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;
}
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);
}
int MultiFitter::MainF()
{
multifit_fdfsolver_type = gsl_multifit_fdfsolver_lmsder;
sf = gsl_multifit_fsolver_alloc (multifit_fsolver_type, n, p);
gsl_multifit_fsolver_set (sf, &Ff, &x.vector);
do
{
iter++;
status = gsl_multifit_fsolver_iterate (sf);
status = gsl_multifit_test_delta (sf->dx, sf->x, epsabs, epsrel);
}
while (status == GSL_CONTINUE && iter < max_iter);
return status;
}
int
gsl_multilarge_nlinear_test (const double xtol, const double gtol,
const double ftol, int *info,
const gsl_multilarge_nlinear_workspace * w)
{
int status;
double gnorm, fnorm, phi;
*info = 0;
status = gsl_multifit_test_delta(w->dx, w->x, xtol*xtol, xtol);
if (status == GSL_SUCCESS)
{
*info = 1;
return GSL_SUCCESS;
}
/* compute gnorm = max_i( g_i * max(x_i, 1) ) */
gnorm = scaled_infnorm(w->x, w->g);
/* compute fnorm = ||f|| */
fnorm = gsl_blas_dnrm2(w->f);
phi = 0.5 * fnorm * fnorm;
#if 0
fprintf(stderr, "gnorm = %.12e fnorm = %.12e gnorm/phi = %.12e\n", gnorm, fnorm, gnorm / phi);
#endif
if (gnorm <= gtol * GSL_MAX(phi, 1.0))
{
*info = 2;
return GSL_SUCCESS;
}
#if 0
if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))
{
*info = 3;
return GSL_SUCCESS;
}
#endif
return GSL_CONTINUE;
}
static int gauss_fit(dist_t *dist, int ngauss, double *params)
{
data_t *dat = &dist->dat;
dat->ngauss = ngauss;
gsl_multifit_function_fdf mfunc;
mfunc.f = &func_f;
mfunc.df = &func_df;
mfunc.fdf = &func_set;
mfunc.n = dat->nvals;
mfunc.p = ngauss*3; // number of fitting parameters
mfunc.params = dat;
const gsl_multifit_fdfsolver_type *solver_type;
gsl_multifit_fdfsolver *solver;
gsl_vector_view vview = gsl_vector_view_array(params, mfunc.p);
solver_type = gsl_multifit_fdfsolver_lmsder;
solver = gsl_multifit_fdfsolver_alloc(solver_type, dat->nvals, mfunc.p);
gsl_multifit_fdfsolver_set(solver, &mfunc, &vview.vector);
int i, status;
size_t iter = 0;
do
{
status = gsl_multifit_fdfsolver_iterate(solver);
if ( status ) break;
status = gsl_multifit_test_delta(solver->dx, solver->x, 1e-4, 1e-4);
}
while (status == GSL_CONTINUE && iter++ < 500);
for (i=0; i<mfunc.p; i++)
params[i] = gsl_vector_get(solver->x, i);
gsl_multifit_fdfsolver_free(solver);
return iter>500 ? -1 : 0;
}
int LevenbergMarquardtMinimizer::hasConverged()
{
return gsl_multifit_test_delta(m_gslSolver->dx, m_gslSolver->x, 1e-4, 1e-4);
}
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;
}
void ImageTile::FitBackground()
{
// Chose to use the Levenberg-Marquardt solver with scaling
const gsl_multifit_fdfsolver_type * T = gsl_multifit_fdfsolver_lmsder;
// Construct solver
gsl_multifit_fdfsolver *solver = gsl_multifit_fdfsolver_alloc (T, _channelCount * _scanCount, _timeOrder + _freqOrder + 1);
if(solver == 0) throw std::exception();
// Initialize function information structure
gsl_multifit_function_fdf functionInfo;
/*if(_useMPF) {
functionInfo.f = &BaselineFunctionMPF;
functionInfo.df = &BaselineDerivativeMPF;
functionInfo.fdf = &BaselineCombinedMPF;
// chose 256 bits precision for intermediate values in the evaluation of the function and its derivative
mpf_set_default_prec (256);
} else {*/
functionInfo.f = &BaselineFunction;
functionInfo.df = &BaselineDerivative;
functionInfo.fdf = &BaselineCombined;
//}
functionInfo.n = _channelCount * _scanCount;
functionInfo.p = _timeOrder + _freqOrder + 1;
functionInfo.params = this;
// Initialize initial value of parameters
//gsl_vector x;
double x_init[_timeOrder + _freqOrder + 1];
for(int i = 0;i < _timeOrder + _freqOrder + 1;++i)
x_init[i] = _baselineConsts[i];
gsl_vector_view x_view = gsl_vector_view_array (x_init, _timeOrder + _freqOrder + 1);
gsl_multifit_fdfsolver_set (solver, &functionInfo, &x_view.vector);
// Start iterating
int status, iter=0;
do {
iter++;
status = gsl_multifit_fdfsolver_iterate(solver);
//PrintState(iter, solver);
if (status && status != GSL_CONTINUE) {
// std::cout << "Error: status = " << gsl_strerror (status) << std::endl;
break;
}
status = gsl_multifit_test_delta(solver->dx, solver->x, 0, 0);
} while (status == GSL_CONTINUE && iter < 250);
// Save coefficients
for(int i = 0;i<_freqOrder + _timeOrder + 1;++i)
this->_baselineConsts[i] = gsl_vector_get(solver->x, i);
//PrintState(iter, solver);
// Clean up
gsl_multifit_fdfsolver_free(solver);
}
GammaDistributionFitter::GammaDistributionFitResult GammaDistributionFitter::fit(vector<DPosition<2> > & input)
{
const gsl_multifit_fdfsolver_type * T = NULL;
gsl_multifit_fdfsolver * s = NULL;
int status = 0;
size_t iter = 0;
const size_t p = 2;
gsl_multifit_function_fdf f;
double x_init[2] = { init_param_.b, init_param_.p };
gsl_vector_view x = gsl_vector_view_array(x_init, p);
