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/*
* post-refinement.c
*
* Post refinement
*
* (c) 2006-2011 Thomas White <taw@physics.org>
*
* Part of CrystFEL - crystallography with a FEL
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdlib.h>
#include <assert.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_linalg.h>
#include "image.h"
#include "post-refinement.h"
#include "peaks.h"
#include "symmetry.h"
#include "geometry.h"
#include "cell.h"
/* Maximum number of iterations of NLSq to do for each image per macrocycle. */
#define MAX_CYCLES (10)
/* Refineable parameters */
enum {
REF_ASX,
NUM_PARAMS,
REF_BSX,
REF_CSX,
REF_ASY,
REF_BSY,
REF_CSY,
REF_ASZ,
REF_BSZ,
REF_CSZ,
REF_DIV,
REF_R,
};
/* Returns dp/dr at "r" */
static double partiality_gradient(double r, double profile_radius)
{
double q, dpdq, dqdr;
/* Calculate degree of penetration */
q = (r + profile_radius)/(2.0*profile_radius);
/* dp/dq */
dpdq = 6.0*(q-pow(q, 2.0));
/* dq/dr */
dqdr = 1.0 / (2.0*profile_radius);
return dpdq * dqdr;
}
/* Returns dp/drad at "r" */
static double partiality_rgradient(double r, double profile_radius)
{
double q, dpdq, dqdrad;
/* Calculate degree of penetration */
q = (r + profile_radius)/(2.0*profile_radius);
/* dp/dq */
dpdq = 6.0*(q-pow(q, 2.0));
/* dq/drad */
dqdrad = 0.5 * (1.0 - r * pow(profile_radius, -2.0));
return dpdq * dqdrad;
}
/* Return the gradient of parameter 'k' given the current status of 'image'. */
static double gradient(struct image *image, int k, Reflection *refl, double r)
{
double ds, tt, azi;
double nom, den;
double g;
double asx, asy, asz;
double bsx, bsy, bsz;
double csx, csy, csz;
double xl, yl, zl;
signed int hs, ks, ls;
double r1, r2, p;
int clamp_low, clamp_high;
get_symmetric_indices(refl, &hs, &ks, &ls);
cell_get_reciprocal(image->indexed_cell, &asx, &asy, &asz,
&bsx, &bsy, &bsz,
&csx, &csy, &csz);
xl = hs*asx + ks*bsx + ls*csx;
yl = hs*asy + ks*bsy + ls*csy;
zl = hs*asz + ks*bsz + ls*csz;
ds = 2.0 * resolution(image->indexed_cell, hs, ks, ls);
tt = angle_between(0.0, 0.0, 1.0, xl, yl, zl+1.0/image->lambda);
azi = angle_between(1.0, 0.0, 0.0, xl, yl, 0.0);
get_partial(refl, &r1, &r2, &p, &clamp_low, &clamp_high);
/* Calculate the gradient of partiality wrt excitation error. */
g = 0.0;
if ( clamp_low == 0 ) {
g += partiality_gradient(r1, r);
}
if ( clamp_high == 0 ) {
g += partiality_gradient(r2, r);
}
/* For many gradients, just multiply the above number by the gradient
* of excitation error wrt whatever. */
switch ( k ) {
case REF_DIV :
nom = sqrt(2.0) * ds * sin(image->div/2.0);
den = sqrt(1.0 - cos(image->div/2.0));
return (nom/den) * g;
case REF_R :
g = 0.0;
if ( clamp_low == 0 ) {
g += partiality_rgradient(r1, r);
}
if ( clamp_high == 0 ) {
g += partiality_rgradient(r2, r);
}
return g;
/* Cell parameters and orientation */
case REF_ASX :
return hs * sin(tt) * cos(azi) * g;
case REF_BSX :
return ks * sin(tt) * g;
case REF_CSX :
return ls * sin(tt) * g;
case REF_ASY :
return hs * sin(tt) * g;
case REF_BSY :
