CoCalc -- p_formspace.c

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap4r8 / pkg / carat / carat-2.1b1 / functions / Bravais / p_formspace.c
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#include"typedef.h"
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#include"matrix.h"
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#include"longtools.h"
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/**************************************************************************\
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@---------------------------------------------------------------------------
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@---------------------------------------------------------------------------
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@ FILE: p_formspace.c
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@---------------------------------------------------------------------------
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@---------------------------------------------------------------------------
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@
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\**************************************************************************/
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/**************************************************************************\
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@---------------------------------------------------------------------------
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@ matrix_TYP **p_formspace(B, Banz, prime, sym_opt, fdim)
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@ matrix_TYP **B;
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@ int Banz, prime, sym_opt, *fdim;
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@
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@ The same as formspace, just module the prime.
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@---------------------------------------------------------------------------
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@
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\**************************************************************************/
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matrix_TYP **p_formspace(B, Banz, prime, sym_opt, fdim)
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matrix_TYP **B;
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int Banz, prime, sym_opt, *fdim;
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{
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  int i,j,k,l,m, no, p;
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  int dim, dd, anz;
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  matrix_TYP *X, **Xk, **E;
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  int **XX, **Bi;
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  int **pos, **sign;
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  p = prime;
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  dim = B[0]->cols;
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  if(B[0]->rows != dim)
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  {
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    printf("error in formspace: non-square matrix in group 'B'\n");
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    exit(3);
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  }
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  for(i=1;i<Banz;i++)
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  {
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     if(B[i]->rows != dim || B[i]->cols != dim)
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     {
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       printf("error in formspace: different dimesion of group elements\n");
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       exit(3);
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     }
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  }
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  if(sym_opt == 1)
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    dd = (dim *(dim+1))/2;
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  if(sym_opt == -1)
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    dd = (dim *(dim-1))/2;
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  if(sym_opt == 0)
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    dd = dim * dim;
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  if( (pos = (int **)malloc(dim *sizeof(int *))) == NULL)
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  {
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     printf("malloc of 'pos' in 'formspace' failed\n");
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     exit(2);
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  }
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  for(i=0;i<dim;i++)
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  {
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    if( (pos[i] = (int *)malloc(dim *sizeof(int))) == NULL)
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    {
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       printf("malloc of 'pos[%d]' in 'formspace' failed\n", i);
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       exit(2);
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    }
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  }
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  if( (sign = (int **)malloc(dim *sizeof(int *))) == NULL)
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  {
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     printf("malloc of 'sign' in 'formspace' failed\n");
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     exit(2);
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  }
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  for(i=0;i<dim;i++)
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  {
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    if( (sign[i] = (int *)malloc(dim *sizeof(int))) == NULL)
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    {
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       printf("malloc of 'sign[%d]' in 'formspace' failed\n", i);
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       exit(2);
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    }
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  }
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  if(sym_opt == 0)
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  {
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     no = 0;
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     for(i=0;i<dim;i++)
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       for(j=0;j<dim;j++)
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       { pos[i][j] = no; sign[i][j] = 1; no++;}
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  }
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  if(sym_opt == 1)
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  {
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     no = 0;
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     for(i=0;i<dim;i++)
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       for(j=0;j<=i;j++)
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       { pos[i][j] = no; sign[i][j] = 1; no++;}
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     no = 0;
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     for(i=0;i<dim;i++)
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       for(j=0;j<=i;j++)
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       { pos[j][i] = no; sign[j][i] = 1; no++;}
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  }
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  if(sym_opt == -1)
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  {
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     no = 0;
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     for(i=0;i<dim;i++)
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       for(j=0;j<i;j++)
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       { pos[i][j] = no; sign[i][j] = 1; no++;}
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     no = 0;
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     for(i=0;i<dim;i++)
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       for(j=0;j<i;j++)
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       { pos[j][i] = no; sign[j][i] = -1; no++;}
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     for(i=0;i<dim;i++)
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     { pos[i][i] = 0; sign[i][i] = 0;}
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  }
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  X = init_mat(dd * Banz, dd, "");
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  XX = X->array.SZ;
