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;
}