const gsl_rng_type * type = NULL;
gsl_rng * r = NULL;
gsl_rng_env_setup();
type = gsl_rng_default;
r = gsl_rng_alloc(type);
f.f = &gammaDistributionFitterf_;
f.df = &gammaDistributionFitterdf_;
f.fdf = &gammaDistributionFitterfdf_;
f.n = input.size();
f.p = p;
f.params = &input;
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc(T, input.size(), p);
gsl_multifit_fdfsolver_set(s, &f, &x.vector);
#ifdef GAMMA_DISTRIBUTION_FITTER_VERBOSE
printState_(iter, s);
#endif
do
{
++iter;
status = gsl_multifit_fdfsolver_iterate(s);
#ifdef GAMMA_DISTRIBUTION_FITTER_VERBOSE
printf("status = %s\n", gsl_strerror(status));
printState_(iter, s);
#endif
if (status)
{
break;
}
status = gsl_multifit_test_delta(s->dx, s->x, 1e-4, 1e-4);
#ifdef GAMMA_DISTRIBUTION_FITTER_VERBOSE
printf("Status = '%s'\n", gsl_strerror(status));
#endif
}
while (status == GSL_CONTINUE && iter < 1000);
#ifdef GAMMA_DISTRIBUTION_FITTER_VERBOSE
printf("Final status = '%s'\n", gsl_strerror(status));
#endif
if (status != GSL_SUCCESS)
{
gsl_rng_free(r);
gsl_multifit_fdfsolver_free(s);
throw Exception::UnableToFit(__FILE__, __LINE__, __PRETTY_FUNCTION__, "UnableToFit-GammaDistributionFitter", "Could not fit the gamma distribution to the data");
}
// write the result in a GammaDistributionFitResult struct
GammaDistributionFitResult result;
result.b = gsl_vector_get(s->x, 0);
result.p = gsl_vector_get(s->x, 1);
// build a formula with the fitted parameters for gnuplot
stringstream formula;
formula << "f(x)=" << "(" << result.b << " ** " << result.p << ") / gamma(" << result.p << ") * x ** (" << result.p << " - 1) * exp(- " << result.b << " * x)";
gnuplot_formula_ = formula.str();
#ifdef GAMMA_DISTRIBUTION_FITTER_VERBOSE
cout << gnuplot_formula_ << endl;
#endif
gsl_rng_free(r);
gsl_multifit_fdfsolver_free(s);
return result;
}
//------------------------------------------------------------------------------
// 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);
}
int kstfit_general_levenberg_marquardt(const double *const inArrays[], const int inArrayLens[],
const double inScalars[], double *outArrays[], int outArrayLens[],
double outScalars[], const char* inStrings[], char *outStrings[])
{
KST_UNUSED(outStrings);
int iReturn = -1;
if (inArrayLens[X] >= 2 && inArrayLens[Y] >= 2) {
mu::Parser parser;
double* pResult[4];
double* pDelete = 0L;
double* pInputX;
double* pInputY;
double *parameters;
double tolerance = inScalars[0];
double xvar;
char *token;
char *toSplit;
char *endPtr;
int maxIterations = (int)inScalars[1];
int n = inArrayLens[0];
int paramsNumber = 2;
int startsNumber = 0;
int iLengthData;
int i;
int j;
iLengthData = inArrayLens[X];
if( inArrayLens[Y] > iLengthData ) {
iLengthData = inArrayLens[Y];
}
if (inArrayLens[X] == iLengthData) {
pInputX = (double*)inArrays[X];
} else {
pDelete = (double*)malloc(iLengthData * sizeof( double ));
pInputX = pDelete;
for( i=0; i<iLengthData; i++) {
pInputX[i] = interpolate( i, iLengthData, inArrays[X], inArrayLens[X] );
}
}
if (inArrayLens[Y] == iLengthData) {
pInputY = (double*)inArrays[Y];
} else {
pDelete = (double*)malloc(iLengthData * sizeof( double ));
pInputY = pDelete;
for( i=0; i<iLengthData; i++) {
pInputY[i] = interpolate( i, iLengthData, inArrays[Y], inArrayLens[Y] );
}
}
//
// count the number of parameter names
//
toSplit = strdup(inStrings[1]);
token = strtok( toSplit, ",;:" );
while( token != NULL ) {
paramsNumber++;
token = strtok( NULL, ",;:" );
}
free(toSplit);
if( iLengthData > paramsNumber ) {
if( outArrayLens[0] != iLengthData ) {
pResult[0] = (double*)realloc( outArrays[0], iLengthData * sizeof( double ) );
} else {
pResult[0] = outArrays[0];
}
if( outArrayLens[1] != iLengthData ) {
pResult[1] = (double*)realloc( outArrays[1], iLengthData * sizeof( double ) );
} else {
pResult[1] = outArrays[1];
}
if( outArrayLens[2] != paramsNumber ) {
pResult[2] = (double*)realloc( outArrays[2], paramsNumber * sizeof( double ) );
} else {
pResult[2] = outArrays[2];
}
if( outArrayLens[3] != paramsNumber * paramsNumber ) {
pResult[3] = (double*)realloc( outArrays[3], paramsNumber * paramsNumber * sizeof( double ) );
} else {
pResult[3] = outArrays[3];
}
if( pResult[0] != NULL &&
pResult[1] != NULL &&
pResult[2] != NULL &&
pResult[3] != NULL ) {
outArrays[0] = pResult[0];
outArrayLens[0] = iLengthData;
outArrays[1] = pResult[1];
outArrayLens[1] = iLengthData;
outArrays[2] = pResult[2];
outArrayLens[2] = paramsNumber;
outArrays[3] = pResult[3];
outArrayLens[3] = paramsNumber * paramsNumber;
parameters = new double[paramsNumber];
for (i=0; i<paramsNumber; i++) {
parameters[i] = 0.0;
}
paramsNumber = 0;
//
// set the parameter names
//
toSplit = strdup(inStrings[1]);
token = strtok( toSplit, ",;:" );
