gsl_matrix_alloc(numOfPara, numOfPara); gsl_multifit_covar(J, 0.0, covar); //Get the covariance matrix. double fitErr[numOfPara]; for (int iterpara = 0; iterpara<numOfPara; ++iterpara) //err_i=\sqrt{c_{ii}} { fitErr[iterpara]=sqrt(gsl_matrix_get(covar, iterpara, iterpara)); } gsl_matrix_free(covar); for (int iter = 0; iter < numOfPara; ++iter) { double relerr = abs(fitErr[iter] / x->data[iter]); if (relerr>tol) { return GSL_CONTINUE; } } return GSL_SUCCESS; }
void test_lmder (gsl_multifit_function_fdf * f, double x0[], double * X, double F[], double * cov) { const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; const size_t n = f->n; const size_t p = f->p; int status; size_t iter = 0, i; gsl_vector_view x = gsl_vector_view_array (x0, p); T = gsl_multifit_fdfsolver_lmsder; s = gsl_multifit_fdfsolver_alloc (T, n, p); gsl_multifit_fdfsolver_set (s, f, &x.vector); do { status = gsl_multifit_fdfsolver_iterate (s); for (i = 0 ; i < p; i++) { gsl_test_rel (gsl_vector_get (s->x, i), X[p*iter+i], 1e-5, "lmsder, iter=%u, x%u", iter, i); } gsl_test_rel (gsl_blas_dnrm2 (s->f), F[iter], 1e-5, "lmsder, iter=%u, f", iter); iter++; } while (iter < 20); { size_t i, j; gsl_matrix * covar = gsl_matrix_alloc (4, 4); gsl_multifit_covar (s->J, 0.0, covar); for (i = 0; i < 4; i++) { for (j = 0; j < 4; j++) { gsl_test_rel (gsl_matrix_get(covar,i,j), cov[i*p + j], 1e-7, "gsl_multifit_covar cov(%d,%d)", i, j) ; } } gsl_matrix_free (covar); } gsl_multifit_fdfsolver_free (s); }
double *Fit::fitGslMultimin(int &iterations, int &status) { double *result = new double[d_p]; // declare input data struct FitData data = {static_cast<size_t>(d_n), static_cast<size_t>(d_p), d_x, d_y, d_y_errors, this}; gsl_multimin_function f; f.f = d_fsimplex; f.n = d_p; f.params = &data; // step size (size of the simplex) // can be increased for faster convergence gsl_vector *ss = gsl_vector_alloc(f.n); gsl_vector_set_all(ss, 10.0); // initialize minimizer const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex; gsl_multimin_fminimizer *s_min = gsl_multimin_fminimizer_alloc(T, f.n); gsl_multimin_fminimizer_set(s_min, &f, d_param_init, ss); // iterate minimization algorithm for (iterations = 0; iterations < d_max_iterations; iterations++) { status = gsl_multimin_fminimizer_iterate(s_min); if (status) break; double size = gsl_multimin_fminimizer_size(s_min); status = gsl_multimin_test_size(size, d_tolerance); if (status != GSL_CONTINUE) break; } // grab results for (int i = 0; i < d_p; i++) result[i] = gsl_vector_get(s_min->x, i); chi_2 = s_min->fval; gsl_matrix *J = gsl_matrix_alloc(d_n, d_p); d_df(s_min->x, (void *)f.params, J); gsl_multifit_covar(J, 0.0, covar); if (d_y_error_source == UnknownErrors) { // multiply covar by variance of residuals, which is used as an estimate for // the // statistical errors (this relies on the Y errors being set to 1.0) gsl_matrix_scale(covar, chi_2 / (d_n - d_p)); } // free previously allocated memory gsl_matrix_free(J); gsl_multimin_fminimizer_free(s_min); gsl_vector_free(ss); return result; }
///Calculates covariance matrix - not implemented void SimplexMinimizer::calCovarianceMatrix(double epsrel, gsl_matrix * covar) { gsl_matrix * holdCalculatedJacobian; holdCalculatedJacobian = gsl_matrix_alloc (m_gslLeastSquaresContainer.n, m_gslLeastSquaresContainer.p); int dummy = m_gslLeastSquaresContainer.df(m_gslSolver->x, m_gslLeastSquaresContainer.params, holdCalculatedJacobian); (void) dummy; gsl_multifit_covar (holdCalculatedJacobian, epsrel, covar); gsl_matrix_free (holdCalculatedJacobian); }
int NonLinearLSQ::curvefit() { size_t n(nSize()); size_t p(nParms()); // Initialize the solver function information _nlsqPointer d = { this }; gsl_multifit_function_fdf mf; mf.f = &f; mf.df = &df; mf.fdf = &fdf; mf.n = n; mf.p = p; mf.params = &d; const gsl_multifit_fdfsolver_type *T = gsl_multifit_fdfsolver_lmsder; gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc(T, n, p); _fitParms = guess(); gsl_vector *x = NlsqTogsl(_fitParms); gsl_matrix *covar = gsl_matrix_alloc(p, p); gsl_multifit_fdfsolver_set(s, &mf, x); _nIters = 0; checkIteration(_nIters, gslToNlsq(s->x), NLVector(p,999.0), gsl_blas_dnrm2(s->f), GSL_CONTINUE); do { _nIters++; _status = gsl_multifit_fdfsolver_iterate(s); _fitParms = gslToNlsq(s->x); gsl_multifit_covar(s->J, 0.0, covar); _uncert = getUncertainty(covar); _status = checkIteration(_nIters, _fitParms, _uncert, gsl_blas_dnrm2(s->f), _status); if ( _status ) { break; } if(!doContinue()) { break; } _status = gsl_multifit_test_delta(s->dx, s->x, absErr(), relErr()); } while ((_status == GSL_CONTINUE) && (_nIters < _maxIters)); // Clean up gsl_multifit_fdfsolver_free(s); gsl_matrix_free(covar); return (_status); }
/** * Calculates covariance matrix for fitting function's active parameters. */ void CostFuncFitting::calActiveCovarianceMatrix(GSLMatrix &covar, double epsrel) { // construct the jacobian GSLJacobian J(m_function, m_values->size()); size_t na = this->nParams(); // number of active parameters assert(J.getJ()->size2 == na); covar.resize(na, na); // calculate the derivatives m_function->functionDeriv(*m_domain, J); // let the GSL to compute the covariance matrix gsl_multifit_covar(J.getJ(), epsrel, covar.gsl()); }
void FittingPerfomanceInfo::GetSolverResults( gsl_multifit_fdfsolver *s ) { double chi, dof, c; size_t p=s->x->size, n=s->f->size; gsl_matrix *covar = gsl_matrix_alloc (p, p); if(covar!=NULL) { gsl_multifit_covar (s->J, 0.0, covar); chi = gsl_blas_dnrm2(s->f); dof = n - p; c = GSL_MAX_DBL(1, chi / sqrt(dof)); chisq_dof=chi*chi / dof; for(size_t i=0;i<p;i++) { a[i]=gsl_vector_get(s->x, i); da[i]=fabs(c*sqrt(gsl_matrix_get(covar,i,i))); } gsl_matrix_free(covar); } }
static void test_fdf_checksol(const char *sname, const char *pname, const double epsrel, gsl_multifit_fdfsolver *s, test_fdf_problem *problem) { gsl_multifit_function_fdf *fdf = problem->fdf; const double *sigma = problem->sigma; gsl_vector *f = gsl_multifit_fdfsolver_residual(s); gsl_vector *x = gsl_multifit_fdfsolver_position(s); double sumsq; /* check solution vector x and sumsq = ||f||^2 */ gsl_blas_ddot(f, f, &sumsq); (problem->checksol)(x->data, sumsq, epsrel, sname, pname); #if 1 /* check variances */ if (sigma) { const size_t n = fdf->n; const size_t p = fdf->p; size_t i; gsl_matrix * J = gsl_matrix_alloc(n, p); gsl_matrix * covar = gsl_matrix_alloc (p, p); gsl_multifit_fdfsolver_jac (s, J); gsl_multifit_covar(J, 0.0, covar); for (i = 0; i < p; i++) { double ei = sqrt(sumsq/(n-p))*sqrt(gsl_matrix_get(covar,i,i)); gsl_test_rel (ei, sigma[i], epsrel, "%s/%s, sigma(%d)", sname, pname, i) ; } gsl_matrix_free (J); gsl_matrix_free (covar); } #endif }
int cspl_qrs_fit (void * params) { int status; unsigned int iter; struct cspl_qrs_data * data = (struct cspl_qrs_data *) params; /* This is the data to be fitted */ gsl_multifit_function_fdf f; // const gsl_rng_type * type; // gsl_rng * r; // gsl_rng_env_setup(); // type = gsl_rng_default; // r = gsl_rng_alloc (type); f.f = &cspl_qrs_f; f.df = &cspl_qrs_df; f.fdf = &cspl_qrs_fdf; f.n = data->n; f.p = data->p; f.params = data; gsl_multifit_fdfsolver_set (data->s, &f, &data->x.vector); iter = 0; //print_state (iter, data->s); do { iter++; status = gsl_multifit_fdfsolver_iterate (data->s); #ifdef DEBUG printf ("status = %s\n", gsl_strerror (status)); print_state (iter, data->s); #endif if (status) break; status = gsl_multifit_test_delta (data->s->dx, data->s->x, 1e-12, 1e-12); } while (status == GSL_CONTINUE && iter < 500); gsl_multifit_covar (data->s->J, 0.0, data->covar); double chi = gsl_blas_dnrm2(data->s->f); double dof = data->n - data->p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); data->c = c; data->chisq_pdof = pow(chi, 2.0) / dof; #ifdef DEBUG #define FIT(i) gsl_vector_get(data->s->x, i) #define ERR(i) sqrt(gsl_matrix_get(data->covar,i,i)) printf("chisq/dof = %g\n", pow(chi, 2.0) / dof); printf ("A = %.5f +/- %.5f\n", FIT(0), c*ERR(0)); printf ("t_beat = %.5f +/- %.5f\n", FIT(1), c*ERR(1)); printf ("S_0 = %.5f +/- %.5f\n", FIT(2), c*ERR(2)); printf ("S_1 = %.5f +/- %.5f\n", FIT(3), c*ERR(3)); printf ("status = %s\n", gsl_strerror (status)); #endif // gsl_rng_free (r); return GSL_SUCCESS; }
