/**
* The destructor only deletes the pointers if count reaches zero.
*/
~fdfsolver(){
if( count == 0 or --*count == 0 ){
// could have allocated null pointer
if( ccgsl_pointer != 0 ) gsl_multifit_fdfsolver_free( ccgsl_pointer );
delete count;
}
}
void
magcal_free(magcal_workspace *w)
{
if (w->Ex)
free(w->Ex);
if (w->Ey)
free(w->Ey);
if (w->Ez)
free(w->Ez);
if (w->F)
free(w->F);
if (w->fdf_s)
gsl_multifit_fdfsolver_free(w->fdf_s);
if (w->fdf_ridge)
gsl_multifit_fdfridge_free(w->fdf_ridge);
if (w->covar)
gsl_matrix_free(w->covar);
free(w);
}
static int
magcal_init(const satdata_mag *data, magcal_workspace *w)
{
int s = 0;
size_t i;
size_t n = 0;
for (i = 0; i < data->n; ++i)
{
/* don't store flagged data */
if (data->flags[i])
continue;
/* don't process high latitude data */
if (fabs(data->latitude[i]) > MAGCAL_MAX_LATITUDE)
continue;
w->Ex[n] = SATDATA_VEC_X(data->B_VFM, i);
w->Ey[n] = SATDATA_VEC_Y(data->B_VFM, i);
w->Ez[n] = SATDATA_VEC_Z(data->B_VFM, i);
w->F[n] = data->F[i];
++n;
}
if (n < 200)
{
fprintf(stderr, "magcal_init: insufficient data points for calibration: %zu\n",
n);
return -1;
}
if (n != w->n)
{
gsl_multifit_fdfsolver_free(w->fdf_s);
gsl_multifit_fdfridge_free(w->fdf_ridge);
w->fdf_s = gsl_multifit_fdfsolver_alloc(w->fdf_type, n, w->p);
w->fdf_ridge = gsl_multifit_fdfridge_alloc(w->fdf_type, n, w->p);
w->n = n;
}
#if MAGCAL_SCALE
w->B_s = GSL_MAX(gsl_stats_sd(w->Ex, 1, n),
GSL_MAX(gsl_stats_sd(w->Ey, 1, n),
gsl_stats_sd(w->Ez, 1, n)));
#endif
/* center and scale data arrays */
for (i = 0; i < n; ++i)
{
w->Ex[i] /= w->B_s;
w->Ey[i] /= w->B_s;
w->Ez[i] /= w->B_s;
w->F[i] /= w->B_s;
}
return s;
} /* magcal_init() */
/**
* The assignment operator. This copies elementwise.
* @param v The fdfsolver to copy
*/
fdfsolver& operator=( fdfsolver const& v ){
// first, possibly delete anything pointed to by this
if( count == 0 or --*count == 0 ){
if( ccgsl_pointer != 0 ) gsl_multifit_fdfsolver_free( ccgsl_pointer );
delete count;
} // Then copy
ccgsl_pointer = v.ccgsl_pointer; count = v.count; if( count != 0 ) ++*count; return *this;
}
Vector MultiSolver::NLLeastSquareSolver(MultiSolverInput *input)
{
/**/condition.analyzer->solverSolving.startTimer(); // ---- ---- T5 start
const gsl_multifit_fdfsolver_type *T;
gsl_multifit_fdfsolver *s;
gsl_multifit_function_fdf f;
double x_init[3] = {0.0, 0.0, 150.0};
// x_init[0] = input->initLocation.x;
// x_init[1] = input->initLocation.y;
// x_init[2] = input->initLocation.z;
gsl_vector_view x = gsl_vector_view_array(x_init, 3);
int n = (int)input->data.size();
// sort restriction..
// n = 3;
int p = 3;
f.f = &ms_f;
f.df = &ms_df;
f.fdf = &ms_fdf;
f.n = n;
f.p = p;
f.params = input;
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc(T, n, p);
gsl_multifit_fdfsolver_set(s, &f, &x.vector);
gsl_vector *gradt = gsl_vector_alloc(p);
int iter = 0;
int status;
do
{
iter ++;
status = gsl_multifit_fdfsolver_iterate(s);
if (status) break;
/// status = gsl_multifit_test_delta(s->dx, s->x, 1e-4, 1e-4);
gsl_multifit_gradient(s->J, s->f, gradt);
status = gsl_multifit_test_gradient(gradt, 1e-6);
}
while (status == GSL_CONTINUE && iter < 500);
Vector point = Vector(gsl_vector_get(s->x, 0), gsl_vector_get(s->x, 1), gsl_vector_get(s->x, 2));
gsl_vector_free(gradt);
gsl_multifit_fdfsolver_free(s);
/**/condition.analyzer->solverSolving.stopTimer(); // ---- ---- T5 end
return point;
}
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);
}
static void
ncm_fit_gsl_ls_finalize (GObject *object)
{
NcmFitGSLLS *fit_gsl_ls = NCM_FIT_GSL_LS (object);
gsl_multifit_fdfsolver_free (fit_gsl_ls->ls);
/* Chain up : end */
G_OBJECT_CLASS (ncm_fit_gsl_ls_parent_class)->finalize (object);
}
/**
* The default constructor creates a new fdfsolver with n elements.
