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extract.c
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extract.c
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#include <typedef.h>
#include <getput.h>
#include <matrix.h>
#include <orbit.h>
#include <bravais.h>
#include <base.h>
#include <tools.h>
#include <zass.h>
#include <datei.h>
#include <presentation.h>
int main(int argc,char **argv){
bravais_TYP *G,
*H;
matrix_TYP *X,
**XX,
**base,
*T,
**COZ;
bahn **strong;
int i,
j,
k,
type, /* TRUE iff the function has been called via
...Standart_affine_form */
kgv,
cozanz;
char comment[1000],
file[1000];
G = NULL;
H = NULL;
X = NULL;
T = NULL;
read_header(argc,argv);
#define OTHER_NAME "Standard_affine_form"
if (strlen(argv[0]) < strlen(OTHER_NAME)){
/* it can't have been called via .....OTHER_NAME */
type = FALSE;
}
else{
type = (strcmp(argv[0]+(strlen(argv[0])-strlen(OTHER_NAME)),
OTHER_NAME) == 0);
}
if ((type && FILEANZ < 1) ||
(!type && ((is_option('h') && optionnumber('h')==0)||
(FILEANZ < 1) ||
((FILEANZ < 2) && (is_option('r')))))){
if (type){
printf("Usage: %s 'file1' 'file2' [-t]\n",argv[0]);
printf("\n");
printf("file1: bravais_TYP containing a space group G.\n");
printf("file2: matrix_TYP contatining a presentation of the point\n");
printf(" group of G.\n");
printf("\n");
printf("Transforms the space group with generators in file1 into standard\n");
printf("form, ie. the translation lattice is transformed to Z^n.\n");
printf("In case the translation subgroup has dimension smaller than n, i.\n");
printf("e. the group is not an n-dimensional space group, the program\n");
printf("will indicate an error, gives the rank, and exit.\n");
printf("\n");
printf("Options:\n");
printf("-t : The transforming matrix will be given as well.\n");
printf("\n");
printf("Cf. Extensions, Vector_systems\n");
printf("Note: This program is a synonym for Extract -t.\n");
}
else{
printf("Usage: %s 'file1' ['file2'] [-c] [-p] [-f] [-r [-D]] [-t=n]\n",argv[0]);
printf("\n");
printf("file1: bravais_TYP containing a space or (in case of option -r) a point group.\n");
printf("file2: matrix_TYP only used with options -r and -t, cf. below. \n");
printf("\n");
printf("Extracts the linear part of the affine (space) group in file1.\n");
printf("Note this is the point group of the space group in case the space \n");
printf("group is given in standard form.\n");
printf("\n");
printf("Options:\n");
printf("-p : extracts the linear part (default).\n");
printf("-c : extracts the translational part as a vector system (1-cocycle).\n");
printf("-f : do not calculate the formspace of the point group.\n");
printf("-r : reverses the process: Reads in the generators of the point group \n");
printf(" of file1 and multiple vector systems for these generators from file2 \n");
printf(" and outputs the resulting space groups. Overwrites any other option.\n");
printf("-D : this option only works together with '-r'. The spacegroups are written\n");
printf(" to 'file.i' with i = 1, ...\n");
printf("-t=n : transform the space group with generators in file1 into standard\n");
printf(" form, ie. the translation lattice is transformed to Z^n. If a \n");
printf(" parameter n>0 is specified, the transforming matrix will be\n");
printf(" given as well. NOTE: For the -t-option file2 must contain a \n");
printf(" presentation for the point group. If the translation lattice \n");
printf(" is of smaller rank, it will give the rank. Synonymous command:\n");
printf(" Standard_affine_form\n");
printf("-T : RESERVED\n");
printf("\n");
printf("Cf. Extensions, Vector_systems\n");
}
if (is_option('h')){
exit(0);
}
else{
exit(31);
}
}
INFO_LEVEL = optionnumber('h');
G = get_bravais(FILENAMES[0]);
if (is_option('t') || type){
if (FILEANZ == 2){
XX = mget_mat(FILENAMES[1],&i);
if (i>1){
fprintf(stderr,"you should only give a single matrix as presention\n");
exit(3);
}
X = XX[0];
free(XX);
}
else{
/* get the point group */
H = init_bravais(G->dim-1);
H->gen_no = G->gen_no;
H->gen = (matrix_TYP **) malloc(H->gen_no * sizeof(matrix_TYP *));
for (i=0;i<H->gen_no;i++){
H->gen[i] = copy_mat(G->gen[i]);
