cannon_forw_template.c 47.5 KB
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// it seems, that we need those two levels of indirection to correctly expand macros
#define cannons_reduction_impl_expand2(SUFFIX) cannons_reduction_##SUFFIX
#define cannons_reduction_impl_expand1(SUFFIX) cannons_reduction_impl_expand2(SUFFIX)
#define cannons_reduction_impl cannons_reduction_impl_expand1(ELPA_IMPL_SUFFIX)
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#define cannons_reduction_c_impl_expand2(SUFFIX) cannons_reduction_c_##SUFFIX
#define cannons_reduction_c_impl_expand1(SUFFIX) cannons_reduction_c_impl_expand2(SUFFIX)
#define cannons_reduction_c_impl cannons_reduction_c_impl_expand1(ELPA_IMPL_SUFFIX)
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void cannons_reduction_impl(double* A, double* U, int np_rows, int np_cols, int my_prow, int my_pcol,
                         int* a_desc, double *Res, int ToStore, MPI_Comm row_comm, MPI_Comm col_comm)
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{
   // Input matrices: 
      // - A: full matrix
      // - U: upper triangular matrix U(-1)
   // Output matrix: 
      // - Res = U(-H)*A*U(-1)
   // row_comm: communicator along rows
   // col_comm: communicator along columns
  
   int na, nblk, i, j, Size_send_A, Size_receive_A, Size_send_U, Size_receive_U, Buf_rows, Buf_cols, where_to_send_A, from_where_to_receive_A, where_to_send_U, from_where_to_receive_U, last_proc_row, last_proc_col, cols_in_buffer_A, rows_in_buffer_A, intNumber;
   double *Buf_to_send_A, *Buf_to_receive_A, *Buf_to_send_U, *Buf_to_receive_U, *double_ptr, *Buf_A, *Buf_pos, *U_local_start, *Res_ptr, *M, *M_T, *A_local_start, *U_local_start_curr, *U_stored, *CopyTo, *CopyFrom, *U_to_calc;
   int ratio, num_of_iters, cols_in_buffer, rows_in_block, rows_in_buffer, curr_col_loc, cols_in_block, curr_col_glob, curr_row_loc, Size_receive_A_now, Nb, owner, cols_in_buffer_A_now;
   int  row_of_origin_U, rows_in_block_U, num_of_blocks_in_U_buffer, k, startPos, cols_in_buffer_U, rows_in_buffer_U, col_of_origin_A, curr_row_loc_res, curr_row_loc_A, curr_col_glob_res; 
   int curr_col_loc_res, curr_col_loc_buf, proc_row_curr, curr_col_loc_U, A_local_index, LDA_A, LDA_A_new, index_row_A_for_LDA, ii, rows_in_block_U_curr, width, row_origin_U, rows_in_block_A, cols_in_buffer_A_my_initial, rows_in_buffer_A_my_initial, proc_col_min;
   int *SizesU;
   int Size_U_skewed, Size_U_stored, Curr_pos_in_U_stored, rows_in_buffer_A_now;
   double done = 1.0;
   double dzero = 0.0;
   int one = 1; 
   int zero = 0; 
   int na_rows, na_cols;
        
   MPI_Status status;
   MPI_Request request_A_Recv; 
   MPI_Request request_A_Send;
   MPI_Request request_U_Recv; 
   MPI_Request request_U_Send;
      
   na = a_desc[2];
   nblk = a_desc[4];
   na_rows = numroc_(&na, &nblk, &my_prow, &zero, &np_rows);
   na_cols = numroc_(&na, &nblk, &my_pcol, &zero, &np_cols); 
   
   if(ToStore > (np_rows -1))
      if((my_prow == 0)&&(my_pcol == 0))
         printf("Buffering level is larger than (np_rows-1) !!!\n");
   if((my_prow == 0)&&(my_pcol == 0))
         printf("Buffering level = %d\n", ToStore); 
   
//////////////////////////////////////////// Start of algorithm //////////////////////////////////////////////////////////////////////////////
   if (np_cols%np_rows != 0)
   {
      if((my_prow == 0)&& (my_pcol ==0))
         printf("!!!!! np_cols must be a multiple of np_rows!!!!! I do nothing! \n");
      return;
   }
   if (np_cols < np_rows != 0)
   {
      if((my_prow == 0)&& (my_pcol ==0))
         printf("np_cols < np_rows \n");
      return;
   }
   
   ratio = np_cols/np_rows; 
   last_proc_row = ((na-1)/nblk) % np_rows;          // processor row having the last block-row of matrix
   last_proc_col = ((na-1)/nblk) % np_cols;          // processor column having the last block-column of matrix
   
   /////////////////////////memory allocation area//////////////////////////////////////////////////////////////
   if(na%nblk == 0)
      if(my_pcol <= last_proc_col)
         Buf_cols = na_cols;
      else
         Buf_cols = na_cols + nblk;      
   else
      if(my_pcol < last_proc_col)
         Buf_cols = na_cols;
      else if(my_pcol > last_proc_col)
         Buf_cols = na_cols + nblk; 
      else  // if my_pcol == last_proc_col
         Buf_cols = na_cols + nblk - na_cols%nblk;     
   
  if(na%nblk == 0)
      if(my_prow <= last_proc_row)
         Buf_rows = na_rows;
      else
         Buf_rows = na_rows + nblk;      
   else
      if(my_prow < last_proc_row)
         Buf_rows = na_rows;
      else if(my_prow > last_proc_row)
         Buf_rows = na_rows + nblk; 
      else  // if my_prow == last_proc_row
         Buf_rows = na_rows + nblk - na_rows%nblk;  
      
   intNumber = ceil((double)na/(double)(np_cols*nblk));   // max. possible number of the local block columns of U
   Size_U_stored = ratio*nblk*nblk*intNumber*(intNumber+1)/2 + 2;   // number of local elements from the upper triangular part that every proc. has (max. possible value among all the procs.)
   
