/******************************************************************************
 * Copyright 1998-2019 Lawrence Livermore National Security, LLC and other
 * HYPRE Project Developers. See the top-level COPYRIGHT file for details.
 *
 * SPDX-License-Identifier: (Apache-2.0 OR MIT)
 ******************************************************************************/

#include "_hypre_parcsr_ls.h"
 
#ifndef M_PI
#define M_PI 3.14159265358979
#endif

/* examples in Ruge & Stuben paper */
static HYPRE_Int rs_example = 1;
static HYPRE_Real rs_l = 3.0;

/*--------------------------------------------------------------------------
 * hypre_GenerateVarDifConv: with the FD discretization and examples 
 *                           in Ruge-Stuben's paper ``Algebraic Multigrid''
 *--------------------------------------------------------------------------*/

HYPRE_ParCSRMatrix 
GenerateRSVarDifConv( MPI_Comm comm,
                 HYPRE_BigInt   nx,
                 HYPRE_BigInt   ny,
                 HYPRE_BigInt   nz, 
                 HYPRE_Int      P,
                 HYPRE_Int      Q,
                 HYPRE_Int      R,
                 HYPRE_Int      p,
                 HYPRE_Int      q,
                 HYPRE_Int      r,
                 HYPRE_Real eps,
		 HYPRE_ParVector *rhs_ptr,
                 HYPRE_Int type)
{
   hypre_ParCSRMatrix *A;
   hypre_CSRMatrix *diag;
   hypre_CSRMatrix *offd;
   hypre_ParVector *par_rhs;
   hypre_Vector *rhs;
   HYPRE_Real *rhs_data;

   HYPRE_Int    *diag_i;
   HYPRE_Int    *diag_j;
   HYPRE_Real *diag_data;

   HYPRE_Int    *offd_i;
   HYPRE_Int    *offd_j;
   HYPRE_BigInt *big_offd_j;
   HYPRE_Real *offd_data;

   HYPRE_BigInt *global_part;
   HYPRE_BigInt ix, iy, iz;
   HYPRE_Int cnt, o_cnt;
   HYPRE_Int local_num_rows; 
   HYPRE_BigInt *col_map_offd;
   HYPRE_Int row_index;
   HYPRE_Int i,j;

   HYPRE_Int nx_local, ny_local, nz_local;
   HYPRE_Int num_cols_offd;
   HYPRE_BigInt grid_size;


   HYPRE_BigInt *nx_part;
   HYPRE_BigInt *ny_part;
   HYPRE_BigInt *nz_part;

   HYPRE_Int num_procs, my_id;
   HYPRE_Int P_busy, Q_busy, R_busy;

   HYPRE_Real hhx, hhy, hhz;
   HYPRE_Real xx, yy, zz;
   HYPRE_Real afp, afm, bfp, bfm, cfp, cfm, di, ai, mux, ei, bi,
              muy, fi, ci, muz, dfm, dfp, efm, efp, ffm, ffp, gi;

   hypre_MPI_Comm_size(comm,&num_procs);
   hypre_MPI_Comm_rank(comm,&my_id);

   if (type >= 1 && type <= 3)
   {
     rs_example = type;
   }

   grid_size = nx*ny*nz;

   hypre_GeneratePartitioning(nx,P,&nx_part);
   hypre_GeneratePartitioning(ny,Q,&ny_part);
   hypre_GeneratePartitioning(nz,R,&nz_part);

   nx_local = (HYPRE_Int)(nx_part[p+1] - nx_part[p]);
   ny_local = (HYPRE_Int)(ny_part[q+1] - ny_part[q]);
   nz_local = (HYPRE_Int)(nz_part[r+1] - nz_part[r]);

   local_num_rows = nx_local*ny_local*nz_local;


#ifdef HYPRE_NO_GLOBAL_PARTITION

   global_part = hypre_CTAlloc(HYPRE_BigInt,2,HYPRE_MEMORY_HOST);
   global_part[0] = nz_part[r]*nx*ny+(ny_part[q]*nx+nx_part[p]*ny_local)*nz_local;
   global_part[1] = global_part[0] + (HYPRE_BigInt)local_num_rows;

#else
   HYPRE_Int nx_size, ny_size, nz_size;
   HYPRE_Int jx, jy, jz;

   global_part = hypre_CTAlloc(HYPRE_BigInt, P*Q*R+1, HYPRE_MEMORY_HOST);

   global_part[0] = 0;
   cnt = 1;
   for (jz = 0; jz < R; jz++)
   {
      nz_size = (HYPRE_Int)(nz_part[jz+1]-nz_part[jz]);
      for (jy = 0; jy < Q; jy++)
      {
         ny_size = (HYPRE_Int)(ny_part[jy+1]-ny_part[jy]);
         for (jx = 0; jx < P; jx++)
         {
            nx_size = (HYPRE_Int)(nx_part[jx+1] - nx_part[jx]);
            global_part[cnt] = global_part[cnt-1];
            global_part[cnt++] += (HYPRE_BigInt)(nx_size*ny_size*nz_size);
         }
      }
   }

