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/*
* refine-lsq.c
*
* Refinement by Simple LSQ
*
* (c) 2006-2007 Thomas White <taw27@cam.ac.uk>
*
* synth2d - Two-Dimensional Crystallographic Fourier Synthesis
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <stdio.h>
#include <stdlib.h>
#include "refine.h"
#include "model.h"
#include "reflist.h"
#include "statistics.h"
static AtomicModel *refine_model_from_parameters(const gsl_vector *parameters, RefinementSpec spec, AtomicModel *template) {
unsigned int j, idx;
AtomicModel *model;
model = model_copy(template);
idx = 1; /* Ignore scale factor */
for ( j=0; j<model->n_atoms; j++ ) {
if ( model->atoms[j].refine ) {
if ( spec & REFINE_SPEC_X ) model->atoms[j].x = fmod(gsl_vector_get(parameters, idx++), 1);
if ( model->atoms[j].x < 0 ) model->atoms[j].x = 1 + model->atoms[j].x;
if ( spec & REFINE_SPEC_Y ) model->atoms[j].y = fmod(gsl_vector_get(parameters, idx++), 1);
if ( model->atoms[j].y < 0 ) model->atoms[j].y = 1 + model->atoms[j].y;
if ( spec & REFINE_SPEC_Z ) model->atoms[j].z = fmod(gsl_vector_get(parameters, idx++), 1);
if ( model->atoms[j].z < 0 ) model->atoms[j].z = 1 + model->atoms[j].z;
if ( spec & REFINE_SPEC_B ) model->atoms[j].B = gsl_vector_get(parameters, idx++);
if ( model->atoms[j].B < 0 ) model->atoms[j].B = 0;
if ( spec & REFINE_SPEC_OCC ) model->atoms[j].occ = gsl_vector_get(parameters, idx++);
if ( model->atoms[j].occ < 0 ) model->atoms[j].occ = 0;
}
}
return model;
}
static double refine_lsq_gradient(const gsl_vector *parameters, const ReflectionList *obs, RefinementSpec spec,
size_t param_idx, size_t obs_idx, ReflectionList *f_calc, AtomicModel *model) {
unsigned int j, idx;
double f_calc_new, gradient;
AtomicModel *model_new;
double scale;
if ( spec & REFINE_SPEC_INTENSITIES ) {
if ( param_idx == 0 ) return f_calc->refs[obs_idx].amplitude*f_calc->refs[obs_idx].amplitude; /* Scale factor */
} else {
if ( param_idx == 0 ) return f_calc->refs[obs_idx].amplitude; /* Scale factor */
}
scale = gsl_vector_get(parameters, 0);
idx = 0;
model_new = model_copy(model);
for ( j=0; j<model->n_atoms; j++ ) {
if ( !(model->atoms[j].refine) ) continue;
if ( spec & REFINE_SPEC_X ) idx++;
if ( idx == param_idx ) {
model->atoms[j].x += LSQ_MSLS_SHIFT;
break;
}
if ( spec & REFINE_SPEC_Y ) idx++;
if ( idx == param_idx ) {
model->atoms[j].y += LSQ_MSLS_SHIFT;
break;
}
if ( spec & REFINE_SPEC_Z ) idx++;
if ( idx == param_idx ) {
model->atoms[j].z += LSQ_MSLS_SHIFT;
break;
}
if ( spec & REFINE_SPEC_B ) idx++;
if ( idx == param_idx ) {
model->atoms[j].B += LSQ_MSLS_SHIFT;
break;
}
if ( spec & REFINE_SPEC_OCC ) idx++;
if ( idx == param_idx ) {
model->atoms[j].occ += LSQ_MSLS_SHIFT;
break;
}
}
f_calc_new = model_mod_f(model, f_calc->refs[obs_idx].h, f_calc->refs[obs_idx].k, f_calc->refs[obs_idx].l);
if ( spec & REFINE_SPEC_INTENSITIES ) {
gradient = ((f_calc->refs[obs_idx].amplitude*f_calc->refs[obs_idx].amplitude) - (f_calc_new*f_calc_new))/LSQ_MSLS_SHIFT;
} else {
gradient = (f_calc->refs[obs_idx].amplitude - f_calc_new)/LSQ_MSLS_SHIFT;
}
model_free(model_new);
return scale*gradient;
}
static gsl_matrix *refine_lsq_B(const gsl_vector *parameters, const ReflectionList *obs, RefinementSpec spec, AtomicModel *model, ReflectionList *f_calc) {
gsl_matrix *B;
size_t j;
int n_params, n_obs;
n_params = parameters->size;
n_obs = obs->n_reflections - 1;
B = gsl_matrix_alloc(n_params, n_params);
for ( j=0; j<n_params; j++ ) {
size_t k;
for ( k=0; k<n_params; k++ ) {
int i;
double total_grad = 0;
for ( i=1; i<=n_obs; i++ ) {
double grad1, grad2;
grad1 = refine_lsq_gradient(parameters, obs, spec, j, i, f_calc, model);
grad2 = refine_lsq_gradient(parameters, obs, spec, k, i, f_calc, model);
total_grad += grad1 * grad2;
}
gsl_matrix_set(B, j, k, total_grad);
}
}
return B;
}
static gsl_matrix *refine_lsq_D(const gsl_vector *parameters, ReflectionList *obs, RefinementSpec spec, AtomicModel *model, ReflectionList *f_calc) {
gsl_matrix *D;
size_t j;
int n_params, n_obs;
double scale;
n_params = parameters->size;
n_obs = obs->n_reflections - 1;
scale = gsl_vector_get(parameters, 0);
D = gsl_matrix_alloc(n_params, 1);
for ( j=0; j<n_params; j++ ) {
int i;
double total = 0;
for ( i=1; i<=n_obs; i++ ) {
double grad;
double res;
grad = refine_lsq_gradient(parameters, obs, spec, j, i, f_calc, model);