* @param T The fdfsolver type.
* @param n The number of elements in the fdfsolver.
* @param p The number of predictor variables
*/
explicit fdfsolver( type const* T, size_t const n, size_t const p ){
ccgsl_pointer = gsl_multifit_fdfsolver_alloc( T, n, p );
// just plausibly we could allocate fdfsolver but not count
try { count = new size_t; } catch( std::bad_alloc& e ){
// try to tidy up before rethrowing
gsl_multifit_fdfsolver_free( ccgsl_pointer );
throw e;
}
*count = 1; // initially there is just one reference to ccgsl_pointer
}
void
gsl_multifit_fdfridge_free(gsl_multifit_fdfridge *work)
{
if (work->s)
gsl_multifit_fdfsolver_free(work->s);
if (work->wts)
gsl_vector_free(work->wts);
free(work);
}
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);
}
static void
_ncm_fit_gsl_ls_reset (NcmFit *fit)
{
/* Chain up : start */
NCM_FIT_CLASS (ncm_fit_gsl_ls_parent_class)->reset (fit);
{
NcmFitGSLLS *fit_gsl_ls = NCM_FIT_GSL_LS (fit);
if (fit_gsl_ls->f.p != fit->fstate->fparam_len || fit_gsl_ls->f.n != fit->fstate->data_len)
{
gsl_multifit_fdfsolver_free (fit_gsl_ls->ls);
fit_gsl_ls->f.p = fit->fstate->fparam_len;
fit_gsl_ls->f.n = fit->fstate->data_len;
fit_gsl_ls->ls = gsl_multifit_fdfsolver_alloc (fit_gsl_ls->T,
fit_gsl_ls->f.n,
fit_gsl_ls->f.p);
}
}
}
void MLFitterGSL::initfitter(){
//do first whatever the fitter wants to do here
Fitter::initfitter();
#ifdef FITTER_DEBUG
std::cout <<"mlfitter_gsl::initfitter called\n";
#endif
//createmodelinfo(); //update number of free parameters etc if a model has changed
const int n=modelptr->getnpoints();
try{
//delete old solver and create new one
if (solver!=0) gsl_multifit_fdfsolver_free (solver);
const gsl_multifit_fdfsolver_type * T = gsl_multifit_fdfsolver_lmsder; //Scaled Levenberg Marquardt
solver= gsl_multifit_fdfsolver_alloc (T,n,modelptr->getnroffreeparameters());
//reallocate memory for parameter vector x and covariance matrix covar
if (initialparameters!=0) gsl_vector_free (initialparameters);
if (covar!=0) gsl_matrix_free (covar);
initialparameters=gsl_vector_calloc (modelptr->getnroffreeparameters()); //allocate space for vector x, containing param values
covar=gsl_matrix_calloc (modelptr->getnroffreeparameters(), modelptr->getnroffreeparameters());
//init the link with the function to be fitted
initfdf();
//load the current parameters in the x vector
initparameters();
//reinit the solver
gsl_multifit_fdfsolver_set(solver,&f,initialparameters);
}
catch(...){
//problems with memory? -> kill this
Saysomething mysay(0,"Error","Unable to allocate memory, exit MLFitterGSL",true);
delete(this);
}
}
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;
}
/*******************************************************************************
* 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 PlaneDetector::solve()
{
// prepare calculation data
DetectionData baseData;
// prepare gsl variables
const gsl_multifit_fdfsolver_type *T;
gsl_multifit_fdfsolver *s;
int n = (int)data.size();
#ifdef VECTOR_SOLVER
const int p = 4;
double x_init[p] = {0.0, 0.0, 1.0, 0.0};
#endif
#ifdef ANGLE_SOLVER
const int p = 3;
// double x_init[p] = {0.0, 0.0, 0.0};
double x_init[p] = {0.0, 90.0 / 180.0 * M_PI, 0.0};
#endif
#ifdef VECTOR2_SOLVER
const int p = 6;
// double x_init[p] = {1.0, 0.0, 0.0, 500.0, 0.0, 0.0};
double x_init[p] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
#endif
#ifdef ANGLE2_SOLVER
const int p = 5;
double x_init[p] = {0.0, M_PI / 2.0 + 0.1, 000.0, 0.0, 0.0};
#endif
gsl_multifit_function_fdf f;
f.f = &pd_func_f;