int magcal_proc(gsl_vector *m, const satdata_mag *data, magcal_workspace *w) { int s; gsl_multifit_function_fdf f; gsl_multifit_fdfsolver *fdf_s; magcal_params params; gsl_vector_view v; const double xtol = 1e-10; const double gtol = 1e-10; const double ftol = 0.0; int info; /* copy data arrays */ s = magcal_init(data, w); if (s) return s; /* scale parameters to dimensionless units */ magcal_scale(1, m, w); params.w = w; f.f = &magcal_f; f.df = &magcal_df; f.n = w->n; f.p = w->p; f.params = ¶ms; v = gsl_vector_subvector(m, MAGCAL_IDX_DT, w->p); gsl_multifit_fdfsolver_set (w->fdf_s, &f, &v.vector); gsl_multifit_fdfridge_set (w->fdf_ridge, &f, &v.vector, w->lambda); #if 0 s = gsl_multifit_fdfsolver_driver(w->fdf_s, 500, xtol, gtol, ftol, &info); fdf_s = w->fdf_s; #else s = gsl_multifit_fdfridge_driver(w->fdf_ridge, 500, xtol, gtol, ftol, &info); fdf_s = w->fdf_ridge->s; #endif if (s != GSL_SUCCESS) { fprintf(stderr, "magcal_proc: error computing parameters: %s\n", gsl_strerror(s)); } else { magcal_print_state (w, fdf_s); fprintf(stderr, "magcal_proc: total data processed: %zu\n", w->n); fprintf(stderr, "magcal_proc: number of iterations: %zu\n", fdf_s->niter); fprintf(stderr, "magcal_proc: function evaluations: %zu\n", fdf_s->fdf->nevalf); fprintf(stderr, "magcal_proc: jacobian evaluations: %zu\n", fdf_s->fdf->nevaldf); fprintf(stderr, "magcal_proc: reason for convergence: %d\n", info); /* save calibration parameters */ gsl_vector_memcpy(&v.vector, fdf_s->x); /* restore time shift parameter */ gsl_vector_set(m, MAGCAL_IDX_DT, 0.0); /* scale offsets back to nT */ magcal_scale(-1, m, w); #if 0 /* compute covariance matrix */ gsl_multifit_covar(fdf_s->J, 0.0, w->covar); #endif } return s; } /* magcal_proc() */
int InterpolaVPR_GSL::interpola_VPR(const float* vpr, int hvprmax, int livmin) { LOG_CATEGORY("radar.vpr"); static const unsigned N = 10; const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; int status; unsigned int i; const size_t n = N; const size_t p = 5; char file_vprint[512]; gsl_matrix *covar = gsl_matrix_alloc (p, p); double a[5]; struct data d(N); gsl_multifit_function_fdf f; double x_init[5] = { 4, 0.2, 3. , 1.4, -0.4 }; gsl_vector_view x = gsl_vector_view_array (x_init, p); ////////////////////////////////////////////////////////////////////////////// int ier_int=0; double xint,yint; /* punti interessanti per inizializzare parametri*/ int in1=(int)((hvprmax-TCK_VPR/2)/TCK_VPR); //indice del massimo int in2=(int)((hvprmax+HALF_BB)/TCK_VPR); //indice del massimo + 500 m int in3=in2+1; int in4=in2+5; //indice del massimo + 1000 m if (in4 > NMAXLAYER-1) { ier_int=1; return ier_int; } B=vpr[in1]-vpr[in2]; E=hvprmax/1000.; G=0.25; C=vpr[in2-1]; F=vpr[in4]<vpr[in3]?(vpr[in4]-vpr[in3])/((in4-in3)*TCK_VPR/1000.):0.; // fprintf(stderr, "const unsigned NMAXLAYER=%d;\n", NMAXLAYER); // fprintf(stderr, "float vpr[] = {"); // for (unsigned i = 0; i < NMAXLAYER; ++i) // fprintf(stderr, "%s%f", i==0?"":",", (double)vpr[i]); // fprintf(stderr, "};\n"); x_init[0]= a[0]=B; x_init[1]= a[1]=E; x_init[2]= a[2]=G; x_init[3]= a[3]=C; x_init[4]= a[4]=F; ///////////////////////////////////////////////////////////////////////////////////////////////////////// f.f = &expb_f; f.df = &expb_df; f.fdf = &expb_fdf; f.n = n; f.p = p; f.params = &d; /* This is the data to be fitted */ for (i = 0; i < n; i++) { d.t[i]= ((hvprmax-1000.)>livmin)? (i*TCK_VPR+(hvprmax-800)-TCK_VPR)/1000. : (livmin+i*TCK_VPR)/1000.; d.y[i]= ((hvprmax-1000.)>livmin)? vpr[i+(int)(((hvprmax-800)-TCK_VPR)/TCK_VPR)] : vpr[i+(int)(livmin/TCK_VPR)]; d.sigma[i] = 0.5; }; T = gsl_multifit_fdfsolver_lmsder; s = gsl_multifit_fdfsolver_alloc (T, n, p); gsl_multifit_fdfsolver_set (s, &f, &x.vector); //print_state (0, s); bool found = false; for (unsigned iter = 0; !found && iter < 500; ++iter) { //fprintf(stderr, "Iter %d\n", iter); //d.print(); int status = gsl_multifit_fdfsolver_iterate (s); if (status != 0) { LOG_ERROR("gsl_multifit_fdfsolver_iterate: %s", gsl_strerror(status)); return 1; } //print_state (iter, s); status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4); switch (status) { case GSL_SUCCESS: found = true; break; case GSL_CONTINUE: break; default: LOG_ERROR("gsl_multifit_test_delta: %s", gsl_strerror(status)); return 1; } } #if GSL_MAJOR_VERSION == 2 // Use of GSL 2.0 taken from https://sft.its.cern.ch/jira/browse/ROOT-7776 gsl_matrix* J = gsl_matrix_alloc(s->fdf->n, s->fdf->p); gsl_multifit_fdfsolver_jac(s, J); gsl_multifit_covar(J, 0.0, covar); #else gsl_multifit_covar(s->J, 0.0, covar); #endif #define FIT(i) gsl_vector_get(s->x, i) #define ERR(i) sqrt(gsl_matrix_get(covar,i,i)) { double chi = gsl_blas_dnrm2(s->f); double dof = n - p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); // printf("chisq/dof = %g\n", pow(chi, 2.0) / dof); // printf ("B = %.5f +/- %.5f\n", FIT(0), c*ERR(0)); // printf ("E = %.5f +/- %.5f\n", FIT(1), c*ERR(1)); // printf ("G = %.5f +/- %.5f\n", FIT(2), c*ERR(2)); // printf ("C = %.5f +/- %.5f\n", FIT(3), c*ERR(3)); // printf ("F = %.5f +/- %.5f\n", FIT(4), c*ERR(4)); } B = a[0] = FIT(0); E = a[1] = FIT(1); G = a[2] = FIT(2); C = a[3] = FIT(3); F = a[4] = FIT(4); gsl_multifit_fdfsolver_free (s); gsl_matrix_free (covar); ///////////////////////////////////////////////////////// if (testfit(a) == 1) return 1; for (i=1; i<=N; i++) { xint=(i*TCK_VPR-TCK_VPR/2)/1000.; yint= lineargauss(xint, a); vpr_int[i-1] = yint; } return 0; }
f_all_sol do_fit_duplex(f_info *f, int n, real *t_min, real *t_max, bool bVerbose, bool bUpdate) { int i,j,k; int iter=0; int tot_points=0; int status; int tot_abs=0; int tot_inv_t=0; real inv_t=0; real tss_inv=0; real mean_inv_t=0; real abs_t=0; real mean_abs_t=0; real tss_abs=0; real tss_tot=0; f_all_sol fit; f_info *local_f; snew(local_f,n); // count points within boundaries, allocate // and copy to new array. Only copy the xp (derivative) // as is the one that matters for the fitting for(i=0; i<n; i++){ for(j=0; j<f[i].nts; j++){ if( f[i].xp[0][j] >= t_min[i] && f[i].xp[0][j] <= t_max[i] ) { local_f[i].nts++ ; } } snew(local_f[i].xp[0],local_f[i].nts); snew(local_f[i].xp[1],local_f[i].nts); } // now copy the data // not only the derivatives of the absorbance, also the conc k=0; for(i=0; i<n; i++){ local_f[i].conc = f[i].conc ; for(j=0; j<f[i].nts; j++){ if( f[i].xp[0][j] >= t_min[i] && f[i].xp[0][j] <= t_max[i] ) { local_f[i].xp[0][k] = f[i].xp[0][j] ; local_f[i].xp[1][k] = f[i].xp[1][j] ; // we use this loop to compute the TSS, the total sum of squares of the // "y" data, to be used for r_squared after we know chi_sq abs_t += local_f[i].xp[1][k] ; tot_abs++; k++; } } k=0; } // Total number of points to fit size_t pp = 4; const gsl_multifit_fdfsolver_type *T; T = gsl_multifit_fdfsolver_lmsder; gsl_multifit_fdfsolver *s; // do a fit for each triplex curve for (i=0; i<n; i++){ // Total number of points to fit if (bVerbose){printf("Working on curve n %d\n",i);} struct fit_data d = { n,i, local_f}; tot_points = local_f[i].nts ; gsl_matrix *covar = gsl_matrix_alloc (pp, pp); gsl_multifit_function_fdf ff; gsl_vector *x; x = gsl_vector_alloc(pp); gsl_vector_set(x,0,f[i].tm2); gsl_vector_set(x,1,f[i].c); gsl_vector_set(x,2,-70); gsl_vector_set(x,3,-0.1); s = gsl_multifit_fdfsolver_alloc (T, tot_points, pp); // copy data to function ff.f = &eq_fit; ff.df = NULL; ff.fdf = NULL; ff.p = pp; // total number of points is total of points // in the curve plus the number of points for the inv. fit ff.n = tot_points; ff.params = &d; gsl_multifit_fdfsolver_set (s, &ff, x); iter=0; do { iter++; status = gsl_multifit_fdfsolver_iterate (s); if(bVerbose){ printf ("iter: %3u x = % 15.8f % 15.8f %15.8f " "|f(x)| = %g\n",iter, gsl_vector_get (s->x, 0), gsl_vector_get (s->x, 1), gsl_vector_get (s->x, 2), gsl_blas_dnrm2 (s->f)); } if (status) break; status = gsl_multifit_test_delta (s->dx, s->x, 1e-8, 1e-8); } while (status == GSL_CONTINUE && iter < 500); gsl_multifit_covar (s->J, 0.0, covar); gsl_matrix_free (covar); gsl_vector_free(x); // copy tm2 data adjusted from each curve local_f[i].tm2 = gsl_vector_get(s->x, 0); } //free first solver gsl_multifit_fdfsolver_free (s); // do the 1/tm vs ln(ct) fitting const gsl_multifit_fdfsolver_type *Tl; gsl_multifit_fdfsolver *sl; // fit params in the straight line int ppl = 2; gsl_matrix *covarl = gsl_matrix_alloc (ppl, ppl); struct fit_data dl = { n,i, local_f}; gsl_multifit_function_fdf ffl; gsl_vector *xl; xl = gsl_vector_alloc(ppl); // DH and DS gsl_vector_set(xl,0,-70); gsl_vector_set(xl,1,-0.1); Tl = gsl_multifit_fdfsolver_lmsder; sl = gsl_multifit_fdfsolver_alloc (Tl, n, ppl); // copy data to function ffl.f=&eq_fit_straight; ffl.df = NULL; ffl.fdf = NULL; ffl.p = ppl; // total number of points the number of curves ffl.n = n; ffl.params = &dl; gsl_multifit_fdfsolver_set (sl, &ffl, xl); iter=0; do { iter++; status = gsl_multifit_fdfsolver_iterate (sl); if(bVerbose){ printf ("iter: %3u x = % 15.8f % 15.8f " "|f(x)| = %g\n",iter, gsl_vector_get (sl->x, 0), gsl_vector_get (sl->x, 1), gsl_blas_dnrm2 (sl->f)); } if (status) break; status = gsl_multifit_test_delta (sl->dx, sl->x, 1e-8, 1e-8); } while (status == GSL_CONTINUE && iter < 500); gsl_multifit_covar (sl->J, 0.0, covarl); #define FIT(i) gsl_vector_get(sl->x, i) #define ERR(i) sqrt(gsl_matrix_get(covarl,i,i)) // compute contribution of inverse temperature to TSS for(i=0;i<n;i++){ inv_t += ((real)1.0/(real)local_f[i].tm2); tot_inv_t++; } mean_inv_t = inv_t / (real)tot_inv_t; for(i=0;i<n;i++){ tss_inv += (1.0/(real)local_f[i].tm2 - mean_inv_t ) * (1.0/(real)local_f[i].tm2 - mean_inv_t); } if (bUpdate){ fit.dh2 = gsl_vector_get(sl->x, 0); fit.ds2 = gsl_vector_get(sl->x, 1); fit.dg2 = fit.dh2 - 298.15*fit.ds2; for(i=0; i<n; i++){ f[i].tm2 = local_f[i].tm2 ; } } tss_tot = tss_inv ; double chi = gsl_blas_dnrm2(sl->f); fit.r2 = 1.0 - ( chi*chi / tss_tot ) ; double dof = n - ppl; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); if(bVerbose) { printf ("chisq/dof = %g\n", pow(chi, 2.0) / dof); printf ("r2 = %g\n", fit.r2); printf ("DH3 = %.5f +/- %.5f\n", FIT(0), c*ERR(0)); printf ("DS3 = %.5f +/- %.5f\n", FIT(1), c*ERR(1)); printf ("DG3 = %.5f +/- %.5f\n", FIT(0)-298*FIT(1),c*ERR(1)+c*298*ERR(0)); printf ("status = %s\n", gsl_strerror (status)); } gsl_multifit_fdfsolver_free (sl); gsl_matrix_free (covarl); gsl_vector_free(xl); return fit; }
