/*
    DFT++ is a density functional package developed by the research group
    of Professor Tomas Arias

    Copyright 1996-2003 Sohrab Ismail-Beigi

    This file is part of DFT++.

    DFT++ 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.

    DFT++ 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 DFT++; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    Please see the file CREDITS for a list of authors.

    For academic users, we request that publications using results obtained with
    this software reference

    "New algebraic formulation of density functional calculation," by Sohrab Ismail-Beigi
    and T.A. Arias, Computer Physics Communications 128:1-2, 1-45 (June 2000).

    and, if using the wavelet basis, further reference

    "Multiresolution analysis of electronic structure: semicardinal and wavelet bases,"
    T.A. Arias, Reviews of Modern Physics 71:1, 267-311 (January 1999).

    and 

    "Robust ab initio calculation of condensed matter: transparent convergence through
    semicardinal multiresolution analysis,'' I.P. Daykov, T.A. Arias, and
    Torkel D. Engeness, Physical Review Letters, 90:21, 216402 (May 2003).

    For your convenience, preprints of the above articles may be obtained from
    http://arXiv.org/abs/cond-mat/9909130, 9805262, and 0204411, respectively.
*/

#include "header.h"

// Symmetrizes the grid 'in' w..r.t. the symmetries of the system
// As a beginning map the old wavelet symemtrizer as closely as
// possible: transform the symmetry matrices from 'Symmetries'
// to integer matrices that the wavelet code uses
//
// TODO: clean-up - change the wavelet code so that it uses
// the class 'Symmetries' directly
// THINK if it's necessary to call symmetrize_accum()
// in real space - probably any space will be alright
void symmetrize_n(WL_ComplexColumn &in, Symmetries *symm)
{

//  return;

  // Symmetrization always happens in COEFFSPACE
  // go there if in REALSPACE
  int inputspace = in.representation; // initial space (REAL/COEFFSPACE)
  if(inputspace == REALSPACE)
    apply_J(in, in);

  Gridspec *gridspec;
  
  switch(in.embedding){
    case SPARSE:
      gridspec = in.basis_spec->gridspec;
      break;
    case DENSE:
      gridspec = in.basis_spec->gridspec_dense;
      break;
    default:
      die("symmetrize_n: Unknown  input embedding %d\n",in.embedding);
  }


  int i,j;
  struct Ivec R; // symmetry center that the old wl code understands
  // compute it from the Symemtry object
  R.x=(int)(symm->Rsym.v[0]*gridspec[0].dim.x);
  R.y=(int)(symm->Rsym.v[1]*gridspec[0].dim.y);
  R.z=(int)(symm->Rsym.v[2]*gridspec[0].dim.z);

  // these should be all integers
  if( fmod(symm->Rsym.v[0]*gridspec[0].dim.x, 1) > MIN_SYMM_TOL ||
      fmod(symm->Rsym.v[1]*gridspec[0].dim.y, 1) > MIN_SYMM_TOL ||
      fmod(symm->Rsym.v[2]*gridspec[0].dim.x, 1) > MIN_SYMM_TOL )
    die("WL_symm:  wrong center of symemtry\n");


  // symemtry matrices in the form that the old wl code likes
  int *symgroup[48]; // pointers to the matrices (to loop over)
  int symmetryop[48][9]; // the actual matrices

  // translate the dft++ symmetries to old-wl language
  for(i=0; i<48;i++)
    for(j=0; j<9; j++)
      symmetryop[i][j] = (int)*(&symm->sym[i].m[0][0] +j);

  // set the pointers to the correct positions
  for(i=0; i<symm->nrot;i++)
      symgroup[i]=&symmetryop[i][0];

  // Now create the grids that we'll symmetrize
  Grid *n = mkgridnew(gridspec,NULL); //input
  Grid *ns = mkgridnew(gridspec,NULL); //output
  evalgrid(ns,NULLDVEC, zero);// initialize the output


  // zero-out the coefficients, that do not have partners
  // (perform the transforms inplace on the wl_column objects)
  {
    GetRe(n, in); // initialize the input grid
    setsymzero(n);
    PutRe(n,in);
    // now we return back in real space
    apply_I(in, in);
    GetRe(n, in);
  }

  // ACCUMULATE S[i](n) on ns
  for (int i=0; i<symm->nrot; i++)
    symmetrize_accum(ns, n, symgroup[i], R);
  
  // make sure the boundaries on the lower levels are consistent
  adjustdown(ns);