#endif

   diag_i = hypre_CTAlloc(HYPRE_Int,  local_num_rows+1, HYPRE_MEMORY_HOST);
   offd_i = hypre_CTAlloc(HYPRE_Int,  local_num_rows+1, HYPRE_MEMORY_HOST);
   rhs_data = hypre_CTAlloc(HYPRE_Real,  local_num_rows, HYPRE_MEMORY_HOST);

   P_busy = hypre_min(nx,P);
   Q_busy = hypre_min(ny,Q);
   R_busy = hypre_min(nz,R);

   num_cols_offd = 0;
   if (p) num_cols_offd += ny_local*nz_local;
   if (p < P_busy-1) num_cols_offd += ny_local*nz_local;
   if (q) num_cols_offd += nx_local*nz_local;
   if (q < Q_busy-1) num_cols_offd += nx_local*nz_local;
   if (r) num_cols_offd += nx_local*ny_local;
   if (r < R_busy-1) num_cols_offd += nx_local*ny_local;

   if (!local_num_rows) num_cols_offd = 0;

   col_map_offd = hypre_CTAlloc(HYPRE_BigInt,  num_cols_offd, HYPRE_MEMORY_HOST);

   hhx = 1.0/(HYPRE_Real)(nx+1);
   hhy = 1.0/(HYPRE_Real)(ny+1);
   hhz = 1.0/(HYPRE_Real)(nz+1);

   cnt = 1;
   o_cnt = 1;
   diag_i[0] = 0;
   offd_i[0] = 0;
   for (iz = nz_part[r]; iz < nz_part[r+1]; iz++)
   {
      for (iy = ny_part[q];  iy < ny_part[q+1]; iy++)
      {
         for (ix = nx_part[p]; ix < nx_part[p+1]; ix++)
         {
            diag_i[cnt] = diag_i[cnt-1];
            offd_i[o_cnt] = offd_i[o_cnt-1];
            diag_i[cnt]++;
            if (iz > nz_part[r]) 
               diag_i[cnt]++;
            else
            {
               if (iz) 
               {
                  offd_i[o_cnt]++;
               }
            }
            if (iy > ny_part[q]) 
               diag_i[cnt]++;
            else
            {
               if (iy) 
               {
                  offd_i[o_cnt]++;
               }
            }
            if (ix > nx_part[p]) 
               diag_i[cnt]++;
            else
            {
               if (ix) 
               {
                  offd_i[o_cnt]++; 
               }
            }
            if (ix+1 < nx_part[p+1]) 
               diag_i[cnt]++;
            else
            {
               if (ix+1 < nx) 
               {
                  offd_i[o_cnt]++; 
               }
            }
            if (iy+1 < ny_part[q+1]) 
               diag_i[cnt]++;
            else
            {
               if (iy+1 < ny) 
               {
                  offd_i[o_cnt]++;
               }
            }
            if (iz+1 < nz_part[r+1]) 
               diag_i[cnt]++;
            else
            {
               if (iz+1 < nz) 
               {
                  offd_i[o_cnt]++;
               }
            }
            cnt++;
            o_cnt++;
         }
      }
   }

   diag_j = hypre_CTAlloc(HYPRE_Int,  diag_i[local_num_rows], HYPRE_MEMORY_HOST);
   diag_data = hypre_CTAlloc(HYPRE_Real,  diag_i[local_num_rows], HYPRE_MEMORY_HOST);

   if (num_procs > 1)
   {
      big_offd_j = hypre_CTAlloc(HYPRE_BigInt,  offd_i[local_num_rows], HYPRE_MEMORY_HOST);
      offd_j = hypre_CTAlloc(HYPRE_Int,  offd_i[local_num_rows], HYPRE_MEMORY_HOST);
      offd_data = hypre_CTAlloc(HYPRE_Real,  offd_i[local_num_rows], HYPRE_MEMORY_HOST);
   }