   U_stored = malloc((Size_U_stored*(ToStore+1))*sizeof(double));
   SizesU = malloc(ToStore*sizeof(int));  // here will be stored the sizes of the buffers of U that I have stored     
   Buf_to_send_A = malloc(ratio*Buf_cols*Buf_rows*sizeof(double));
   Buf_to_receive_A = malloc(ratio*Buf_cols*Buf_rows*sizeof(double));
   Buf_to_send_U = malloc(Size_U_stored*sizeof(double));
   Buf_to_receive_U = malloc(Size_U_stored*sizeof(double));
   if(ratio != 1)
      Buf_A = malloc(Buf_cols*Buf_rows*sizeof(double));   // in this case we will receive data into initial buffer and after place block-columns to the needed positions of buffer for calculation
   M = malloc(na_rows*na_cols*sizeof(double));
   M_T = malloc(na_rows*na_cols*sizeof(double));
   for(i = 0; i < na_rows*na_cols; i++)
      M[i] = 0; 
        
   ////////////////////////////////////////////////////////////// initial reordering of A ///////////////////////////////////////////////////////////////////////////////////////// 
   
   // here we assume, that np_rows < np_cols; then I will send to the number of processors equal to <ratio> with the "leap" equal to np_rows; the same holds for receive  
   if(ratio != 1)
      dlacpy_("A", &na_rows, &na_cols, A, &na_rows, Buf_to_send_A, &na_rows);   // copy my buffer to send
   Size_receive_A = 0; 
   
   // receive from different processors and place in my buffer for calculation;
   for(i = 0; i < ratio; i++)
   {
      where_to_send_A = (my_pcol - my_prow - i*np_rows + np_cols)%np_cols;                
      from_where_to_receive_A = (my_pcol + my_prow + i*np_rows)%np_cols;
      
      // send and receive in the row_comm
      if(ratio != 1)   // if grid is not square
      {
         if(where_to_send_A != my_pcol)
         {
            MPI_Sendrecv(Buf_to_send_A, na_cols*na_rows, MPI_DOUBLE, where_to_send_A, 0, Buf_A, na_rows*Buf_cols, MPI_DOUBLE, from_where_to_receive_A, 0, row_comm, &status);
            MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_A_now);
            Size_receive_A_now = Size_receive_A_now/na_rows;       // how many columns of A I have received
         }
         else
            Size_receive_A_now = na_cols;
         Size_receive_A = Size_receive_A + Size_receive_A_now;  // here accumulate number of columns of A that I will receive

         // now I need to copy the received block to my buffer for A
         intNumber = from_where_to_receive_A/np_rows; // how many blocks I will receive, such that I will need to put them before the just received block         
         
         CopyTo = &Buf_to_receive_A[intNumber*na_rows*nblk];  // here I will start copying the received buffer
         if(where_to_send_A != my_pcol)
            CopyFrom = Buf_A; 
         else
            CopyFrom = A;
         
         intNumber = ceil((double)Size_receive_A_now/(double)nblk);   // how many block-columns I have received
         for(j = 0; j < intNumber; j++)
         {
            width = nblk; // width of the current block column
            if(nblk*(j+1) > Size_receive_A_now)
               width = Size_receive_A_now - nblk*j; 
            dlacpy_("A", &na_rows, &width, CopyFrom, &na_rows, CopyTo, &na_rows);
            CopyTo = CopyTo + na_rows*nblk*ratio; 
            CopyFrom = CopyFrom + na_rows*nblk; 
         }
      }
      else  // if grid is square then simply receive from one processor to a calculation buffer
         if(my_prow > 0)
         {
            dlacpy_("A", &na_rows, &na_cols, A, &na_rows, Buf_to_send_A, &na_rows);   // copy my buffer to send
            MPI_Sendrecv(Buf_to_send_A, na_cols*na_rows, MPI_DOUBLE, where_to_send_A, 0, Buf_to_receive_A, na_rows*Buf_cols, MPI_DOUBLE, from_where_to_receive_A, 0, row_comm, &status);
            MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_A);
            Size_receive_A = Size_receive_A/na_rows;       // how many columns of A I have received
         }
         else
         {
            dlacpy_("A", &na_rows, &na_cols, A, &na_rows, Buf_to_receive_A, &na_rows);   // copy A to the received buffer if I do not need to send
            Size_receive_A = na_cols; 
         }
   }
   
   ////////////////////////////////////////////////////////////// initial reordering of U //////////////////////////////////////////////////////
     
   // form array to send by block-columns
   num_of_iters = ceil((double)na_cols/(double)nblk);             // number my of block-columns
   
   where_to_send_U = (my_prow - my_pcol + np_cols)%np_rows;                 // shift = my_pcol; we assume that np_cols%np_rows = 0
   from_where_to_receive_U = (my_pcol + my_prow)%np_rows;
   
   if(where_to_send_U == my_prow)    // if I will not need to send my local part of U, then copy my local data to the "received" buffer
      Buf_pos = Buf_to_receive_U;
   else
      Buf_pos = Buf_to_send_U;         // else form the array to send
   
   // find the first local block belonging to the upper part of matrix U
   if(my_pcol >= my_prow)  // if I am in the upper part of proc. grid
      curr_col_loc = 0;    // my first local block-column has block from the upper part of matrix
   else
      curr_col_loc = 1;   //ceil((double)(((double)my_prow - (double)my_pcol)/(double)np_cols)) always will give 1 since np_cols > np_rows 
      
   num_of_iters = num_of_iters - curr_col_loc;   // I will exclude the first <curr_col_loc> block-columns since they do not have blocks from the upper part of matrix U
   curr_col_loc = curr_col_loc*nblk;             // local index of the found block-column

   if(my_pcol >= my_prow )
      rows_in_block = ceil(((double)(my_pcol + 1) - (double)my_prow)/(double)np_rows)*nblk;
   else
      rows_in_block = ratio*nblk;
   
   Size_send_U = 0; 
   for(i = 0; i < num_of_iters; i++)       // loop over my block-columns, which have blocks in the upepr part of U
   {      
      if(rows_in_block > na_rows)
         rows_in_block = na_rows; 

      if ((na_cols - curr_col_loc) < nblk)
         cols_in_block = na_cols - curr_col_loc;     // how many columns do I have in the current block-column
      else
         cols_in_block = nblk; 
      
      if((rows_in_block > 0)&&(cols_in_block > 0))
      {
         double_ptr = &U[curr_col_loc*na_rows];   // pointer to start of the current block-column to be copied to buffer
         dlacpy_("A", &rows_in_block, &cols_in_block, double_ptr, &na_rows, Buf_pos, &rows_in_block);     // copy upper part of block-column in the buffer with LDA = length of the upper part of block-column 
         Buf_pos = Buf_pos + rows_in_block*cols_in_block;                         // go to the position where the next block-column will be copied                                             
         Size_send_U = Size_send_U + rows_in_block*cols_in_block; 
      }
      curr_col_loc = curr_col_loc + nblk;      // go to the next local block-column of my local array U 
      rows_in_block = rows_in_block + ratio*nblk;
   }
   rows_in_buffer = rows_in_block - ratio*nblk;    // remove redundant addition from the previous loop 
   *Buf_pos = (double)rows_in_buffer; // write number of the rows at the end of the buffer; we will need this for further multiplications on the other processors
   Size_send_U = Size_send_U + 1;
   