while( token != NULL ) {
char *paramName = strdup(token);
char *paramPointer = paramName;
while (paramPointer[0] == ' ') {
paramPointer++;
}
while (paramPointer[strlen(paramPointer)] == ' ') {
paramPointer[strlen(paramPointer)] = '\0';
}
try {
parser.DefineVar(paramPointer, ¶meters[paramsNumber]);
} catch (mu::Parser::exception_type &e) {
}
paramsNumber++;
token = strtok( NULL, ",;:" );
free( paramName );
}
free(toSplit);
//
// set parameter initial guesses
//
double pInit[paramsNumber];
toSplit = strdup(inStrings[2]);
token = strtok( toSplit, ",;:" );
while( token != NULL ) {
pInit[startsNumber] = strtod(token, &endPtr);
startsNumber++;
token = strtok( NULL, ",;:" );
}
free(toSplit);
for (i=startsNumber; i<paramsNumber; i++) {
pInit[i] = 0.0;
}
if (strstr(inStrings[0], "pi") != 0L) {
parser.DefineConst("pi", M_PI);
}
if (strstr(inStrings[0], "Pi") != 0L) {
parser.DefineConst("Pi", M_PI);
}
if (strstr(inStrings[0], "PI") != 0L) {
parser.DefineConst("PI", M_PI);
}
parser.DefineVar("x", &xvar);
parser.SetExpr(inStrings[0]);
gsl_vector_view x = gsl_vector_view_array(pInit, paramsNumber);
struct fit d = { n, inArrays[0], inArrays[1], outArrays[0], &xvar, parameters, paramsNumber, &parser };
const gsl_multifit_fdfsolver_type *T = gsl_multifit_fdfsolver_lmsder;
gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc(T, n, paramsNumber);
if (s != 0L) {
gsl_multifit_function_fdf f;
gsl_matrix *covar = gsl_matrix_alloc(paramsNumber, paramsNumber);
if (covar != 0L) {
f.f = &function_f;
f.df = &function_df;
f.fdf = &function_fdf;
f.n = n;
f.p = paramsNumber;
f.params = &d;
gsl_multifit_fdfsolver_set(s, &f, &x.vector);
int status;
int iteration = 0;
do {
iteration++;
status = gsl_multifit_fdfsolver_iterate(s);
if (status) {
break;
}
status = gsl_multifit_test_delta(s->dx, s->x, tolerance, tolerance);
} while (status == GSL_CONTINUE && iteration < maxIterations);
gsl_multifit_covar(s->J, 0.0, covar);
for( i=0; i<n; i++ ) {
xvar = inArrays[0][i];
try {
outArrays[0][i] = parser.Eval();
outArrays[1][i] = inArrays[1][i] - outArrays[0][i];
} catch (mu::Parser::exception_type &e) {
outArrays[0][i] = 0.0;
outArrays[1][i] = 0.0;
}
}
for (i=0; i<paramsNumber; i++) {
outArrays[2][i] = parameters[i];
for (j=0; j<paramsNumber; j++) {
outArrays[3][(i*paramsNumber)+j] = gsl_matrix_get( covar, i, j );
}
}
//
// determine the value of chi^2/nu
//
outScalars[0] = gsl_blas_dnrm2( s->f );
iReturn = 0;
gsl_matrix_free(covar);
}
gsl_multifit_fdfsolver_free(s);
}
}
}
if( pDelete )
{
free( pDelete );
}
}
return iReturn;
}
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;
}
/** 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;
}
/*
* 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 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;
}
/*******************************************************************************
* 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;
}
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);
}
static int MLalgo(struct dataStruct *data) {
/* declare solvers */
const gsl_multifit_fdfsolver_type *T;
gsl_multifit_fdfsolver *s;
gsl_vector_view x = gsl_vector_view_array(data->x_init, data->np);
const gsl_rng_type *type;
gsl_rng_env_setup();
type = gsl_rng_default;
gsl_multifit_function_fdf f;
f.f = &gaussian_f;
f.df = &gaussian_df;
f.fdf = &gaussian_fdf;
f.n = data->nValid;
f.p = data->np;
f.params = data;
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc(T, data->nValid, data->np);
gsl_multifit_fdfsolver_set(s, &f, &x.vector);
int status, status2;
int iter = 0;
gsl_vector *gradt = gsl_vector_alloc(data->np);
do {
iter++;
status = gsl_multifit_fdfsolver_iterate(s);
if (status)
break;
status = gsl_multifit_test_delta(s->dx, s->x, data->eAbs, data->eRel);
gsl_multifit_gradient(s->J, s->f, gradt);
status2 = gsl_multifit_test_gradient(gradt, data->eAbs);
}
while ((status == GSL_CONTINUE || status2 == GSL_CONTINUE) && iter < data->maxIter);
gsl_vector_free(gradt);
int i;
for (i=0; i<data->np; ++i) {
data->prmVect[data->estIdx[i]] = gsl_vector_get(s->x, i);
}
data->prmVect[3] = fabs(data->prmVect[3]);
/* copy residuals */
data->residuals = gsl_vector_alloc(data->nValid);
gsl_vector_memcpy(data->residuals, s->f);
/* copy Jacobian */
data->J = gsl_matrix_alloc(data->nValid, data->np);
gsl_matrix_memcpy(data->J, s->J);
gsl_multifit_fdfsolver_free(s);
return 0;
}
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 */
}
int OptimizationOptions::lmpinvOptimize( NLSFunction *F, gsl_vector* x_vec,
IterationLogger *itLog ) {
int status, status_dx, status_grad, k;
double g_norm, x_norm;
if (this->maxiter < 0 || this->maxiter > 5000) {
throw new Exception("opt.maxiter should be in [0;5000].\n");
}
