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/*
* symmetry.c
*
* Symmetry
*
* (c) 2006-2010 Thomas White <taw@physics.org>
*
* Part of CrystFEL - crystallography with a FEL
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "utils.h"
#ifdef DEBUG
#define SYM_DEBUG STATUS
#else /* DEBUG */
#define SYM_DEBUG(...)
#endif /* DEBUG */
/* Check if a reflection is in the asymmetric unit cell */
static int check_cond(signed int h, signed int k, signed int l, const char *sym)
{
if ( strcmp(sym, "1") == 0 )
return ( 1 );
if ( strcmp(sym, "-1") == 0 )
return ( 1 );
if ( strcmp(sym, "6") == 0 )
return ( ((h>0) && (k>=0)) || ((h==0) && (k==0)) );
if ( strcmp(sym, "6/m") == 0 )
return ( (((h>0) && (k>=0)) || ((h==0) && (k==0))) && (l>=0) );
if ( strcmp(sym, "6/mmm") == 0 )
return ( (((h>0) && (k>=0)) || ((h==0) && (k==0))) && (l>=0)
&& (h>=k) );
/* TODO: Add more groups here */
return 1;
}
/* Macros for checking the above conditions and returning if satisfied */
#define CHECK_COND(h, k, l, sym) \
if ( check_cond((h), (k), (l), (sym)) ) { \
*hp = (h); *kp = (k); *lp = (l); \
return; \
}
int num_equivs(signed int h, signed int k, signed int l, const char *sym)
{
/* 000 is always unique */
if ( (h==0) && (k==0) && (l==0) ) return 1;
if ( strcmp(sym, "1") == 0 ) return 1;
if ( strcmp(sym, "-1") == 0 ) return 2;
if ( strcmp(sym, "6") == 0 ) {
if ( (h==0) && (k==0) ) return 1; /* a */
return 6; /* b */
}
if ( strcmp(sym, "6/m") == 0 ) {
if ( (h==0) && (k==0) ) return 2; /* a */
if ( l == 0 ) return 6; /* b */
return 12; /* c */
}
if ( strcmp(sym, "6/mmm") == 0 ) {
if ( (h==0) && (k==0) ) return 2; /* a */
if ( (l==0) && (h==k) ) return 6; /* b */
if ( (l==0) && (k==0) ) return 6; /* c */
if ( h == k ) return 12; /* d */
if ( k == 0 ) return 12; /* e */
if ( l == 0 ) return 12; /* f */
return 24; /* g */
}
/* TODO: Add more groups here */
return 1;
}
void get_equiv(signed int h, signed int k, signed int l,
signed int *he, signed int *ke, signed int *le,
const char *sym, int idx)
{
signed int i = -h-k;
if ( strcmp(sym, "1") == 0 ) {
*he = h; *ke = k; *le = l; return;
}
if ( strcmp(sym, "-1") == 0 ) {
switch ( idx ) {
case 0 : *he = h; *ke = k; *le = l; return;
case 1 : *he = -h; *ke = -k; *le = -l; return;
}
}
if ( strcmp(sym, "6") == 0 ) {
/* a */
if ( (h==0) && (k==0) ) {
switch ( idx ) {
case 0 : *he = 0; *ke = 0; *le = l; return;
}
}
/* b */
switch ( idx ) {
case 0 : *he = h; *ke = k; *le = l; return;
case 1 : *he = i; *ke = h; *le = l; return;
case 2 : *he = k; *ke = i; *le = l; return;
case 3 : *he = -h; *ke = -k; *le = l; return;
case 4 : *he = -i; *ke = -h; *le = l; return;
case 5 : *he = -k; *ke = -i; *le = l; return;
}
}
if ( strcmp(sym, "6/m") == 0 ) {
/* a */
if ( (h==0) && (k==0) ) {
switch ( idx ) {
case 0 : *he = 0; *ke = 0; *le = l; return;
case 1 : *he = 0; *ke = 0; *le = -l; return;
}
}
/* b-c */
switch ( idx ) {
case 0 : *he = h; *ke = k; *le = l; return;
case 1 : *he = i; *ke = h; *le = l; return;
case 2 : *he = k; *ke = i; *le = l; return;
case 3 : *he = -h; *ke = -k; *le = l; return;
case 4 : *he = -i; *ke = -h; *le = l; return;
case 5 : *he = -k; *ke = -i; *le = l; return;
case 6 : *he = h; *ke = k; *le = -l; return;
case 7 : *he = i; *ke = h; *le = -l; return;
case 8 : *he = k; *ke = i; *le = -l; return;
case 9 : *he = -h; *ke = -k; *le = -l; return;
case 10 : *he = -i; *ke = -h; *le = -l; return;
case 11 : *he = -k; *ke = -i; *le = -l; return;
}
}
if ( strcmp(sym, "6/mmm") == 0 ) {
/* a */
if ( (h==0) && (k==0) ) {
switch ( idx ) {
case 0 : *he = 0; *ke = 0; *le = l; return;
case 1 : *he = 0; *ke = 0; *le = -l; return;
}
}
/* b-g */
switch ( idx ) {
case 0 : *he = h; *ke = k; *le = l; return;
case 1 : *he = i; *ke = h; *le = l; return;
case 2 : *he = k; *ke = i; *le = l; return;
case 3 : *he = -h; *ke = -k; *le = l; return;
case 4 : *he = -i; *ke = -h; *le = l; return;
case 5 : *he = -k; *ke = -i; *le = l; return;
case 6 : *he = k; *ke = h; *le = -l; return;
case 7 : *he = h; *ke = i; *le = -l; return;
case 8 : *he = i; *ke = k; *le = -l; return;