return ks * sin(tt) * g;
case REF_CSY :
return ls * sin(tt) * g;
case REF_ASZ :
return hs * cos(tt) * g;
case REF_BSZ :
return ks * cos(tt) * g;
case REF_CSZ :
return ls * cos(tt) * g;
}
ERROR("No gradient defined for parameter %i\n", k);
abort();
}
static void apply_cell_shift(UnitCell *cell, int k, double shift)
{
double asx, asy, asz;
double bsx, bsy, bsz;
double csx, csy, csz;
cell_get_reciprocal(cell, &asx, &asy, &asz,
&bsx, &bsy, &bsz,
&csx, &csy, &csz);
switch ( k )
{
case REF_ASX : asx += shift; break;
case REF_ASY : asy += shift; break;
case REF_ASZ : asz += shift; break;
case REF_BSX : bsx += shift; break;
case REF_BSY : bsy += shift; break;
case REF_BSZ : bsz += shift; break;
case REF_CSX : csx += shift; break;
case REF_CSY : csy += shift; break;
case REF_CSZ : csz += shift; break;
}
cell_set_reciprocal(cell, asx, asy, asz,
bsx, bsy, bsz,
csx, csy, csz);
if ( k == REF_CSZ ) {
double a, b, c, al, be, ga;
cell_get_parameters(cell, &a, &b, &c, &al, &be, &ga);
STATUS("New cell: %5.2f %5.2f %5.2f nm %5.2f %5.2f %5.2f deg\n",
a/1.0e-9, b/1.0e-9, c/1.0e-9,
rad2deg(al), rad2deg(be), rad2deg(ga));
}
}
/* Apply the given shift to the 'k'th parameter of 'image'. */
static void apply_shift(struct image *image, int k, double shift)
{
switch ( k ) {
case REF_DIV :
image->div += shift;
break;
case REF_R :
image->profile_radius += shift;
break;
case REF_ASX :
case REF_ASY :
case REF_ASZ :
case REF_BSX :
case REF_BSY :
case REF_BSZ :
case REF_CSX :
case REF_CSY :
case REF_CSZ :
apply_cell_shift(image->indexed_cell, k, shift);
break;
default :
ERROR("No shift defined for parameter %i\n", k);
abort();
}
}
/* Perform one cycle of post refinement on 'image' against 'full' */
static double pr_iterate(struct image *image, const RefList *full,
const char *sym)
{
gsl_matrix *M;
gsl_vector *v;
gsl_vector *shifts;
int param;
Reflection *refl;
RefListIterator *iter;
RefList *reflections;
double max_shift;
reflections = image->reflections;
M = gsl_matrix_calloc(NUM_PARAMS, NUM_PARAMS);
v = gsl_vector_calloc(NUM_PARAMS);
/* Construct the equations, one per reflection in this image */
for ( refl = first_refl(reflections, &iter);
refl != NULL;
refl = next_refl(refl, iter) ) {
signed int ha, ka, la;
double I_full, delta_I;
double I_partial;
int k;
double p;
Reflection *match;
double gradients[NUM_PARAMS];
if ( !get_scalable(refl) ) continue;
/* Find the full version */
get_indices(refl, &ha, &ka, &la);
match = find_refl(full, ha, ka, la);
assert(match != NULL); /* Never happens because all scalable
* reflections had their LSQ intensities
* calculated in lsq_intensities(). */
I_full = image->osf * get_intensity(match);
/* Actual measurement of this reflection from this pattern? */
I_partial = get_intensity(refl);
p = get_partiality(refl);
delta_I = I_partial - (p * I_full);
/* Calculate all gradients for this reflection */
for ( k=0; k<NUM_PARAMS; k++ ) {
double gr;
gr = gradient(image, k, refl, image->profile_radius);
gradients[k] = gr;
}
for ( k=0; k<NUM_PARAMS; k++ ) {