double *Fit::fitGslMultifit(int &iterations, int &status) { double *result = new double[d_p]; // declare input data struct FitData data = {static_cast<size_t>(d_n), static_cast<size_t>(d_p), d_x, d_y, d_y_errors, this}; gsl_multifit_function_fdf f; f.f = d_f; f.df = d_df; f.fdf = d_fdf; f.n = d_n; f.p = d_p; f.params = &data; // initialize solver const gsl_multifit_fdfsolver_type *T; switch (d_solver) { case ScaledLevenbergMarquardt: T = gsl_multifit_fdfsolver_lmsder; break; case UnscaledLevenbergMarquardt: T = gsl_multifit_fdfsolver_lmder; break; default: break; } gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc(T, d_n, d_p); gsl_multifit_fdfsolver_set(s, &f, d_param_init); // iterate solver algorithm for (iterations = 0; iterations < d_max_iterations; iterations++) { status = gsl_multifit_fdfsolver_iterate(s); if (status) break; status = gsl_multifit_test_delta(s->dx, s->x, d_tolerance, d_tolerance); if (status != GSL_CONTINUE) break; } // grab results for (int i = 0; i < d_p; i++) result[i] = gsl_vector_get(s->x, i); gsl_blas_ddot(s->f, s->f, &chi_2); #if GSL_MAJOR_VERSION < 2 gsl_multifit_covar(s->J, 0.0, covar); #else { gsl_matrix J; gsl_multifit_fdfsolver_jac(s, &J); gsl_multifit_covar(&J, 0.0, covar); } #endif if (d_y_error_source == UnknownErrors) { // multiply covar by variance of residuals, which is used as an estimate for // the // statistical errors (this relies on the Y errors being set to 1.0, so that // s->f is properly normalized) gsl_matrix_scale(covar, chi_2 / (d_n - d_p)); } // free memory allocated for fitting gsl_multifit_fdfsolver_free(s); return result; }
/** * C++ version of gsl_multifit_covar(). * @param J The Jacobian matrix * @param epsrel relative error (for removing linearly dependent columns) * @param covar The covariance matrix (return value) * @return Error code on failure */ inline int covar( matrix const& J, double epsrel, matrix& covar ){ return gsl_multifit_covar( J.get(), epsrel, covar.get() ); }
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { /* inputs: * image array * prmVect * mode * {options} */ dataStruct_t data; /* check inputs */ if (nrhs < 3) mexErrMsgTxt("Inputs should be: data, prmVect, mode."); if (!mxIsDouble(prhs[0])) mexErrMsgTxt("Data input must be double array."); size_t nx = mxGetN(prhs[0]); size_t ny = mxGetM(prhs[0]); if (nx != ny) mexErrMsgTxt("Input image must be a square."); if (!(nx % 2)) mexErrMsgTxt("The side of the input image must be odd."); int N = nx*ny; if (mxGetNumberOfElements(prhs[1])!=NPARAMS || !mxIsDouble(prhs[1])) mexErrMsgTxt("Incorrect parameter vector format."); if (!mxIsChar(prhs[2])) mexErrMsgTxt("Mode needs to be a string."); if (nrhs < 4) { data.maxIter = 500; data.eAbs = 1e-8; data.eRel = 1e-8; } else { if (!mxIsDouble(prhs[3]) || mxGetNumberOfElements(prhs[3])!=3) mexErrMsgTxt("Options must must be double array with 3 elements."); double *options = mxGetPr(prhs[3]); data.maxIter = options[0]; data.eAbs = options[1]; data.eRel = options[2]; } /* read mode input */ int np = (int)mxGetNumberOfElements(prhs[2]); char *mode; mode = (char*)malloc(sizeof(char)*(np+1)); mxGetString(prhs[2], mode, np+1); int i; for (i=0; i<strlen(mode); ++i) { mode[i] = tolower(mode[i]); } np = 0; /* number of parameters to fit */ for (i=0; i<NPARAMS; ++i) { if (strchr(mode, refMode[i])!=NULL) { np++; } } if (np==0) mexErrMsgTxt("Unknown mode."); /* allocate */ data.nx = nx; data.np = np; data.pixels = mxGetPr(prhs[0]); data.gx = (double*)malloc(sizeof(double)*nx); data.gy = (double*)malloc(sizeof(double)*nx); data.estIdx = (int*)malloc(sizeof(int)*np); memcpy(data.prmVect, mxGetPr(prhs[1]), NPARAMS*sizeof(double)); data.dfunc = (pfunc_t*) malloc(sizeof(pfunc_t) * np); /* read mask/pixels */ data.nValid = N; for (i=0; i<N; ++i) { data.nValid -= (int)mxIsNaN(data.pixels[i]); } if (data.nValid < 5) mexErrMsgTxt("Input image must contain at least 5 data points."); data.idx = (int*)malloc(sizeof(int)*data.nValid); int *nanIdx = (int*)malloc(sizeof(int)*(N-data.nValid)); int k = 0, l = 0; for (i=0; i<N; ++i) { if (!mxIsNaN(data.pixels[i])) { data.idx[k++] = i; } else { nanIdx[l++] = i; } } np = 0; if (strchr(mode, 'x')!=NULL) {data.estIdx[np] = 0; data.dfunc[np++] = df_dx;} if (strchr(mode, 'y')!=NULL) {data.estIdx[np] = 1; data.dfunc[np++] = df_dy;} if (strchr(mode, 'a')!=NULL) {data.estIdx[np] = 2; data.dfunc[np++] = df_dA;} if (strchr(mode, 's')!=NULL) {data.estIdx[np] = 3; data.dfunc[np++] = df_ds;} if (strchr(mode, 'c')!=NULL) {data.estIdx[np] = 4; data.dfunc[np++] = df_dc;} data.x_init = (double*)malloc(sizeof(double)*np); for (i=0; i<np; ++i) { data.x_init[i] = data.prmVect[data.estIdx[i]]; } MLalgo(&data); /* parameters */ if (nlhs > 0) { plhs[0] = mxCreateDoubleMatrix(1, NPARAMS, mxREAL); memcpy(mxGetPr(plhs[0]), data.prmVect, NPARAMS*sizeof(double)); } /* standard dev. of parameters & covariance matrix */ double RSS = 0.0; double* resValid = NULL; if (nlhs > 1) { resValid = (double*)malloc(data.nValid*sizeof(double)); for (i=0; i<data.nValid; ++i) { resValid[i] = gsl_vector_get(data.residuals, i); RSS += resValid[i]*resValid[i]; } gsl_matrix *covar = gsl_matrix_alloc(np, np); gsl_multifit_covar(data.J, 0.0, covar); double iRSS = RSS/(data.nValid - data.np - 1); plhs[1] = mxCreateDoubleMatrix(1, data.np, mxREAL); double *prmStd = mxGetPr(plhs[1]); for (i=0; i<data.np; ++i) { prmStd[i] = sqrt(iRSS*gsl_matrix_get(covar, i, i)); } if (nlhs > 2) { plhs[2] = mxCreateDoubleMatrix(np, np, mxREAL); /* cov. matrix is symmetric, no need to transpose */ memcpy(mxGetPr(plhs[2]), covar->data, np*np*sizeof(double)); } gsl_matrix_free(covar); } /* residuals */ if (nlhs > 3) { const char *fieldnames[] = {"data", "hAD", "mean", "std", "RSS"}; mwSize dims[2] = {1, 1}; plhs[3] = mxCreateStructArray(2, dims, 5, fieldnames); mxArray *val = mxCreateDoubleMatrix(nx, nx, mxREAL); double* res = mxGetPr(val); double mean = 0.0, std = 0.0; for (i=0; i<data.nValid; ++i) { res[data.idx[i]] = resValid[i]; mean += resValid[i]; } std = sqrt((RSS-mean*mean/data.nValid)/(data.nValid-1)); mean /= data.nValid; for (i=0; i<N-data.nValid; ++i) { res[nanIdx[i]] = mxGetNaN(); } // A-D test, case 2: mean known unsigned char hAD = adtest(resValid, data.nValid, 2, 0.0, std, 0.05); mxSetFieldByNumber(plhs[3], 0, 0, val); mxSetFieldByNumber(plhs[3], 0, 1, mxCreateLogicalScalar(hAD)); mxSetFieldByNumber(plhs[3], 0, 2, mxCreateDoubleScalar(mean)); mxSetFieldByNumber(plhs[3], 0, 3, mxCreateDoubleScalar(std)); mxSetFieldByNumber(plhs[3], 0, 4, mxCreateDoubleScalar(RSS)); } /* Jacobian */ if (nlhs > 4) { /* convert row-major double* data.J->data to column-major double* */ plhs[4] = mxCreateDoubleMatrix(N, np, mxREAL); double *J = mxGetPr(plhs[4]); int k; for (k=0; k<np; ++k) { for (i=0; i<data.nValid; ++i) { J[data.idx[i]+k*N] = gsl_matrix_get(data.J, i, k); } for (i=0; i<N-data.nValid; ++i) { J[nanIdx[i]+k*N] = mxGetNaN(); } } } free(resValid); gsl_matrix_free(data.J); gsl_vector_free(data.residuals); free(data.x_init); free(nanIdx); free(data.idx); free(data.dfunc); free(data.estIdx); free(data.gy); free(data.gx); free(mode); }
static int lmniel_covar(void *vstate, const double epsrel, gsl_matrix * covar) { lmniel_state_t *state = (lmniel_state_t *) vstate; return gsl_multifit_covar(state->J, epsrel, covar); }
void test_fdf (const char * name, gsl_multifit_function_fdf * f, double x0[], double x_final[], double f_sumsq, double sigma[]) { const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; const size_t n = f->n; const size_t p = f->p; int status; size_t iter = 0; gsl_vector_view x = gsl_vector_view_array (x0, p); T = gsl_multifit_fdfsolver_lmsder; s = gsl_multifit_fdfsolver_alloc (T, n, p); gsl_multifit_fdfsolver_set (s, f, &x.vector); do { status = gsl_multifit_fdfsolver_iterate (s); #ifdef DEBUG printf("iter = %d status = %d |f| = %.18e x = \n", iter, status, gsl_blas_dnrm2 (s->f)); gsl_vector_fprintf(stdout, s->x, "%.8e"); #endif status = gsl_multifit_test_delta (s->dx, s->x, 0.0, 1e-7); iter++; } while (status == GSL_CONTINUE && iter < 1000); { size_t i; gsl_matrix * covar = gsl_matrix_alloc (p, p); gsl_multifit_covar (s->J, 0.0, covar); for (i = 0 ; i < p; i++) { gsl_test_rel (gsl_vector_get (s->x, i), x_final[i], 1e-5, "%s, lmsder, x%u", name, i); } { double s2 = pow(gsl_blas_dnrm2 (s->f), 2.0); gsl_test_rel (s2, f_sumsq, 1e-5, "%s, lmsder, |f|^2", name); for (i = 0; i < p; i++) { double ei = sqrt(s2/(n-p))*sqrt(gsl_matrix_get(covar,i,i)); gsl_test_rel (ei, sigma[i], 1e-4, "%s, sigma(%d)", name, i) ; } } gsl_matrix_free (covar); } gsl_multifit_fdfsolver_free (s); }
