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/*
* symmetry.c
*
* Symmetry stuff
*
* (c) 2006-2008 Thomas White <taw27@cam.ac.uk>
*
* synth2d - Two-Dimensional Crystallographic Fourier Synthesis
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <assert.h>
#include "symmetry.h"
#include "reflist.h"
#include "model.h"
#define is_odd(a) ((a)%2==1)
/* Return a list of atoms containing the given atom and all its symmetry equivalents */
AtomicModel *symmetry_generate_equivalent_atoms(AtomicModel *model, size_t j, ModelTarget target) {
AtomicModel *list;
list = model_new();
list->atoms[list->n_atoms] = model->atoms[j]; list->n_atoms++;
if ( target == MODEL_TARGET_DISPLAY ) {
if ( model->atoms[j].x == 0 ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = 1.0;
list->n_atoms++;
}
if ( model->atoms[j].y == 0 ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].y = 1.0;
list->n_atoms++;
}
if ( (model->atoms[j].x == 0) && (model->atoms[j].y == 0) ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = 1.0;
list->atoms[list->n_atoms].y = 1.0;
list->n_atoms++;
}
}
if ( model->sym & SYMMETRY_CENTRE ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = 1-list->atoms[list->n_atoms].x;
list->atoms[list->n_atoms].y = 1-list->atoms[list->n_atoms].y;
list->n_atoms++;
}
if ( model->sym & SYMMETRY_MIRROR_HORIZONTAL ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].y = 1-list->atoms[list->n_atoms].y;
list->n_atoms++;
}
if ( model->sym & SYMMETRY_MIRROR_VERTICAL ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = 1-list->atoms[list->n_atoms].x;
list->n_atoms++;
}
if ( model->sym & SYMMETRY_GLIDE_HORIZONTAL ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = fmod(0.5 + list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = 1-list->atoms[list->n_atoms].y;
list->n_atoms++;
}
if ( model->sym & SYMMETRY_GLIDE_VERTICAL ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = 1-list->atoms[list->n_atoms].x;
list->atoms[list->n_atoms].y = fmod(0.5 + list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
}
if ( model->sym & SYMMETRY_GLIDE_HORIZONTAL_QUARTER ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = fmod(0.5 + list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = fmod(1.5 - list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
}
if ( model->sym & SYMMETRY_GLIDE_VERTICAL_QUARTER ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = fmod(1.5 - list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = fmod(0.5 + list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
}
/* Fix cm */
if ( (model->sym & SYMMETRY_GLIDE_HORIZONTAL_QUARTER) && (model->sym & SYMMETRY_MIRROR_HORIZONTAL) ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = fmod(0.5 + list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = 1 - fmod(1.5 - list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
} else if ( (model->sym & SYMMETRY_GLIDE_VERTICAL_QUARTER) && (model->sym & SYMMETRY_MIRROR_VERTICAL) ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = 1 - fmod(1.5 - list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = fmod(0.5 + list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
}
/* Fix c2mm */
if ( (model->sym & SYMMETRY_GLIDE_VERTICAL_QUARTER) && (model->sym & SYMMETRY_MIRROR_HORIZONTAL) ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = fmod(1.5 - list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = 1 - fmod(0.5 + list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
}
if ( model->sym & SYMMETRY_MIRROR_HORIZONTAL_QUARTER ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = list->atoms[list->n_atoms].x;
list->atoms[list->n_atoms].y = fmod(1.5 - list->atoms[list->n_atoms].y, 1);
list->n_atoms++;
}
if ( model->sym & SYMMETRY_MIRROR_VERTICAL_QUARTER ) {
list->atoms[list->n_atoms] = model->atoms[j];
list->atoms[list->n_atoms].x = fmod(1.5 - list->atoms[list->n_atoms].x, 1);
list->atoms[list->n_atoms].y = list->atoms[list->n_atoms].y;
list->n_atoms++;
}
return list;
}
ReflectionList *symmetry_generate_equivalent_reflections(Symmetry sym, signed int h, signed int k, signed int l) {
ReflectionList *result;
result = reflist_new();
/* Remove the minus in front of 'l' to make even HOLZ conditional transforms real.
