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symmetry.c
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/*
* Brute force symmetry analyzer.
* This is actually C++ program, masquerading as a C one!
*
* (C) 1996, 2003 S. Patchkovskii, [email protected]
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*
* $Log: symmetry.c,v $
* Revision 1.16 2003/04/04 13:05:03 patchkov
* Revision 1.15 2000/01/25 16:47:17 patchkov
* Revision 1.14 2000/01/25 16:39:08 patchkov
* Revision 1.13 1996/05/24 12:32:08 ps
* Revision 1.12 1996/05/23 16:10:47 ps
* First reasonably stable version.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#ifndef M_PI
#define M_PI 3.1415926535897932384626433832795028841971694
#endif
#define DIMENSION 3
#define MAXPARAM 7
typedef struct {
int type ;
double x[ DIMENSION ] ;
} ATOM ;
/*
* All specific structures should have corresponding elements in the
* same position generic structure does.
*
* Planes are characterized by the surface normal direction
* (taken in the direction *from* the coordinate origin)
* and distance from the coordinate origin to the plane
* in the direction of the surface normal.
*
* Inversion is characterized by location of the inversion center.
*
* Rotation is characterized by a vector (distance+direction) from the origin
* to the rotation axis, axis direction and rotation order. Rotations
* are in the clockwise direction looking opposite to the direction
* of the axis. Note that this definition of the rotation axis
* is *not* unique, since an arbitrary multiple of the axis direction
* can be added to the position vector without changing actual operation.
*
* Mirror rotation is defined by the same parameters as normal rotation,
* but the origin is now unambiguous since it defines the position of the
* plane associated with the axis.
*
*/
typedef struct _SYMMETRY_ELEMENT_ {
void (*transform_atom)( struct _SYMMETRY_ELEMENT_ *el, ATOM *from, ATOM *to ) ;
int * transform ; /* Correspondence table for the transformation */
int order ; /* Applying transformation this many times is identity */
int nparam ; /* 4 for inversion and planes, 7 for axes */
double maxdev ; /* Larges error associated with the element */
double distance ;
double normal[ DIMENSION ] ;
double direction[ DIMENSION ] ;
} SYMMETRY_ELEMENT ;
typedef struct {
char * group_name ; /* Canonical group name */
char * symmetry_code ; /* Group symmetry code */
int (*check)( void ) ; /* Additional verification routine, not used */
} POINT_GROUP ;
double ToleranceSame = 1e-3 ;
double TolerancePrimary = 5e-2 ;
double ToleranceFinal = 1e-4 ;
double MaxOptStep = 5e-1 ;
double MinOptStep = 1e-7 ;
double GradientStep = 1e-7 ;
double OptChangeThreshold = 1e-10 ;
double CenterOfSomething[ DIMENSION ] ;
double * DistanceFromCenter = NULL ;
int verbose = 0 ;
int MaxOptCycles = 200 ;
int OptChangeHits = 5 ;
int MaxAxisOrder = 20 ;
int AtomsCount = 0 ;
ATOM * Atoms = NULL ;
int PlanesCount = 0 ;
SYMMETRY_ELEMENT ** Planes = NULL ;
SYMMETRY_ELEMENT * MolecularPlane = NULL ;
int InversionCentersCount = 0 ;
SYMMETRY_ELEMENT ** InversionCenters = NULL ;
int NormalAxesCount = 0 ;
SYMMETRY_ELEMENT ** NormalAxes = NULL ;
int ImproperAxesCount = 0 ;
SYMMETRY_ELEMENT ** ImproperAxes = NULL ;
int * NormalAxesCounts = NULL ;
int * ImproperAxesCounts = NULL ;
int BadOptimization = 0 ;
char * SymmetryCode = "" ;
/*
* Statistics
*/
long StatTotal = 0 ;
long StatEarly = 0 ;
long StatPairs = 0 ;
long StatDups = 0 ;
long StatOrder = 0 ;
long StatOpt = 0 ;
long StatAccept = 0 ;
/*
* Point groups I know about
*/
int true(void){ return 1 ; }
POINT_GROUP PointGroups[] = {