int main (void) { const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; int status; unsigned int i, iter = 0; const size_t n = N; const size_t p = 3; gsl_matrix *covar = gsl_matrix_alloc (p, p); double y[N], sigma[N]; struct data d = { n, y, sigma}; gsl_multifit_function_fdf f; double x_init[3] = { 1.0, 0.0, 0.0 }; gsl_vector_view x = gsl_vector_view_array (x_init, p); const gsl_rng_type * type; gsl_rng * r; gsl_rng_env_setup(); type = gsl_rng_default; r = gsl_rng_alloc (type); f.f = &expb_f; f.df = &expb_df; f.fdf = &expb_fdf; f.n = n; f.p = p; f.params = &d; /* This is the data to be fitted */ for (i = 0; i < n; i++) { double t = i; y[i] = 1.0 + 5 * exp (-0.1 * t) + gsl_ran_gaussian (r, 0.1); sigma[i] = 0.1; printf ("data: %u %g %g\n", i, y[i], sigma[i]); }; T = gsl_multifit_fdfsolver_lmsder; s = gsl_multifit_fdfsolver_alloc (T, n, p); gsl_multifit_fdfsolver_set (s, &f, &x.vector); print_state (iter, s); do { iter++; status = gsl_multifit_fdfsolver_iterate (s); printf ("status = %s\n", gsl_strerror (status)); print_state (iter, s); if (status) break; status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4); } while (status == GSL_CONTINUE && iter < 500); gsl_multifit_covar (s->J, 0.0, covar); #define FIT(i) gsl_vector_get(s->x, i) #define ERR(i) sqrt(gsl_matrix_get(covar,i,i)) { double chi = gsl_blas_dnrm2(s->f); double dof = n - p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); printf("chisq/dof = %g\n", pow(chi, 2.0) / dof); printf ("A = %.5f +/- %.5f\n", FIT(0), c*ERR(0)); printf ("lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1)); printf ("b = %.5f +/- %.5f\n", FIT(2), c*ERR(2)); } printf ("status = %s\n", gsl_strerror (status)); gsl_multifit_fdfsolver_free (s); gsl_matrix_free (covar); gsl_rng_free (r); return 0; }
/******************************************************************************* * fit_gaussian * Fit data to a guassian and return the results. Ideally, this should give the * same results as scipy.optimize.curve_fit. * Input: * hist: Histogram to fit the gaussian to * Output: * chisq: Chi^2 of the histogram * ndf: Number of degrees of freedom of the fit * fit_params: Fit parameters ******************************************************************************/ gsl_vector *fit_gaussian(gsl_histogram *hist, double *chisq, long *ndf, gsl_matrix *covar){ double tol; double *hbin, *hrange, bin_width, xdata, min, max; double magnitude, mean, sigma; double error, ythr; int status; long gpars, nonzero, nbins; long i; gsl_vector *pars, *fit_params; gsl_multifit_fdfsolver *gfit; gsl_multifit_function_fdf gaus; const gsl_multifit_fdfsolver_type *ftype; /* Allowed relative error is what scipy uses */ /* tol = 1.49012e-8; scipy least squares default */ tol = 1e-14; /* get number of bins containing data */ nbins = hist -> n; hbin = hist -> bin; hrange = hist -> range; nonzero = 0; for (i=0; i<nbins; i++){ if (hbin[i]) nonzero++; } /* Set the function */ gaus.f = &gaus_f; gaus.df = &gaus_df; gaus.fdf = &gaus_fdf; gaus.n = nonzero; gaus.p = 3; gaus.params = hist; /* Initialize the solver */ gpars = 3; pars = gsl_vector_alloc(gpars); gsl_vector_set_all(pars, 1.0); ftype = gsl_multifit_fdfsolver_lmsder; gfit = gsl_multifit_fdfsolver_alloc(ftype, nonzero, gpars); gsl_multifit_fdfsolver_set(gfit, &gaus, pars); /* loop the solver and solve this thing */ do { status = gsl_multifit_fdfsolver_iterate(gfit); status = gsl_multifit_test_delta(gfit -> dx, gfit -> x, 0, tol); } while (status == GSL_CONTINUE); magnitude = gsl_vector_get(gfit -> x, 0); mean = gsl_vector_get(gfit -> x, 1); /* The fitted sigma might be negative, but it is squared when computing the * gaussian, so taking the absolute value of sigma is ok */ sigma = fabs(gsl_vector_get(gfit -> x, 2)); /* Compute the chi^2 */ min = hrange[0]; max = hrange[nbins]; bin_width = (max - min) / nbins; *chisq = 0; for (i = 0; i<nbins; i++){ if (hbin[i]){ xdata = hrange[i] + bin_width/2.0; error = sqrt(hbin[i]); ythr = gaussian(xdata, magnitude, mean, sigma); *chisq += pow((hbin[i] - ythr)/error, 2); } } *ndf = nonzero - gpars; /* Copy results to return vector */ fit_params = gsl_vector_alloc(gpars); gsl_vector_memcpy(fit_params, gfit -> x); /* Compute the covariance matrix */ gsl_multifit_covar(gfit -> J, 0.0, covar); /* Free the solver's memory */ gsl_vector_free(pars); gsl_multifit_fdfsolver_free(gfit); /* Return the results of the fit */ return fit_params; }
/* Calculates covariance matrix * * @param epsrel :: Is used to remove linear-dependent columns * @param covar :: Returned covariance matrix, here as */ void LevenbergMarquardtMinimizer::calCovarianceMatrix(double epsrel, gsl_matrix * covar) { gsl_multifit_covar (m_gslSolver->J, epsrel, covar); }
//Fitting. Allow fitting multiple q curves simultaneously to decrease the chance of converging to local minimum. void ddm::fitting() { int cnum_fit=num_fit; int ctimeWindow=timeWindow; //Find the truncation time if time window is set for (int itert=0; itert<num_fit; ++itert) { if (tau[itert]>ctimeWindow) { cnum_fit=itert; break; } } //Local variables int cqsize=qsize-qIncreList[num_qCurve-1]; //number of fitting result int cnum_qCurve=num_qCurve; int ctnum_fit=cnum_fit*num_qCurve; int cnumOfPara=numOfPara+2*num_qCurve; //Total number of parameters fittedPara=gsl_matrix_alloc(cqsize, cnumOfPara); //To store the fitting result and error. fitErr=gsl_matrix_alloc(cqsize, cnumOfPara); status = new int[cqsize]; //Record the status of fitting. //Using Levenberg-Marquardt algorithm as implemented in the scaled lmder routine in minpack. Jacobian is given. const gsl_multifit_fdfsolver_type *solverType = gsl_multifit_fdfsolver_lmsder; int progress=0; //Indicator of progress. //Objects to do numerical inverse Laplace transformation #ifdef ISFRTD NILT NILT1(OMP_NUM_THREADS), NILT2(OMP_NUM_THREADS), NILT3(OMP_NUM_THREADS), NILT4(OMP_NUM_THREADS); #endif #ifdef ISFRTDP NILT NILT1(OMP_NUM_THREADS), NILT2(OMP_NUM_THREADS), NILT3(OMP_NUM_THREADS), NILT4(OMP_NUM_THREADS), NILT5(OMP_NUM_THREADS); #endif #ifdef ISFRTDPTT NILT NILT1(OMP_NUM_THREADS), NILT2(OMP_NUM_THREADS), NILT3(OMP_NUM_THREADS), NILT4(OMP_NUM_THREADS), NILT5(OMP_NUM_THREADS), NILT6(OMP_NUM_THREADS); #endif #ifdef ISFRTDPfix NILT NILT1(OMP_NUM_THREADS), NILT2(OMP_NUM_THREADS); const long double vbar=vbarGuess; const long double sigma=sigmaGuess; const long double vbsigma2=vbar/sigma/sigma; const long double vb2sigma2=vbsigma2*vbar; const long double logvbsigma2=log(vbsigma2); const long double logfactor=vb2sigma2*logvbsigma2-gsl_sf_lngamma(vb2sigma2); const long double cpsiz1=logvbsigma2-gsl_sf_psi(vb2sigma2); const long double vb2sigma3=vb2sigma2/sigma; #endif #ifdef ISFRTDPTTfix NILT NILT1(OMP_NUM_THREADS), NILT2(OMP_NUM_THREADS), NILT3(OMP_NUM_THREADS); const long double vbar=vbarGuess; const long double sigma=sigmaGuess; const long double vbsigma2=vbar/sigma/sigma; const long double vb2sigma2=vbsigma2*vbar; const long double logvbsigma2=log(vbsigma2); const long double logfactor=vb2sigma2*logvbsigma2-gsl_sf_lngamma(vb2sigma2); const long double cpsiz1=logvbsigma2-gsl_sf_psi(vb2sigma2); const long double vb2sigma3=vb2sigma2/sigma; #endif #pragma omp parallel for for (int iterq=0; iterq<cqsize; ++iterq) { //Data array which is going to present to the fitting algorithm double* datafit=new double[ctnum_fit]; double* qList=new double[cnum_qCurve]; double* time=new double[ctnum_fit]; //Truncate the data, and put multiple curves into one array for (int iterqc=0; iterqc<cnum_qCurve; ++iterqc) { for (int iterf = 0; iterf < cnum_fit; ++iterf) { datafit[iterf+iterqc*cnum_fit]=(gsl_matrix_get(datag, iterq+qIncreList[iterqc], iterf)); //Fitting in log scale. time[iterf+iterqc*cnum_fit]=tau[iterf]; } qList[iterqc]=qabs[iterq+qIncreList[iterqc]]; } gsl_multifit_function_fdf fitfun; //Pointer of function to fit. dataStruct sdata; //GSL data structure //Data is passed to ISFfun by sdata sdata.data=datafit; sdata.tau=time; sdata.q=qList; sdata.num_fit=cnum_fit; sdata.num_qCurve=cnum_qCurve; #ifdef ISFRTD sdata.ISFILT=&NILT1; sdata.dvISFILT=&NILT2; sdata.dDISFILT=&NILT3; sdata.dlambdaISFILT=&NILT4; #endif #ifdef ISFRTDP sdata.ISFILT=&NILT1; sdata.dvbarISFILT=&NILT2; sdata.dsigmaISFILT=&NILT3; sdata.dDISFILT=&NILT4; sdata.dlambdaISFILT=&NILT5; #endif #ifdef ISFRTDPTT sdata.ISFILT=&NILT1; sdata.dvbarISFILT=&NILT2; sdata.dsigmaISFILT=&NILT3; sdata.dDISFILT=&NILT4; sdata.dlambdaISFILT=&NILT5; sdata.dTTISFILT=&NILT6; #endif #ifdef ISFRTDPfix sdata.alpha=alphaGuess; sdata.D=DGuess; sdata.vbar=vbar; sdata.sigma=sigma; sdata.vbsigma2=vbsigma2; sdata.logfactor=logfactor; sdata.vb2sigma2=vb2sigma2; sdata.cpsiz1=cpsiz1; sdata.vb2sigma3=vb2sigma3; sdata.ISFILT=&NILT1; sdata.dlambdaISFILT=&NILT2; #endif #ifdef ISFRTDPTTfix sdata.alpha=alphaGuess; sdata.D=DGuess; sdata.vbar=vbar; sdata.sigma=sigma; sdata.vbsigma2=vbsigma2; sdata.logfactor=logfactor; sdata.vb2sigma2=vb2sigma2; sdata.cpsiz1=cpsiz1; sdata.vb2sigma3=vb2sigma3; sdata.ISFILT=&NILT1; sdata.dlambdaISFILT=&NILT2; sdata.dTTISFILT=&NILT3; #endif //API fitfun.f=&ISFfun; #ifdef NoJacobian fitfun.df=0; fitfun.fdf=0; #else fitfun.df=&dISFfun; fitfun.fdf=&fdISFfun; #endif fitfun.n=ctnum_fit; fitfun.p=cnumOfPara; fitfun.params=&sdata; //Initialization of the parameters double* localinipara=new double[cnumOfPara]; for (int iterp=0; iterp<numOfPara; ++iterp) { localinipara[iterp]=inipara[iterp]; } //Estimation of A(q) and B(q) for (int iterqc=0; iterqc<num_qCurve; ++iterqc) { localinipara[numOfPara+1+2*iterqc] = gsl_matrix_get(datag, iterq+qIncreList[iterqc], 0); localinipara[numOfPara+2*iterqc] = gsl_matrix_get(datag, iterq+qIncreList[iterqc], num_fit-1)-localinipara[numOfPara+1+2*iterqc]; } //Initiallization of the solver gsl_vector_view para=gsl_vector_view_array(localinipara, cnumOfPara); gsl_multifit_fdfsolver* solver = gsl_multifit_fdfsolver_alloc(solverType, ctnum_fit, cnumOfPara); gsl_multifit_fdfsolver_set(solver, &fitfun, ¶.vector); int iter=0; //gsl_vector* g=gsl_vector_alloc(numOfPara); //For debugging and monitering the iterations // cout << qList[0] << ' ' << qList[1] << '\n'; // for (int iterpara=0; iterpara<cnumOfPara; ++iterpara) // { // cout << gsl_vector_get(solver->x, iterpara) << '\n'; // } // cout << '\n'; int cstatus=GSL_CONTINUE; //Current status do { gsl_multifit_fdfsolver_iterate(solver); //Iterate one step. cstatus = norm0_rel_test(solver->dx, solver->x, 1e-7, 1e-7); //Test the exiting criteria //For debugging and monitering the iterations // for (int iterpara=0; iterpara<cnumOfPara; ++iterpara) // { // cout << gsl_vector_get(solver->x, iterpara) << '\n'; // } // cout << '\n'; //If to use other exiting criteria //gsl_multifit_gradient(solver->J,solver->f, g); //status[iterq-1]=gsl_multifit_test_gradient(g, 1e-5); // status[iterq - 1] = covar_rel_test(solver->J, solver->x, 1e-4); ++iter; //Number of iterations exceed certain limitation if (iter>maxIter) { cstatus=GSL_EMAXITER; } } while (cstatus == GSL_CONTINUE); status[iterq]=cstatus; //gsl_vector_free(g); //Estimating the error. gsl_matrix* covar=gsl_matrix_alloc(cnumOfPara, cnumOfPara); gsl_multifit_covar(solver->J, 0.0, covar); for (int iterpara=0; iterpara<cnumOfPara; ++iterpara) //Record result. { gsl_matrix_set(fittedPara, iterq, iterpara, gsl_vector_get(solver->x, iterpara) ); gsl_matrix_set(fitErr, iterq, iterpara, sqrt(gsl_matrix_get(covar, iterpara, iterpara)) ); //Not presice in log scale } gsl_matrix_free(covar); gsl_multifit_fdfsolver_free(solver); //Output to standard I/O progress+=1; cout << "Fitted q=" << qabs[iterq] << " at iter=" << iter << ", " << 100.0*progress / qsize << "% completed from thread No." << omp_get_thread_num() << ", "<< gsl_strerror(status[iterq]) << "." << '\n'; for (int iterpara=0; iterpara<cnumOfPara; ++iterpara) { cout << gsl_matrix_get(fittedPara, iterq, iterpara) << '\n'; } cout << '\n'; delete [] datafit; delete [] qList; delete [] localinipara; delete [] time; } }
/** Executes the algorithm * * @throw runtime_error Thrown if algorithm cannot execute */ void Fit1D::exec() { // Custom initialization prepare(); // check if derivative defined in derived class bool isDerivDefined = true; gsl_matrix *M = NULL; try { const std::vector<double> inTest(m_parameterNames.size(), 1.0); std::vector<double> outTest(m_parameterNames.size()); const double xValuesTest = 0; JacobianImpl J; M = gsl_matrix_alloc(m_parameterNames.size(), 1); J.setJ(M); // note nData set to zero (last argument) hence this should avoid further // memory problems functionDeriv(&(inTest.front()), &J, &xValuesTest, 0); } catch (Exception::NotImplementedError &) { isDerivDefined = false; } gsl_matrix_free(M); // Try to retrieve optional properties int histNumber = getProperty("WorkspaceIndex"); const int maxInterations = getProperty("MaxIterations"); // Get the input workspace MatrixWorkspace_const_sptr localworkspace = getProperty("InputWorkspace"); // number of histogram is equal to the number of spectra const size_t numberOfSpectra = localworkspace->getNumberHistograms(); // Check that the index given is valid if (histNumber >= static_cast<int>(numberOfSpectra)) { g_log.warning("Invalid Workspace index given, using first Workspace"); histNumber = 0; } // Retrieve the spectrum into a vector const MantidVec &XValues = localworkspace->readX(histNumber); const MantidVec &YValues = localworkspace->readY(histNumber); const MantidVec &YErrors = localworkspace->readE(histNumber); // Read in the fitting range data that we were sent double startX = getProperty("StartX"); double endX = getProperty("EndX"); // check if the values had been set, otherwise use defaults if (isEmpty(startX)) { startX = XValues.front(); modifyStartOfRange(startX); // does nothing by default but derived class may // provide a more intelligent value } if (isEmpty(endX)) { endX = XValues.back(); modifyEndOfRange(endX); // does nothing by default but derived class may // previde a more intelligent value } int m_minX; int m_maxX; // Check the validity of startX if (startX < XValues.front()) { g_log.warning("StartX out of range! Set to start of frame."); startX = XValues.front(); } // Get the corresponding bin boundary that comes before (or coincides with) // this value for (m_minX = 0; XValues[m_minX + 1] < startX; ++m_minX) { } // Check the validity of endX and get the bin boundary that come after (or // coincides with) it if (endX >= XValues.back() || endX < startX) { g_log.warning("EndX out of range! Set to end of frame"); endX = XValues.back(); m_maxX = static_cast<int>(YValues.size()); } else { for (m_maxX = m_minX; XValues[m_maxX] < endX; ++m_maxX) { } } afterDataRangedDetermined(m_minX, m_maxX); // create and populate GSL data container warn user if l_data.n < l_data.p // since as a rule of thumb this is required as a minimum to obtained // 'accurate' // fitting parameter values. FitData l_data(this, getProperty("Fix")); l_data.n = m_maxX - m_minX; // m_minX and m_maxX are array index markers. I.e. e.g. 0 & 19. if (l_data.n == 0) { g_log.error("The data set is empty."); throw std::runtime_error("The data set is empty."); } if (l_data.n < l_data.p) { g_log.error( "Number of data points less than number of parameters to be fitted."); throw std::runtime_error( "Number of data points less than number of parameters to be fitted."); } l_data.X = new double[l_data.n]; l_data.sigmaData = new double[l_data.n]; l_data.forSimplexLSwrap = new double[l_data.n]; l_data.parameters = new double[nParams()]; // check if histogram data in which case use mid points of histogram bins const bool isHistogram = localworkspace->isHistogramData(); for (unsigned int i = 0; i < l_data.n; ++i) { if (isHistogram) l_data.X[i] = 0.5 * (XValues[m_minX + i] + XValues[m_minX + i + 1]); // take mid-point if histogram bin else l_data.X[i] = XValues[m_minX + i]; } l_data.Y = &YValues[m_minX]; // check that no error is negative or zero for (unsigned int i = 0; i < l_data.n; ++i) { if (YErrors[m_minX + i] <= 0.0) { l_data.sigmaData[i] = 1.0; } else l_data.sigmaData[i] = YErrors[m_minX + i]; } // create array of fitted parameter. Take these to those input by the user. // However, for doing the // underlying fitting it might be more efficient to actually perform the // fitting on some of other // form of the fitted parameters. For instance, take the Gaussian sigma // parameter. In practice it // in fact more efficient to perform the fitting not on sigma but 1/sigma^2. // The methods // modifyInitialFittedParameters() and modifyFinalFittedParameters() are used // to allow for this; // by default these function do nothing. m_fittedParameter.clear(); for (size_t i = 0; i < nParams(); i++) { m_fittedParameter.push_back(getProperty(m_parameterNames[i])); } modifyInitialFittedParameters( m_fittedParameter); // does nothing except if overwritten by derived class for (size_t i = 0; i < nParams(); i++) { l_data.parameters[i] = m_fittedParameter[i]; } // set-up initial guess for fit parameters gsl_vector *initFuncArg; initFuncArg = gsl_vector_alloc(l_data.p); for (size_t i = 0, j = 0; i < nParams(); i++) { if (l_data.active[i]) gsl_vector_set(initFuncArg, j++, m_fittedParameter[i]); } // set-up GSL container to be used with GSL simplex algorithm gsl_multimin_function gslSimplexContainer; gslSimplexContainer.n = l_data.p; // n here refers to number of parameters gslSimplexContainer.f = &gsl_costFunction; gslSimplexContainer.params = &l_data; // set-up GSL least squares container gsl_multifit_function_fdf f; f.f = &gsl_f; f.df = &gsl_df; f.fdf = &gsl_fdf; f.n = l_data.n; f.p = l_data.p; f.params = &l_data; // set-up remaining GSL machinery for least squared const gsl_multifit_fdfsolver_type *T = gsl_multifit_fdfsolver_lmsder; gsl_multifit_fdfsolver *s = NULL; if (isDerivDefined) { s = gsl_multifit_fdfsolver_alloc(T, l_data.n, l_data.p); gsl_multifit_fdfsolver_set(s, &f, initFuncArg); } // set-up remaining GSL machinery to use simplex algorithm const