   row_index = 0;
   cnt = 0;
   o_cnt = 0;
   for (iz = nz_part[r]; iz < nz_part[r+1]; iz++)
   {
      zz = (HYPRE_Real)(iz+1)*hhz;
      for (iy = ny_part[q]; iy < ny_part[q+1]; iy++)
      {
         yy = (HYPRE_Real)(iy+1)*hhy;
         for (ix = nx_part[p]; ix < nx_part[p+1]; ix++)
         {
            xx = (HYPRE_Real)(ix+1)*hhx;
	    afp = -eps*afun_rs(xx+0.5*hhx,yy,zz)/hhx/hhx;
	    afm = -eps*afun_rs(xx-0.5*hhx,yy,zz)/hhx/hhx;
	    bfp = -eps*bfun_rs(xx,yy+0.5*hhy,zz)/hhy/hhy;
	    bfm = -eps*bfun_rs(xx,yy-0.5*hhy,zz)/hhy/hhy;
	    cfp = -eps*cfun_rs(xx,yy,zz+0.5*hhz)/hhz/hhz;
	    cfm = -eps*cfun_rs(xx,yy,zz-0.5*hhz)/hhz/hhz;
            /* first order terms */
            /* x-direction */
            di = dfun_rs(xx, yy, zz);
            ai = afun_rs(xx, yy, zz);
            if (di * hhx > eps * ai)
            {
              mux = eps * ai / (2.0 * di * hhx);
            }
            else if (di * hhx < -eps * ai)
            {
              mux = 1.0 + eps * ai / (2.0 * di * hhx);
            }
            else
            {
              mux = 0.5;
            }
            /* y-direction */
            ei = efun_rs(xx, yy, zz);
            bi = bfun_rs(xx, yy, zz);
            if (ei * hhy > eps * bi)
            {
              muy = eps * bi / (2.0 * ei * hhy);
            }
            else if (ei * hhy < -eps * bi)
            {
              muy = 1.0 + eps * bi / (2.0 * ei * hhy);
            }
            else
            {
              muy = 0.5;
            }
            /* z-direction */
            fi = ffun_rs(xx, yy, zz);
            ci = cfun_rs(xx, yy, zz);
            if (fi * hhz > eps * ci)
            {
              muz = eps * ci / (2.0 * fi * hhz);
            }
            else if (fi * hhz < -eps * ci)
            {
              muz = 1.0 + eps * ci / (2.0 * fi * hhz);
            }
            else
            {
              muz = 0.5;
            }

	    dfm = di * (mux - 1.0) / hhx;
            dfp = di * mux / hhx;
	    efm = ei * (muy - 1.0) / hhy;
            efp = ei * muy / hhy;
            ffm = fi * (muz - 1.0) / hhz;
	    ffp = fi * muz / hhz;
	    gi = gfun_rs(xx, yy, zz);
            /* stencil: center */
            diag_j[cnt] = row_index;
            diag_data[cnt++] = -(afp + afm + bfp + bfm + cfp + cfm  +
                                 dfp + dfm + efp + efm + ffp + ffm) + gi;
            /* rhs vector */
	    rhs_data[row_index] = rfun_rs(xx,yy,zz);
	    /* apply boundary conditions */
            if (ix == 0)    rhs_data[row_index] -= (afm+dfm) * bndfun_rs(0,yy,zz);
	    if (iy == 0)    rhs_data[row_index] -= (bfm+efm) * bndfun_rs(xx,0,zz);
	    if (iz == 0)    rhs_data[row_index] -= (cfm+ffm) * bndfun_rs(xx,yy,0);
	    if (ix+1 == nx) rhs_data[row_index] -= (afp+dfp) * bndfun_rs(1.0,yy,zz);
	    if (iy+1 == ny) rhs_data[row_index] -= (bfp+efp) * bndfun_rs(xx,1.0,zz);
	    if (iz+1 == nz) rhs_data[row_index] -= (cfp+ffp) * bndfun_rs(xx,yy,1.0);
            /* stencil: z- */
            if (iz > nz_part[r]) 
            {
               diag_j[cnt] = row_index - nx_local*ny_local;
               diag_data[cnt++] = cfm + ffm;
            }
            else
            {
               if (iz) 
               {
                  big_offd_j[o_cnt] = hypre_map(ix,iy,iz-1,p,q,r-1,nx,ny,
                                            nx_part,ny_part,nz_part);
                  offd_data[o_cnt++] = cfm + ffm;
               }
            }
            /* stencil: y- */
            if (iy > ny_part[q]) 
            {
               diag_j[cnt] = row_index - nx_local;
               diag_data[cnt++] = bfm + efm;
            }
            else
            {
               if (iy) 
               {
                  big_offd_j[o_cnt] = hypre_map(ix,iy-1,iz,p,q-1,r,nx,ny,
                                            nx_part,ny_part,nz_part);
                  offd_data[o_cnt++] = bfm + efm;
               }
            }
            /* stencil: x- */
            if (ix > nx_part[p]) 
            {
               diag_j[cnt] = row_index - 1;
               diag_data[cnt++] = afm + dfm;
            }
            else
            {
               if (ix) 
               {
                  big_offd_j[o_cnt] = hypre_map(ix-1,iy,iz,p-1,q,r,nx,ny,
                                            nx_part,ny_part,nz_part);
                  offd_data[o_cnt++] = afm + dfm;
               }
            }
            /* stencil: x+ */
            if (ix+1 < nx_part[p+1]) 
            {
               diag_j[cnt] = row_index + 1;
               diag_data[cnt++] = afp + dfp;
            }
            else
            {
               if (ix+1 < nx) 
               {
                  big_offd_j[o_cnt] = hypre_map(ix+1,iy,iz,p+1,q,r,nx,ny,
                                            nx_part,ny_part,nz_part);
                  offd_data[o_cnt++] = afp + dfp;
               }
            }
            /* stencil: y+ */
            if (iy+1 < ny_part[q+1]) 
            {
               diag_j[cnt] = row_index + nx_local;
               diag_data[cnt++] = bfp + efp;
            }
            else
            {
               if (iy+1 < ny) 
               {
                  big_offd_j[o_cnt] = hypre_map(ix,iy+1,iz,p,q+1,r,nx,ny,
                                            nx_part,ny_part,nz_part);
                  offd_data[o_cnt++] = bfp + efp;
               }
            }
            /* stencil: z+ */
            if (iz+1 < nz_part[r+1]) 
            {
               diag_j[cnt] = row_index + nx_local*ny_local;
               diag_data[cnt++] = cfp + ffp;
            }
            else
            {
               if (iz+1 < nz) 
               {
                  big_offd_j[o_cnt] = hypre_map(ix,iy,iz+1,p,q,r+1,nx,ny,
                                            nx_part,ny_part,nz_part);
                  offd_data[o_cnt++] = cfp + ffp;
               }
            }
            /* done with this row */
            row_index++;
         }
      }
   }