int scaled = 1; //this->submethod;
/* LM */
gsl_matrix *jac = gsl_matrix_alloc(F->getNsq(), F->getNvar());
gsl_vector *func = gsl_vector_alloc(F->getNsq());
gsl_vector *g = gsl_vector_alloc(F->getNvar());
gsl_vector *x_cur = gsl_vector_alloc(F->getNvar());
gsl_vector *x_new = gsl_vector_alloc(F->getNvar());
gsl_vector *dx = gsl_vector_alloc(F->getNvar());
gsl_vector *scaling = scaled ? gsl_vector_alloc(F->getNvar()) : NULL;
gsl_matrix *tempv = gsl_matrix_alloc(jac->size2, jac->size2);
gsl_vector *tempufuncsig = gsl_vector_alloc(jac->size2);
gsl_vector *templm = gsl_vector_alloc(jac->size2);
gsl_vector *sig = gsl_vector_alloc(mymin(jac->size1, jac->size2));
double lambda2 = 0, f_new;
int start_lm = 1;
/* Determine optimal work */
size_t status_svd = 0, minus1 = -1;
double tmp;
dgesvd_("A", "O", &jac->size2, &jac->size1, jac->data, &jac->tda, sig->data,
tempv->data, &tempv->size2, NULL, &jac->size1, &tmp, &minus1, &status_svd);
gsl_vector *work_vec = gsl_vector_alloc(tmp);
/* 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;
gsl_vector_memcpy(x_cur, x_vec);
F->computeFuncAndJac(x_cur, func, jac);
gsl_multifit_gradient(jac, func, g);
gsl_vector_scale(g, 2);
gsl_blas_ddot(func, func, &this->fmin);
if (itLog != NULL) {
itLog->reportIteration(0, x_cur, this->fmin, g);
}
{
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);
}
while (status_dx == GSL_CONTINUE &&
status_grad == GSL_CONTINUE &&
status == GSL_SUCCESS &&
this->iter < this->maxiter) {
/* Check convergence criteria (except dx) */
if (this->maxx > 0) {
if (gsl_vector_max(x_cur) > this->maxx || gsl_vector_min(x_cur) < -this->maxx ){
break;
}
}
this->iter++;
if (scaling != NULL) {
normalizeJacobian(jac, scaling);
}
/* Compute the SVD */
dgesvd_("A", "O", &jac->size2, &jac->size1, jac->data, &jac->tda, sig->data,
tempv->data, &tempv->size2, NULL, &jac->size1, work_vec->data,
&work_vec->size, &status_svd);
gsl_blas_dgemv(CblasTrans, -1.0, jac, func, 0.0, tempufuncsig);
gsl_vector_mul(tempufuncsig, sig);
while (1) {
moveGN(tempv, sig, tempufuncsig, lambda2, dx, F->getNEssVar(), scaling);
gsl_vector_memcpy(x_new, x_cur);
gsl_vector_add(x_new, dx);
F->computeFuncAndGrad(x_new, &f_new, NULL);
if (f_new <= this->fmin + 1e-16) {
lambda2 = 0.4 * lambda2;
break;
}
if (lambda2 > 1e100) {
status = GSL_ENOPROG;
break;
}
/* Else: update lambda */
if (start_lm) {
lambda2 = gsl_vector_get(sig, 0) * gsl_vector_get(sig, 0);
start_lm = 0;
} else {
lambda2 = 10 * lambda2;
Log::lprintf(Log::LOG_LEVEL_ITER, "lambda: %f\n", lambda2);
}
}
/* check the dx convergence criteria */
if (this->epsabs != 0 || this->epsrel != 0) {
status_dx = gsl_multifit_test_delta(dx, x_cur, this->epsabs, this->epsrel);
}
gsl_vector_memcpy(x_cur, x_new);
F->computeFuncAndJac(x_cur, func, jac);
gsl_multifit_gradient(jac, func, g);
gsl_vector_scale(g, 2);
gsl_blas_ddot(func, func, &this->fmin);
if (itLog != NULL) {
itLog->reportIteration(this->iter, x_cur, this->fmin, g);
}
status_grad = gsl_multifit_test_gradient(g, this->epsgrad);
}
if (this->iter >= this->maxiter) {
status = EITER;
}
gsl_blas_ddot(func, func, &this->fmin);
/* 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");
}
}
}
gsl_vector_memcpy(x_vec, x_cur);
gsl_vector_free(work_vec);
gsl_matrix_free(jac);
gsl_vector_free(func);
gsl_vector_free(g);
gsl_vector_free(x_cur);
gsl_vector_free(x_new);
if (scaling != NULL) {
gsl_vector_free(scaling);
}
gsl_vector_free(dx);
gsl_matrix_free(tempv);
gsl_vector_free(tempufuncsig);
gsl_vector_free(templm);
gsl_vector_free(sig);
return GSL_SUCCESS; /* <- correct with status */
}
/* Removes the ballistic term from the beginning of the ACF,
* just like in Omer's paper.
*/
extern void takeAwayBallistic(double *ct, double *t, int len, real tMax, int nexp, gmx_bool bDerivative)
{
/* Use nonlinear regression with GSL instead.
* Fit with 4 exponentials and one constant term,
* subtract the fatest exponential. */
int nData,i,status, iter;
balData *BD;
double *guess, /* Initial guess. */
*A, /* The fitted parameters. (A1, B1, A2, B2,... C) */
a[2],
ddt[2];
gmx_bool sorted;
size_t n;
size_t p;
nData = 0;
do {
nData++;
} while (t[nData]<tMax+t[0] && nData<len);
p = nexp*2+1; /* Number of parameters. */
#ifdef HAVE_LIBGSL
const gsl_multifit_fdfsolver_type *T
= gsl_multifit_fdfsolver_lmsder;
gsl_multifit_fdfsolver *s; /* The solver itself. */
gsl_multifit_function_fdf fitFunction; /* The function to be fitted. */
gsl_matrix *covar; /* Covariance matrix for the parameters.
* We'll not use the result, though. */
gsl_vector_view theParams;
nData = 0;
do {
nData++;
} while (t[nData]<tMax+t[0] && nData<len);
guess = NULL;
n = nData;
snew(guess, p);
snew(A, p);
covar = gsl_matrix_alloc (p, p);
/* Set up an initial gess for the parameters.