{ "C1", "", true },
{ "Cs", "(sigma) ", true },
{ "Ci", "(i) ", true },
{ "C2", "(C2) ", true },
{ "C3", "(C3) ", true },
{ "C4", "(C4) (C2) ", true },
{ "C5", "(C5) ", true },
{ "C6", "(C6) (C3) (C2) ", true },
{ "C7", "(C7) ", true },
{ "C8", "(C8) (C4) (C2) ", true },
{ "D2", "3*(C2) ", true },
{ "D3", "(C3) 3*(C2) ", true },
{ "D4", "(C4) 5*(C2) ", true },
{ "D5", "(C5) 5*(C2) ", true },
{ "D6", "(C6) (C3) 7*(C2) ", true },
{ "D7", "(C7) 7*(C2) ", true },
{ "D8", "(C8) (C4) 9*(C2) ", true },
{ "C2v", "(C2) 2*(sigma) ", true },
{ "C3v", "(C3) 3*(sigma) ", true },
{ "C4v", "(C4) (C2) 4*(sigma) ", true },
{ "C5v", "(C5) 5*(sigma) ", true },
{ "C6v", "(C6) (C3) (C2) 6*(sigma) ", true },
{ "C7v", "(C7) 7*(sigma) ", true },
{ "C8v", "(C8) (C4) (C2) 8*(sigma) ", true },
{ "C2h", "(i) (C2) (sigma) ", true },
{ "C3h", "(C3) (S3) (sigma) ", true },
{ "C4h", "(i) (C4) (C2) (S4) (sigma) ", true },
{ "C5h", "(C5) (S5) (sigma) ", true },
{ "C6h", "(i) (C6) (C3) (C2) (S6) (S3) (sigma) ", true },
{ "C7h", "(C7) (S7) (sigma) ", true },
{ "C8h", "(i) (C8) (C4) (C2) (S8) (S4) (sigma) ", true },
{ "D2h", "(i) 3*(C2) 3*(sigma) ", true },
{ "D3h", "(C3) 3*(C2) (S3) 4*(sigma) ", true },
{ "D4h", "(i) (C4) 5*(C2) (S4) 5*(sigma) ", true },
{ "D5h", "(C5) 5*(C2) (S5) 6*(sigma) ", true },
{ "D6h", "(i) (C6) (C3) 7*(C2) (S6) (S3) 7*(sigma) ", true },
{ "D7h", "(C7) 7*(C2) (S7) 8*(sigma) ", true },
{ "D8h", "(i) (C8) (C4) 9*(C2) (S8) (S4) 9*(sigma) ", true },
{ "D2d", "3*(C2) (S4) 2*(sigma) ", true },
{ "D3d", "(i) (C3) 3*(C2) (S6) 3*(sigma) ", true },
{ "D4d", "(C4) 5*(C2) (S8) 4*(sigma) ", true },
{ "D5d", "(i) (C5) 5*(C2) (S10) 5*(sigma) ", true },
{ "D6d", "(C6) (C3) 7*(C2) (S12) (S4) 6*(sigma) ", true },
{ "D7d", "(i) (C7) 7*(C2) (S14) 7*(sigma) ", true },
{ "D8d", "(C8) (C4) 9*(C2) (S16) 8*(sigma) ", true },
{ "S4", "(C2) (S4) ", true },
{ "S6", "(i) (C3) (S6) ", true },
{ "S8", "(C4) (C2) (S8) ", true },
{ "T", "4*(C3) 3*(C2) ", true },
{ "Th", "(i) 4*(C3) 3*(C2) 4*(S6) 3*(sigma) ", true },
{ "Td", "4*(C3) 3*(C2) 3*(S4) 6*(sigma) ", true },
{ "O", "3*(C4) 4*(C3) 9*(C2) ", true },
{ "Oh", "(i) 3*(C4) 4*(C3) 9*(C2) 4*(S6) 3*(S4) 9*(sigma) ", true },
{ "Cinfv", "(Cinf) (sigma) ", true },
{ "Dinfh", "(i) (Cinf) (C2) 2*(sigma) ", true },
{ "I", "6*(C5) 10*(C3) 15*(C2) ", true },
{ "Ih", "(i) 6*(C5) 10*(C3) 15*(C2) 6*(S10) 10*(S6) 15*(sigma) ", true },
{ "Kh", "(i) (Cinf) (sigma) ", true },
} ;
#define PointGroupsCount (sizeof(PointGroups)/sizeof(POINT_GROUP))
char * PointGroupRejectionReason = NULL ;
/*
* Generic functions
*/
double
pow2( double x )
{
return x * x ;
}
int
establish_pairs( SYMMETRY_ELEMENT *elem )
{
int i, j, k, best_j ;
char * atom_used = calloc( AtomsCount, 1 ) ;
double distance, best_distance ;
ATOM symmetric ;
if( atom_used == NULL ){
fprintf( stderr, "Out of memory for tagging array in establish_pairs()\n" ) ;
exit( EXIT_FAILURE ) ;
}
for( i = 0 ; i < AtomsCount ; i++ ){
if( elem->transform[i] >= AtomsCount ){ /* No symmetric atom yet */
if( verbose > 2 ) printf( " looking for a pair for %d\n", i ) ;
elem->transform_atom( elem, Atoms+i, &symmetric ) ;
if( verbose > 2 ) printf( " new coordinates are: (%g,%g,%g)\n",
symmetric.x[0], symmetric.x[1], symmetric.x[2] ) ;
best_j = i ;
best_distance = 2*TolerancePrimary ;/* Performance value we'll reject */
for( j = 0 ; j < AtomsCount ; j++ ){
if( Atoms[j].type != symmetric.type || atom_used[j] )
continue ;
for( k = 0, distance = 0 ; k < DIMENSION ; k++ ){
distance += pow2( symmetric.x[k] - Atoms[j].x[k] ) ;
}
distance = sqrt( distance ) ;
if( verbose > 2 ) printf( " distance to %d is %g\n", j, distance ) ;