  // Rescale by the nymber of symemtry operators
  // use the c style to save on memory
  scalarmultnew(ns, 1./((double) symm->nrot), ns);
  
  
  // zero-out the coefficients, that do not have partners
  // (perform the transforms inplace on the wl_column objects)
  {
    // first go to COEFFSPACE
    PutRe(ns,in);
    apply_J(in,in);
    //again zero-out the ones w/o a partner
    GetRe(ns,in);
    setsymzero(ns);
    PutRe(ns,in);
  }

  // Return to REALSPACE if started there
  if(inputspace == REALSPACE)
    apply_I(in,in);

  // Kill the grids we created!
  killgridnew(n); killgridnew(ns);
}


int check_basis_symm_compatibility(Symmetries &symm, const WL_Basis &basis)
{
  return 0;
}



//the dag of symmetrize_n()
// since the symmetrizewr is nonhermetian in the DFT gradient one must use
// the daggered version
void symmetrize_n_dag(WL_ComplexColumn &in, Symmetries *symm)
{

//  return;

  // Symmetrization always happens in COEFFSPACE
  // go there if in REALSPACE
  int inputspace = in.representation; // initial space (REAL/COEFFSPACE)
  if(inputspace == REALSPACE)
    apply_Idag(in, in);

  Gridspec *gridspec;
  
  switch(in.embedding){
    case SPARSE:
      gridspec = in.basis_spec->gridspec;
      break;
    case DENSE:
      gridspec = in.basis_spec->gridspec_dense;
      break;
    default:
      die("symmetrize_n: Unknown  input embedding %d\n",in.embedding);
  }


  int i,j;
  struct Ivec R; // symmetry center that the old wl code understands
  // compute it from the Symemtry object
  R.x=(int)(symm->Rsym.v[0]*gridspec[0].dim.x);
  R.y=(int)(symm->Rsym.v[1]*gridspec[0].dim.y);
  R.z=(int)(symm->Rsym.v[2]*gridspec[0].dim.z);

  // these should be all integers
  if( fmod(symm->Rsym.v[0]*gridspec[0].dim.x, 1) > MIN_SYMM_TOL ||
      fmod(symm->Rsym.v[1]*gridspec[0].dim.y, 1) > MIN_SYMM_TOL ||
      fmod(symm->Rsym.v[2]*gridspec[0].dim.x, 1) > MIN_SYMM_TOL )
    die("WL_symm:  wrong center of symemtry\n");


  // symemtry matrices in the form that the old wl code likes
  int *symgroup[48]; // pointers to the matrices (to loop over)
  int symmetryop[48][9]; // the actual matrices

  // translate the dft++ symmetries to old-wl language
  for(i=0; i<48;i++)
    for(j=0; j<9; j++)
      symmetryop[i][j] = (int)*(&symm->sym[i].m[0][0] +j);

  // set the pointers to the correct positions
  for(i=0; i<symm->nrot;i++)
      symgroup[i]=&symmetryop[i][0];

  // Now create the grids that we'll symmetrize
  Grid *n = mkgridnew(gridspec,NULL); //input
  Grid *ns = mkgridnew(gridspec,NULL); //output
  evalgrid(ns,NULLDVEC, zero);// initialize the output


  // zero-out the coefficients, that do not have partners
  // (perform the transforms inplace on the wl_column objects)
  {
    GetRe(n, in); // initialize the input grid
    setsymzero(n);
    PutRe(n,in);
    // now we return back in real space
    apply_Jdag(in, in);
    GetRe(n, in);
  }

  // ACCUMULATE S[i](n) on ns
  for (int i=0; i<symm->nrot; i++)
    symmetrize_accum(ns, n, symgroup[i], R);
  
  // make sure the boundaries on the lower levels are consistent
  adjustdown(ns);

  // Rescale by the nymber of symemtry operators
  // use the c style to save on memory
  scalarmultnew(ns, 1./((double) symm->nrot), ns);
  
  
  // zero-out the coefficients, that do not have partners
  // (perform the transforms inplace on the wl_column objects)
  {
    // first go to COEFFSPACE
    PutRe(ns,in);
    apply_Idag(in,in);
    //again zero-out the ones w/o a partner
    GetRe(ns,in);
    setsymzero(ns);
    PutRe(ns,in);
  }

  // Return to REALSPACE if started there
  if(inputspace == REALSPACE)
    apply_Jdag(in,in);

  // Kill the grids we created!
  killgridnew(n); killgridnew(ns);
}