* This is generally the wrong thing to do. */
if ( sym & SYMMETRY_FRIEDEL ) reflist_addref_deltatheta(result, -h, -k, -l, 0, -1);
if ( sym & SYMMETRY_MIRROR_HORIZONTAL ) reflist_addref_deltatheta(result, h, -k, l, 0, 1);
if ( sym & SYMMETRY_MIRROR_VERTICAL ) reflist_addref_deltatheta(result, -h, k, l, 0, 1);
if ( sym & SYMMETRY_MIRROR_DIAGONAL ) reflist_addref_deltatheta(result, -h, -k, l, 0, 1);
if ( sym & SYMMETRY_GLIDE_HORIZONTAL ) reflist_addref_deltatheta(result, h, -k, l, M_PI, 1);
if ( sym & SYMMETRY_GLIDE_VERTICAL ) reflist_addref_deltatheta(result, -h, k, l, M_PI, 1);
if ( sym & SYMMETRY_GLIDE_HORIZONTAL_QUARTER ) {
if ( is_odd(abs(h)+abs(k)) ) {
reflist_addref_deltatheta(result, h, -k, l, M_PI, 1);
} else {
reflist_addref_deltatheta(result, h, -k, l, 0, 1);
}
}
if ( sym & SYMMETRY_GLIDE_VERTICAL_QUARTER ) {
if ( is_odd(abs(h)+abs(k)) ) {
reflist_addref_deltatheta(result, -h, k, l, M_PI, 1);
} else {
reflist_addref_deltatheta(result, -h, k, l, 0, 1);
}
}
if ( sym & SYMMETRY_ROTATION_4 ) {
if ( sym & SYMMETRY_GLIDE_DIAGONAL ) {
if ( is_odd(abs(h)+abs(k)) ) {
reflist_addref_deltatheta(result, h, -k, l, M_PI, 1);
reflist_addref_deltatheta(result, -h, k, l, M_PI, 1);
reflist_addref_deltatheta(result, -h, -k, l, 0, 1);
reflist_addref_deltatheta(result, k, h, l, 0, 1);
reflist_addref_deltatheta(result, -k, h, l, M_PI, 1);
reflist_addref_deltatheta(result, k, -h, l, M_PI, 1);
reflist_addref_deltatheta(result, -k, -h, l, 0, 1);
} else {
reflist_addref_deltatheta(result, h, -k, l, 0, 1);
reflist_addref_deltatheta(result, -h, k, l, 0, 1);
reflist_addref_deltatheta(result, -h, -k, l, 0, 1);
reflist_addref_deltatheta(result, k, h, l, 0, 1);
reflist_addref_deltatheta(result, -k, h, l, 0, 1);
reflist_addref_deltatheta(result, k, -h, l, 0, 1);
reflist_addref_deltatheta(result, -k, -h, l, 0, 1);
}
} else {
reflist_addref_deltatheta(result, -h, -k, l, 0, 1);
reflist_addref_deltatheta(result, -h, k, l, 0, 1);
reflist_addref_deltatheta(result, h, -k, l, 0, 1);
}
}
return result;
}
static double symmetry_realphase(double phk) {
if ( (phk >= 0) && (phk < M_PI_2) ) phk = 0;
else if ( (phk > M_PI_2) && (phk < M_PI) ) phk = M_PI;
else if ( (phk < 0) && (phk > -M_PI/2) ) phk = 0;
else if ( (phk <= -M_PI_2) && (phk > -M_PI) ) phk = M_PI;
return phk;
}
void symmetry_centricity(ReflectionList *reflections, unsigned int i, Symmetry sym, SymFlags flags) {
double am, ph;
signed int h, k;
ph = 0;
h = reflections->refs[i].h;
k = reflections->refs[i].k;
am = reflections->refs[i].amplitude;
if ( flags & SYMFLAG_PHASES_KNOWN ) ph = fmod(reflections->refs[i].phase_known, 2*M_PI);
if ( flags & SYMFLAG_PHASES_CALC ) ph = fmod(reflections->refs[i].phase_calc, 2*M_PI);
if ( (sym & SYMMETRY_MIRROR_HORIZONTAL) && (sym & SYMMETRY_FRIEDEL) && (h == 0) ) {
ph = symmetry_realphase(ph);
}
if ( (sym & SYMMETRY_MIRROR_VERTICAL) && (sym & SYMMETRY_FRIEDEL) && (k == 0) ) {
ph = symmetry_realphase(ph);
}
if ( (sym & SYMMETRY_CENTRE) && (sym & SYMMETRY_FRIEDEL) ) {
ph = symmetry_realphase(ph);
}