if( distance < best_distance ){
best_j = j ;
best_distance = distance ;
}
}
if( best_distance > TolerancePrimary ){ /* Too bad, there is no symmetric atom */
if( verbose > 0 )
printf( " no pair for atom %d - best was %d with err = %g\n", i, best_j, best_distance ) ;
free( atom_used ) ;
return -1 ;
}
elem->transform[i] = best_j ;
atom_used[best_j] = 1 ;
if( verbose > 1 ) printf( " atom %d transforms to the atom %d, err = %g\n", i, best_j, best_distance ) ;
}
}
free( atom_used ) ;
return 0 ;
}
int
check_transform_order( SYMMETRY_ELEMENT *elem )
{
int i, j, k ;
void rotate_reflect_atom( SYMMETRY_ELEMENT *, ATOM *, ATOM *) ;
for( i = 0 ; i < AtomsCount ; i++ ){
if( elem->transform[i] == i ) /* Identity transform is Ok for any order */
continue ;
if( elem->transform_atom == rotate_reflect_atom ){
j = elem->transform[i] ;
if( elem->transform[j] == i )
continue ; /* Second-order transform is Ok for improper axis */
}
for( j = elem->order - 1, k = elem->transform[i] ; j > 0 ; j--, k = elem->transform[k] ){
if( k == i ){
if( verbose > 0 ) printf( " transform looped %d steps too early from atom %d\n", j, i ) ;
return -1 ;
}
}
if( k != i && elem->transform_atom == rotate_reflect_atom ){
/* For improper axes, the complete loop may also take twice the order */
for( j = elem->order ; j > 0 ; j--, k = elem->transform[k] ){
if( k == i ){
if( verbose > 0 ) printf( " (improper) transform looped %d steps too early from atom %d\n", j, i ) ;
return -1 ;
}
}
}
if( k != i ){
if( verbose > 0 ) printf( " transform failed to loop after %d steps from atom %d\n", elem->order, i ) ;
return -1 ;
}
}
return 0 ;
}
int
same_transform( SYMMETRY_ELEMENT *a, SYMMETRY_ELEMENT *b )
{
int i, j ;
int code ;
if( ( a->order != b->order ) || ( a->nparam != b->nparam ) || ( a->transform_atom != b->transform_atom ) )
return 0 ;
for( i = 0, code = 1 ; i < AtomsCount ; i++ ){
if( a->transform[i] != b->transform[i] ){
code = 0 ;
break ;
}
}
if( code == 0 && a->order > 2 ){ /* b can also be a reverse transformation for a */
for( i = 0 ; i < AtomsCount ; i++ ){
j = a->transform[i] ;
if( b->transform[j] != i )
return 0 ;
}
return 1 ;
}
return code ;
}
SYMMETRY_ELEMENT *
alloc_symmetry_element( void )
{
SYMMETRY_ELEMENT * elem = calloc( 1, sizeof( SYMMETRY_ELEMENT ) ) ;
int i ;
if( elem == NULL ){
fprintf( stderr, "Out of memory allocating symmetry element\n" ) ;
exit( EXIT_FAILURE ) ;
}
elem->transform = calloc( AtomsCount, sizeof( int ) ) ;
if( elem->transform == NULL ){
fprintf( stderr, "Out of memory allocating transform table for symmetry element\n" ) ;
exit( EXIT_FAILURE ) ;
}
for( i = 0 ; i < AtomsCount ; i++ ){
elem->transform[i] = AtomsCount + 1 ; /* An impossible value */
}
return elem ;
}
void
destroy_symmetry_element( SYMMETRY_ELEMENT *elem )
{
if( elem != NULL ){
if( elem->transform != NULL )
free( elem->transform ) ;
free( elem ) ;
}
}
int
check_transform_quality( SYMMETRY_ELEMENT *elem )
{
int i, j, k ;
ATOM symmetric ;
double r, max_r ;
for( i = 0, max_r = 0 ; i < AtomsCount ; i++ ){
j = elem->transform[i] ;
elem->transform_atom( elem, Atoms + i, &symmetric ) ;
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
r += pow2( symmetric.x[k] - Atoms[j].x[k] ) ;
}
r = sqrt( r ) ;
if( r > ToleranceFinal ){
if( verbose > 0 ) printf( " distance to symmetric atom (%g) is too big for %d\n", r, i ) ;
return -1 ;
}
if( r > max_r ) max_r = r ;
}
elem->maxdev = max_r ;
return 0 ;
}
double
eval_optimization_target_function( SYMMETRY_ELEMENT *elem, int *finish )
{
int i, j, k ;
ATOM symmetric ;
double target, r, maxr ;
if( elem->nparam >= 4 ){