   //send and receive
   if(where_to_send_U != my_prow)
   {   
      // send and receive in the col_comm
      MPI_Sendrecv(Buf_to_send_U, Size_send_U, MPI_DOUBLE, where_to_send_U, 0, Buf_to_receive_U, Buf_rows*na_cols, MPI_DOUBLE, from_where_to_receive_U, 0, col_comm, &status); 
      MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_U); // find out how many elements I have received 
   }
   else // if I do not need to send 
      Size_receive_U = Size_send_U;         // how many elements I "have received"; the needed data I have already copied to the "receive" buffer
      
   for(i = 0; i < Size_receive_U; i++)
      U_stored[i] = Buf_to_receive_U[i];
   Size_U_skewed = Size_receive_U; 
   Curr_pos_in_U_stored = Size_U_skewed;

   //////////////////////////////////////////////////////////////////////// main loop /////////////////////////////////////////////////////
   where_to_send_A = (my_pcol - 1 + np_cols)%np_cols;
   from_where_to_receive_A = (my_pcol + 1)%np_cols;
   where_to_send_U = (my_prow - 1 + np_rows)%np_rows;
   from_where_to_receive_U = (my_prow + 1)%np_rows;
   
   for(j = 1; j < np_rows; j++)
   {
      // at this moment I need to send to neighbour what I have in the "received" arrays; that is why exchange pointers of the "received" and "send" arrays
      double_ptr = Buf_to_send_A; 
      Buf_to_send_A = Buf_to_receive_A; 
      Buf_to_receive_A = double_ptr; 
      
      double_ptr = Buf_to_send_U; 
      Buf_to_send_U = Buf_to_receive_U; 
      Buf_to_receive_U = double_ptr;
      
      ///// shift for A ////////////////////////////////////////////////////////////
      Size_send_A = Size_receive_A;  // number of block-columns of A and block-rows of U to send (that I have received on the previous step) 
      MPI_Isend(Buf_to_send_A, Size_send_A*na_rows, MPI_DOUBLE, where_to_send_A, 0, row_comm, &request_A_Send); 
      MPI_Irecv(Buf_to_receive_A, Buf_cols*na_rows*ratio, MPI_DOUBLE, from_where_to_receive_A, 0, row_comm, &request_A_Recv);
         
      ///// shift for U /////////////////////////////////////////////
      Size_send_U = Size_receive_U; 
      MPI_Isend(Buf_to_send_U, Size_send_U, MPI_DOUBLE, where_to_send_U, 0, col_comm, &request_U_Send); 
      MPI_Irecv(Buf_to_receive_U, Buf_rows*na_cols, MPI_DOUBLE, from_where_to_receive_U, 0, col_comm, &request_U_Recv); 
      
      ///// multiplication ////////////////////////////////////////////////////////////////////////////////////////////
      rows_in_buffer = (int)Buf_to_send_U[Size_receive_U-1];
      row_origin_U = (my_pcol + my_prow + np_cols + j - 1)%np_rows;
      
      if((my_pcol >= my_prow)&&(my_pcol >= row_origin_U))   // if I and sender are from the upper part of grid
      {
         cols_in_buffer = na_cols;                          // then we have the same number of columns in the upper triangular part
         curr_col_loc_res = 0;                              // all my block-columns have parts in the upper triangular part
         curr_col_loc_buf = 0;                              // I use all the block-columns of the received buffer
      }
      if((my_pcol < my_prow)&&(my_pcol < row_origin_U))     // if I and sender are from the lower part of grid
      {
         cols_in_buffer = na_cols - nblk;                   // then we have the same number of columns in the upper triangular part, but the first block-column was not included
         curr_col_loc_res = nblk;                           // I start update from the second block-column since the first on is in the lower triangular part
         curr_col_loc_buf = 0;                              // I use all the block-columns of the received buffer
      }
      if((my_pcol >= my_prow)&&(my_pcol < row_origin_U))    // if I am from the upper part of grid and sender is from the lower part
      {
         cols_in_buffer = na_cols - nblk;                   // then I have received one block-column less than I have
         curr_col_loc_res = nblk;                           // all my block-columns have parts in the upper triangular part, but the first block-column of the received buffers corresponds to my second one
         curr_col_loc_buf = 0;                              // I use all the block-columns of the received buffer
      }
      if((my_pcol < my_prow)&&(my_pcol >= row_origin_U))    // if I am from the lower part of grid and sender is from the upper part
      {
         cols_in_buffer = na_cols;                          // then I have received the full set of block-columns
         curr_col_loc_res = nblk;                           // I start update from the second block-column since the first on is in the lower triangular part
         curr_col_loc_buf = nblk;                           // I skip the first block-column of the buffer, since my first block-column is in the lower part
      }
    
      num_of_blocks_in_U_buffer = ceil(((double)cols_in_buffer - (double)curr_col_loc_buf)/(double)nblk); 
      
      startPos = (curr_col_loc_buf + nblk)*curr_col_loc_buf/2;
      U_local_start = &Buf_to_send_U[startPos];
      Res_ptr = &M[curr_col_loc_res*na_rows];
  
      for (i = 0; i < num_of_blocks_in_U_buffer; i++)
      { 
         curr_col_glob = (curr_col_loc_res/nblk)*nblk*np_cols + my_pcol*nblk;
         proc_row_curr = (curr_col_glob/nblk)%np_rows; 
         rows_in_block_A = (curr_col_glob/(nblk*np_rows))*nblk;     // in A; not to go down beyond  the upper triangular part
         if(my_prow <= proc_row_curr)
            rows_in_block_A = rows_in_block_A + nblk; 
         
         if(rows_in_block_A > na_rows)
            rows_in_block_A = na_rows; 
      
         if((curr_col_loc_buf + nblk) <= cols_in_buffer)
            cols_in_block = nblk;      // number columns in block of U which will take part in this calculation
         else
            cols_in_block = cols_in_buffer - curr_col_loc_buf; 
      