* The solver is somewhat sensitive to the initial guess,
* but this worked fine for a TIP3P box with -geminate dd
* EDIT: In fact, this seems like a good starting pont for other watermodels too. */
for (i=0; i<nexp; i++)
{
guess[i*2] = 0.1;
guess[i*2+1] = -0.5 + (((double)i)/nexp - 0.5)*0.3;
}
guess[nexp * 2] = 0.01;
theParams = gsl_vector_view_array(guess, p);
snew(BD,1);
BD->n = n;
BD->y = ct;
BD->tDelta = t[1]-t[0];
BD->nexp = nexp;
fitFunction.f = &balFunc_f;
fitFunction.df = &balFunc_df;
fitFunction.fdf = &balFunc_fdf;
fitFunction.n = nData;
fitFunction.p = p;
fitFunction.params = BD;
s = gsl_multifit_fdfsolver_alloc (T, nData, p);
if (s==NULL)
gmx_fatal(FARGS, "Could not set up the nonlinear solver.");
gsl_multifit_fdfsolver_set(s, &fitFunction, &theParams.vector);
/* \=============================================/ */
iter = 0;
do
{
iter++;
status = gsl_multifit_fdfsolver_iterate (s);
if (status)
break;
status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4);
}
while (iter < 5000 && status == GSL_CONTINUE);
if (iter == 5000)
{
fprintf(stderr, "The non-linear fitting did not converge in 5000 steps.\n"
"Check the quality of the fit!\n");
}
else
{
fprintf(stderr, "Non-linear fitting of ballistic term converged in %d steps.\n\n", (int)iter);
}
for (i=0; i<nexp; i++) {
fprintf(stdout, "%c * exp(%c * t) + ", 'A'+(char)i*2, 'B'+(char)i*2);
}
fprintf(stdout, "%c\n", 'A'+(char)nexp*2);
fprintf(stdout, "Here are the actual numbers for A-%c:\n", 'A'+nexp*2);
for (i=0; i<nexp; i++)
{
A[i*2] = gsl_vector_get(s->x, i*2);
A[i*2+1] = gsl_vector_get(s->x, i*2+1);
fprintf(stdout, " %g*exp(%g * x) +", A[i*2], A[i*2+1]);
}
A[i*2] = gsl_vector_get(s->x, i*2); /* The last and constant term */
fprintf(stdout, " %g\n", A[i*2]);
fflush(stdout);
/* Implement some check for parameter quality */
for (i=0; i<nexp; i++)
{
if (A[i*2]<0 || A[i*2]>1) {
fprintf(stderr, "WARNING: ----------------------------------\n"
" | A coefficient does not lie within [0,1].\n"
" | This may or may not be a problem.\n"
" | Double check the quality of the fit!\n");
}
if (A[i*2+1]>0) {
fprintf(stderr, "WARNING: ----------------------------------\n"
" | One factor in the exponent is positive.\n"
" | This could be a problem if the coefficient\n"
" | is large. Double check the quality of the fit!\n");
}
}
if (A[i*2]<0 || A[i*2]>1) {
fprintf(stderr, "WARNING: ----------------------------------\n"
" | The constant term does not lie within [0,1].\n"
" | This may or may not be a problem.\n"
" | Double check the quality of the fit!\n");
}
/* Sort the terms */
sorted = (nexp > 1) ? FALSE : TRUE;
while (!sorted)
{
sorted = TRUE;
for (i=0;i<nexp-1;i++)
{
ddt[0] = A[i*2] * A[i*2+1];
ddt[1] =A[i*2+2] * A[i*2+3];
if ((bDerivative && (ddt[0]<0 && ddt[1]<0 && ddt[0]>ddt[1])) || /* Compare derivative at t=0... */
(!bDerivative && (A[i*2+1] > A[i*2+3]))) /* Or just the coefficient in the exponent */
{
sorted = FALSE;
a[0] = A[i*2]; /* coefficient */
a[1] = A[i*2+1]; /* parameter in the exponent */
A[i*2] = A[i*2+2];
A[i*2+1] = A[i*2+3];
A[i*2+2] = a[0];
A[i*2+3] = a[1];
}
}
}
/* Subtract the fastest component */
fprintf(stdout, "Fastest component is %g * exp(%g * t)\n"
"Subtracting fastest component from ACF.\n", A[0], A[1]);
for (i=0; i<len; i++) {
ct[i] = (ct[i] - A[0] * exp(A[1] * i*BD->tDelta)) / (1-A[0]);
}
sfree(guess);
sfree(A);
gsl_multifit_fdfsolver_free(s);
gsl_matrix_free(covar);
fflush(stdout);
#else
/* We have no gsl. */
fprintf(stderr, "Sorry, can't take away ballistic component without gsl. "
"Recompile using --with-gsl.\n");
return;
#endif /* HAVE_LIBGSL */
}
int LevenbergMarquardtMinimizer::hasConverged() {
return gsl_multifit_test_delta(m_gslSolver->dx, m_gslSolver->x, m_absError,
m_relError);
}
gsl_vector* least_square_nl_fit(struct data dat, struct parameters par, gsl_multifit_function_fdf f)
{
size_t n, p;
int status, i, iter = 0;
double *x_init;
const gsl_rng_type * type;
const gsl_multifit_fdfsolver_type *T;
gsl_multifit_fdfsolver *s;
n = dat.n;
p = par.n;
gsl_matrix *covar = gsl_matrix_alloc(p,p);
x_init = (double *) calloc(par.n, sizeof(double));
for(i=0; i<par.n; i++)
x_init[i] = par.guess_p[i];
gsl_vector_view x = gsl_vector_view_array (x_init, p);
gsl_rng * r;
gsl_rng_env_setup();
type = gsl_rng_default;
r = gsl_rng_alloc (type);
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc(T, n, p);
gsl_multifit_fdfsolver_set(s, &f, &x.vector);
#ifdef PRINT_INFO
print_state (iter, s);
#endif
do
{
iter++;
status = gsl_multifit_fdfsolver_iterate (s);
#ifdef PRINT_INFO
print_state (iter, s);
#endif
if (status)
break;
status = gsl_multifit_test_delta (s->dx, s->x,
1e-6, 1e-6);
}
while (status == GSL_CONTINUE && iter < 500);
#ifdef PRINT_INFO
print_state (iter, s);
#endif
gsl_multifit_covar (s->J, 0.0, covar);
{
gsl_matrix_free (covar);
gsl_rng_free (r);
}
return s->x;
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;
}
/**
* C++ version of gsl_multifit_test_delta().