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
r += elem->normal[k]*elem->normal[k] ;
}
r = sqrt( r ) ;
if( r < ToleranceSame ){
fprintf( stderr, "Normal collapced!\n" ) ;
exit( EXIT_FAILURE ) ;
}
for( k = 0 ; k < DIMENSION ; k++ ){
elem->normal[k] /= r ;
}
if( elem->distance < 0 ){
elem->distance = -elem->distance ;
for( k = 0 ; k < DIMENSION ; k++ ){
elem->normal[k] = -elem->normal[k] ;
}
}
}
if( elem->nparam >= 7 ){
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
r += elem->direction[k]*elem->direction[k] ;
}
r = sqrt( r ) ;
if( r < ToleranceSame ){
fprintf( stderr, "Direction collapced!\n" ) ;
exit( EXIT_FAILURE ) ;
}
for( k = 0 ; k < DIMENSION ; k++ ){
elem->direction[k] /= r ;
}
}
for( i = 0, target = maxr = 0 ; i < AtomsCount ; i++ ){
elem->transform_atom( elem, Atoms + i, &symmetric ) ;
j = elem->transform[i] ;
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
r += pow2( Atoms[j].x[k] - symmetric.x[k] ) ;
}
if( r > maxr ) maxr = r ;
target += r ;
}
if( finish != NULL ){
*finish = 0 ;
if( sqrt( maxr ) < ToleranceFinal )
*finish = 1 ;
}
return target ;
}
void
get_params( SYMMETRY_ELEMENT *elem, double values[] )
{
memcpy( values, &elem->distance, elem->nparam * sizeof( double ) ) ;
}
void
set_params( SYMMETRY_ELEMENT *elem, double values[] )
{
memcpy( &elem->distance, values, elem->nparam * sizeof( double ) ) ;
}
void
optimize_transformation_params( SYMMETRY_ELEMENT *elem )
{
double values[ MAXPARAM ] ;
double grad [ MAXPARAM ] ;
double force [ MAXPARAM ] ;
double step [ MAXPARAM ] ;
double f, fold, fnew, fnew2, fdn, fup, snorm ;
double a, b, x ;
int vars = elem->nparam ;
int cycle = 0 ;
int i, finish ;
int hits = 0 ;
if( vars > MAXPARAM ){
fprintf( stderr, "Catastrophe in optimize_transformation_params()!\n" ) ;
exit( EXIT_FAILURE ) ;
}
f = 0 ;
do {
fold = f ;
f = eval_optimization_target_function( elem, &finish ) ;
/* Evaluate function, gradient and diagonal force constants */
if( verbose > 1 ) printf( " function value = %g\n", f ) ;
if( finish ){
if( verbose > 1 ) printf( " function value is small enough\n" ) ;
break ;
}
if( cycle > 0 ){
if( fabs( f-fold ) > OptChangeThreshold )
hits = 0 ;
else hits++ ;
if( hits >= OptChangeHits ){
if( verbose > 1 ) printf( " no progress is made, stop optimization\n" ) ;
break ;
}
}
get_params( elem, values ) ;
for( i = 0 ; i < vars ; i++ ){
values[i] -= GradientStep ;
set_params( elem, values ) ;
fdn = eval_optimization_target_function( elem, NULL ) ;
values[i] += 2*GradientStep ;
set_params( elem, values ) ;
fup = eval_optimization_target_function( elem, NULL ) ;
values[i] -= GradientStep ;
grad[i] = ( fup - fdn ) / ( 2 * GradientStep ) ;
force[i] = ( fup + fdn - 2*f ) / ( GradientStep * GradientStep ) ;
if( verbose > 1 ) printf( " i = %d, grad = %12.6e, force = %12.6e\n", i, grad[i], force[i] ) ;
}
/* Do a quasy-Newton step */
for( i = 0, snorm = 0 ; i < vars ; i++ ){
if( force[i] < 0 ) force[i] = -force[i] ;
if( force[i] < 1e-3 ) force[i] = 1e-3 ;
if( force[i] > 1e3 ) force[i] = 1e3 ;
step[i] = - grad[i]/force[i] ;
snorm += step[i] * step[i] ;
}
snorm = sqrt( snorm ) ;
if( snorm > MaxOptStep ){ /* Renormalize step */
for( i = 0 ; i < vars ; i++ )
step[i] *= MaxOptStep/snorm ;
snorm = MaxOptStep ;
}
do {
for( i = 0 ; i < vars ; i++ ){
values[i] += step[i] ;
}
set_params( elem, values ) ;
fnew = eval_optimization_target_function( elem, NULL ) ;
if( fnew < f )
break ;
for( i = 0 ; i < vars ; i++ ){
values[i] -= step[i] ;
step [i] /= 2 ;
}
set_params( elem, values ) ;
snorm /= 2 ;
} while( snorm > MinOptStep ) ;
if( (snorm > MinOptStep) && (snorm < MaxOptStep / 2) ){ /* try to do quadratic interpolation */