         rows_in_block_U = (curr_col_glob/(nblk*np_rows))*nblk;    // corresponds to columns in A;
         if(proc_row_curr >= row_origin_U)
            rows_in_block_U = rows_in_block_U + nblk; 
         
         if(rows_in_block_U > rows_in_buffer)
            rows_in_block_U = rows_in_buffer;

         if ((rows_in_block_A > 0)&&(cols_in_block > 0))
            if (j == 1)
               dgemm_("N", "N", &rows_in_block_A, &cols_in_block, &rows_in_block_U, &done, Buf_to_send_A, &na_rows, U_local_start, &rows_in_block_U, &dzero, Res_ptr, &na_rows);
            else 
               dgemm_("N", "N", &rows_in_block_A, &cols_in_block, &rows_in_block_U, &done, Buf_to_send_A, &na_rows, U_local_start, &rows_in_block_U, &done, Res_ptr, &na_rows);
      
         U_local_start = U_local_start + rows_in_block_U*cols_in_block;
         curr_col_loc_res = curr_col_loc_res + nblk;
         Res_ptr = &M[curr_col_loc_res*na_rows];
         curr_col_loc_buf = curr_col_loc_buf + nblk;  
      } 
     
      MPI_Wait(&request_A_Send, &status);
      MPI_Wait(&request_A_Recv, &status);
      MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_A); // find out how many elements I have received 
      Size_receive_A = Size_receive_A/na_rows;
      
      MPI_Wait(&request_U_Send, &status);
      MPI_Wait(&request_U_Recv, &status);
      MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_U); // find out how many elements I have received  
      
       //// write in the buffer for later use //////////////////////////////7
      if(j <= ToStore)
      {
         for(k = 0; k < Size_receive_U; k++)
            U_stored[Curr_pos_in_U_stored + k] = Buf_to_receive_U[k]; 
         Curr_pos_in_U_stored = Curr_pos_in_U_stored + Size_receive_U; 
         SizesU[j-1] = Size_receive_U; 
      }
   }
   
   /////// do the last multiplication //////////////
   rows_in_buffer = (int)Buf_to_receive_U[Size_receive_U-1];
   row_origin_U = (my_pcol + my_prow + np_cols + np_rows -1)%np_rows;

   if((my_pcol >= my_prow)&&(my_pcol >= row_origin_U))   // if I and sender are from the upper part of grid
   {
      cols_in_buffer = na_cols;                          // then we have the same number of columns in the upper triangular part
      curr_col_loc_res = 0;                              // all my block-columns have parts in the upper triangular part
      curr_col_loc_buf = 0;                              // I use all the block-columns of the received buffer
   }
   if((my_pcol < my_prow)&&(my_pcol < row_origin_U))     // if I and sender are from the lower part of grid
   {
      cols_in_buffer = na_cols - nblk;                   // then we have the same number of columns in the upper triangular part, but the first block-column was not included
      curr_col_loc_res = nblk;                           // I start update from the second block-column since the first on is in the lower triangular part
      curr_col_loc_buf = 0;                              // I use all the block-columns of the received buffer
   }
   if((my_pcol >= my_prow)&&(my_pcol < row_origin_U))    // if I am from the upper part of grid and sender is from the lower part
   {
      cols_in_buffer = na_cols - nblk;                   // then I have received one block-column less than I have
      curr_col_loc_res = nblk;                           // all my block-columns have parts in the upper triangular part, but the first block-column of the received buffers corresponds to my second one
      curr_col_loc_buf = 0;                              // I use all the block-columns of the received buffer
   }
   if((my_pcol < my_prow)&&(my_pcol >= row_origin_U))    // if I am from the lower part of grid and sender is from the upper part
   {
      cols_in_buffer = na_cols;                          // then I have received the full set of block-columns
      curr_col_loc_res = nblk;                           // I start update from the second block-column since the first on is in the lower triangular part
      curr_col_loc_buf = nblk;                           // I skip the first block-column of the buffer, since my first block-column is in the lower part
   }
    
   num_of_blocks_in_U_buffer = ceil(((double)cols_in_buffer - (double)curr_col_loc_buf)/(double)nblk); 
      
   startPos = (curr_col_loc_buf + nblk)*curr_col_loc_buf/2;
   U_local_start = &Buf_to_receive_U[startPos];
   Res_ptr = &M[curr_col_loc_res*na_rows];
  
   for (i = 0; i < num_of_blocks_in_U_buffer; i++)
   { 
      curr_col_glob = (curr_col_loc_res/nblk)*nblk*np_cols + my_pcol*nblk;
      proc_row_curr = (curr_col_glob/nblk)%np_rows; 
      rows_in_block_A = (curr_col_glob/(nblk*np_rows))*nblk;     // in A; not to go down beyond  the upper triangular part
      if(my_prow <= proc_row_curr)
         rows_in_block_A = rows_in_block_A + nblk; 
         
      if(rows_in_block_A > na_rows)
         rows_in_block_A = na_rows; 
      
      if((curr_col_loc_buf + nblk) <= cols_in_buffer)
         cols_in_block = nblk;      // number columns in block of U which will take part in this calculation
      else
         cols_in_block = cols_in_buffer - curr_col_loc_buf; 
      
      rows_in_block_U = (curr_col_glob/(nblk*np_rows))*nblk;    // corresponds to columns in A;
      if(proc_row_curr >= row_origin_U)
         rows_in_block_U = rows_in_block_U + nblk; 
        
      if(rows_in_block_U > rows_in_buffer)
         rows_in_block_U = rows_in_buffer; 

      if ((rows_in_block_A > 0)&&(cols_in_block > 0))
         if (j == 1)
            dgemm_("N", "N", &rows_in_block_A, &cols_in_block, &rows_in_block_U, &done, Buf_to_receive_A, &na_rows, U_local_start, &rows_in_block_U, &dzero, Res_ptr, &na_rows);
         else 
            dgemm_("N", "N", &rows_in_block_A, &cols_in_block, &rows_in_block_U, &done, Buf_to_receive_A, &na_rows, U_local_start, &rows_in_block_U, &done, Res_ptr, &na_rows);
      
      U_local_start = U_local_start + rows_in_block_U*cols_in_block;
      curr_col_loc_res = curr_col_loc_res + nblk;
      Res_ptr = &M[curr_col_loc_res*na_rows];
      curr_col_loc_buf = curr_col_loc_buf + nblk;  
   }  
   