if (( ( (sym & SYMMETRY_GLIDE_HORIZONTAL) && (sym & SYMMETRY_MIRROR_VERTICAL) )
|| ( (sym & SYMMETRY_GLIDE_HORIZONTAL_QUARTER) && (sym & SYMMETRY_MIRROR_VERTICAL) )
|| ( (sym & SYMMETRY_GLIDE_VERTICAL) && (sym & SYMMETRY_MIRROR_HORIZONTAL) )
|| ( (sym & SYMMETRY_GLIDE_VERTICAL_QUARTER) && (sym & SYMMETRY_MIRROR_HORIZONTAL) ) )
&& (is_odd(abs(h)+abs(k))) ) {
if ( (ph >= 0) && (ph < M_PI) ) ph = M_PI_2;
else if ( (ph >= M_PI_2) && (ph < 2*M_PI) ) ph = -M_PI_2;
else if ( (ph < 0) && (ph > -M_PI) ) ph = -M_PI_2;
else if ( (ph <= -M_PI) ) ph = M_PI_2;
}
if ( flags & SYMFLAG_PHASES_KNOWN ) reflections->refs[i].phase_known = ph;
if ( flags & SYMFLAG_PHASES_CALC ) reflections->refs[i].phase_calc = ph;
}
unsigned int symmetry_reflection_allowed(signed int h, signed int k, signed int l, Symmetry sym) {
if ( (sym & SYMMETRY_GLIDE_HORIZONTAL) && (h == 0) && (k % 2) ) return 0;
if ( (sym & SYMMETRY_GLIDE_HORIZONTAL_QUARTER) && (h == 0) && (k % 2) ) return 0;
if ( (sym & SYMMETRY_GLIDE_VERTICAL) && (k == 0) && (h % 2) ) return 0;
if ( (sym & SYMMETRY_GLIDE_VERTICAL_QUARTER) && (k == 0) && (h % 2) ) return 0;
if ( (sym & SYMMETRY_ROTATION_4 ) && ( sym & SYMMETRY_GLIDE_DIAGONAL ) && (k == 0) && (h % 2) ) return 0;
if ( (sym & SYMMETRY_ROTATION_4 ) && ( sym & SYMMETRY_GLIDE_DIAGONAL ) && (h == 0) && (k % 2) ) return 0;
return 1;
}
/* Symmetrise a list of reflections (expanding all equivalents to P1) */
double symmetry_symmetrise(ReflectionList *reflections, Symmetry sym, SymFlags flags) {
unsigned int i = 0;
double r_sym = 0;
double r_sym_norm = 0;
unsigned int new_ref = 0;
unsigned int elim_ref = 0;
double am_elim = 0;
unsigned int n = reflections->n_reflections;
for ( i=1; i<n; i++ ) { /* Don't symmetrise 000 */
signed int h, k, l;
h = reflections->refs[i].h;
k = reflections->refs[i].k;
l = reflections->refs[i].l;
if ( (h==0) && (k==0) && (l==0) ) continue;
if ( symmetry_reflection_allowed(h, k, l, sym) ) {
double ph = 69;
unsigned int j;
double av;
unsigned int av_n;
ReflectionList *equivalents;
equivalents = symmetry_generate_equivalent_reflections(sym, h, k, l);
symmetry_centricity(reflections, i, sym, flags);
/* First pass: calculate average amplitude, determine phase */
av = reflections->refs[i].amplitude; av_n = 1;
for ( j=1; j<equivalents->n_reflections; j++ ) {
unsigned int p;
p = reflist_inlist(reflections, equivalents->refs[j].h, equivalents->refs[j].k, equivalents->refs[j].l);
if ( p ) {
av += reflections->refs[p].amplitude;
av_n++;
}
}
av = av / av_n;
r_sym += fabs(av - reflections->refs[i].amplitude);
r_sym_norm += reflections->refs[i].amplitude;
if ( flags & SYMFLAG_PHASES_KNOWN ) ph = fmod(reflections->refs[i].phase_known, 2*M_PI);
if ( flags & SYMFLAG_PHASES_CALC ) ph = fmod(reflections->refs[i].phase_calc, 2*M_PI);
//printf("Phase of %3i %3i %3i is %f\n", h, k, l, ph);
/* Second pass: set all equivalent reflections to the average amplitude */
reflections->refs[i].amplitude = av;
for ( j=1; j<equivalents->n_reflections; j++ ) {
unsigned int p;
double phn;