for( i = 0 ; i < vars ; i++ )
values[i] += step[i] ;
set_params( elem, values ) ;
fnew2 = eval_optimization_target_function( elem, NULL ) ;
if( verbose > 1 ) printf( " interpolation base points: %g, %g, %g\n", f, fnew, fnew2 ) ;
for( i = 0 ; i < vars ; i++ )
values[i] -= 2*step[i] ;
a = ( 4*f - fnew2 - 3*fnew ) / 2 ;
b = ( f + fnew2 - 2*fnew ) / 2 ;
if( verbose > 1 ) printf( " linear interpolation coefficients %g, %g\n", a, b ) ;
if( b > 0 ){
x = -a/(2*b) ;
if( x > 0.2 && x < 1.8 ){
if( verbose > 1 ) printf( " interpolated: %g\n", x ) ;
for( i = 0 ; i < vars ; i++ )
values[i] += x*step[i] ;
}
else b = 0 ;
}
if( b <= 0 ){
if( fnew2 < fnew ){
for( i = 0 ; i < vars ; i++ )
values[i] += 2*step[i] ;
}
else {
for( i = 0 ; i < vars ; i++ )
values[i] += step[i] ;
}
}
set_params( elem, values ) ;
}
} while( snorm > MinOptStep && ++cycle < MaxOptCycles ) ;
f = eval_optimization_target_function( elem, NULL ) ;
if( cycle >= MaxOptCycles ) BadOptimization = 1 ;
if( verbose > 0 ) {
if( cycle >= MaxOptCycles )
printf( " maximum number of optimization cycles made\n" ) ;
printf( " optimization completed after %d cycles with f = %g\n", cycle, f ) ;
}
}
int
refine_symmetry_element( SYMMETRY_ELEMENT *elem, int build_table )
{
int i ;
if( build_table && (establish_pairs( elem ) < 0) ){
StatPairs++ ;
if( verbose > 0 ) printf( " no transformation correspondence table can be constructed\n" ) ;
return -1 ;
}
for( i = 0 ; i < PlanesCount ; i++ ){
if( same_transform( Planes[i], elem ) ){
StatDups++ ;
if( verbose > 0 ) printf( " transformation is identical to plane %d\n", i ) ;
return -1 ;
}
}
for( i = 0 ; i < InversionCentersCount ; i++ ){
if( same_transform( InversionCenters[i], elem ) ){
StatDups++ ;
if( verbose > 0 ) printf( " transformation is identical to inversion center %d\n", i ) ;
return -1 ;
}
}
for( i = 0 ; i < NormalAxesCount ; i++ ){
if( same_transform( NormalAxes[i], elem ) ){
StatDups++ ;
if( verbose > 0 ) printf( " transformation is identical to normal axis %d\n", i ) ;
return -1 ;
}
}
for( i = 0 ; i < ImproperAxesCount ; i++ ){
if( same_transform( ImproperAxes[i], elem ) ){
StatDups++ ;
if( verbose > 0 ) printf( " transformation is identical to improper axis %d\n", i ) ;
return -1 ;
}
}
if( check_transform_order( elem ) < 0 ){
StatOrder++ ;
if( verbose > 0 ) printf( " incorrect transformation order\n" ) ;
return -1 ;
}
optimize_transformation_params( elem ) ;
if( check_transform_quality( elem ) < 0 ){
StatOpt++ ;
if( verbose > 0 ) printf( " refined transformation does not pass the numeric threshold\n" ) ;
return -1 ;
}
StatAccept++ ;
return 0 ;
}
/*
* Plane-specific functions
*/
void
mirror_atom( SYMMETRY_ELEMENT *plane, ATOM *from, ATOM *to )
{
int i ;
double r ;
for( i = 0, r = plane->distance ; i < DIMENSION ; i++ ){
r -= from->x[i] * plane->normal[i] ;
}
to->type = from->type ;
for( i = 0 ; i < DIMENSION ; i++ ){
to->x[i] = from->x[i] + 2*r*plane->normal[i] ;
}
}
SYMMETRY_ELEMENT *
init_mirror_plane( int i, int j )
{
SYMMETRY_ELEMENT * plane = alloc_symmetry_element() ;
double dx[ DIMENSION ], midpoint[ DIMENSION ], rab, r ;
int k ;
if( verbose > 0 ) printf( "Trying mirror plane for atoms %d,%d\n", i, j ) ;
StatTotal++ ;
plane->transform_atom = mirror_atom ;
plane->order = 2 ;
plane->nparam = 4 ;
for( k = 0, rab = 0 ; k < DIMENSION ; k++ ){
dx[k] = Atoms[i].x[k] - Atoms[j].x[k] ;
midpoint[k] = ( Atoms[i].x[k] + Atoms[j].x[k] ) / 2.0 ;
rab += dx[k]*dx[k] ;
}
rab = sqrt(rab) ;
if( rab < ToleranceSame ){
fprintf( stderr, "Atoms %d and %d coincide (r = %g)\n", i, j, rab ) ;
exit( EXIT_FAILURE ) ;
}