   ///////////////////// Now M has an upper part of A*U(-1) ///////////////////////////////////////////////
   
   pdtran_(&na, &na, &done, M, &one, &one, a_desc, &dzero, M_T, &one, &one, a_desc);     // now M_T has lower part of U(-H)*A 
 
   ////////////////////////////////////////////////// start algorithm to find lower part of U(-H)*A*U(-1) //////////////////////////
           
   /////////////////////////////////////////////////////////////// initial reordering of A ////////////////////////////////////////////////
   
   // here we assume, that np_rows < np_cols; then I will send to the number of processors equal to <ratio> with the "leap" equal to np_rows; the same holds for receive  
   if((ratio != 1)||(my_prow != 0))   // if grid is rectangular or my_prow is not 0
      Buf_pos = Buf_to_send_A;     // I will copy to the send buffer
   else
      Buf_pos = Buf_to_receive_A;  // if grid is square and my_prow is 0, then I will copy to the received buffer
   
   // form array to send by block-columns; we need only lower triangular part
   num_of_iters = ceil((double)na_cols/(double)nblk);             // number my of block-columns
   
   cols_in_buffer_A_my_initial = 0;
   Size_send_A = 0; 
   
   if(my_pcol <= my_prow)  // if I am from the lower part of grid
   {
      curr_row_loc = 0;     // I will copy all my block-rows
      rows_in_buffer_A_my_initial = na_rows;
   }
   else
   {
      curr_row_loc = ceil((double)(((double)my_pcol - (double)my_prow)/(double)np_rows))*nblk; // I will skip some of my block-rows
      rows_in_buffer_A_my_initial = na_rows - curr_row_loc;   
   }
       
   for(i = 0; i < num_of_iters; i++)       // loop over my block-columns
   {
      curr_col_loc = i*nblk;      // local index of start of the current block-column 
      rows_in_block = na_rows - curr_row_loc;    // how many rows do I have in the lower part of the current block-column
      
      if ((na_cols - curr_col_loc) < nblk)
         cols_in_block = na_cols - curr_col_loc;     // how many columns do I have in the block-column
      else
         cols_in_block = nblk; 
      
      if((rows_in_block > 0)&&(cols_in_block > 0))
      {
         A_local_start = &M_T[curr_col_loc*na_rows + curr_row_loc];
         dlacpy_("A", &rows_in_block, &cols_in_block, A_local_start, &na_rows, Buf_pos, &rows_in_block);     // copy lower part of block-column in the buffer with LDA = length of the lower part of block-column 
         Buf_pos = Buf_pos + rows_in_block*cols_in_block;
         Size_send_A = Size_send_A + rows_in_block*cols_in_block; 
         cols_in_buffer_A_my_initial = cols_in_buffer_A_my_initial + cols_in_block; 
      }
      curr_row_loc = curr_row_loc + ratio*nblk;
   }
   *Buf_pos = (double)cols_in_buffer_A_my_initial; // write number of the columns at the end of the buffer; we will need this for furhter multiplications on the other processors
   Size_send_A = Size_send_A + 1;
   
   // now we have the local buffer to send
   // find the lowest processor column among those who will send me
   proc_col_min = np_cols; 
   for(i = 0; i < ratio; i++)
   {
      from_where_to_receive_A = (my_pcol + my_prow + i*np_rows)%np_cols;
      if(from_where_to_receive_A < proc_col_min)
         proc_col_min = from_where_to_receive_A;
   }
   // do communications and form local buffers for calculations
   Size_receive_A = 0;       // size of the accumulated buffer
   cols_in_buffer_A = 0;     // number of columns in the accumulated buffer
   rows_in_buffer_A = 0;     // number of rows in the accumulated buffer
   for(i = 0; i < ratio; i++)
   {
      where_to_send_A = (my_pcol - my_prow - i*np_rows + np_cols)%np_cols;                
      from_where_to_receive_A = (my_pcol + my_prow + i*np_rows)%np_cols;
      
      // send and receive in the row_comm
      if(ratio != 1)   // if grid is not square
      {
         if(where_to_send_A != my_pcol)   // if I need to send and receive on this step
         {
            MPI_Sendrecv(Buf_to_send_A, Size_send_A, MPI_DOUBLE, where_to_send_A, 0, Buf_A, Size_U_stored, MPI_DOUBLE, from_where_to_receive_A, 0, row_comm, &status);
            MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_A_now);
            Size_receive_A = Size_receive_A + Size_receive_A_now - 1; // we need only number of elements, so exclude information about cols_in_buffer_A
            
            cols_in_buffer_A_now = Buf_A[Size_receive_A_now-1];
            cols_in_buffer_A = cols_in_buffer_A + cols_in_buffer_A_now; 
            
            // determine number of rows in the received buffer
            if(from_where_to_receive_A <= my_prow)  // if source is from the lower part of grid
            {
               rows_in_buffer_A_now = na_rows;
            }
            else
            {
               rows_in_buffer_A_now = na_rows - ceil((double)(((double)from_where_to_receive_A - (double)my_prow)/(double)np_rows))*nblk; // some of the block-rows have been skipped
            }
            if(rows_in_buffer_A < rows_in_buffer_A_now)
               rows_in_buffer_A = rows_in_buffer_A_now; 

            intNumber = from_where_to_receive_A/np_rows; // how many processors will send me blocks, such that they will be placed before the current blocks  
            if(proc_col_min <= my_prow)   // if among procs who will send me there is one with the full sets of block-rows in the lower part
               CopyTo = &Buf_to_receive_A[nblk*(na_rows*intNumber - nblk*(intNumber-1)*intNumber/2)];  // here I will copy to; formula based on arithm. progression
            else
               CopyTo = &Buf_to_receive_A[nblk*(na_rows*intNumber - nblk*intNumber*(intNumber+1)/2)];  // otherwise, the first block-column will be shorter by one block
            CopyFrom = Buf_A; 
         }
         else  // if I need to send to myself on this step, then I will copy from Buf_to_send_L to Buf_to_receive_A
         {
            cols_in_buffer_A_now = cols_in_buffer_A_my_initial;
            cols_in_buffer_A = cols_in_buffer_A + cols_in_buffer_A_now; 
            
            rows_in_buffer_A_now = rows_in_buffer_A_my_initial;
            if(rows_in_buffer_A < rows_in_buffer_A_now)
               rows_in_buffer_A = rows_in_buffer_A_now; 

            intNumber = my_pcol/np_rows; // how many processors will send me blocks, such that they will be placed before the current blocks  
            if(proc_col_min <= my_prow)   // if among procs who will send me there is one with the full sets of block-rows in the lower part
               CopyTo = &Buf_to_receive_A[nblk*(na_rows*intNumber - nblk*(intNumber-1)*intNumber/2)];  // here I will copy to; formula based on arithm. progression
            else
               CopyTo = &Buf_to_receive_A[nblk*(na_rows*intNumber - nblk*intNumber*(intNumber+1)/2)];  // otherwise, the first block-column will be shorter by one block
            CopyFrom = Buf_to_send_A;  