p = reflist_inlist(reflections, equivalents->refs[j].h, equivalents->refs[j].k, equivalents->refs[j].l);
if ( p ) {
r_sym += fabs(av - reflections->refs[p].amplitude);
r_sym_norm += reflections->refs[p].amplitude;
reflections->refs[p].amplitude = av;
} else {
p = reflist_addref_am(reflections, equivalents->refs[j].h, equivalents->refs[j].k, equivalents->refs[j].l, av);
//printf("SY: Generating %3i %3i %3i am=%f\n", equivalents->refs[j].h,
// equivalents->refs[j].k, equivalents->refs[j].l, av);
new_ref++;
}
phn = (ph + equivalents->refs[j].delta_theta) * equivalents->refs[j].multiplier;
if ( flags & SYMFLAG_PHASES_KNOWN ) {
reflections->refs[p].phase_known = phn;
reflections->refs[p].phase_known_set = 1;
}
if ( flags & SYMFLAG_PHASES_CALC ) {
reflections->refs[p].phase_calc = phn;
reflections->refs[p].phase_calc_set = 1;
}
//printf("Set phase of %3i %3i %3i to %f (dt=%f, mul=%i)\n", equivalents->refs[j].h,
//equivalents->refs[j].k, equivalents->refs[j].l,
//phn, equivalents->refs[j].delta_theta, equivalents->refs[j].multiplier);
}
reflist_free(equivalents);
} else {
am_elim += reflections->refs[i].amplitude;
reflist_delref(reflections, h, k, l);
//printf("SY: Eliminating systematically absent reflection %i %i %i\n", h, k, l);
elim_ref++;
i--;
}
}
if ( r_sym > 0 ) {
r_sym = r_sym / r_sym_norm;
}
//printf("SY: R_sym = %.2f%%, %i reflections generated, %i reflections eliminated (total amplitude %f)\n", r_sym*100, new_ref, elim_ref, am_elim);
return r_sym;
}
Symmetry symmetry_encode(const char *symmetry) {
if ( strcmp(symmetry, "p1") == 0 ) return PLANEGROUP_P1;
if ( strcmp(symmetry, "p2") == 0 ) return PLANEGROUP_P2;
if ( strcmp(symmetry, "pm (m // x)") == 0 ) return PLANEGROUP_PM_X;
if ( strcmp(symmetry, "pm (m // y)") == 0 ) return PLANEGROUP_PM_Y;
if ( strcmp(symmetry, "pg (g // x)") == 0 ) return PLANEGROUP_PG_X;
if ( strcmp(symmetry, "pg (g // y)") == 0 ) return PLANEGROUP_PG_Y;
if ( strcmp(symmetry, "cm (m // x)") == 0 ) return PLANEGROUP_CM_X;
if ( strcmp(symmetry, "cm (m // y)") == 0 ) return PLANEGROUP_CM_Y;
if ( strcmp(symmetry, "p2mm") == 0 ) return PLANEGROUP_P2MM;
if ( strcmp(symmetry, "p2mg (m // x)") == 0 ) return PLANEGROUP_P2MG_X;
if ( strcmp(symmetry, "p2mg (m // y)") == 0 ) return PLANEGROUP_P2MG_Y;
if ( strcmp(symmetry, "p2gg") == 0 ) return PLANEGROUP_P2GG;
if ( strcmp(symmetry, "c2mm") == 0 ) return PLANEGROUP_C2MM;
if ( strcmp(symmetry, "p4") == 0 ) return PLANEGROUP_P4;
if ( strcmp(symmetry, "p4mm") == 0 ) return PLANEGROUP_P4MM;
if ( strcmp(symmetry, "p4gm") == 0 ) return PLANEGROUP_P4GM;
if ( strcmp(symmetry, "p3") == 0 ) return PLANEGROUP_P3;
if ( strcmp(symmetry, "p3m1") == 0 ) return PLANEGROUP_P3M1;
if ( strcmp(symmetry, "p31m") == 0 ) return PLANEGROUP_P31M;
if ( strcmp(symmetry, "p6") == 0 ) return PLANEGROUP_P6;
if ( strcmp(symmetry, "p6mm") == 0 ) return PLANEGROUP_P6MM;
fprintf(stderr, "Unrecognised symmetry identifier '%s'\n", symmetry);
return SYMMETRY_IDENTITY;
}
const char *symmetry_decode(Symmetry sym) {
if ( sym == PLANEGROUP_P1 ) return "p1";