real_mat(H->gen[i],G->dim,G->dim-1);
real_mat(H->gen[i],G->dim-1,G->dim-1);
}
/* calculate a presentation */
base = get_base(H);
strong = strong_generators(base,H,TRUE);
X = pres(strong,H,NULL);
for (i=0;i<H->dim;i++){
free_mat(base[i]);
free_bahn(strong[i]);
free(strong[i]);
}
free(strong);
free(base);
free_bravais(H); H = NULL;
}
if (is_option('T')){
real_mat(X,X->rows+G->dim-1,X->cols);
for (i=0;i<G->dim-1;i++){
X->array.SZ[X->rows-G->dim+1+i][0] = G->gen_no - i ;
}
}
/* set the transformation matrix */
T = translation_lattice(G->gen,G->gen_no,X);
free_mat(X);
X = NULL;
/* echo the rank if needed */
if (T->rows != T->cols){
fprintf(stderr,"The rank of the translation lattice is %d\n",T->cols);
exit(0);
}
real_mat(T,T->rows+1,T->cols+1);
/* paranoia */
rat2kgv(T);
T->array.SZ[T->rows-1][T->cols-1] = T->kgv;
Check_mat(T);
if ((optionnumber('t')>0 && !type) ||
(is_option('t') && type)){
sprintf(comment,"transformation matrix for space group in %s",
FILENAMES[0]);
put_mat(T,NULL,comment,2);
}
/* we should also calculate a positive definite, point group
invariant form, and transform the group according to a mink_red
of this form. left for further development */
/* now transform the group */
H = init_bravais(G->dim);
H->gen = (matrix_TYP **) malloc(G->gen_no * sizeof(matrix_TYP *));
H->gen_no = G->gen_no;
X = mat_inv(T);
for (i=0;i<H->gen_no;i++){
H->gen[i] = mat_kon(X,G->gen[i],T);
}
sprintf(comment,"space group of %s on Z^n",
FILENAMES[0]);
put_bravais(H,NULL,NULL);
}
else{
if (is_option('r')){
COZ = mget_mat(FILENAMES[1], &cozanz);
for (k = 0; k < cozanz; k++){
rat2kgv(COZ[k]);
Check_mat(COZ[k]);
convert_cocycle_to_column(&COZ[k],1,G->dim,G->gen_no);
/* is it a valid cocycle? */
if ((G->dim * G->gen_no != COZ[k]->rows) || (COZ[k]->cols != 1)){
fprintf(stderr,"The cocycle is not compatible to this point group\n");
fprintf(stderr,"It should have %d * %d = %d rows\n",G->dim,G->gen_no,
G->dim*G->gen_no);
exit(3);
}
H = init_bravais(G->dim+1);
H->gen_no = G->gen_no;
H->gen = (matrix_TYP **) malloc(G->gen_no * sizeof(matrix_TYP *));
for (i=0;i<H->gen_no;i++){
H->gen[i] = copy_mat(G->gen[i]);
rat2kgv(H->gen[i]);
Check_mat(H->gen[i]);
real_mat(H->gen[i],H->dim,H->dim);
iscal_mul(H->gen[i],COZ[k]->kgv);
H->gen[i]->kgv = H->gen[i]->kgv * COZ[k]->kgv;
for (j=0;j<H->dim-1;j++)
H->gen[i]->array.SZ[j][H->dim-1] = COZ[k]->array.SZ[i*(H->dim-1)+j][0];
H->gen[i]->array.SZ[H->dim-1][H->dim-1] = COZ[k]->kgv;
Check_mat(H->gen[i]);
}
if (is_option('D')){
sprintf(file, "%s.%d", FILENAMES[0], k + 1);
sprintf(comment, "space group to the point group of %s and the %d-th cocycle of %s",
FILENAMES[0], k+1, FILENAMES[1]);
put_bravais(H, file, comment);
}
else{
sprintf(comment, "space group to the point group of %s and the %d-th cocycle of %s",
FILENAMES[0], k+1, FILENAMES[1]);
put_bravais(H, NULL, comment);
}
free_bravais(H);
free_mat(COZ[k]);
}
H = NULL;
free(COZ);
}
else if (is_option('p') || (!is_option('p') && ! is_option('c'))){
/* extract the point group */
H = init_bravais(G->dim-1);
H->gen_no = G->gen_no;
H->gen = (matrix_TYP **) malloc(G->gen_no * sizeof(matrix_TYP *));
for (i=0;i<H->gen_no;i++){
H->gen[i] = copy_mat(G->gen[i]);
real_mat(H->gen[i],H->dim,G->dim);
real_mat(H->gen[i],H->dim,H->dim);
rat2kgv(H->gen[i]);
Check_mat(H->gen[i]);
}
if (!is_option('f'))
H->form = formspace(H->gen,H->gen_no,1,&H->form_no);
/* output */
sprintf(comment,"point group to the space group of %s",FILENAMES[0]);
put_bravais(H,NULL,comment);
free_bravais(H);
H = NULL;
}
if (is_option('c')){
X = init_mat(G->gen_no * (G->dim-1),1,"");
kgv = 1;
for (i=0;i<G->gen_no;i++){
rat2kgv(G->gen[i]);
kgv = kgv*G->gen[i]->kgv/GGT(kgv,G->gen[i]->kgv);
}
/* set the cocycle */
X->kgv = kgv;
for(i=0;i<G->gen_no;i++)
for (j=0;j<G->dim-1;j++)
X->array.SZ[i*(G->dim-1)+j][0] = X->kgv/G->gen[i]->kgv *
G->gen[i]->array.SZ[j][G->dim-1];
Check_mat(X);
sprintf(comment,"cocycle to the group of %s",FILENAMES[0]);
put_cocycle(X,G->dim-1,G->gen_no,NULL,comment);
}
}
/* cleaning up */
if (G!=NULL) free_bravais(G);
if (H!=NULL) free_bravais(H);
if (X!=NULL) free_mat(X);
if (T!=NULL) free_mat(T);
exit(0);
} /* main */