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
plane->normal[k] = dx[k]/rab ;
r += midpoint[k]*plane->normal[k] ;
}
if( r < 0 ){ /* Reverce normal direction, distance is always positive! */
r = -r ;
for( k = 0 ; k < DIMENSION ; k++ ){
plane->normal[k] = -plane->normal[k] ;
}
}
plane->distance = r ;
if( verbose > 0 ) printf( " initial plane is at %g from the origin\n", r ) ;
if( refine_symmetry_element( plane, 1 ) < 0 ){
if( verbose > 0 ) printf( " refinement failed for the plane\n" ) ;
destroy_symmetry_element( plane ) ;
return NULL ;
}
return plane ;
}
SYMMETRY_ELEMENT *
init_ultimate_plane( void )
{
SYMMETRY_ELEMENT * plane = alloc_symmetry_element() ;
double d0[ DIMENSION ], d1[ DIMENSION ], d2[ DIMENSION ] ;
double p[ DIMENSION ] ;
double r, s0, s1, s2 ;
double * d ;
int i, j, k ;
if( verbose > 0 ) printf( "Trying whole-molecule mirror plane\n" ) ;
StatTotal++ ;
plane->transform_atom = mirror_atom ;
plane->order = 1 ;
plane->nparam = 4 ;
for( k = 0 ; k < DIMENSION ; k++ )
d0[k] = d1[k] = d2[k] = 0 ;
d0[0] = 1 ; d1[1] = 1 ; d2[2] = 1 ;
for( i = 1 ; i < AtomsCount ; i++ ){
for( j = 0 ; j < i ; j++ ){
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
p[k] = Atoms[i].x[k] - Atoms[j].x[k] ;
r += p[k]*p[k] ;
}
r = sqrt(r) ;
for( k = 0, s0=s1=s2=0 ; k < DIMENSION ; k++ ){
p[k] /= r ;
s0 += p[k]*d0[k] ;
s1 += p[k]*d1[k] ;
s2 += p[k]*d2[k] ;
}
for( k = 0 ; k < DIMENSION ; k++ ){
d0[k] -= s0*p[k] ;
d1[k] -= s1*p[k] ;
d2[k] -= s2*p[k] ;
}
}
}
for( k = 0, s0=s1=s2=0 ; k < DIMENSION ; k++ ){
s0 += d0[k] ;
s1 += d1[k] ;
s2 += d2[k] ;
}
d = NULL ;
if( s0 >= s1 && s0 >= s2 ) d = d0 ;
if( s1 >= s0 && s1 >= s2 ) d = d1 ;
if( s2 >= s0 && s2 >= s1 ) d = d2 ;
if( d == NULL ){
fprintf( stderr, "Catastrophe in init_ultimate_plane(): %g, %g and %g have no ordering!\n", s0, s1, s2 ) ;
exit( EXIT_FAILURE ) ;
}
for( k = 0, r = 0 ; k < DIMENSION ; k++ )
r += d[k]*d[k] ;
r = sqrt(r) ;
if( r > 0 ){
for( k = 0 ; k < DIMENSION ; k++ )
plane->normal[k] = d[k]/r ;
}
else {
for( k = 1 ; k < DIMENSION ; k++ )
plane->normal[k] = 0 ;
plane->normal[0] = 1 ;
}
for( k = 0, r = 0 ; k < DIMENSION ; k++ )
r += CenterOfSomething[k]*plane->normal[k] ;
plane->distance = r ;
for( k = 0 ; k < AtomsCount ; k++ )
plane->transform[k] = k ;
if( refine_symmetry_element( plane, 0 ) < 0 ){
if( verbose > 0 ) printf( " refinement failed for the plane\n" ) ;
destroy_symmetry_element( plane ) ;
return NULL ;
}
return plane ;
}
/*
* Inversion-center specific functions
*/
void
invert_atom( SYMMETRY_ELEMENT *center, ATOM *from, ATOM *to )
{
int i ;
to->type = from->type ;
for( i = 0 ; i < DIMENSION ; i++ ){
to->x[i] = 2*center->distance*center->normal[i] - from->x[i] ;
}
}
SYMMETRY_ELEMENT *
init_inversion_center( void )
{
SYMMETRY_ELEMENT * center = alloc_symmetry_element() ;
int k ;
double r ;
if( verbose > 0 ) printf( "Trying inversion center at the center of something\n" ) ;
StatTotal++ ;
center->transform_atom = invert_atom ;
center->order = 2 ;
center->nparam = 4 ;
for( k = 0, r = 0 ; k < DIMENSION ; k++ )
r += CenterOfSomething[k]*CenterOfSomething[k] ;
r = sqrt(r) ;
if( r > 0 ){
for( k = 0 ; k < DIMENSION ; k++ )
center->normal[k] = CenterOfSomething[k]/r ;
}
else {
center->normal[0] = 1 ;
for( k = 1 ; k < DIMENSION ; k++ )
center->normal[k] = 0 ;
}
center->distance = r ;
if( verbose > 0 ) printf( " initial inversion center is at %g from the origin\n", r ) ;
if( refine_symmetry_element( center, 1 ) < 0 ){
if( verbose > 0 ) printf( " refinement failed for the inversion center\n" ) ;
destroy_symmetry_element( center ) ;
return NULL ;
}
return center ;
}
/*
* Normal rotation axis-specific routines.