gsl_multimin_fminimizer_type *simplexType = gsl_multimin_fminimizer_nmsimplex; gsl_multimin_fminimizer *simplexMinimizer = NULL; gsl_vector *simplexStepSize = NULL; if (!isDerivDefined) { simplexMinimizer = gsl_multimin_fminimizer_alloc(simplexType, l_data.p); simplexStepSize = gsl_vector_alloc(l_data.p); gsl_vector_set_all(simplexStepSize, 1.0); // is this always a sensible starting step size? gsl_multimin_fminimizer_set(simplexMinimizer, &gslSimplexContainer, initFuncArg, simplexStepSize); } // finally do the fitting int iter = 0; int status; double finalCostFuncVal; double dof = static_cast<double>( l_data.n - l_data.p); // dof stands for degrees of freedom // Standard least-squares used if derivative function defined otherwise // simplex Progress prog(this, 0.0, 1.0, maxInterations); if (isDerivDefined) { do { iter++; status = gsl_multifit_fdfsolver_iterate(s); if (status) // break if error break; status = gsl_multifit_test_delta(s->dx, s->x, 1e-4, 1e-4); prog.report(); } while (status == GSL_CONTINUE && iter < maxInterations); double chi = gsl_blas_dnrm2(s->f); finalCostFuncVal = chi * chi / dof; // put final converged fitting values back into m_fittedParameter for (size_t i = 0, j = 0; i < nParams(); i++) if (l_data.active[i]) m_fittedParameter[i] = gsl_vector_get(s->x, j++); } else { do { iter++; status = gsl_multimin_fminimizer_iterate(simplexMinimizer); if (status) // break if error break; double size = gsl_multimin_fminimizer_size(simplexMinimizer); status = gsl_multimin_test_size(size, 1e-2); prog.report(); } while (status == GSL_CONTINUE && iter < maxInterations); finalCostFuncVal = simplexMinimizer->fval / dof; // put final converged fitting values back into m_fittedParameter for (unsigned int i = 0, j = 0; i < m_fittedParameter.size(); i++) if (l_data.active[i]) m_fittedParameter[i] = gsl_vector_get(simplexMinimizer->x, j++); } modifyFinalFittedParameters( m_fittedParameter); // do nothing except if overwritten by derived class // Output summary to log file std::string reportOfFit = gsl_strerror(status); g_log.information() << "Iteration = " << iter << "\n" << "Status = " << reportOfFit << "\n" << "Chi^2/DoF = " << finalCostFuncVal << "\n"; for (size_t i = 0; i < m_fittedParameter.size(); i++) g_log.information() << m_parameterNames[i] << " = " << m_fittedParameter[i] << " \n"; // also output summary to properties setProperty("OutputStatus", reportOfFit); setProperty("OutputChi2overDoF", finalCostFuncVal); for (size_t i = 0; i < m_fittedParameter.size(); i++) setProperty(m_parameterNames[i], m_fittedParameter[i]); std::string output = getProperty("Output"); if (!output.empty()) { // calculate covariance matrix if derivatives available gsl_matrix *covar(NULL); std::vector<double> standardDeviations; std::vector<double> sdExtended; if (isDerivDefined) { covar = gsl_matrix_alloc(l_data.p, l_data.p); gsl_multifit_covar(s->J, 0.0, covar); int iPNotFixed = 0; for (size_t i = 0; i < nParams(); i++) { sdExtended.push_back(1.0); if (l_data.active[i]) { sdExtended[i] = sqrt(gsl_matrix_get(covar, iPNotFixed, iPNotFixed)); iPNotFixed++; } } modifyFinalFittedParameters(sdExtended); for (size_t i = 0; i < nParams(); i++) if (l_data.active[i]) standardDeviations.push_back(sdExtended[i]); declareProperty( new WorkspaceProperty<API::ITableWorkspace>( "OutputNormalisedCovarianceMatrix", "", Direction::Output), "The name of the TableWorkspace in which to store the final " "covariance matrix"); setPropertyValue("OutputNormalisedCovarianceMatrix", output + "_NormalisedCovarianceMatrix"); Mantid::API::ITableWorkspace_sptr m_covariance = Mantid::API::WorkspaceFactory::Instance().createTable( "TableWorkspace"); m_covariance->addColumn("str", "Name"); std::vector<std::string> paramThatAreFitted; // used for populating 1st "name" column for (size_t i = 0; i < nParams(); i++) { if (l_data.active[i]) { m_covariance->addColumn("double", m_parameterNames[i]); paramThatAreFitted.push_back(m_parameterNames[i]); } } for (size_t i = 0; i < l_data.p; i++) { Mantid::API::TableRow row = m_covariance->appendRow(); row << paramThatAreFitted[i]; for (size_t j = 0; j < l_data.p; j++) { if (j == i) row << 1.0; else { row << 100.0 * gsl_matrix_get(covar, i, j) / sqrt(gsl_matrix_get(covar, i, i) * gsl_matrix_get(covar, j, j)); } } } setProperty("OutputNormalisedCovarianceMatrix", m_covariance); } declareProperty(new WorkspaceProperty<API::ITableWorkspace>( "OutputParameters", "", Direction::Output), "The name of the TableWorkspace in which to store the " "final fit parameters"); declareProperty( new WorkspaceProperty<MatrixWorkspace>("OutputWorkspace", "", Direction::Output), "Name of the output Workspace holding resulting simlated spectrum"); setPropertyValue("OutputParameters", output + "_Parameters"); setPropertyValue("OutputWorkspace", output + "_Workspace"); // Save the final fit parameters in the output table workspace Mantid::API::ITableWorkspace_sptr m_result = Mantid::API::WorkspaceFactory::Instance().createTable("TableWorkspace"); m_result->addColumn("str", "Name"); m_result->addColumn("double", "Value"); if (isDerivDefined) m_result->addColumn("double", "Error"); Mantid::API::TableRow row = m_result->appendRow(); row << "Chi^2/DoF" << finalCostFuncVal; for (size_t i = 0; i < nParams(); i++) { Mantid::API::TableRow row = m_result->appendRow(); row << m_parameterNames[i] << m_fittedParameter[i]; if (isDerivDefined && l_data.active[i]) { // perhaps want to scale standard deviations with sqrt(finalCostFuncVal) row << sdExtended[i]; } } setProperty("OutputParameters", m_result); // Save the fitted and simulated spectra in the output workspace MatrixWorkspace_const_sptr inputWorkspace = getProperty("InputWorkspace"); int iSpec = getProperty("WorkspaceIndex"); const MantidVec &inputX = inputWorkspace->readX(iSpec); const MantidVec &inputY = inputWorkspace->readY(iSpec); int histN = isHistogram ? 1 : 0; Mantid::DataObjects::Workspace2D_sptr ws = boost::dynamic_pointer_cast<Mantid::DataObjects::Workspace2D>( Mantid::API::WorkspaceFactory::Instance().create( "Workspace2D", 3, l_data.n + histN, l_data.n)); ws->setTitle(""); ws->getAxis(0)->unit() = inputWorkspace->getAxis(0) ->unit(); // UnitFactory::Instance().create("TOF"); for (int i = 0; i < 3; i++) ws->dataX(i) .assign(inputX.begin() + m_minX, inputX.begin() + m_maxX + histN); ws->dataY(0).assign(inputY.begin() + m_minX, inputY.begin() + m_maxX); MantidVec &Y = ws->dataY(1); MantidVec &E = ws->dataY(2); double *lOut = new double[l_data.n]; // to capture output from call to function() modifyInitialFittedParameters(m_fittedParameter); // does nothing except if // overwritten by derived // class function(&m_fittedParameter[0], lOut, l_data.X, l_data.n); modifyInitialFittedParameters(m_fittedParameter); // reverse the effect of // modifyInitialFittedParameters - if any for (unsigned int i = 0; i < l_data.n; i++) { Y[i] = lOut[i]; E[i] = l_data.Y[i] - Y[i]; } delete[] lOut; setProperty("OutputWorkspace", boost::dynamic_pointer_cast<MatrixWorkspace>(ws)); if (isDerivDefined) gsl_matrix_free(covar); } // clean up dynamically allocated gsl stuff if (isDerivDefined) gsl_multifit_fdfsolver_free(s); else { gsl_vector_free(simplexStepSize); gsl_multimin_fminimizer_free(simplexMinimizer); } delete[] l_data.X; delete[] l_data.sigmaData; delete[] l_data.forSimplexLSwrap; delete[] l_data.parameters; gsl_vector_free(initFuncArg); return; }
int OptimizationOptions::gslOptimize( NLSFunction *F, gsl_vector* x_vec, gsl_matrix *v, IterationLogger *itLog ) { const gsl_multifit_fdfsolver_type *Tlm[] = { gsl_multifit_fdfsolver_lmder, gsl_multifit_fdfsolver_lmsder }; const gsl_multimin_fdfminimizer_type *Tqn[] = { gsl_multimin_fdfminimizer_vector_bfgs, gsl_multimin_fdfminimizer_vector_bfgs2, gsl_multimin_fdfminimizer_conjugate_fr, gsl_multimin_fdfminimizer_conjugate_pr }; const gsl_multimin_fminimizer_type *Tnm[] = { gsl_multimin_fminimizer_nmsimplex, gsl_multimin_fminimizer_nmsimplex2, gsl_multimin_fminimizer_nmsimplex2rand }; int gsl_submethod_max[] = { sizeof(Tlm) / sizeof(Tlm[0]), sizeof(Tqn) / sizeof(Tqn[0]), sizeof(Tnm) / sizeof(Tnm[0]) }; int status, status_dx, status_grad, k; double g_norm, x_norm; /* vectorize x row-wise */ size_t max_ind, min_ind; double max_val, min_val, abs_max_val = 0, abs_min_val; if (this->method < 0 || this->method > sizeof(gsl_submethod_max)/sizeof(gsl_submethod_max[0]) || this->submethod < 0 || this->submethod > gsl_submethod_max[this->method]) { throw new Exception("Unknown optimization method.\n"); } if (this->maxiter < 0 || this->maxiter > 5000) { throw new Exception("opt.maxiter should be in [0;5000].