   if (num_procs > 1)
   {
      for (i=0; i < num_cols_offd; i++)
         col_map_offd[i] = big_offd_j[i];
   	
      hypre_BigQsort0(col_map_offd, 0, num_cols_offd-1);

      for (i=0; i < num_cols_offd; i++)
         for (j=0; j < num_cols_offd; j++)
            if (big_offd_j[i] == col_map_offd[j])
            {
               offd_j[i] = j;
               break;
            }
      hypre_TFree(big_offd_j, HYPRE_MEMORY_HOST);
   }

   par_rhs = hypre_ParVectorCreate(comm, grid_size, global_part);
   hypre_ParVectorOwnsPartitioning(par_rhs) = 0;
   rhs = hypre_ParVectorLocalVector(par_rhs);
   hypre_VectorData(rhs) = rhs_data;

   A = hypre_ParCSRMatrixCreate(comm, grid_size, grid_size,
                                global_part, global_part, num_cols_offd,
                                diag_i[local_num_rows],
                                offd_i[local_num_rows]);

   hypre_ParCSRMatrixColMapOffd(A) = col_map_offd;

   diag = hypre_ParCSRMatrixDiag(A);
   hypre_CSRMatrixI(diag) = diag_i;
   hypre_CSRMatrixJ(diag) = diag_j;
   hypre_CSRMatrixData(diag) = diag_data;

   offd = hypre_ParCSRMatrixOffd(A);
   hypre_CSRMatrixI(offd) = offd_i;
   if (num_cols_offd)
   {
      hypre_CSRMatrixJ(offd) = offd_j;
      hypre_CSRMatrixData(offd) = offd_data;
   }

   hypre_TFree(nx_part, HYPRE_MEMORY_HOST);
   hypre_TFree(ny_part, HYPRE_MEMORY_HOST);
   hypre_TFree(nz_part, HYPRE_MEMORY_HOST);

   *rhs_ptr = (HYPRE_ParVector) par_rhs;

   return (HYPRE_ParCSRMatrix) A;
}

HYPRE_Real afun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = 1.0;
   return value;
}

HYPRE_Real bfun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = 1.0;
   return value;
}

HYPRE_Real cfun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = 1.0;
   return value;
}

HYPRE_Real dfun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   if (rs_example == 1)
   {
     value = sin(rs_l*M_PI/8.0);
   }
   else if (rs_example == 2)
   {
     value = (2.0*yy-1.0)*(1.0-xx*xx);
   }
   else
   {
     value = 4.0*xx*(xx-1.0)*(1.0-2.0*yy);
   }
   return value;
}

HYPRE_Real efun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   if (rs_example == 1)
   {
     value = cos(rs_l*M_PI/8.0);
   }
   else if (rs_example == 2)
   {
     value = 2.0*xx*yy*(yy-1.0);
   }
   else
   {
     value = -4.0*yy*(yy-1.0)*(1.0-2.0*xx);
   }
   return value;
}

HYPRE_Real ffun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = efun_rs(xx, yy, zz);
   return value;
}

HYPRE_Real gfun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = 0.0;
   return value;
}

HYPRE_Real rfun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = 1.0;
   return value;
}

HYPRE_Real bndfun_rs(HYPRE_Real xx, HYPRE_Real yy, HYPRE_Real zz)
{
   HYPRE_Real value;
   value = 0.0;
   return value;
}