f.df = &pd_func_df;
f.fdf = &pd_func_fdf;
f.n = n;
f.p = p;
f.params = &data;
gsl_vector_view x = gsl_vector_view_array(x_init, p);
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc(T, n, p);
gsl_multifit_fdfsolver_set(s, &f, &x.vector);
gsl_vector *gradt = gsl_vector_alloc(p);
int iter = 0;
int status;
do
{
iter ++;
status = gsl_multifit_fdfsolver_iterate(s);
if (status)
{
// printf ("error: %s\n", gsl_strerror (status));
break;
}
gsl_multifit_gradient(s->J, s->f, gradt);
status = gsl_multifit_test_gradient(gradt, 1e-6);
} while (status == GSL_CONTINUE && iter < 10000);
#ifdef VECTOR_SOLVER
vN = Vector(
gsl_vector_get(s->x, 0),
gsl_vector_get(s->x, 1),
gsl_vector_get(s->x, 2)).getUnitVector();
fD = gsl_vector_get(s->x, 3);
#endif
#ifdef ANGLE_SOLVER
double theta = gsl_vector_get(s->x, 0);
double pi = gsl_vector_get(s->x, 1);
vN = Vector(sin(pi)*cos(theta), sin(pi)*sin(theta), cos(pi));
double d = gsl_vector_get(s->x, 2);
fD = - ((vN & vListener) + d);
#endif
#ifdef VECTOR2_SOLVER
vN = Vector(
gsl_vector_get(s->x, 0),
gsl_vector_get(s->x, 1),
gsl_vector_get(s->x, 2)).getUnitVector();
Vector vX1 = Vector(
gsl_vector_get(s->x, 3),
gsl_vector_get(s->x, 4),
gsl_vector_get(s->x, 5));
fD = -(vN & vX1);
#endif
#ifdef ANGLE2_SOLVER
double theta = gsl_vector_get(s->x, 0);
double pi = gsl_vector_get(s->x, 1);
vN = Vector(sin(pi)*cos(theta), sin(pi)*sin(theta), cos(pi));
Vector vX1 = Vector(
gsl_vector_get(s->x, 2),
gsl_vector_get(s->x, 3),
gsl_vector_get(s->x, 4));
fD = -(vN & vX1);
#endif
#if 0
for (double pp = 0; pp < M_PI; pp += 0.1)
{
for (double tt = 0; tt < M_PI; tt += 0.1)
{
Vector vNN = Vector(sin(pp)*cos(tt), sin(pp)*sin(tt), cos(pp));
printf("vN = ");
vNN.print();
double sum = 0;
for (size_t i = 0; i < data.size(); i++)
{
sum += pow(data[i].getF(tt, pp, fD), 2);
}
printf(" , sum = %f\n", sum);
}
}
#endif
#if 0
double sqrsum = 0;
for (size_t i = 0; i < data.size(); i++)
{
#ifdef VECTOR_SOLVER
sqrsum += pow(data[i].getF(vN, fD), 2);
#endif
#ifdef ANGLE_SOLVER
sqrsum += pow(data[i].getF(theta, pi, fD), 2);
#endif
#ifdef VECTOR2_SOLVER
sqrsum += pow(data[i].getF(vN, fD), 2);
#endif
// printf ("%f/", sqrsum);
}
vN.print();
printf(" %f %f\n", fD, sqrt(sqrsum));
#endif
// for (size_t i = 0; i < data.size(); i++)
// printf ("F_%d = %f\n", i, data[i].getF(vN));
gsl_vector_free(gradt);
gsl_multifit_fdfsolver_free(s);
vP.clear();
for (size_t i = 0; i < data.size(); i++)
{
vP.push_back(data[i].getP(vN));
}
}
/** 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;
}
/* 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 */
}
/*
* 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);
}
void FitModel::train()
{
if (descriptor_matrix_.cols() == 0)
{
throw Exception::InconsistentUsage(__FILE__, __LINE__, "Data must be read into the model before training!");
}
if (allEquations_.empty())
{
cout<<"ERROR: No equations specified! Use method setEquations first."<<endl;
return;
}
training_result_.resize(descriptor_matrix_.cols(), Y_.cols());
for (c = 0; c < (unsigned int)Y_.cols(); c++)
{
fitY = new Eigen::MatrixXd(Y_.rows(), 1);
for (int n = 0; n < Y_.rows(); n++)
{
(*fitY)(n, 0) = Y_(n, c);
}
fitX = &descriptor_matrix_;
equation = &allEquations_[c];
if (allDiffEquations_.size() < c)
{
diffEquations = &allDiffEquations_[c];
}
else
{
diffEquations = NULL;
}
const gsl_multifit_fdfsolver_type* T = gsl_multifit_fdfsolver_lmsder;
gsl_multifit_fdfsolver* s = gsl_multifit_fdfsolver_alloc(T, fitX->rows(), fitX->cols());
const size_t n = descriptor_matrix_.rows();
const size_t p = descriptor_matrix_.cols();