            Size_receive_A = Size_receive_A + Size_send_A - 1;
         }
            
         // copy by block-columns
         intNumber = ceil((double)cols_in_buffer_A_now/(double)nblk);  // how many block-columns I have received on this iteration
         rows_in_block = rows_in_buffer_A_now; 
         for(j = 0; j < intNumber; j++)
         {
            if((j+1)*nblk < cols_in_buffer_A_now)
               cols_in_block = nblk; 
            else
               cols_in_block = cols_in_buffer_A_now - j*nblk;
               
            dlacpy_("A", &rows_in_block, &cols_in_block, CopyFrom, &rows_in_block, CopyTo, &rows_in_block);

            CopyFrom = CopyFrom + rows_in_block*cols_in_block; 
            CopyTo = CopyTo + nblk*(ratio*rows_in_block - nblk*(ratio-1)*ratio/2);  // I need to leave place for ratio block-columns of the other procs. of the lengths rows_in_block, (rows_in_block-nblk), (rows_in_block-2*nblk) and so on
            rows_in_block = rows_in_block - ratio*nblk;     // number of rows in the next block-columns
         }
      }
      else    // if grid is square
      {
         if(my_prow > 0)
         {
            MPI_Sendrecv(Buf_to_send_A, Size_send_A, MPI_DOUBLE, where_to_send_A, 0, Buf_to_receive_A, Size_U_stored, MPI_DOUBLE, from_where_to_receive_A, 0, row_comm, &status);
            MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_A);
            cols_in_buffer_A = (int)Buf_to_receive_A[Size_receive_A-1];
            if(from_where_to_receive_A <= my_prow)  // if source is from the lower part of grid
            {
               rows_in_buffer_A = na_rows;
            }
            else
            {
               rows_in_buffer_A = na_rows - ceil((double)(((double)from_where_to_receive_A - (double)my_prow)/(double)np_rows))*nblk; // some of the block-rows have been skipped
            }
         }
         else    // if my_prow == 0, then I have already everything in my Buf_to_receive_A buffer
         {
            Size_receive_A = Size_send_A;
            rows_in_buffer_A = rows_in_buffer_A_my_initial;
            cols_in_buffer_A = cols_in_buffer_A_my_initial;
         }
      }
   }
   if(ratio != 1)
   {
      Buf_to_receive_A[Size_receive_A] = cols_in_buffer_A;
      Buf_to_receive_A[Size_receive_A + 1] = rows_in_buffer_A;
      Size_receive_A = Size_receive_A + 2;
   }
   else
   {
      Buf_to_receive_A[Size_receive_A] = rows_in_buffer_A;
      Size_receive_A = Size_receive_A + 1;
   }

   ////////////////////////////////////////////////////////////// initial reordering of U: restore skewed U from the first multiplication ///////////////////////////
   
   Size_receive_U = Size_U_skewed;
   U_to_calc = U_stored;
   
   //////////////////////////////////////////////////////////////////////// main loop ////////////////////////////////////////////////////////////////////////////////
   
   where_to_send_A = (my_pcol - 1 + np_cols)%np_cols;
   from_where_to_receive_A = (my_pcol + 1)%np_cols;
   where_to_send_U = (my_prow - 1 + np_rows)%np_rows;
   from_where_to_receive_U = (my_prow + 1)%np_rows;
   Curr_pos_in_U_stored = Size_U_skewed;
  
   for(j = 1; j < np_rows; j++)
   {
      // at this moment I need to send to neighbour what I have in the "received" arrays; that is why exchange pointers of the "received" and "send" arrays
      double_ptr = Buf_to_send_A; 
      Buf_to_send_A = Buf_to_receive_A; 
      Buf_to_receive_A = double_ptr; 
      
      if (j > ToStore)
      {
         double_ptr = Buf_to_send_U; 
         Buf_to_send_U = Buf_to_receive_U; 
         Buf_to_receive_U = double_ptr;
      }
        
      ///// shift for A ////////////////////////////////////////////////////////////
      Size_send_A = Size_receive_A; 
      MPI_Isend(Buf_to_send_A, Size_send_A, MPI_DOUBLE, where_to_send_A, 0, row_comm, &request_A_Send); 
      MPI_Irecv(Buf_to_receive_A, ratio*Size_U_stored, MPI_DOUBLE, from_where_to_receive_A, 0, row_comm, &request_A_Recv);
         
      ///// shift for U /////////////////////////////////////////////
      Size_send_U = Size_receive_U; 
      if (j > ToStore)
      {
         if(j > ToStore + 1)
         {
            MPI_Isend(Buf_to_send_U, Size_send_U, MPI_DOUBLE, where_to_send_U, 0, col_comm, &request_U_Send); 
            U_to_calc = Buf_to_send_U;
         }
         else
            MPI_Isend(U_to_calc, Size_send_U, MPI_DOUBLE, where_to_send_U, 0, col_comm, &request_U_Send);
         MPI_Irecv(Buf_to_receive_U, Size_U_stored, MPI_DOUBLE, from_where_to_receive_U, 0, col_comm, &request_U_Recv);
      }
      
      ///// multiplication ////////////////////////////////////////////////////////////////////////////////////////////
      rows_in_buffer_U = (int)U_to_calc[Size_receive_U-1];
      row_of_origin_U = (my_pcol + my_prow + np_cols + j - 1)%np_rows;
      if(my_pcol >= row_of_origin_U)
         cols_in_buffer_U = na_cols;
      else
         cols_in_buffer_U = na_cols - nblk;
      
      cols_in_buffer_A = (int)Buf_to_send_A[Size_receive_A-2];
      rows_in_buffer_A = (int)Buf_to_send_A[Size_receive_A-1];
      // find the minimal pcol among those who have sent A for this iteration
      col_of_origin_A = np_cols; 
      for(i = 0; i < ratio; i++)
      {
         intNumber = (my_pcol + my_prow + i*np_rows + np_cols + j - 1)%np_cols;
         if(intNumber < col_of_origin_A)
            col_of_origin_A = intNumber;
      }
      
      ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
      // find block-column of the result to start update with
      if (my_pcol >= row_of_origin_U)   // if origin of U is from the upper part 
         curr_col_loc_res = 0;          // then I update all columns of Result    
      else
         curr_col_loc_res = nblk;       // the first block column of U corresponds to my second one and I do not need to update the first block-column
      
      num_of_blocks_in_U_buffer = ceil((double)((double)cols_in_buffer_U/(double)nblk)); 
      if(my_pcol >= row_of_origin_U)    // if origin of U is from the upper part
         rows_in_block_U = ceil(((double)(my_pcol + 1) - (double)row_of_origin_U)/(double)np_rows)*nblk;  // blocks in the first block-column of U buffer
      else
         rows_in_block_U = ratio*nblk;
      
      U_local_start = U_to_calc;
      
      for (i = 0; i < num_of_blocks_in_U_buffer; i++)
      { 
         // find block-row of the result to start update with; we need to update only lower triangular part of result
         curr_col_glob_res = np_cols*nblk*(curr_col_loc_res/nblk) + curr_col_loc_res%nblk + ((np_cols+my_pcol)%np_cols)*nblk;   // global index of the first column to be updated
         // now we need to find the smallest my local row index, such that the corresponding global index is larger of equal to <curr_col_glob_res>
         Nb = curr_col_glob_res/nblk;    // how many global block-rows are before the needed one
         owner = Nb%np_rows;             // proc. row index of the owner of row with the global index equal to <curr_col_glob_res> (it is not necessarily me)
         curr_row_loc_res = (Nb/np_rows)*nblk; 
         if(my_prow < owner)
            curr_row_loc_res = curr_row_loc_res + nblk; 
      
         curr_row_loc_A = curr_row_loc_res;     // it is impossible, that both col_of_origin_L and row_of_origin_U are from upper part
         if(col_of_origin_A > my_prow)
            curr_row_loc_A = curr_row_loc_A - nblk;  
        
         rows_in_block = rows_in_buffer_A - curr_row_loc_A;    // rows in current block of A
              
         curr_col_loc_U = i*nblk;   // local index in the buffer U of the current column
      
         if((curr_col_loc_U + nblk) <= cols_in_buffer_U)
            cols_in_block = nblk;      // number columns in block of U which will take part in this calculation
         else
            cols_in_block = cols_in_buffer_U - curr_col_loc_U; 
      
         if(rows_in_block_U > rows_in_buffer_U)
            rows_in_block_U = rows_in_buffer_U;     // rows in current column of U; also a leading dimension for U
 
         A_local_index = curr_row_loc_A;
         A_local_start = &Buf_to_send_A[A_local_index];
         Res_ptr = &Res[curr_col_loc_res*na_rows + curr_row_loc_res];

         LDA_A = rows_in_buffer_A;
         LDA_A_new = LDA_A;
         if ((rows_in_block > 0)&&(cols_in_block > 0))
         {
            U_local_start_curr = U_local_start; 
 
            // loop over block-columns of the "active" part of L buffer
            for (ii = 0; ii < ceil((double)rows_in_block_U/(double)nblk); ii++)
            {
               if((ii+1)*nblk <= cols_in_buffer_A)
                  rows_in_block_U_curr = nblk; 
               else
                  rows_in_block_U_curr = cols_in_buffer_A - ii*nblk;  

               if((j == 1)&&(ii == 0))
                  dgemm_("N", "N", &rows_in_block, &cols_in_block, &rows_in_block_U_curr, &done, A_local_start, &LDA_A, U_local_start_curr, &rows_in_block_U, &dzero, Res_ptr, &na_rows); 
               else 
                  dgemm_("N", "N", &rows_in_block, &cols_in_block, &rows_in_block_U_curr, &done, A_local_start, &LDA_A, U_local_start_curr, &rows_in_block_U, &done, Res_ptr, &na_rows);

               LDA_A_new = LDA_A_new - nblk;
      
               U_local_start_curr = U_local_start_curr + rows_in_block_U_curr; 
               A_local_index = A_local_index - LDA_A + LDA_A*nblk + LDA_A_new; 
               A_local_start = &Buf_to_send_A[A_local_index];
               LDA_A = LDA_A_new; 
            }
         }
      
         U_local_start = U_local_start + rows_in_block_U*cols_in_block;
         curr_col_loc_res = curr_col_loc_res + nblk; 
         rows_in_block_U = rows_in_block_U + ratio*nblk;
      }    
      
      MPI_Wait(&request_A_Send, &status);
      MPI_Wait(&request_A_Recv, &status);
      MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_A); // find out how many elements I have received 
      
      if (j <= ToStore)
      {
         U_to_calc = &U_stored[Curr_pos_in_U_stored];
         Curr_pos_in_U_stored = Curr_pos_in_U_stored + SizesU[j-1]; 
         Size_receive_U =  SizesU[j-1];
      }
      else
      {
         MPI_Wait(&request_U_Send, &status);
         MPI_Wait(&request_U_Recv, &status);
         MPI_Get_count(&status, MPI_DOUBLE, &Size_receive_U); // find out how many elements I have received  
      }
   }
   
   /////// do the last multiplication //////////////
   if(ToStore < np_rows - 1)
      U_to_calc = Buf_to_receive_U;
   rows_in_buffer_U = (int)U_to_calc[Size_receive_U-1];
   row_of_origin_U = (my_pcol + my_prow + np_cols + j - 1)%np_rows;     
   if(my_pcol >= row_of_origin_U)
      cols_in_buffer_U = na_cols;
   else
      cols_in_buffer_U = na_cols - nblk;
      
   cols_in_buffer_A = (int)Buf_to_receive_A[Size_receive_A-2];
   rows_in_buffer_A = (int)Buf_to_receive_A[Size_receive_A-1];
   // find the minimal pcol among those who have sent A for this iteration
   col_of_origin_A = np_cols; 
   for(i = 0; i < ratio; i++)
   {
      intNumber = (my_pcol + my_prow + i*np_rows + np_cols + np_rows - 1)%np_cols;
      if(intNumber < col_of_origin_A)
         col_of_origin_A = intNumber;
   }
   