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  no = 0;
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  if(sym_opt == 0)
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  {
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    no = 0;
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    for(i=0;i<Banz;i++)
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    {
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       Bi = B[i]->array.SZ;
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       for(j=0;j<dim;j++)
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         for(k=0;k<dim;k++)
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         {
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           for(l=0;l<dim;l++)
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             for(m=0;m<dim;m++)
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             {
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               XX[no][pos[l][m]] += sign[l][m] * (Bi[l][j]%p) * (Bi[m][k]%p);
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               XX[no][pos[l][m]] %= p;
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             }
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           XX[no][pos[j][k]]--;
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           no++;
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         }
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    }
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  }
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  if(sym_opt == 1)
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  {
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     no = 0;
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     for(i=0;i<Banz;i++)
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     {
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       Bi = B[i]->array.SZ;
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       for(j=0;j<dim;j++)
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         for(k=0;k<=j;k++)
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         {
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           for(l=0;l<dim;l++)
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             for(m=0;m<dim;m++)
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             {
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               XX[no][pos[l][m]] += sign[l][m] * (Bi[l][j]%p) * (Bi[m][k]%p);
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               XX[no][pos[l][m]] %= p;
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             }
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           XX[no][pos[j][k]]--;
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           no++;
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         }
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     }
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  }
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  if(sym_opt == -1)
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  {
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     no = 0;
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     for(i=0;i<Banz;i++)
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     {
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       Bi = B[i]->array.SZ;
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       for(j=0;j<dim;j++)
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         for(k=0;k<j;k++)
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         {
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           for(l=0;l<dim;l++)
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             for(m=0;m<dim;m++)
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             {
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               XX[no][pos[l][m]] += sign[l][m] * (Bi[l][j]%p) * (Bi[m][k]%p);
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               XX[no][pos[l][m]] %= p;
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             }
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           XX[no][pos[j][k]]--;
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           no++;
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         }
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     }
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  }
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  for(i=0;i<X->rows;i++)
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    for(j=0;j<X->cols;j++)
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      X->array.SZ[i][j] %=p;
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  Xk = p_lse_solve(X, NULL, &anz, p);
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  free_mat(X);
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    anz--;
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  if(Xk[0] != NULL)
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    free_mat(Xk[0]);
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  if(anz != 0)
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  {
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    if( (E = (matrix_TYP **)malloc(anz *sizeof(matrix_TYP *))) == NULL)
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    {
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      printf("malloc of 'E' in 'formspace' failed\n");
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      exit(2);
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    }
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  }
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  else
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     E = NULL;
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  for(i=0;i<anz;i++)
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  {
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    E[i] = init_mat(dim, dim, "");
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    if(sym_opt == 0)
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    {
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       for(j=0;j<dim;j++)
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         for(k=0;k<dim;k++)
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            E[i]->array.SZ[j][k] = Xk[i+1]->array.SZ[0][pos[j][k]];
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    }
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    if(sym_opt == 1)
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    {
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       for(j=0;j<dim;j++)
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         for(k=0;k<=j;k++)
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         {
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            E[i]->array.SZ[j][k] = Xk[i+1]->array.SZ[0][pos[j][k]];
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            if(j != k)
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              E[i]->array.SZ[k][j] = E[i]->array.SZ[j][k];
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         }
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    }
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    if(sym_opt == -1)
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    {
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       for(j=0;j<dim;j++)
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         for(k=0;k<j;k++)
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         {
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            E[i]->array.SZ[j][k] = Xk[i+1]->array.SZ[0][pos[j][k]];
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              E[i]->array.SZ[k][j] = -E[i]->array.SZ[j][k];
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         }
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       for(j=0;j<dim;j++)
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        E[i]->array.SZ[j][j] = 0;
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    }
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  }
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  for(i=0;i<anz;i++)
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    Check_mat(E[i]);
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  for(i=0;i<anz;i++)
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    free_mat(Xk[i+1]);
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  for(i=0;i<dim;i++)
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  { free(pos[i]); free(sign[i]);}
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  free(pos); free(sign);
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  *fdim = anz;
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  return(E);
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}
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