\n"); } /* LM */ gsl_multifit_fdfsolver* solverlm; gsl_multifit_function_fdf fdflm = { &(F->_f_ls), &(F->_df_ls), &(F->_fdf_ls), F->getNsq(), F->getNvar(), F }; gsl_vector *g; /* QN */ double stepqn = this->step; gsl_multimin_fdfminimizer* solverqn; gsl_multimin_function_fdf fdfqn = { &(F->_f), &(F->_df), &(F->_fdf), F->getNvar(), F }; /* NM */ double size; gsl_vector *stepnm; gsl_multimin_fminimizer* solvernm; gsl_multimin_function fnm = { &(F->_f), F->getNvar(), F }; /* initialize the optimization method */ switch (this->method) { case SLRA_OPT_METHOD_LM: /* LM */ solverlm = gsl_multifit_fdfsolver_alloc(Tlm[this->submethod], F->getNsq(), F->getNvar()); gsl_multifit_fdfsolver_set(solverlm, &fdflm, x_vec); g = gsl_vector_alloc(F->getNvar()); break; case SLRA_OPT_METHOD_QN: /* QN */ solverqn = gsl_multimin_fdfminimizer_alloc(Tqn[this->submethod], F->getNvar() ); gsl_multimin_fdfminimizer_set(solverqn, &fdfqn, x_vec, stepqn, this->tol); status_dx = GSL_CONTINUE; break; case SLRA_OPT_METHOD_NM: /* NM */ solvernm = gsl_multimin_fminimizer_alloc(Tnm[this->submethod], F->getNvar()); stepnm = gsl_vector_alloc(F->getNvar()); gsl_vector_set_all(stepnm, this->step); gsl_multimin_fminimizer_set( solvernm, &fnm, x_vec, stepnm ); break; } /* optimization loop */ Log::lprintf(Log::LOG_LEVEL_FINAL, "SLRA optimization:\n"); status = GSL_SUCCESS; status_dx = GSL_CONTINUE; status_grad = GSL_CONTINUE; this->iter = 0; switch (this->method) { case SLRA_OPT_METHOD_LM: gsl_blas_ddot(solverlm->f, solverlm->f, &this->fmin); gsl_multifit_gradient(solverlm->J, solverlm->f, g); gsl_vector_scale(g, 2); { gsl_vector *g2 = gsl_vector_alloc(g->size); F->computeFuncAndGrad(x_vec, NULL, g2); gsl_vector_sub(g2, g); if (gsl_vector_max(g2) > 1e-10 || gsl_vector_min(g2) < -1e-10) { Log::lprintf(Log::LOG_LEVEL_NOTIFY, "Gradient error, max = %14.10f, min = %14.10f ...", gsl_vector_max(g2), gsl_vector_min(g2)); print_vec(g2); } gsl_vector_free(g2); } if (itLog != NULL) { itLog->reportIteration(0, solverlm->x, this->fmin, g); } break; case SLRA_OPT_METHOD_QN: this->fmin = gsl_multimin_fdfminimizer_minimum(solverqn); if (itLog != NULL) { itLog->reportIteration(0, solverqn->x, this->fmin, solverqn->gradient); } break; case SLRA_OPT_METHOD_NM: this->fmin = gsl_multimin_fminimizer_minimum( solvernm ); if (itLog != NULL) { itLog->reportIteration(this->iter, solvernm->x, this->fmin, NULL); } break; } while (status_dx == GSL_CONTINUE && status_grad == GSL_CONTINUE && status == GSL_SUCCESS && this->iter < this->maxiter) { if (this->method == SLRA_OPT_METHOD_LM && this->maxx > 0) { if (gsl_vector_max(solverlm->x) > this->maxx || gsl_vector_min(solverlm->x) < -this->maxx ){ break; } } this->iter++; switch (this->method) { case SLRA_OPT_METHOD_LM: /* Levenberg-Marquardt */ status = gsl_multifit_fdfsolver_iterate(solverlm); gsl_multifit_gradient(solverlm->J, solverlm->f, g); gsl_vector_scale(g, 2); /* check the convergence criteria */ if (this->epsabs != 0 || this->epsrel != 0) { status_dx = gsl_multifit_test_delta(solverlm->dx, solverlm->x, this->epsabs, this->epsrel); } else { status_dx = GSL_CONTINUE; } status_grad = gsl_multifit_test_gradient(g, this->epsgrad); gsl_blas_ddot(solverlm->f, solverlm->f, &this->fmin); if (itLog != NULL) { itLog->reportIteration(this->iter, solverlm->x, this->fmin, g); } break; case SLRA_OPT_METHOD_QN: status = gsl_multimin_fdfminimizer_iterate( solverqn ); /* check the convergence criteria */ status_grad = gsl_multimin_test_gradient( gsl_multimin_fdfminimizer_gradient(solverqn), this->epsgrad); status_dx = gsl_multifit_test_delta(solverqn->dx, solverqn->x, this->epsabs, this->epsrel); this->fmin = gsl_multimin_fdfminimizer_minimum(solverqn); if (itLog != NULL) { itLog->reportIteration(this->iter, solverqn->x, this->fmin, solverqn->gradient); } break; case SLRA_OPT_METHOD_NM: status = gsl_multimin_fminimizer_iterate( solvernm ); /* check the convergence criteria */ size = gsl_multimin_fminimizer_size( solvernm ); status_dx = gsl_multimin_test_size( size, this->epsx ); this->fmin = gsl_multimin_fminimizer_minimum( solvernm ); if (itLog != NULL) { itLog->reportIteration(this->iter, solvernm->x, this->fmin, NULL); } break; } } if (this->iter >= this->maxiter) { status = EITER; } switch (this->method) { case SLRA_OPT_METHOD_LM: gsl_vector_memcpy(x_vec, solverlm->x); if (v != NULL) { gsl_multifit_covar(solverlm->J, this->epscov, v); /* ??? Different eps */ } gsl_blas_ddot(solverlm->f, solverlm->f, &this->fmin); break; case SLRA_OPT_METHOD_QN: gsl_vector_memcpy(x_vec, solverqn->x); this->fmin = solverqn->f; break; case SLRA_OPT_METHOD_NM: gsl_vector_memcpy(x_vec, solvernm->x); this->fmin = solvernm->fval; break; } /* print exit information */ if (Log::getMaxLevel() >= Log::LOG_LEVEL_FINAL) { /* unless "off" */ switch (status) { case EITER: Log::lprintf("SLRA optimization terminated by reaching " "the maximum number of iterations.\n" "The result could be far from optimal.\n"); break; case GSL_ETOLF: Log::lprintf("Lack of convergence: " "progress in function value < machine EPS.\n"); break; case GSL_ETOLX: Log::lprintf("Lack of convergence: " "change in parameters < machine EPS.\n"); break; case GSL_ETOLG: Log::lprintf("Lack of convergence: " "change in gradient < machine EPS.\n"); break; case GSL_ENOPROG: Log::lprintf("Possible lack of convergence: no progress.\n"); break; } if (status_grad != GSL_CONTINUE && status_dx != GSL_CONTINUE) { Log::lprintf("Optimization terminated by reaching the convergence " "tolerance for both X and the gradient.\n"); } else { if (status_grad != GSL_CONTINUE) { Log::lprintf("Optimization terminated by reaching the convergence " "tolerance for the gradient.\n"); } else { Log::lprintf("Optimization terminated by reaching the convergence " "tolerance for X.\n"); } } } /* Cleanup */ switch (this->method) { case SLRA_OPT_METHOD_LM: /* LM */ gsl_multifit_fdfsolver_free(solverlm); gsl_vector_free(g); break; case SLRA_OPT_METHOD_QN: /* QN */ gsl_multimin_fdfminimizer_free(solverqn); break; case SLRA_OPT_METHOD_NM: /* NM */ gsl_multimin_fminimizer_free(solvernm); gsl_vector_free(stepnm); break; } return GSL_SUCCESS; /* <- correct with status */ }
//------------------------------------------------------------------------------ // findCorrection () : Uses a GSL Levenberg-Marquardt algorithm to fit the lines // in FittedLines to the wavenumbers in the user-specified calibration standard. // The result is the optimal wavenumber correction factor for the uncalibrated // data, which is stored in the class variable WaveCorrection. Information about // the fit residuals are saved by calling calcDiffStats(). // void ListCal::findCorrection () { // Prepare the GSL Solver and associated objects. A non-linear solver is used, // the precise type of which is determined by SOLVER_TYPE, defined in // MgstFcn.h. const size_t NumParameters = 1; const size_t NumLines = FittedLines.size (); double GuessArr [NumParameters]; for (unsigned int i = 0; i < NumParameters; i ++) { GuessArr[i] = WaveCorrection; } const gsl_multifit_fdfsolver_type *SolverType; gsl_multifit_fdfsolver *Solver; gsl_multifit_function_fdf FitFunction; gsl_matrix *Covariance = gsl_matrix_alloc (NumParameters, NumParameters); gsl_vector_view VectorView = gsl_vector_view_array (GuessArr, NumParameters); FitFunction.f = &fitFn; FitFunction.df = &derivFn; FitFunction.fdf = &fitAndDerivFns; FitFunction.n = NumLines; FitFunction.p = NumParameters; FitFunction.params = &FittedLines; SolverType = SOLVER_TYPE; Solver = gsl_multifit_fdfsolver_alloc(SolverType, NumLines, NumParameters); gsl_multifit_fdfsolver_set (Solver, &FitFunction, &VectorView.vector); // Perform the fitting, one iteration at a time until one of the following // conditions is met: The absolute and relative changes in the fit parameters // become smaller than SOLVER_TOL, or the max number of allowed iterations, // SOLVER_MAX_ITERATIONS, is reached. unsigned int Iteration = 0; int Status; do { Iteration ++; Status = gsl_multifit_fdfsolver_iterate (Solver); if (Status) break; Status = gsl_multifit_test_delta (Solver->dx, Solver->x, SOLVER_TOL, SOLVER_TOL); } while (Status == GSL_CONTINUE && Iteration < SOLVER_MAX_ITERATIONS); // Output all the fit parameters with their associated error. gsl_multifit_covar (Solver -> J, 0.0, Covariance); #define FIT(i) gsl_vector_get (Solver -> x, i) #define ERR(i) sqrt (gsl_matrix_get (Covariance, i, i)) double chi = gsl_blas_dnrm2 (Solver -> f); double dof = NumLines - double(NumParameters); double c = chi / sqrt (dof); cout << "Correction factor: " << FIT(0) << " +/- " << c*ERR(0) << " (" << "reduced chi^2 = " << pow(chi, 2) / dof << ", " << "lines fitted = " << NumLines << ", c = " << c << ")" << endl; // Apply the wavenumber correction to all the lines loaded from the // uncalibrated spectrum WaveCorrection = FIT(0); WaveCorrectionError = c*ERR(0); calcDiffStats (); cout << "dSig/Sig Mean Residual: " << DiffMean / LC_DATA_SCALE << ", StdDev: " << DiffStdDev / LC_DATA_SCALE << ", StdErr: " << DiffStdErr / LC_DATA_SCALE << endl; // Clean up the memory and exit gsl_multifit_fdfsolver_free (Solver); gsl_matrix_free (Covariance); }