*/
void
rotate_atom( SYMMETRY_ELEMENT *axis, ATOM *from, ATOM *to )
{
double x[3], y[3], a[3], b[3], c[3] ;
double angle = axis->order ? 2*M_PI/axis->order : 1.0 ;
double a_sin = sin( angle ) ;
double a_cos = cos( angle ) ;
double dot ;
int i ;
if( DIMENSION != 3 ){
fprintf( stderr, "Catastrophe in rotate_atom!\n" ) ;
exit( EXIT_FAILURE ) ;
}
for( i = 0 ; i < 3 ; i++ )
x[i] = from->x[i] - axis->distance * axis->normal[i] ;
for( i = 0, dot = 0 ; i < 3 ; i++ )
dot += x[i] * axis->direction[i] ;
for( i = 0 ; i < 3 ; i++ )
a[i] = axis->direction[i] * dot ;
for( i = 0 ; i < 3 ; i++ )
b[i] = x[i] - a[i] ;
c[0] = b[1]*axis->direction[2] - b[2]*axis->direction[1] ;
c[1] = b[2]*axis->direction[0] - b[0]*axis->direction[2] ;
c[2] = b[0]*axis->direction[1] - b[1]*axis->direction[0] ;
for( i = 0 ; i < 3 ; i++ )
y[i] = a[i] + b[i]*a_cos + c[i]*a_sin ;
for( i = 0 ; i < 3 ; i++ )
to->x[i] = y[i] + axis->distance * axis->normal[i] ;
to->type = from->type ;
}
SYMMETRY_ELEMENT *
init_ultimate_axis(void)
{
SYMMETRY_ELEMENT * axis = alloc_symmetry_element() ;
double dir[ DIMENSION ], rel[ DIMENSION ] ;
double s ;
int i, k ;
if( verbose > 0 ) printf( "Trying infinity axis\n" ) ;
StatTotal++ ;
axis->transform_atom = rotate_atom ;
axis->order = 0 ;
axis->nparam = 7 ;
for( k = 0 ; k < DIMENSION ; k++ )
dir[k] = 0 ;
for( i = 0 ; i < AtomsCount ; i++ ){
for( k = 0, s = 0 ; k < DIMENSION ; k++ ){
rel[k] = Atoms[i].x[k] - CenterOfSomething[k] ;
s += rel[k]*dir[k] ;
}
if( s >= 0 )
for( k = 0 ; k < DIMENSION ; k++ )
dir[k] += rel[k] ;
else for( k = 0 ; k < DIMENSION ; k++ )
dir[k] -= rel[k] ;
}
for( k = 0, s = 0 ; k < DIMENSION ; k++ )
s += pow2( dir[k] ) ;
s = sqrt(s) ;
if( s > 0 )
for( k = 0 ; k < DIMENSION ; k++ )
dir[k] /= s ;
else dir[0] = 1 ;
for( k = 0 ; k < DIMENSION ; k++ )
axis->direction[k] = dir[k] ;
for( k = 0, s = 0 ; k < DIMENSION ; k++ )
s += pow2( CenterOfSomething[k] ) ;
s = sqrt(s) ;
if( s > 0 )
for( k = 0 ; k < DIMENSION ; k++ )
axis->normal[k] = CenterOfSomething[k]/s ;
else {
for( k = 1 ; k < DIMENSION ; k++ )
axis->normal[k] = 0 ;
axis->normal[0] = 1 ;
}
axis->distance = s ;
for( k = 0 ; k < AtomsCount ; k++ )
axis->transform[k] = k ;
if( refine_symmetry_element( axis, 0 ) < 0 ){
if( verbose > 0 ) printf( " refinement failed for the infinity axis\n" ) ;
destroy_symmetry_element( axis ) ;
return NULL ;
}
return axis ;
}
SYMMETRY_ELEMENT *
init_c2_axis( int i, int j, double support[ DIMENSION ] )
{
SYMMETRY_ELEMENT * axis ;
int k ;
double ris, rjs ;
double r, center[ DIMENSION ] ;
if( verbose > 0 )
printf( "Trying c2 axis for the pair (%d,%d) with the support (%g,%g,%g)\n",
i, j, support[0], support[1], support[2] ) ;
StatTotal++ ;
/* First, do a quick sanity check */
for( k = 0, ris = rjs = 0 ; k < DIMENSION ; k++ ){