case 9 : *he = -k; *ke = -h; *le = -l; return;
case 10 : *he = -h; *ke = -i; *le = -l; return;
case 11 : *he = -i; *ke = -k; *le = -l; return;
case 12 : *he = -h; *ke = -k; *le = -l; return;
case 13 : *he = -i; *ke = -h; *le = -l; return;
case 14 : *he = -k; *ke = -i; *le = -l; return;
case 15 : *he = h; *ke = k; *le = -l; return;
case 16 : *he = i; *ke = h; *le = -l; return;
case 17 : *he = k; *ke = i; *le = -l; return;
case 18 : *he = -k; *ke = -h; *le = l; return;
case 19 : *he = -h; *ke = -i; *le = l; return;
case 20 : *he = -i; *ke = -k; *le = l; return;
case 21 : *he = k; *ke = h; *le = l; return;
case 22 : *he = h; *ke = i; *le = l; return;
case 23 : *he = i; *ke = k; *le = l; return;
}
}
/* TODO: Add more groups here */
ERROR("Unrecognised symmetry '%s'\n", sym);
abort();
}
void get_asymm(signed int h, signed int k, signed int l,
signed int *hp, signed int *kp, signed int *lp,
const char *sym)
{
int nequiv = num_equivs(h, k, l, sym);
int p;
SYM_DEBUG("------ %i %i %i\n", h, k, l);
for ( p=0; p<nequiv; p++ ) {
signed int he, ke, le;
get_equiv(h, k, l, &he, &ke, &le, sym, p);
SYM_DEBUG("%i : %i %i %i\n", p, he, ke, le);
CHECK_COND(he, ke, le, sym);
}
/* Should never reach here */
ERROR("No match found in %s for %i %i %i\n", sym, h, k, l);
abort();
}
static const char *get_holohedral(const char *sym)
{
/* Triclinic */
if ( strcmp(sym, "1") == 0 ) return "-1";
if ( strcmp(sym, "1") == 0 ) return "-1";
/* Hexagonal */
if ( strcmp(sym, "6") == 0 ) return "6/m";
if ( strcmp(sym, "6/m") == 0 ) return "6/mmm";
if ( strcmp(sym, "6/mmm") == 0 ) return "6/mmm";
/* TODO: Add more groups here */
ERROR("Couldn't find holohedral point group for '%s'\n", sym);
abort();
}
/* This is kind of like a "numerical" left coset decomposition.
* Given a reflection index and a point group, it returns the "idx-th"
* twinning possibility for the reflection. It returns "idx" if
* successful. To just count the number of possibilities, set idx=-1.
*
* The sequence of operators producing each possibility is guaranteed to
* be the same for any choice of indices given the same point group. */
static int coset_decomp(signed int hs, signed int ks, signed int ls,
signed int *hp, signed int *kp, signed int *lp,
const char *mero, signed int idx)
{
const char *holo = get_holohedral(mero);
int n_mero, n_holo;
int i;
signed int n_twins = 1;
signed int h, k, l;
ReflItemList *twins;
twins = new_items();
if ( idx == 0 ) {
/* Twin index zero is always the original orientation */
*hp = hs; *kp = ks; *lp = ls;
return 0;
}
get_asymm(hs, ks, ls, &h, &k, &l, mero);
/* How many equivalents in the holohedral point group are not
* equivalents according to the (possibly) merohedral group? */
n_holo = num_equivs(h, k, l, holo);
n_mero = num_equivs(h, k, l, mero);
for ( i=0; i<n_holo; i++ ) {
signed int h_holo, k_holo, l_holo;
signed int hs_holo, ks_holo, ls_holo;
/* Get equivalent according to the holohedral group */
get_equiv(h, k, l, &hs_holo, &ks_holo, &ls_holo, holo, i);
/* Put it into the asymmetric cell for the merohedral group */
get_asymm(hs_holo, ks_holo, ls_holo,
&h_holo, &k_holo, &l_holo, mero);
/* Is this the same reflection as we started with?
* If not, this reflection is 'equivalent by twinning' */
if ( (h_holo != h) || (k_holo != k) || (l_holo != l) ) {
if ( find_item(twins, h_holo, k_holo, l_holo) )
continue;
if ( n_twins == idx ) {
*hp = h_holo;
*kp = k_holo;
*lp = l_holo;
delete_items(twins);
return n_twins;
}
add_item(twins, h_holo, k_holo, l_holo);
n_twins++;
}
}
delete_items(twins);
return n_twins;
}
/* Get the number of twinned "equivalents" for this reflection */
int num_twins(signed int h, signed int k, signed int l, const char *sym)
{
return coset_decomp(h, k, l, NULL, NULL, NULL, sym, -1);
}
void get_twins(signed int h, signed int k, signed int l,
signed int *hp, signed int *kp, signed int *lp,
const char *sym, int idx)
{
if ( coset_decomp(h, k, l, hp, kp, lp, sym, idx) != idx ) {
ERROR("Failed coset decomposition for %i %i %i in %s\n",
h, k, l, sym);
abort();
}
}
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