/* * Gaussian parameters calculation y=A/sqrt(2*pi*sigma^2) exp(-(x-x_0)^2/2/sigma^2), * which approximates the points set pts * Parameters A_, sigma_, x0_ may be NULL (if you don't need any of them) */ void gauss_fit(Points *pts, double *C_, double *A_, double *sigma_, double *x0_){ // VVVV lower parameters may be formed as a structure to change as function argument double epsabs = 1e-8,// absolute error epsrel = 1e-5,// relative error chi_max = 0.01;// max chi value for iterations criteria int max_iter = 300; // limit iterations number of gsl_multifit_fdfsolver size_t N_MIN = 10; // minimum points for approximation double x_init[4]; // AAAA upper parameters may be formed as a structure to change as function argument /* x_init, the best approximations: * x0 - not far from real (the nearest is the better) * sigma - not far from real (the nearest is the better) * A - not large ~10 (it has a weak effect) */ const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; int status; #ifdef EBUG int appNo = 0; #endif int iter; size_t i, j, n = pts->n, oldn; const size_t p = 4; gsl_matrix *covar = gsl_matrix_alloc (p, p); #ifdef EBUG double t0; #endif double *x, *y, *dy, chi, C, A, sigma, x0; if(n < 1) return; x = malloc(n * sizeof(double)); y = malloc(n * sizeof(double)); dy = malloc(n * sizeof(double)); struct data d = {n, x, y, dy}; gsl_multifit_function_fdf f; gsl_vector_view xx = gsl_vector_view_array(x_init, p); const gsl_rng_type *type; gsl_rng *r; gsl_rng_env_setup(); type = gsl_rng_default; r = gsl_rng_alloc (type); f.f = &gauss_f; f.df = &gauss_df; f.fdf = &gauss_fdf; f.n = n; f.p = p; f.params = &d; // fill data structure. Don't forget Okkam's razor!!! { Point *pt = pts->data; double *px = x, *py = y, *pdy = dy, sum = 0.; for(i = 0; i < n; i++, pt++){ *pdy++ = 1.; // I have no idea what is it, so init by 1 *px++ = pt->x; *py++ = pt->y; sum += pt->y; //DBG("point %d: (%g, %g)", i, pt->x, pt->y); } // fill x_init: x0, sigma, C, A (it can be a funtion parameter) x_init[3] = (*(--px) + *x) / 2.; x_init[2] = fabs((*x - *px) / 4.); x_init[0] = sum/(double)n; x_init[1] = sum; DBG("\nInitial parameters: x0=%.1f, sigma=%.1f, A=%.1f, C=%.1f", x_init[3], x_init[2], x_init[1], x_init[0]); } T = gsl_multifit_fdfsolver_lmder; // or also gsl_multifit_fdfsolver_lmsder s = gsl_multifit_fdfsolver_alloc(T, n, p); #ifdef EBUG t0 = dtime(); #endif do{ double dof, tres, c; DBG("\n************ Approximation %d ******************\n", appNo++); iter = 0; gsl_multifit_fdfsolver_set(s, &f, &xx.vector); do{ iter++; status = gsl_multifit_fdfsolver_iterate(s); if(status) break; status = gsl_multifit_test_delta(s->dx, s->x, epsabs, epsrel); }while(status == GSL_CONTINUE && iter < max_iter); DBG("time=%g\n", dtime()-t0); gsl_multifit_covar(s->J, 0.0, covar); chi = gsl_blas_dnrm2(s->f); dof = n - p; tres = chi; c = chi / sqrt(dof); // GSL_MAX_DBL(1., chi / sqrt(dof)); C = FIT(0), A = FIT(1), sigma = FIT(2), x0 = FIT(3); DBG("Number of iteratons = %d\n", iter); DBG("chi = %g, chi/dof = %g\n", chi, chi / sqrt(dof)); DBG("C = %.5f +/- %.5f\n", C, c*ERR(0)); DBG("A = %.5f +/- %.5f\n", A, c*ERR(1)); DBG("sigma = %.5f +/- %.5f\n", sigma, c*ERR(2)); DBG("x0 = %.5f +/- %.5f\n", x0, c*ERR(3)); j = 0; oldn = n; if(c < chi_max) break; // throw out bad (by chi) data for(i = 0; i < n; i++){ if(fabs(FN(i)) < tres){ if(i != j){ x[j] = x[i]; y[j] = y[i]; dy[j] = dy[i]; } j++; continue; } } if(j != n){ DBG("Chi tresholding %g, %zd points of %zd\n", tres, j, n); n = j; d.n = n; } }while(chi > chi_max && n != oldn && n > N_MIN); if(C_) *C_ = C; if(A_) *A_ = A; if(sigma_) *sigma_ = sigma; if(x0_) *x0_ = x0; //printf ("status = %s\n", gsl_strerror (status)); gsl_multifit_fdfsolver_free(s); gsl_matrix_free(covar); gsl_rng_free(r); free(x); free(y); free(dy); }
int main (void) { const gsl_multifit_fdfsolver_type *T = gsl_multifit_fdfsolver_lmsder; gsl_multifit_fdfsolver *s; int status, info; size_t i; const size_t n = N; const size_t p = 3; gsl_matrix *J = gsl_matrix_alloc(n, p); gsl_matrix *covar = gsl_matrix_alloc (p, p); double y[N], weights[N]; struct data d = { n, y }; gsl_multifit_function_fdf f; double x_init[3] = { 1.0, 0.0, 0.0 }; gsl_vector_view x = gsl_vector_view_array (x_init, p); gsl_vector_view w = gsl_vector_view_array(weights, n); const gsl_rng_type * type; gsl_rng * r; gsl_vector *res_f; double chi, chi0; const double xtol = 1e-8; const double gtol = 1e-8; const double ftol = 0.0; gsl_rng_env_setup(); type = gsl_rng_default; r = gsl_rng_alloc (type); f.f = &expb_f; f.df = &expb_df; /* set to NULL for finite-difference Jacobian */ f.n = n; f.p = p; f.params = &d; /* This is the data to be fitted */ for (i = 0; i < n; i++) { double t = i; double yi = 1.0 + 5 * exp (-0.1 * t); double si = 0.1 * yi; double dy = gsl_ran_gaussian(r, si); weights[i] = 1.0 / (si * si); y[i] = yi + dy; printf ("data: %zu %g %g\n", i, y[i], si); }; s = gsl_multifit_fdfsolver_alloc (T, n, p); /* initialize solver with starting point and weights */ gsl_multifit_fdfsolver_wset (s, &f, &x.vector, &w.vector); /* compute initial residual norm */ res_f = gsl_multifit_fdfsolver_residual(s); chi0 = gsl_blas_dnrm2(res_f); /* solve the system with a maximum of 20 iterations */ status = gsl_multifit_fdfsolver_driver(s, 20, xtol, gtol, ftol, &info); gsl_multifit_fdfsolver_jac(s, J); gsl_multifit_covar (J, 0.0, covar); /* compute final residual norm */ chi = gsl_blas_dnrm2(res_f); #define FIT(i) gsl_vector_get(s->x, i) #define ERR(i) sqrt(gsl_matrix_get(covar,i,i)) fprintf(stderr, "summary from method '%s'\n", gsl_multifit_fdfsolver_name(s)); fprintf(stderr, "number of iterations: %zu\n", gsl_multifit_fdfsolver_niter(s)); fprintf(stderr, "function evaluations: %zu\n", f.nevalf); fprintf(stderr, "Jacobian evaluations: %zu\n", f.nevaldf); fprintf(stderr, "reason for stopping: %s\n", (info == 1) ? "small step size" : "small gradient"); fprintf(stderr, "initial |f(x)| = %g\n", chi0); fprintf(stderr, "final |f(x)| = %g\n", chi); { double dof = n - p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); fprintf(stderr, "chisq/dof = %g\n", pow(chi, 2.0) / dof); fprintf (stderr, "A = %.5f +/- %.5f\n", FIT(0), c*ERR(0)); fprintf (stderr, "lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1)); fprintf (stderr, "b = %.5f +/- %.5f\n", FIT(2), c*ERR(2)); } fprintf (stderr, "status = %s\n", gsl_strerror (status)); gsl_multifit_fdfsolver_free (s); gsl_matrix_free (covar); gsl_matrix_free (J); gsl_rng_free (r); return 0; }
double fit_n(set_const* Init, double n0){ const gsl_multifit_fdfsolver_type *T; gsl_multifit_fdfsolver *s; int status; unsigned int i, iter = 0; const size_t n = 11; const size_t p = 5; double k = n0/0.16; gsl_matrix *covar = gsl_matrix_alloc (p, p); double y[11] = {4.45, 6.45 , 9.65, 13.29, 17.94, 22.92, 27.49, 38.82, 54.95, 75.13, 99.75}; double t[11] = {k*0.02,k*0.04, k*0.08,k*0.12,k*0.16,k*0.2,k*0.24, k*0.32, k*0.4,k*0.48, k*0.56}; struct data d = { n, y, t, Init}; gsl_multifit_function_fdf f; double x_init[5] = {Init->C_s,Init->C_o, Init->b,Init->c, Init->C_r}; //double x_init[6] = {11.56279437,7.49931859,0.00871711,0.00267620,0.86859184,0.5}; //double x_init[4] = { sqrt(130.746),sqrt(120.7244),1.0,10.0}; gsl_vector_view x = gsl_vector_view_array (x_init, p); const gsl_rng_type * type; gsl_rng * r; gsl_rng_env_setup(); type = gsl_rng_default; r = gsl_rng_alloc (type); f.f = &func_fit_n; f.df = NULL; f.fdf = NULL; f.n = n; f.p = p; f.params = &d; /* This is the data to be fitted */ /*for (i = 0; i < n; i++) { double t = i; y[i] = 1.0 + 5 * exp (-0.1 * t) + gsl_ran_gaussian (r, 0.1); sigma[i] = 0.1; printf ("data: %u %g %g\n", i, y[i], sigma[i]); };*/ T = gsl_multifit_fdfsolver_lmsder; s = gsl_multifit_fdfsolver_alloc (T, n, p); gsl_multifit_fdfsolver_set (s, &f, &x.vector); print_state (iter, s); do { iter++; status = gsl_multifit_fdfsolver_iterate (s); //printf ("status = %s\n", gsl_strerror (status)); print_state (iter, s); if (status) break; status = gsl_multifit_test_delta (s->dx, s->x, 1e-15, 0.0); } while (status == GSL_CONTINUE && iter < 2000); gsl_multifit_covar (s->J, 0.0, covar); #define FIT(i) gsl_vector_get(s->x, i) #define ERR(i) sqrt(gsl_matrix_get(covar,i,i)) cond(Init, FIT(0), FIT(1), FIT(2), FIT(3), FIT(4)); { double chi = gsl_blas_dnrm2(s->f); double dof = n - p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); //double c = 1.0; /*printf("chisq/dof = %g\n", pow(chi, 2.0) / dof); printf ("Cs = %.5f +/- %.5f\n", Init->C_s, c*ERR(0)); printf ("Co = %.5f +/- %.5f\n", Init->C_o, c*ERR(1)); printf ("b = %.5f +/- %.5f\n", Init->c, c*ERR(2)); printf ("c = %.5f +/- %.5f\n", Init->b, c*ERR(3)); printf ("Cr = %.5f +/- %.5f\n", Init->C_r, c*ERR(4));*/ } // printf ("status = %s\n", gsl_strerror (status)); double z = 0.65; gsl_matrix_free (covar); gsl_rng_free (r); double yi = 0; /*for (int i = 0; i < 11; i++){ double yi = EoS::t_E(t[i],0, Init)/(D*t[i]) - m_n ; printf("n = %.3f, %.3f %.3f %.3f \n", t[i], yi, y[i], yi-y[i]); }*/ /*return *(new set_const("APR_fit return constant set",FIT(0), FIT(1), 10.0, FIT(2),abs(FIT(3)), z, [](double f){return (1-f);}, [](double f){return 1.0;}, [=](double f){return eta_o(f);}, [](double f){return 1.0;}));*/ double rr = gsl_blas_dnrm2(s->x); gsl_multifit_fdfsolver_free (s); return rr; }