gsl_multifit_function_fdf fdf;
fdf = make_fdf(&setF, &setDf, &setFdf, n, p, 0);
double* g = new double[initial_guess_.size()];
for (unsigned int m = 0; m < initial_guess_.size(); m++)
{
g[m] = initial_guess_[m];
}
gsl_vector_view ini = gsl_vector_view_array (g, p);
gsl_multifit_fdfsolver_set(s, &fdf, &ini.vector);
int status;
for (unsigned int i = 0; i < 50; i++)
{
status = gsl_multifit_fdfsolver_iterate(s);
}
// save the predicted coefficients
for (unsigned int m = 0; m < s->x->size; m++)
{
training_result_(m, c) = gsl_vector_get(s->x, m);
}
delete fitY;
delete [] g;
gsl_multifit_fdfsolver_free(s);
}
cout <<training_result_<<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;
}
void pv_step2(int exists, double ** seeds, int seeds_size, double ** bg, struct data * d, int n_param)
{
//variables generales del programa
int i, j;
double H, eta;
double * shift_eta = vector_double_alloc((*d).numrings);
//variables del solver
int status = 0;
const gsl_multifit_fdfsolver_type * T;
gsl_multifit_fdfsolver * s;
gsl_multifit_function_fdf pv; //funcion a fitear
//gsl_matrix * covar = gsl_matrix_alloc (n_param, n_param);//matriz covariante
double * x_init = vector_double_alloc(n_param);
//printf("Inicializando los parametros\n");
j = 0;
for(i = 2; i < seeds_size; i += 4)
{
x_init[j] = seeds[1][i]; j++; //theta_0
x_init[j] = seeds[1][i + 1]; j++; //Intensity
x_init[j] = seeds[1][i + 2]; j++; //Shift_H
}
for(i = 0; i < (*d).n_bg; i++)
{
x_init[j] = bg[1][i]; j++;
}
gsl_vector_view x = gsl_vector_view_array (x_init, n_param); //inicializo el vector con los datos a fitear
//Estructura con los parametros fijos del fiteo
H = seeds[1][0];
eta = seeds[exists][1];
j = 0;
for(i = 2; i < seeds_size; i += 4)
{
shift_eta[j] = seeds[exists][i + 3]; j++;
}
data_s2 d2 = {*d, H, eta, shift_eta};
//inicializo la funcion pseudo-voigt
pv.f = &pv_f_step2; //definicion de la funcion
pv.df = NULL; //al apuntar la funcion con el jacobiano de la funcion a NULL, hago que la derivada de la funcion se calcule por el metodo de diferencias finitas
pv.fdf = NULL; //idem anterior
pv.n = (*d).n; //numero de puntos experimentales
pv.p = n_param; //variables a fitear (debe cumplir <= pv.n)
pv.params = &d2; //parametros fijos
//inicializo el solver
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc (T, (*d).n, n_param);
gsl_multifit_fdfsolver_set (s, &pv, &x.vector);
solver_iterator(&status, s, T);
//printf("Salida de los resultados del paso 2\n");
j = 0;
for(i = 2; i < seeds_size; i += 4)
{
seeds[1][i] = gsl_vector_get(s -> x, j); j++; //theta_0
seeds[1][i + 1] = gsl_vector_get(s -> x, j); j++; //Intensity
seeds[1][i + 2] = gsl_vector_get(s -> x, j); j++; //Shift_H
}
for(i = 0; i < (*d).n_bg; i++)
{
bg[1][i] = gsl_vector_get(s -> x, j); j++;
}
free(x_init);
gsl_multifit_fdfsolver_free (s);
//printf("Final del paso 2\n");
}
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;
}
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;
}
//------------------------------------------------------------------------------
// 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);
}
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;
}
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;
}
void MultiFitter::CleanUp()
{
if(s!=NULL) { gsl_multifit_fdfsolver_free (s); s=NULL; }
if(sf!=NULL) { gsl_multifit_fsolver_free (sf); sf=NULL; }
}
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);
}
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;
}
//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;
}
}