ris += pow2( Atoms[i].x[k] - support[k] ) ;
rjs += pow2( Atoms[j].x[k] - support[k] ) ;
}
ris = sqrt( ris ) ;
rjs = sqrt( rjs ) ;
if( fabs( ris - rjs ) > TolerancePrimary ){
StatEarly++ ;
if( verbose > 0 ) printf( " Support can't actually define a rotation axis\n" ) ;
return NULL ;
}
axis = alloc_symmetry_element() ;
axis->transform_atom = rotate_atom ;
axis->order = 2 ;
axis->nparam = 7 ;
for( k = 0, r = 0 ; k < DIMENSION ; k++ )
r += CenterOfSomething[k]*CenterOfSomething[k] ;
r = sqrt(r) ;
if( r > 0 ){
for( k = 0 ; k < DIMENSION ; k++ )
axis->normal[k] = CenterOfSomething[k]/r ;
}
else {
axis->normal[0] = 1 ;
for( k = 1 ; k < DIMENSION ; k++ )
axis->normal[k] = 0 ;
}
axis->distance = r ;
for( k = 0, r = 0 ; k < DIMENSION ; k++ ){
center[k] = ( Atoms[i].x[k] + Atoms[j].x[k] ) / 2 - support[k] ;
r += center[k]*center[k] ;
}
r = sqrt(r) ;
if( r <= TolerancePrimary ){ /* c2 is underdefined, let's do something special */
if( MolecularPlane != NULL ){
if( verbose > 0 ) printf( " c2 is underdefined, but there is a molecular plane\n" ) ;
for( k = 0 ; k < DIMENSION ; k++ )
axis->direction[k] = MolecularPlane->normal[k] ;
}
else {
if( verbose > 0 ) printf( " c2 is underdefined, trying random direction\n" ) ;
for( k = 0 ; k < DIMENSION ; k++ )
center[k] = Atoms[i].x[k] - Atoms[j].x[k] ;
if( fabs( center[2] ) + fabs( center[1] ) > ToleranceSame ){
axis->direction[0] = 0 ;
axis->direction[1] = center[2] ;
axis->direction[2] = -center[1] ;
}
else {
axis->direction[0] = -center[2] ;
axis->direction[1] = 0 ;
axis->direction[2] = center[0] ;
}
for( k = 0, r = 0 ; k < DIMENSION ; k++ )
r += axis->direction[k] * axis->direction[k] ;
r = sqrt(r) ;
for( k = 0 ; k < DIMENSION ; k++ )
axis->direction[k] /= r ;
}
}
else { /* direction is Ok, renormalize it */
for( k = 0 ; k < DIMENSION ; k++ )
axis->direction[k] = center[k]/r ;
}
if( refine_symmetry_element( axis, 1 ) < 0 ){
if( verbose > 0 ) printf( " refinement failed for the c2 axis\n" ) ;
destroy_symmetry_element( axis ) ;
return NULL ;
}
return axis ;
}
SYMMETRY_ELEMENT *
init_axis_parameters( double a[3], double b[3], double c[3] )
{
SYMMETRY_ELEMENT * axis ;
int i, order, sign ;
double ra, rb, rc, rab, rbc, rac, r ;
double angle ;
ra = rb = rc = rab = rbc = rac = 0 ;
for( i = 0 ; i < DIMENSION ; i++ ){
ra += a[i]*a[i] ;
rb += b[i]*b[i] ;
rc += c[i]*c[i] ;
}
ra = sqrt(ra) ; rb = sqrt(rb) ; rc = sqrt(rc) ;
if( fabs( ra - rb ) > TolerancePrimary || fabs( ra - rc ) > TolerancePrimary || fabs( rb - rc ) > TolerancePrimary ){
StatEarly++ ;
if( verbose > 0 ) printf( " points are not on a sphere\n" ) ;
return NULL ;
}
for( i = 0 ; i < DIMENSION ; i++ ){
rab += (a[i]-b[i])*(a[i]-b[i]) ;
rac += (a[i]-c[i])*(a[i]-c[i]) ;
rbc += (c[i]-b[i])*(c[i]-b[i]) ;
}
rab = sqrt(rab) ;
rac = sqrt(rac) ;