int g;
double v_c, v_curr;
double gr;
for ( g=0; g<NUM_PARAMS; g++ ) {
double M_c, M_curr;
M_c = gradients[g] * gradients[k];
M_c *= pow(I_full, 2.0);
M_curr = gsl_matrix_get(M, g, k);
gsl_matrix_set(M, g, k, M_curr + M_c);
}
gr = gradients[k];
v_c = delta_I * I_full * gr;
v_curr = gsl_vector_get(v, k);
gsl_vector_set(v, k, v_curr + v_c);
}
}
double tg = gsl_matrix_get(M, 0, 0);
STATUS("total gradient = %e\n", tg);
//show_matrix_eqn(M, v, NUM_PARAMS);
shifts = gsl_vector_alloc(NUM_PARAMS);
max_shift = 0.0;
if ( gsl_linalg_HH_solve(M, v, shifts) ) {
ERROR("Couldn't solve normal equations!\n");
} else {
for ( param=0; param<NUM_PARAMS; param++ ) {
double shift = gsl_vector_get(shifts, param);
apply_shift(image, param, shift);
if ( fabs(shift) > max_shift ) max_shift = fabs(shift);
}
}
gsl_matrix_free(M);
gsl_vector_free(v);
gsl_vector_free(shifts);
return max_shift;
}
static double mean_partial_dev(struct image *image,
const RefList *full, const char *sym)
{
double dev = 0.0;
/* For each reflection */
Reflection *refl;
RefListIterator *iter;
for ( refl = first_refl(image->reflections, &iter);
refl != NULL;
refl = next_refl(refl, iter) ) {
double G, p;
signed int h, k, l;
Reflection *full_version;
double I_full, I_partial;
if ( !get_scalable(refl) ) continue;
get_indices(refl, &h, &k, &l);
assert ((h!=0) || (k!=0) || (l!=0));
full_version = find_refl(full, h, k, l);
assert(full_version != NULL);
G = image->osf;
p = get_partiality(refl);
I_partial = get_intensity(refl);
I_full = get_intensity(full_version);
//STATUS("%3i %3i %3i %5.2f %5.2f %5.2f %5.2f %5.2f\n",
// h, k, l, G, p, I_partial, I_full,
// I_partial - p*G*I_full);
dev += pow(I_partial - p*G*I_full, 2.0);
}
return sqrt(dev);
}
static void plot_curve(struct image *image, const RefList *full,
const char *sym)
{
double ax, ay, az;
double bx, by, bz;
double cx, cy, cz;
UnitCell *cell = image->indexed_cell;
double shval, origval;
int i;
cell_get_reciprocal(cell, &ax, &ay, &az, &bx, &by, &bz, &cx, &cy, &cz);
shval = 0.001*ax;
origval = ax;
for ( i=-10; i<=10; i++ ) {
double dev;
cell_get_reciprocal(cell, &ax, &ay, &az, &bx,
&by, &bz, &cx, &cy, &cz);
ax = origval + (double)i*shval;
cell_set_reciprocal(cell, ax, ay, az, bx, by, bz, cx, cy, cz);
update_partialities(image, sym, NULL, NULL, NULL, NULL);
dev = mean_partial_dev(image, full, sym);
STATUS("%i %e %e\n", i, ax, dev);
}
}
void pr_refine(struct image *image, const RefList *full, const char *sym)
{
double max_shift, dev;
int i;
/* FIXME: This is for debugging */
//plot_curve(image, full, sym);
//return;
dev = mean_partial_dev(image, full, sym);
STATUS("PR starting dev = %5.2f\n", dev);
i = 0;
do {
double dev;
max_shift = pr_iterate(image, full, sym);
update_partialities(image, sym, NULL, NULL, NULL, NULL);
dev = mean_partial_dev(image, full, sym);
STATUS("PR Iteration %2i: max shift = %5.2f dev = %5.2f\n",
i, max_shift, dev);
i++;
} while ( (max_shift > 0.01) && (i < MAX_CYCLES) );
}
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