   // find block-column of the result to start update with
   if (my_pcol >= row_of_origin_U)   // if origin of U is from the upper part 
      curr_col_loc_res = 0;          // then I update all columns of Result    
   else
      curr_col_loc_res = nblk;       // the first block column of U corresponds to my second one and I do not need to update the first block-column
      
   num_of_blocks_in_U_buffer = ceil((double)((double)cols_in_buffer_U/(double)nblk));
   if(my_pcol >= row_of_origin_U)    // if origin of U is from the upper part
      rows_in_block_U = ceil(((double)(my_pcol + 1) - (double)row_of_origin_U)/(double)np_rows)*nblk;  // blocks in the first block-column of U buffer
   else
      rows_in_block_U = ratio*nblk;
      
   U_local_start = U_to_calc;
      
   for (i = 0; i < num_of_blocks_in_U_buffer; i++)
   { 
      // find block-row of the result to start update with; we need to update only lower triangular part of result
      curr_col_glob_res = np_cols*nblk*(curr_col_loc_res/nblk) + curr_col_loc_res%nblk + ((np_cols+my_pcol)%np_cols)*nblk;   // global index of the first column to be updated
      // now we need to find the smallest my local row index, such that the corresponding global index is larger of equal to <curr_col_glob_res>
      Nb = curr_col_glob_res/nblk;    // how many global block-rows are before the needed one
      owner = Nb%np_rows;             // proc. row index of the owner of row with the global index equal to <curr_col_glob_res> (it is not necessarily me)
      curr_row_loc_res = (Nb/np_rows)*nblk; 
      if(my_prow < owner)
         curr_row_loc_res = curr_row_loc_res + nblk; 
      
      curr_row_loc_A = curr_row_loc_res;     // it is impossible, that both col_of_origin_L and row_of_origin_U are from upper part
      if(col_of_origin_A > my_prow)
         curr_row_loc_A = curr_row_loc_A - nblk;
      
      rows_in_block = rows_in_buffer_A - curr_row_loc_A;    //rows in current block of  
              
      curr_col_loc_U = i*nblk;   // local index in the buffer U of the current column
      
      if((curr_col_loc_U + nblk) <= cols_in_buffer_U)
         cols_in_block = nblk;      // number columns in block of U which will take part in this calculation
      else
         cols_in_block = cols_in_buffer_U - curr_col_loc_U; 
      
      if(rows_in_block_U > rows_in_buffer_U)
         rows_in_block_U = rows_in_buffer_U; 
 
      A_local_index = curr_row_loc_A;
      A_local_start = &Buf_to_receive_A[A_local_index];
      Res_ptr = &Res[curr_col_loc_res*na_rows + curr_row_loc_res];
      LDA_A = rows_in_buffer_A; 
      LDA_A_new = LDA_A; 
      if ((rows_in_block > 0) &&(cols_in_block > 0))
      {
         U_local_start_curr = U_local_start; 

         // loop over block-columns of the "active" part of L buffer
         for (ii = 0; ii < ceil((double)rows_in_block_U/(double)nblk); ii++)
         {
            if((ii+1)*nblk <= cols_in_buffer_A)
               rows_in_block_U_curr = nblk; 
            else
               rows_in_block_U_curr = cols_in_buffer_A - ii*nblk;  

            if((j == 1)&&(ii == 0))
               dgemm_("N", "N", &rows_in_block, &cols_in_block, &rows_in_block_U_curr, &done, A_local_start, &LDA_A, U_local_start_curr, &rows_in_block_U, &dzero, Res_ptr, &na_rows); 
            else 
               dgemm_("N", "N", &rows_in_block, &cols_in_block, &rows_in_block_U_curr, &done, A_local_start, &LDA_A, U_local_start_curr, &rows_in_block_U, &done, Res_ptr, &na_rows);

            LDA_A_new = LDA_A_new - nblk;
              
            U_local_start_curr = U_local_start_curr + rows_in_block_U_curr; 
            A_local_index = A_local_index - (LDA_A - rows_in_block) + LDA_A*nblk + LDA_A_new - rows_in_block; 
            A_local_start = &Buf_to_receive_A[A_local_index];
            LDA_A = LDA_A_new;
         }
      }
      
      U_local_start = U_local_start + rows_in_block_U*cols_in_block;
      curr_col_loc_res = curr_col_loc_res + nblk; 
      rows_in_block_U = rows_in_block_U + ratio*nblk;
   }
   
   pdtran_(&na, &na, &done, Res, &one, &one, a_desc, &dzero, M, &one, &one, a_desc);
   pdlacpy_("U", &na, &na, M, &one, &one, a_desc, Res, &one, &one, a_desc);
      
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   free(Buf_to_send_A);
   free(Buf_to_receive_A);
   free(Buf_to_send_U);
   free(Buf_to_receive_U);
   free(M); 
   free(M_T);
   if(ratio != 1)
      free(Buf_A);
   free(U_stored);
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   free(SizesU);
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}

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void cannons_reduction_c_impl(double* A, double* U, int local_rows, int local_cols,
                         int* a_desc, double *Res, int ToStore, int row_comm, int col_comm)
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{
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#ifdef WITH_MPI
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  MPI_Comm c_row_comm = MPI_Comm_f2c(row_comm);
  MPI_Comm c_col_comm = MPI_Comm_f2c(col_comm);
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Pavel Kus committed
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  int my_prow, my_pcol, np_rows, np_cols;
  MPI_Comm_rank(c_row_comm, &my_prow);
  MPI_Comm_size(c_row_comm, &np_rows);
  MPI_Comm_rank(c_col_comm, &my_pcol);
  MPI_Comm_size(c_col_comm, &np_cols);
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  // BEWARE
  // in the cannons algorithm, column and row communicators are exchanged
  // What we usually call row_comm in elpa, is thus passed to col_comm parameter of the function and vice versa
  // (order is swapped in the following call)
  // It is a bit unfortunate, maybe it should be changed in the Cannon algorithm to comply with ELPA standard notation?
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  cannons_reduction_impl(A, U, np_rows, np_cols, my_prow, my_pcol, a_desc, Res, ToStore, c_col_comm, c_row_comm);
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#else
  printf("Internal error: Cannons algorithm should not be called without MPI, stopping...\n");
  exit(1);
#endif
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}