* @param dx Last step
* @param x Current estimate of x
* @param epsabs Absolute error bounds
* @param epsrel Relative error bounds
* @return GSL_SUCCESS if test condition reached
*/
inline int delta( vector const& dx, vector const& x, double epsabs, double epsrel ){
return gsl_multifit_test_delta( dx.get(), x.get(), epsabs, epsrel ); }
SEXP multifit_cor(SEXP par, SEXP Thalf, SEXP x, SEXP y, SEXP err, SEXP tr,
SEXP prec, SEXP N, SEXP max_iter, SEXP no_masses)
{
int npar, nx, ny, i, iter_max;
double p1, p2, m;
double *yp, *errp, *parp, *precp, *statep;
double chi_square, red_chi_square;
int dof;
int * xp, *Thalfp, *trp, *Np, *mip, *nmp;
SEXP state;
const gsl_multifit_fdfsolver_type *solver_type =
gsl_multifit_fdfsolver_lmsder;
/* Allocate the solver. */
gsl_multifit_fdfsolver *solver;
/* Initialize the data structure. */
struct data data_struct;
gsl_multifit_function_fdf function_fdf;
gsl_matrix *covar;
double * para_initial, c=1.;
gsl_vector_view para_initial_;
int status, iter=0, no_points=0;
PROTECT(par = AS_NUMERIC(par));
PROTECT(Thalf = AS_INTEGER(Thalf));
PROTECT(x = AS_INTEGER(x));
PROTECT(y = AS_NUMERIC(y));
PROTECT(err = AS_NUMERIC(err));
PROTECT(tr = AS_INTEGER(tr));
PROTECT(prec = AS_NUMERIC(prec));
PROTECT(N = AS_INTEGER(N));
PROTECT(max_iter = AS_INTEGER(max_iter));
PROTECT(no_masses = AS_INTEGER(no_masses));
xp = INTEGER_POINTER(x);
Thalfp = INTEGER_POINTER(Thalf);
trp = INTEGER_POINTER(tr);
Np = INTEGER_POINTER(N);
yp = NUMERIC_POINTER(y);
errp = NUMERIC_POINTER(err);
parp = NUMERIC_POINTER(par);
precp = NUMERIC_POINTER(prec);
mip = INTEGER_POINTER(max_iter);
nmp = INTEGER_POINTER(no_masses);
iter_max = mip[0];
npar = LENGTH(par);
nx = LENGTH(x);
ny = LENGTH(y);
assert(npar == nmp[0]*(Np[0]+1));
PROTECT(state = NEW_NUMERIC(5+npar));
statep = NUMERIC_POINTER(state);
/* PROTECT(gradient = allocMatrix(REALSXP, npar, npar)); */
if(Np[0] == 2) no_points = 3*trp[0];
if(Np[0] == 4) no_points = 10*trp[0];
if(Np[0] == 6) no_points = 21*trp[0];
solver = gsl_multifit_fdfsolver_alloc(solver_type, ny, npar);
data_struct.x = (double*) malloc(nx*sizeof(double));
data_struct.y = (double*) malloc(ny*sizeof(double));
data_struct.err = (double*) malloc(ny*sizeof(double));
para_initial = (double*) malloc(npar*sizeof(double));
for(i = 0; i < nx; i++) {
data_struct.x[i] = (double)xp[i];
}
for(i = 0; i < ny; i++) {
data_struct.y[i] = yp[i];
data_struct.err[i] = errp[i];
}
data_struct.Thalf = Thalfp[0];
data_struct.tr = trp[0];
data_struct.N = Np[0];
data_struct.no_masses = nmp[0];
// The ansatz.
function_fdf.f = &exp_f;
function_fdf.df = &exp_df;
function_fdf.fdf = &exp_fdf;
function_fdf.n = ny;
function_fdf.p = npar;
function_fdf.params = &data_struct;
for(i = 0; i < npar; i++) {
para_initial[i] = parp[i];
}
para_initial_ = gsl_vector_view_array(para_initial, npar);
gsl_multifit_fdfsolver_set(solver, &function_fdf, ¶_initial_.vector);
// Perform the fit.
// Print the initial state.
#ifdef _DEBUG
Print_State_Mass_Fit_Helper_1(iter, solver);
#endif
do {
iter++;
/* Do a solver iteration. */
status = gsl_multifit_fdfsolver_iterate(solver);
#ifdef _DEBUG
fprintf(stderr, "status = %s.\n", gsl_strerror(status));
Print_State_Mass_Fit_Helper_1(iter, solver);
#endif
if(status) {
break;
}
status = gsl_multifit_test_delta(solver->dx, solver->x,
precp[0], precp[1]);
}
while(status == GSL_CONTINUE && iter < iter_max);
#ifdef _DEBUG
fprintf(stderr, "\n");
#endif
// *****
// Compute the covariance matrix.
covar = gsl_matrix_alloc(npar, npar);
gsl_multifit_covar(solver->J, 0.0, covar);
// Output.
chi_square = pow(gsl_blas_dnrm2(solver->f), 2.0);
#ifdef _DEBUG
fprintf(stderr, "chi_square = %13.6lf.\n", chi_square);
#endif
dof = no_points - npar;
#ifdef _DEBUG
fprintf(stderr, "dof = %d\n", dof);
#endif
red_chi_square = chi_square / (double)dof;
#ifdef _DEBUG
fprintf(stderr, "red_chi_square = %13.6lf.\n", red_chi_square);
fprintf(stderr, "\n");
#endif
p1 = gsl_vector_get(solver->x, 0);
p2 = gsl_vector_get(solver->x, 1);
m = gsl_vector_get(solver->x, npar-1);
if(red_chi_square > 1.0)
c = sqrt(red_chi_square);
#ifdef _DEBUG
fprintf(stderr, "p1 = %+9.6lf +/- %9.6lf.\n",
p1, c * sqrt(gsl_matrix_get(covar, 0, 0)));
fprintf(stderr, "p2 = %+9.6lf +/- %9.6lf.\n",
p2, c * sqrt(gsl_matrix_get(covar, 1, 1)));
fprintf(stderr, "m = %+9.6lf +/- %9.6lf.\n",
m, c * sqrt(gsl_matrix_get(covar, npar-1, npar-1)));
fprintf(stderr, "\n");
fprintf(stderr, "status = %s.\n", gsl_strerror(status));
fprintf(stderr, "\n");
#endif
for(i = 0; i < npar; i++) {