if ( sym == PLANEGROUP_P2 ) return "p2";
if ( sym == PLANEGROUP_PM_X ) return "pm (m // x)";
if ( sym == PLANEGROUP_PM_Y ) return "pm (m // y)";
if ( sym == PLANEGROUP_PG_X ) return "pg (g // x)";
if ( sym == PLANEGROUP_PG_Y ) return "pg (g // y)";
if ( sym == PLANEGROUP_CM_X ) return "cm (m // x)";
if ( sym == PLANEGROUP_CM_Y ) return "cm (m // y)";
if ( sym == PLANEGROUP_P2MM ) return "p2mm";
if ( sym == PLANEGROUP_P2MG_X ) return "p2mg (m // x)";
if ( sym == PLANEGROUP_P2MG_Y ) return "p2mg (m // y)";
if ( sym == PLANEGROUP_P2GG ) return "p2gg";
if ( sym == PLANEGROUP_C2MM ) return "c2mm";
if ( sym == PLANEGROUP_P4 ) return "p4";
if ( sym == PLANEGROUP_P4MM ) return "p4mm";
if ( sym == PLANEGROUP_P4GM ) return "p4gm";
if ( sym == PLANEGROUP_P3 ) return "p3";
if ( sym == PLANEGROUP_P3M1 ) return "p3m1";
if ( sym == PLANEGROUP_P31M ) return "p31m";
if ( sym == PLANEGROUP_P6 ) return "p6";
if ( sym == PLANEGROUP_P6MM ) return "p6mm";
if ( sym == (PLANEGROUP_P1 | SYMMETRY_FRIEDEL) ) return "p1 & Friedel";
if ( sym == (PLANEGROUP_P2 | SYMMETRY_FRIEDEL) ) return "p2 & Friedel";
if ( sym == (PLANEGROUP_PM_X | SYMMETRY_FRIEDEL) ) return "pm (m // x) & Friedel";
if ( sym == (PLANEGROUP_PM_Y | SYMMETRY_FRIEDEL) ) return "pm (m // y) & Friedel";
if ( sym == (PLANEGROUP_PG_X | SYMMETRY_FRIEDEL) ) return "pg (g // x) & Friedel";
if ( sym == (PLANEGROUP_PG_Y | SYMMETRY_FRIEDEL) ) return "pg (g // y) & Friedel";
if ( sym == (PLANEGROUP_CM_X | SYMMETRY_FRIEDEL) ) return "cm (m // x) & Friedel";
if ( sym == (PLANEGROUP_CM_Y | SYMMETRY_FRIEDEL) ) return "cm (m // y) & Friedel";
if ( sym == (PLANEGROUP_P2MM | SYMMETRY_FRIEDEL) ) return "p2mm & Friedel";
if ( sym == (PLANEGROUP_P2MG_X | SYMMETRY_FRIEDEL) ) return "p2mg (m // x) & Friedel";
if ( sym == (PLANEGROUP_P2MG_Y | SYMMETRY_FRIEDEL) ) return "p2mg (m // y) & Friedel";
if ( sym == (PLANEGROUP_P2GG | SYMMETRY_FRIEDEL) ) return "p2gg & Friedel";
if ( sym == (PLANEGROUP_C2MM | SYMMETRY_FRIEDEL) ) return "c2mm & Friedel";
if ( sym == (PLANEGROUP_P4 | SYMMETRY_FRIEDEL) ) return "p4 & Friedel";
if ( sym == (PLANEGROUP_P4MM | SYMMETRY_FRIEDEL) ) return "p4mm & Friedel";
if ( sym == (PLANEGROUP_P4GM | SYMMETRY_FRIEDEL) ) return "p4gm & Friedel";
if ( sym == (PLANEGROUP_P3 | SYMMETRY_FRIEDEL) ) return "p3 & Friedel";
if ( sym == (PLANEGROUP_P3M1 | SYMMETRY_FRIEDEL) ) return "p3m1 & Friedel";
if ( sym == (PLANEGROUP_P31M | SYMMETRY_FRIEDEL) ) return "p31m & Friedel";
if ( sym == (PLANEGROUP_P6 | SYMMETRY_FRIEDEL) ) return "p6 & Friedel";
if ( sym == (PLANEGROUP_P6MM | SYMMETRY_FRIEDEL) ) return "p6mm & Friedel";
return "(unknown symmetry)";
}
void symmetry_symmetrise_array(fftw_complex *in, signed int width, signed int height, Symmetry sym) {
ReflectionList *reflections;
reflections = reflist_new_from_array(in, width, height);
symmetry_symmetrise(reflections, sym, SYMFLAG_PHASES_KNOWN);
reflist_fill_array(in, reflections, width, height);
reflist_free(reflections);
}
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