if ( spec & REFINE_SPEC_INTENSITIES ) {
res = (obs->refs[i].amplitude*obs->refs[i].amplitude) - scale*(f_calc->refs[i].amplitude*f_calc->refs[i].amplitude);
} else {
res = obs->refs[i].amplitude - scale*f_calc->refs[i].amplitude;
}
total += grad*res;
}
gsl_matrix_set(D, j, 0, total);
}
return D;
}
/* Determine and apply shift */
static void refine_lsq_iterate(gsl_vector *parameters, ReflectionList *obs, RefinementSpec spec, AtomicModel *model_template) {
gsl_matrix *B;
gsl_matrix *D;
gsl_matrix *Binv;
gsl_matrix *shift;
gsl_permutation *perm;
int s, n_params;
size_t i;
AtomicModel *model;
ReflectionList *f_calc;
n_params = parameters->size;
model = refine_model_from_parameters(parameters, spec, model_template);
f_calc = model_calculate_f(obs, model, 69);
/* Form 'B' */
//printf("LSQ: Forming B\n");
B = refine_lsq_B(parameters, obs, spec, model, f_calc);
/* Form 'D' */
//printf("LSQ: Forming D\n");
D = refine_lsq_D(parameters, obs, spec, model, f_calc);
/* Invert 'B' */
//printf("LSQ: Inverting B\n");
perm = gsl_permutation_alloc(B->size1);
Binv = gsl_matrix_alloc(B->size1, B->size2);
gsl_linalg_LU_decomp(B, perm, &s);
gsl_linalg_LU_invert(B, perm, Binv);
gsl_permutation_free(perm);
gsl_matrix_free(B);
/* shift = B^-1 D */
//printf("LSQ: Calculating shift\n");
shift = gsl_matrix_alloc(n_params, 1);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Binv, D, 0.0, shift);
gsl_matrix_free(Binv);
gsl_matrix_free(D);
/* Apply shifts */
//printf("LSQ: Applying shifts\n");
for ( i=0; i<n_params; i++ ) {
double old, new;
old = gsl_vector_get(parameters, i);
new = old + gsl_matrix_get(shift, i, 0);
gsl_vector_set(parameters, i, new);
//printf("Parameter %i: %f -> %f\n", i, old, new);
}
gsl_matrix_free(shift);
model_free(model);
//printf("LSQ: Done\n");
}
void refine_lsq(AtomicModel *model_orig, ReflectionList *reflections, RefinementSpec spec) {
gsl_vector *parameters;
unsigned int n_obs, n_params, n_atoms, idx, j, iter;
double scale;
ReflectionList *calc;
AtomicModel *model;
model = model_copy(model_orig);
/* Count the number of parameters to refine */
n_params = 0;
if ( spec & REFINE_SPEC_X ) n_params++;
if ( spec & REFINE_SPEC_Y ) n_params++;
if ( spec & REFINE_SPEC_Z ) n_params++;
if ( spec & REFINE_SPEC_B ) n_params++;
if ( spec & REFINE_SPEC_OCC ) n_params++;
/* Count the number of atoms to refine (having first fixed the origin) */
n_atoms = 0;
if ( (spec & REFINE_SPEC_X) || (spec & REFINE_SPEC_Y) || (spec & REFINE_SPEC_Z) ) model->atoms[0].refine = 0;
for ( j=0; j<model->n_atoms; j++ ) {
if ( model->atoms[j].refine ) n_atoms++;
}
n_obs = reflections->n_reflections-1; /* Number of observations */
n_params = 1 + n_params * n_atoms; /* Number of parameters */
printf("LSQ: Refining %i parameters against %i observations\n", n_params, n_obs);
/* Set initial estimates of the parameters */
parameters = gsl_vector_alloc(n_params);
idx = 0;
/* Initial scale factor */
calc = model_calculate_f(reflections, NULL, 69);
scale = stat_scale(reflections, calc);
reflist_free(calc);
gsl_vector_set(parameters, idx++, scale);
/* Initial atomic coordinates and (iso-)B-factors */
for ( j=0; j<model->n_atoms; j++ ) {
if ( model->atoms[j].refine ) {
if ( spec & REFINE_SPEC_X ) gsl_vector_set(parameters, idx++, model->atoms[j].x);
if ( spec & REFINE_SPEC_Y ) gsl_vector_set(parameters, idx++, model->atoms[j].y);
if ( spec & REFINE_SPEC_Z ) gsl_vector_set(parameters, idx++, model->atoms[j].z);
if ( spec & REFINE_SPEC_B ) gsl_vector_set(parameters, idx++, model->atoms[j].B);
if ( spec & REFINE_SPEC_OCC ) gsl_vector_set(parameters, idx++, model->atoms[j].occ);
}
}
iter = 0;
do {
/* Iterate */
refine_lsq_iterate(parameters, reflections, spec, model);
printf("LSQ: after iteration %i:\tscale=%f\n", iter, gsl_vector_get(parameters, 0));
iter++;
/* Put the parameter vector back into the atomic model */
model_free(model);
model = refine_model_from_parameters(parameters, spec, model);
model_move(model_orig, model);
refine_schedule_update(model);
} while ( (iter < MAX_REFINEMENT_ITERATIONS) && (model->refine_window->run_semaphore) );
printf("%i iterations performed\n", iter);
if ( iter == MAX_REFINEMENT_ITERATIONS ) printf("Reached maximum allowed number of iterations");
gsl_vector_free(parameters);
}
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