statep[5+i] = gsl_vector_get(solver->x, i);
}
statep[0] = chi_square;
statep[1] = gsl_blas_dnrm2(solver->f);
statep[2] = (double)iter;
statep[3] = (double)dof;
statep[4] = (double)status;
gsl_multifit_fdfsolver_free(solver);
#ifdef _DEBUG
gsl_matrix_free(covar);
#endif
free(data_struct.x);
free(data_struct.y);
free(data_struct.err);
free(para_initial);
UNPROTECT(11);
return(state);
}
int main(){
const int max_mu_size=601;
const int zero_pad_size=pow(2,15);
FILE *in;
in= fopen("mean.chi", "r");
gsl_matrix *e = gsl_matrix_alloc(max_mu_size, 4);
gsl_vector * kvar=gsl_vector_alloc(max_mu_size);
gsl_vector * muvar=gsl_vector_alloc(max_mu_size);
gsl_vector * mu_0pad=gsl_vector_alloc(zero_pad_size);
gsl_vector * r_0pad=gsl_vector_alloc(zero_pad_size/2); //half of lenght
gsl_vector * kvar_0pad=gsl_vector_alloc(zero_pad_size);
gsl_matrix_fscanf(in, e);
fclose(in);
gsl_matrix_get_col(kvar,e,0);
gsl_matrix_get_col(muvar,e,1);
gsl_vector_set_zero(mu_0pad);
gsl_matrix_free(e);
double dk=gsl_vector_get (kvar, 1)-gsl_vector_get (kvar, 0);
double dr=M_PI/float(zero_pad_size-1)/dk;
for (int i = 0; i < zero_pad_size; i++)
{
gsl_vector_set (kvar_0pad, i, dk*i);
}
for (int i = 0; i < zero_pad_size/2; i++)
{
gsl_vector_set (r_0pad, i, dr*i);
}
for (int i = 0; i < max_mu_size; i++)
{
gsl_vector_set (mu_0pad, i, gsl_vector_get (muvar, i));
}
gsl_vector *mu_widowed=gsl_vector_alloc(zero_pad_size);
gsl_vector_memcpy (mu_widowed, mu_0pad);
double kmin=4.0, kmax=17.0, dwk=0.8;
hanning(mu_widowed, kvar_0pad, kmin, kmax, dwk);
//FFT transform
double *data = (double *) malloc(zero_pad_size*sizeof(double));
//new double [zero_pad_size] ;
memcpy(data, mu_widowed->data, zero_pad_size*sizeof(double));
gsl_fft_real_radix2_transform(data, 1, zero_pad_size);
//Unpack complex vector
gsl_vector_complex *fourier_data = gsl_vector_complex_alloc (zero_pad_size);
gsl_fft_halfcomplex_radix2_unpack(data, fourier_data->data, 1, zero_pad_size);
gsl_vector *fftR_real = gsl_vector_alloc(fourier_data->size/2);
gsl_vector *fftR_imag = gsl_vector_alloc(fourier_data->size/2);
gsl_vector *fftR_abs = gsl_vector_alloc(fourier_data->size/2);
complex_vector_parts(fourier_data, fftR_real, fftR_imag);
complex_vector_abs(fftR_abs, fftR_real, fftR_imag);
gsl_vector *first_shell=gsl_vector_alloc(fftR_abs->size);
gsl_vector_memcpy (first_shell, fftR_abs);
double rmin=0.2, rmax=3.0, dwr=0.1;
hanning(first_shell, r_0pad, rmin, rmax, dwr);
//feff0001.dat
const int path_lines=68;
e = gsl_matrix_alloc(path_lines, 7);
gsl_vector * k_p =gsl_vector_alloc(path_lines);
gsl_vector * phc_p=gsl_vector_alloc(path_lines);
gsl_vector * mag_p=gsl_vector_alloc(path_lines);
gsl_vector * pha_p=gsl_vector_alloc(path_lines);
gsl_vector * lam_p=gsl_vector_alloc(path_lines);
in= fopen("feff0001.dat", "r");
gsl_matrix_fscanf(in, e);
fclose(in);
gsl_matrix_get_col(k_p ,e,0);
gsl_matrix_get_col(phc_p,e,1);
gsl_matrix_get_col(mag_p,e,2);
gsl_matrix_get_col(pha_p,e,3);
gsl_matrix_get_col(lam_p,e,5);
gsl_matrix_free(e);
gsl_interp_accel *acc = gsl_interp_accel_alloc ();
gsl_spline *k_spline = gsl_spline_alloc (gsl_interp_cspline, path_lines);
gsl_spline *phc_spline = gsl_spline_alloc (gsl_interp_cspline, path_lines);
gsl_spline *mag_spline = gsl_spline_alloc (gsl_interp_cspline, path_lines);
gsl_spline *pha_spline = gsl_spline_alloc (gsl_interp_cspline, path_lines);
gsl_spline *lam_spline = gsl_spline_alloc (gsl_interp_cspline, path_lines);
gsl_spline_init (k_spline , k_p->data, k_p->data , path_lines);
gsl_spline_init (phc_spline, k_p->data, phc_p->data, path_lines);
gsl_spline_init (mag_spline, k_p->data, mag_p->data, path_lines);
gsl_spline_init (pha_spline, k_p->data, pha_p->data, path_lines);
gsl_spline_init (lam_spline, k_p->data, lam_p->data, path_lines);
gsl_vector * mu_p =gsl_vector_alloc(path_lines);
//struct fit_params { student_params t; double kshift; double S02; double N; inter_path splines; };
//student_params t = {2.45681867, 0.02776907, -21.28920008, 9.44741797, 0.0, 0.0, 0.0};
splines.acc=acc; splines.phc_spline=phc_spline; splines.mag_spline=mag_spline;
splines.pha_spline=pha_spline; splines.lam_spline=lam_spline;
fit_params fp = { 2.45681867, 0.02776907, -21.28920008, 9.44741797, 1.0, 0.0};
compute_itegral(k_p, &fp, mu_p);
//mu_data_fit params = { k_p, mu_p};
mu_data.k = kvar_0pad;
mu_data.mu = mu_0pad;
mu_data.mu_ft = first_shell;
mu_data.r = r_0pad;
mu_data.kmin = kmin;
mu_data.kmax = kmax;
mu_data.rmin = rmin;
mu_data.rmax = rmax;
mu_data.dwk = dwk;
mu_data.dwr = dwr;
// initialize the solver
size_t Nparams=6;
gsl_vector *guess0 = gsl_vector_alloc(Nparams);
gsl_vector_set(guess0, 0, 2.4307);
gsl_vector_set(guess0, 1, 0.040969);
gsl_vector_set(guess0, 2, 0.001314);
gsl_vector_set(guess0, 3, 7835);
gsl_vector_set(guess0, 4, 1.0);
gsl_vector_set(guess0, 5, 0.0);
gsl_vector *fit_r = gsl_vector_alloc(r_0pad->size);
compute_itegral_r(&mu_data, fp, fit_r);
gsl_matrix *plotting = gsl_matrix_calloc(r_0pad->size, 3);
gsl_matrix_set_col (plotting, 0, r_0pad);
gsl_matrix_set_col (plotting, 1, first_shell);
gsl_matrix_set_col (plotting, 2, fit_r);
plot_matplotlib(plotting);
gsl_matrix_free (plotting);
gsl_multifit_function_fdf fit_mu_k;
fit_mu_k.f = &resudial_itegral_r;
fit_mu_k.n = MAX_FIT_POINTS;
fit_mu_k.p = Nparams;
fit_mu_k.params = &mu_data;
fit_mu_k.df = NULL;
fit_mu_k.fdf = NULL;
gsl_multifit_fdfsolver *solver = gsl_multifit_fdfsolver_alloc(gsl_multifit_fdfsolver_lmsder, MAX_FIT_POINTS, Nparams);
gsl_multifit_fdfsolver_set(solver, &fit_mu_k, guess0);
size_t iter=0, status;
do{
iter++;
//cout << solver->x->data[0] << " " << solver->x->data[1] <<endl;
status = gsl_multifit_fdfsolver_iterate (solver);
//printf("%12.4f %12.4f %12.4f\n", solver->J->data[0,0], solver->J->data[1,1], solver->J->data[2,2] );
//gsl_multifit_fdfsolver_dif_df (k_p, &fit_mu_k, mu_p, solver->J);
//gsl_multifit_fdfsolver_dif_fdf (k_p, &fit_mu_k, mu_p, solver->J);
for (int i =0; i< solver->x->size; i++){
printf("%14.5f", gsl_vector_get (solver->x, i)) ;
}
printf("\n") ;
if (status) break;
status = gsl_multifit_test_delta (solver->dx, solver->x, 1e-4, 1e-4);
}while (status == GSL_CONTINUE && iter < 100);
gsl_vector * mu_fit =gsl_vector_alloc(path_lines);
fit_params fitp = { solver->x->data[0], solver->x->data[1],\
solver->x->data[2], solver->x->data[3],\
solver->x->data[4], solver->x->data[5]};
compute_itegral(k_p, &fitp, mu_fit);
fp.mu=gsl_vector_get (solver->x, 0);
fp.sig=gsl_vector_get (solver->x, 1);
fp.skew=gsl_vector_get (solver->x, 2);
fp.nu=gsl_vector_get (solver->x, 3);
fp.S02=gsl_vector_get (solver->x, 4);
fp.kshift=gsl_vector_get (solver->x, 5);
compute_itegral_r(&mu_data, fp, fit_r);
//gsl_matrix *plotting = gsl_matrix_calloc(r_0pad->size, 3);
gsl_matrix_set_col (plotting, 0, r_0pad);
gsl_matrix_set_col (plotting, 1, first_shell);
gsl_matrix_set_col (plotting, 2, fit_r);
int min_r=search_max(r_0pad, 0.);
int max_r=search_max(r_0pad, 4.);
gsl_matrix_view plotting_lim = gsl_matrix_submatrix (plotting, min_r, 0, max_r-min_r, plotting->size2);
plot_matplotlib(&plotting_lim.matrix);
gsl_matrix_free (plotting);
//cout << gsl_spline_eval (k_spline, 1.333, acc) << endl;
//cout << gsl_spline_eval (phc_spline, 1.333, acc) << endl;
//cout << data[0] << "\t" << data[1] << "\t" << data[2] << "\t" << endl;
//cout << fourier_data->data[0] << "\t" << fourier_data->data[1] << "\t" << fourier_data->data[2] << "\t" << endl;
//Plotting
/*
gsl_matrix *plotting = gsl_matrix_calloc(zero_pad_size, 3);
gsl_matrix_set_col (plotting, 0, kvar_0pad);
gsl_matrix_set_col (plotting, 1, mu_0pad);
gsl_matrix_set_col (plotting, 2, mu_widowed);
int max_k=search_max(kvar_0pad, 35.);
int min_k=search_max(kvar_0pad, 1.0);
gsl_matrix_view plotting_lim = gsl_matrix_submatrix (plotting, min_k, 0, max_k-min_k, 3);
plot_matplotlib(&plotting_lim.matrix);
gsl_matrix_free (plotting);
*/
/*
gsl_matrix *plotting = gsl_matrix_calloc(zero_pad_size, 2);
gsl_matrix_set_col (plotting, 0, r_0pad);
gsl_matrix_set_col (plotting, 1, mu_0pad);
int max_k=search_max(kvar_0pad, 35.);
int min_k=search_max(kvar_0pad, 1.0);
gsl_matrix_view plotting_lim = gsl_matrix_submatrix (plotting, min_k, 0, max_k-min_k, 3);
plot_matplotlib(&plotting_lim.matrix);
gsl_matrix_free (plotting);
*/
/*
gsl_matrix *plotting = gsl_matrix_calloc(r_0pad->size, 5);
gsl_matrix_set_col (plotting, 0, r_0pad);
gsl_matrix_set_col (plotting, 1, fftR_abs);
gsl_matrix_set_col (plotting, 2, fftR_real);
gsl_matrix_set_col (plotting, 3, fftR_imag);
gsl_matrix_set_col (plotting, 4, first_shell);
int min_r=search_max(r_0pad, 0.);
int max_r=search_max(r_0pad, 5.);
gsl_matrix_view plotting_lim = gsl_matrix_submatrix (plotting, min_r, 0, max_r-min_r, plotting->size2);
plot_matplotlib(&plotting_lim.matrix);
//plot_matplotlib(plotting);
gsl_matrix_free (plotting);
*/
//cout << "Done" << endl;
//cout << data[1] <<"\t" << data[2] << endl;
//for (int i = 0; i < kvar->size; i++)
//{
// cout << gsl_vector_get (kvar, i) <<"\t" << gsl_vector_get (muvar, i) << endl;
//}
}
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;
}